HSSM3204: Engineering Economics & Costing

Module-I: (12 hours)

Engineering Economics – Nature and scope, General concepts on micro & macro economics.

Theory of demand, Demand function, Law of demand and its exceptions, Elasticity of demand,

Law of supply and elasticity of supply. Determination of equilibrium price under perfect

competition (Simple numerical problems to be solved). Theory of production, Law of variable

proportion, Law of returns to scale.

Module-II: (12 hours)

Time value of money – Simple and compound interest, Cash flow diagram, Principle of

economic equivalence. Evaluation of engineering projects – Present worth method, Future worth

method, Annual worth method, internal rate of return method, Cost-benefit analysis in public

projects. Depreciation policy, Depreciation of capital assets, Causes of depreciation, Straight line

method and declining balance method.

Module-III: (12 hours)

Cost concepts, Elements of costs, Preparation of cost sheet, Segregation of costs into fixed and

variable costs. Break-even analysis - Linear approach (Simple numerical problems to be solved).

Banking: Meaning and functions of commercial banks; functions of Reserve Bank of India.

Overview of Indian Financial system.

Text Books:

1. Riggs, Bedworth and Randhwa, “Engineering Economics”, McGraw Hill Education India.

2. D. M. Mithani, Principles of Economics.

Reference Books:

1. Sasmita Mishra, “Engineering Economics & Costing“, PHI

2. Sullivan and Wicks, “Engineering Economics”, Pearson

3. R.Paneerselvam, “Engineering Economics”, PHI

4. Gupta, “Managerial Economics”, TMH

5. Lal and Srivastav, “Cost Accounting”, TM

Introduction to Engineering Economics

Economics:

Economics is the social science that studies the production, distribution, and consumption of

goods and services. The term economics comes from the Greek word oikonomia, ("management

of households”) from (oikos, "house") + (nomos, “Custom” or "law"). Thus, it refers to managing

a household with limited funds.

All economic activities start from the existence of human wants. With the help of resources a

person fulfils his wants and gets satisfaction. Thus, economics is the study of wants, efforts and

satisfaction. In modern economy, wants, efforts and satisfaction are linked through money.

Economics is growing very rapidly as the years pass. As new ideas are being discovered and the

old theories are being revised, it is not possible to give a definition of economics which has a

general acceptance.

The set of definitions given by various economists are generally classified under four heads:

Economics as a science of wealth.

Economics as a science of material welfare.

Economics as a science of scarcity and choice.

Economics as a science of growth and efficiency.

Economics as a Science of Wealth/Classical View:

Adam Smith, the founder of economics, described Economics as a body of knowledge which

relates to wealth. Accordingly to him if a nation has larger amount of wealth, it can help in

achieving its betterment. He defined economics as “The study of nature and causes of generating

wealth of a nation”. He emphasized the production and expansion of wealth as the subject matter

of economics.

Criticisms:

The definitions give primary importance to wealth and secondary importance to man. The

fact is that the study of man is more important than the study of wealth.

The word ‘wealth’ in the definitions means only material goods such as chair, book, pen,

etc. These do not include services of doctors, nurses, soldiers etc. In modern economics,

the word ‘wealth’ includes material as well as non-material goods.

According to the definitions, man works only for his self-interest and social interest is

ignored.

The definitions ignore the importance of man’s welfare. Wealth is not be all and the end

of all human activities.

The definitions lay emphasis on the earning of wealth as an end in itself. They ignore the

means which are scare for the earning of wealth.

Economics as a Science of Material Welfare/Neo-Classical View:

Alfred Marshall in his book, 'Principles of Economics' defined Economics as: “Study of mankind

in the ordinary business of life. It examines that part of individual and social actions which is

closely connected with the attainment and with the use of material requisites of well being”. This

definition clearly states that Economics is on the one side a study of wealth and on the other and

more important side a part of the study of man.

Robbins's Criticisms:

The word “Material” in the definitions considerably narrows down the scope of

economics. There are many things in the world which are not material but they are very

useful for promoting human welfare e.g., the services of doctors, lawyers, teachers,

engineers, professors, etc., satisfy our wants and are scarce in supply.

There are many activities which do not promote human welfare, but they are regarded

economic activities, e.g., the manufacturing and sale of alcohol goods or opium, etc. Here

Robbins says, “Why talk of welfare at all? Why not throw away the mask altogether”?

In his opinion welfare is a vague concept as it is purely subjective. Moreover, he says

what is the use of a concept which can’t be quantitatively measured and on which two

persons can’t agree as to what is conducive to welfare and what is not e.g., manufacturing

of guns, tanks and other war heads, production of opium, liquor etc., are not conducive to

welfare but these are all economic activities.

The definition of welfare is of theoretical nature. It is not possible in practice to divide

man’s activities into material and non-material.

The word ‘Welfare' in the definition involves value judgment and the economists

according to Robbins, are forbidden to pass any verdict.

Economics as a Science of Scarcity and Choice:

Lionel Robbins in his book ‘Nature and Significance of Economics Science' defined Economics

as "A science which studies human behavior as a relationship between ends and scarce means

which have alternative uses".

Main Pillars of Robbins's Definition:

Human wants referred to as ends by Robbins are unlimited. They increase in quantity and

quality over a period of time. They vary among individuals and over time for the same

individual. It is not possible to find a person who will say that his wants for goods and

services have been completely satisfied. This is because of the fact that when one want is

satisfied, it is replaced by another and there is then no end to it.

The ends or wants are of varying importance. They are ranked in order of importance as:

(a) necessaries (b) comforts and (c) luxuries. Man generally satisfies his urgent wants

first and less urgent afterwards in order of their importance.

The resources (Land, labor, capital and entrepreneurship) at the disposal of man are

scarce. They are not found in as much quantity as we need them. Scarcity means that we

do not and cannot have enough income or wealth to satisfy our every desire. Scarcity

exists because human wants always exceed what can be produced with limited resources

and time that Nature makes available to man at any one time.

The scarce resources available to satisfy human wants have alternative uses. They can be

put to one use at one time e.g., if a piece of land is used for the production of sugarcane,

it cannot be utilized for the growth of another crop at the same time. Man, therefore, has

to choose the best way of utilizing the scarce resources which have alternative uses. The

scarce resources and choices are the key problems confronting every society.

Criticisms on Robbins Definition:

Robbins’s definition restricts the scope of economics by treating it as a positive Science

only while in reality it is both a positive and a normative science.

It has widened the scope of economics by covering the whole of economic life, while it is

concerned with that part of human life which is connected with the market price.

Robbins made economics colorless, impersonal and abstract. It is in fact a definition of

economics for economist only.

The study of economic growth process remains outside the scope of economics while it is

through economic growth that living standards improve.

Economics as a Science of Growth and Efficiency:

If we define Economics as a science of administration of scare resources, then its scope becomes

too wide and includes the whole of economics life and not merely that part of it which is

connected with the market price.

The modern economists define economics as "A science of growth and efficiency". According to

Samuelson, "Economics is the study of how people and society end up closing, with or without

the use of money, to employ scarce productive resources that could have alternative uses, to

produce various commodities and distribute them for consumption now or in the future among

various persons and groups in society". It analyses the cost and benefits of improving patterns of

resource allocation.

Efficiency here implies technical efficiency and economic efficiency in the use of scarce

resources for producing a given level of output. The term efficiency also relates to the efficiency

of whole economics system. If one section of the society is made better off without making the

other section worse off, we can say the economic system is operating efficiently".

Thus, Economics can be defined as “A social science which is concerned with the proper use and

allocation of resources for the achievement and maintenance of growth with stability and

efficiency”.

Scope of Economics:

The scope of economics is the area or boundary of the study of economics. In scope of

economics we answer and analyze the following questions:

What is the subject matter of economics?

What is the nature of economics?

Subject Matter of Economics:

There is a difference of opinion among economists regarding the subject-matter of economics.

Adam Smith, the father of modern economic theory, defined economics as a subject, which is

mainly concerned with the study of nature and causes of generation of wealth of nation.

Marshall introduced the concept of welfare in the study of economics. According to Marshall;

economics is a study of mankind in the ordinary business of life. It examines that part of

individual and social actions which is closely connected with the material requisites of well

being. In this definition, Marshall has shifted the emphasis from wealth to man. He gives primary

importance to man and secondary importance to wealth.

The Robbinsian’s concept of the subject-matter of economics is that: “economics is a science

which studies human behavior as a relationship between ends and scarce means which have

alternative uses”. According to Robbins (a) human wants are unlimited (b) means at his disposal

to satisfy these wants are not only limited, (c) but have alternative uses. Man is always busy in

adjusting his limited resources for the satisfaction of unlimited ends. The problems that centre

round such activities constitute the subject-matters of economics.

Paul and Samuelson, however, includes the dynamic aspects of economics in the subject matter.

According to them, "economics is the study of how man and society choose with or without

money, to employ productive uses to produce various commodities over time and distribute them

for consumption now and in future among various people and groups of society”.

Nature of Economics:

The economists are also divided regarding the nature of economics. The following questions are

generally covered in the nature of economics.

Is economics a science or an art?

Is it a positive science or a normative science?

Economics is both a science and an art. Economics is considered as a science because it is a

systematic knowledge derived from observation, study and experimentation. An art is the

practical application of knowledge for achieving definite ends. For example, there is inflation in

a country. This information is derived from positive science. The government takes certain fiscal

and monetary measures to bring down general level of prices in the country. The study of these

fiscal and monetary measures to bring down inflation makes the subject of economics as an art.

After arriving at a conclusion that economics is both a science as well as an art. Here arises

another controversy. Is economics a positive science or a normative science?

Lionel Robbins and his followers have described economics as a positive science. They opined

that economics is based on logic. Marshall, Pigou, Hawtrey, Keynes and many other economists

regard economics as a normative science. According to them, the real function of the science is

to increase the well-being of man. They have given suggestions in their works for promotion of

human welfare.

Economics, in fact, is both a positive and a normative science.

Basic Economics Problems:

Economic problem of mankind owes its origin to the fact that human wants are numerous and of

different kinds. The resources to satisfy the multifarious human wants are limited or scarce. If

the time or resources at our disposal are unlimited so that we could satisfy all our wants, then no

economic problem would have arisen at all. The economic problem has arisen simply because as

one want is satisfied, another want appears on the scene. As wants are unlimited and the means

to satisfy them limited, therefore, in order to get maximum satisfaction we have to fix up a list of

priority. So the two foundation stones on which the subject of Economics rests are:

(1) Multiplicity of human wants.

(2) Scarcity of resources.

Every economy has to solve the following four inter related problems:

What goods to produce? The first function of the society is to decide which goods are to

be produced and in how much quantity. Since the resources at the disposal of the society

are scarce, it has to make a choice between “guns or bread”, or a choice between

necessities and luxuries. The decision about the allocation of resources between

consumer goods and capital goods; their quality and quantity is of utmost importance

from the point of view of economic growth.

How to produce? There are various alternative methods or techniques of producing

goods. The society has to choose the least cost combination of producing the goods. For

instance, cloth can be produced with either handlooms (labor intensive technique) or

power looms (capital intensive technique). The society, depending upon its resources and

the state of technology available to it should use the most efficient method of production.

How to distribute the national income? The distribution of national income among the

members of the community is a burning issue both in the field of economics and politics.

The socialists are of the view that all the people should get fair share by redistribution of

national income. The other view is that, in a free enterprise economy, each individual

should get his share from the total output of goods according to the income available to

him through his genuine efforts.

How to ensure growth? The economic growth can be attained by (a) increasing the rate of

investment (b) replacement of capital goods and (c) by improving the technical processes

of production, A society, therefore, shall have to take timely decisions for allocating

scarce resources for investment, replacement and technological progress. In case a part of

the resources are not diverted for capital accumulation and technological progress, the

rate of growth will go down. The standard of living of the people will fall.

We, thus, conclude that economic problem arises because of scarcity of resources that people

want for the satisfaction of goods. The scarcity of resources involves the problems of choice or

allocation of resources among the competing ends. Economics, in short, is a science of efficiency

in the use of scarce resources.

Basic Economic Problems Facing India Today:

High Inflation Rates - Fueled by rising wages, property prices and food prices, inflation

in India is an increasing problem. With economic growth of 7 % – 8 % per annum,

inflationary pressures are likely to increase, especially with supply side constraints such

as infrastructure.

Poor Infrastructure - Many Indians lack access to basic amenities. Indian public services

are cracking under the strain of bureaucracy and inefficiency. Over 40% of Indian fruit

rots before it reach the market thanks to the supply constraints and inefficiency facing the

Indian economy.

High Levels of Debts - Buoyed by a property boom, the amount of lending in India has

grown by 30% in the past year. However there are concerns about the risk of such loans.

If interest rates rise because of inflation, it will potentially reduce consumer spending in

future.

Inequality Has Risen - So far economic growth of India has been highly uneven

benefiting the skilled and wealthy disproportionately. Many of India’s rural poor are yet

to receive any tangible benefit from the India’s economic growth.

Large Budget Deficit - India has one of the largest budget deficits in the developing

world amounting to nearly 8% of GDP. It thus allows little scope for increasing

investment in public services like health and education.

Micro-Economics and Macro-Economics:

Economics is grouped under two broad categories – Micro-economics and Macro-economics in

order to analyze and understand the economic issues and problems. Micro-economics deals with

operational/internal issues where as macro-economics handles environmental/external issues.

Microeconomics focuses on the market’s supply and demand factors that determine the

economy’s price levels. In other words, microeconomics concentrates on the ‘ups’ and ‘downs’

of the markets for services and goods, and how the price affects the growth of these markets. Its

main importance is to analyze the economic forces, consumer behavior, and methods of

determining the supply and demand of the market. On the other hand, the focus of

macroeconomics is basically on a country’s income, and the position of foreign trades, with the

study of unemployment rates, GDP and price indices. Macroeconomists are often found to make

different types of models, and relationships, between factors such as output, national income,

unemployment, consumption, savings, inflation, international trade, and investment. Overall,

macroeconomics is a vast field that concentrates on two areas, economic growth and changes in

the national income.

There are differences between microeconomics and macroeconomics. As the names imply,

microeconomics facilitates decisions of small groups of individuals such as households, firms

and industries, individual prices and incomes. Macroeconomics, on the other hand, focuses on

entire economy. These two economies are mutually dependent, and together, they develop the

strategy for the overall growth of an organization.

Engineering Economics:

Economics as a science, studies the economic aspects of human life. Engineers, today play an

important role in fulfilling the ultimate aim of economics i.e. to give maximum satisfaction with

minimum use of resources. The job of an engineer, at present is to improve wealth of the country

and proper utilization of resources thus providing maximum utility to the society.

Before 1940, engineers were mainly concerned with the design, construction, and operation of

machines and processes. Many factors like accounting, finance, micro-economics also contribute

to the expansion of engineers’ responsibilities. This field, today, unlike past remains highly

dynamic. Engineers, today act as planners, problem solvers, managers, and decision makers.

Engineering Economics comprise of two parts viz. ‘Engineering’ and ‘Economics’. Engineering

while involves the study and practice of mathematics and natural sciences applied with a view to

economically utilize materials and forces of nature to the benefit of mankind, Economics

involves making decisions in the presence of scarce resources.

Engineering economics, thus, is the discipline that involves application of economic principles to

the engineering problems e.g. comparing costs of two alternative investment projects. The

techniques and models of engineering economics assist engineers to make crucial decisions.

Why Should An Engineer Study Economics?

The increased diversity of technologies, resources and design requires that engineers have

a firm grasp of economics. Economic forces not only provide a rational approach to the

choice among many alternatives in complex situations, but serve to stimulate inventive

process on which so much of the new technology is dependent on.

Engineers in diverse fields need to understand the technicalities of areas beyond their

expertise to effectively communicate such that synergy prevails. Through clear

communication, can only an engineering project be successfully completed.

Engineers need to manage lots of information. An engineer must have a fundamental

understanding of economics to benefit from such shared information.

While money is the medium of exchange, measure of value and means of storing wealth,

engineers should understand that all technical projects take shape with some kind of

finance. Knowledge of economic principles gives engineers means to bring ideas to form.

Studying economics helps engineers develop intellectual creativity. For the engineer who

understands economics, innovation will come more naturally.

Engineering Economics and Costing:

After deciding to invest in a project, the next imperative is to know the expected financial results.

The accounting procedures which properly use financial information achieve the objective of

cost control and other desired financial goals. From the perspective of engineering economic

analysis, cost accounting is more important in the sense, it is concerned with decision making.

Utility Analysis

Cardinal Utility Analysis:

Human wants are unlimited and they are of different intensity. The means at the disposal of a

man are not only scarce but they have alternative uses. As a result of scarcity of recourses, the

consumer cannot satisfy all his wants. He has to choose which want to satisfy first and he is

confronted in making a choice e.g., a man is thirsty. He goes to the market and satisfies his thirst

by purchasing coca cola instead of tea. The consumer buys a commodity because it gives him

satisfaction. In technical term, a consumer purchases a commodity because it has utility for him.

Utility is thus, defined as: "The power of a commodity or service to satisfy human want". e.g.,

cloth has a utility for us because we can wear it. Pen has a utility who can write with it. The

utility is subjective in nature. It differs from person to person. The utility of a bottle of wine is

zero for a person who is non drinker while it has a very high utility for a drinker. Similarly,

poison is injurious to health but it gives subjective satisfaction to a person who wishes to die.

Total Utility and Marginal Utility:

"Total utility (TU) is the total satisfaction obtained from all units of a particular commodity

consumed over a period of time". For example, a person consumes eggs and gains 50 utils of

total utility. This total utility is the sum of utilities from the successive units (30 utils from the

first egg, 15 utils from the second and 5 utils from the third egg).

"Marginal utility (MU) is the change in total utility that results from unit change in consumption

of the commodity within a given period of time". For example, when a person increases the

consumption of eggs from one egg to two eggs, the total utility increases from 30 utils to 45 utils.

The marginal utility here would be the15 utils of the 2nd egg consumed.

As a person consumes more and more units of a commodity, the marginal utility of the additional

units begins to diminish but the total utility goes on increasing at a diminishing rate. When the

marginal utility comes to zero or the point of satiety is reached, the total utility is maximum. If

consumption is increased further from this point of satiety, the marginal utility becomes negative

and total utility begins to diminish.

The relationship between total utility and marginal utility is now explained with the help of

following schedule and a graph.

Schedule:

Units of Apple Consumed/ Day Total Utility in Utils/Day Marginal Utility in Utils/Day

1 7 7

2 11 4 (11-7)

3 13 2 (13-11)

4 14 1 (14-13)

5 14 0 (14-14)

6 13 -1 (13-14)

The above table shows that when a person consumes no apple, he gets no satisfaction. His total

utility is zero. In case he consumes one apple a day, his total utility is 7 and his marginal utility is

also 7. In case he consumes second apple, he gains extra 4 utils. Thus, his total utility is 11 utils

from two apples. His marginal utility has gone down from 7 utils to 4 utils because he has a less

craving for the second apple. Same is the case with the consumption of third apple. In case the

consumer takes fifth apple, his marginal utility falls to zero utils and if he consumes sixth apple

also, marginal utility becomes negative and total utility has diminished.

Curve:

(i) TU curves starts at the origin as zero consumption of apples yield zero utility.

(ii) TU curve reaches at its maximum or a peak of M when MU is zero.

(iii) MU curve falls through the graph. A special point occurs when the consumer

consumes the fifth apple. He gains no marginal utility from it. After this point,

marginal utility becomes negative.

(iv) MU curve can be derived from the total utility curve. It is the slope of the line joining

two adjacent quantities on the curve. For example, the marginal utility of the third

apple is the slope of line joining points a and b.

Law of Diminishing Marginal Utility:

The law of diminishing marginal utility describes a familiar and fundamental tendency of human

behavior. It states that “As a consumer consumes more and more units of a specific commodity,

the utility from the successive units goes on diminishing”. This law is based on Three Facts:

Total wants of a man are unlimited but each single want can be satisfied. As a man gets

more and more units of a commodity, the desire of his for that good goes on falling. A

point is reached when the consumer no longer wants any more units of that good.

Different goods are not perfect substitutes for each other in satisfying various particular

wants. As such the marginal utility will decline as the consumer gets additional units of it

The marginal utility of money is constant given the consumer’s wealth.

The basis of this law is a fundamental feature of wants. It states that when people go to the

market for the purchase of commodities, they do not attach equal importance to all the

commodities which they buy. In case of some of commodities, they are willing to pay more and

in some less.

There are two main reasons for this difference in demand:

The liking of the consumer for the commodity and

The quantity of the commodity which the consumer has with himself.

The more one has of a thing, the less he wants the additional units of it. In other words, the

marginal utility of a commodity diminishes as the consumer gets larger quantities of it. This is

the axiom of law of diminishing marginal utility.

This law can be explained by taking an example. Suppose, a man is very thirsty. He goes to the

market and buys one glass of water. The first glass of water has great utility for him. If he takes

second glass of water after that, the utility will be less than that of the first one. It is because the

edge of his thirst has been blunted to a great extent. If he drinks third glass of water, the utility of

the third glass will be less than that of second and so on. The utility goes on diminishing with the

consumption of every successive glass of water till it drops down to zero. This is the point of

satiety. It is the position of consumer’s equilibrium or maximum satisfaction. If the consumer is

forced further to take a glass of water, it leads to disutility causing total utility to decline. The

marginal utility will become negative. A rational consumer will stop taking water at the point at

which marginal utility becomes negative even if the good is free.

Schedule:

Units Total Utility Marginal Utility

1st glass 20 20

2nd glass 32 12

3rd glass 40 8

4th glass 42 2

5th glass 42 0

6th glass 39 -3

From the above table, it is clear that in a given span of time, the first glass of water to a thirsty

man gives 20 units of utility. When he takes second glass of water, marginal utility goes down to

12 units; When he consumes fifth glass of water, the marginal utility drops down to zero and if

the consumption of water is forced further from this point, the utility changes into disutility (-3).

Diagram:

In the figure (2.2), along OX we measure units of a commodity consumed and along OY is

shown the marginal utility derived from them. The marginal utility of the first glass of water is

called initial utility. It is equal to 20 units. The MU of the 5th glass of water is zero. It is called

satiety point. The MU of the 6th glass of water is negative (-3). The MU curve here lies below

the OX axis. The utility curve MM/ falls from left down to the right showing that the marginal

utility of the successive units of glasses of water is falling.

Assumptions of the Law of Diminishing Marginal Utility:

(i) Rationality: In the cardinal utility analysis, it is assumed that the consumer is rational.

He aims at maximization of utility subject to availability of his income.

(ii) Constant marginal utility of money: Marginal utility of money for purchasing goods

remains constant. If the marginal utility of money changes with the increase or

decrease in income, it can’t yield correct measurement of the marginal utility of good.

(iii) Diminishing marginal utility: The utility gained from the successive units of a

commodity diminishes in a given time period.

(iv) Consumption to be continuous: The consumption of a commodity should be

continuous. If there is interval between consumption of same units of the commodity,

the law may not hold good. E.g., if one takes one glass of water in the morning and

the 2nd at noon, the marginal utility of the 2nd glass of water may increase.

(v) No change to fashion: If there is a sudden change in fashion or customs or taste of a

consumer, it can than make the law inoperative.

(vi) No change in the price of the commodity: There shouldn’t be any change in the price

of the commodity as more units of it are consumed.

The Law of Equi-Marginal Utility:

The law of equi-marginal utility is simply an extension of law of diminishing marginal utility to

two or more than two commodities. This law is stated in the following words: “The household

maximizing the utility will so allocate the expenditure between commodities that the utility of

the last penny spent on each item is equal”.

As we know, every consumer has unlimited wants. However, the income at his disposal at any

time is limited. The consumer is, therefore, faced with a choice among many commodities that

he would like to pay. He, therefore, consciously or unconsciously compresses the satisfaction

which he obtains from purchase of the commodity and the price which he pays for it. If he thinks

the utility of the commodity is greater or at least equal to the loss of utility of money, he buys

that commodity. As he buys more and more of that commodity, the utility of the successive units

begins to diminish. He stops further purchase of the commodity at a point where the marginal

utility of the commodity and its price are just equal. If he pushes the purchase further from his

point of equilibrium, then the marginal utility of the commodity will be less than that of price

and the household will be loser.

A consumer will be in equilibrium with a single commodity symbolically:

MUx = Px

A prudent consumer in order to get the maximum satisfaction from his limited means compares

not only the utility of a particular commodity and the price but also the utility of the other

commodities which he can buy with his scarce resources. If he finds that a particular expenditure

in one use is yielding less utility than that of other, he will try to transfer a unit of expenditure

from the commodity yielding less marginal utility. The consumer will reach his equilibrium

position when it will not be possible for him to increase the total utility by uses. The position of

equilibrium will be reached when the marginal utility of each good is in proportion to its price

and the ratio of the prices of all goods is equal to the ratio of their marginal utilities.

The consumer will maximize total utility from his income when the utility from the last rupee

spent on each good is the same. Algebraically, this is:

MUa / Pa = MUb / Pb = MUc / Pc = MUn = Pn

Here: (a), (b), (c)…. (n) are various goods consumed.

Assumptions of Law of Equi-Marginal Utility:

(i) Independent utilities. The marginal utilities of different commodities are independent

of each other and diminish with more and more purchases.

(ii) Constant marginal utility of money. The marginal utility of money remains constant

to the consumer as he spends more and more of it on the purchase of goods.

(iii) Utility is cardinally measurable.

(iv) Every consumer is rational in the purchase of goods.

The principle of equi-marginal utility can be explained by taking an example. Suppose a person

has Rs. 5 with him whom he wishes to spend on two commodities, tea and coffee. The marginal

utility derived from both these commodities is as under:

Schedule:

Units of Money MU of Tea MU of Coffee

1 10 12

2 8 10

3 6 8

4 4 6

5 2 3

Rs. 5 Total Utility = 30 Total Utility = 39

A rational consumer would like to get maximum satisfaction from Rs. 5. He can spend money in

three ways:

(i) Rs. 5 may be spent on tea only.

(ii) Rs. 5 may be utilized for the purchase of coffee only.

(iii) Some rupees may be spent on the purchase of tea and some on the purchase of cigarettes.

If the prudent consumer spends Rs. 5 on the purchase of tea, he gets 30 utility. If he spends Rs. 5

on the purchase of coffee, the total utility derived is 39 which is higher than tea.

In order to make the best of the limited resources, he adjusts his expenditure.

(i) By spending Rs. 4 on tea and Rs. 1 on coffee, he gets 40 utility (10+8+6+4+12 = 40).

(ii) By spending Rs. 3 on tea and Rs. 2 on coffee, he derives 46 utility (10+8+6+12+10 = 46).

(iii) By spending Rs. 2 on tea and Rs. 3 on coffee, he gets 48 utility (10+8+12+10+8 = 48).

(iv) By spending Rs. 1 on tea and Rs. 4 on coffee, he gets 46 utility (10+12+10+8+6 = 46).

The sensible consumer will spend Rs. 2 on tea and Rs. 3 on coffee and will get maximum

satisfaction. When he spends Rs. 2 on tea and Rs. 3 on coffee, the marginal utilities derived from

both these commodities is equal to 8. When the marginal utilities of the two commodities

equalize, the total utility is then maximum, i.e., 48 as is clear from the schedule given above.

Curve:

In the figure 2.3 MU is the marginal utility curve for tea and KL of coffee. When a consumer

spends OP amount (Rs. 2) on tea and OC (Rs. 3) on coffee, the marginal utility derived from the

consumption of both the items (Tea and Coffee) is equal to 8 units (EP = NC). The consumer

gets the maximum utility when he spends Rs. 2 on tea and Rs. 3 on coffee.

We now assume that the consumer spends Rs. 1 on tea (OC/ amount) and Rs. 4 (OQ

/) on coffee.

If CQ/ more amounts are spent on coffee, the added utility is equal to the area CQ

/ N

/N. On the

other hand, the expenditure on tea falls from OP amount (Rs. 2) to OC/ amount (Rs. 1). There is

a loss of utility equal to the area C/PEE. The loss in utility (tea) is maximum satisfaction except

the combination of expenditure of Rs. 2 on tea and Rs. 3 on coffee.

This law is known as the Law of maximum Satisfaction because a consumer tries to get the

maximum satisfaction from his limited resources by so planning his expenditure that the

marginal utility of a rupee spent in one use is the same as the marginal utility of a rupee spent on

another use.

It is known as the Law of Substitution because consumer continuously substituting one good for

another till he gets the maximum satisfaction.

Demand Analysis

Meanings and Definition of Demand:

Demand in economics means a desire to possess a good supported by willingness and ability to

pay for it. If somebody has desire to buy a certain commodity, say a car, but he/she doesn’t have

the adequate means to pay for it, it will simply be a wish, a desire or a want and not demand.

"Demand means the various quantities of goods that would be purchased per time period at

different prices in a given market".

Characteristics of Demand:

Demand is the amount of a commodity for which a consumer has the willingness and also

the ability to buy.

Demand is always at a price. If we talk of demand without reference to price, it will be

meaningless. The consumer must know both the price and the commodity.

Demand is always per unit of time. The time may be a day, a week, a month, or a year.

Law of Demand:

For every rational consumer, when prices of the commodities fall, they are tempted to purchase

more commodities and when the prices rise, the quantity demanded decreases. There is, thus,

inverse relationship between the price of the commodity and quantity demanded. The economists

have named this inverse relationship between demand and price as the law of demand.

The law of demand states that "Other things remaining the same, the quantity demanded

increases with every fall in the price and decreases with every rise in the price". The functional

relationship between quantity demanded and the price of the commodity can be expressed

mathematically as:

Qx = f (P

x)

Where Qx = Quantity demanded of commodity x.

Px = Price of commodity x.

Demand Schedule:

The demand schedule of an individual for a commodity is a list or table of different amounts of

the commodity that are purchased at different prices per unit of time. An individual demand

schedule for a good say shirt is presented in the table below:

Individual Demand Schedule for Shirts:

Price per shirt (Rs.) 100 80 60 40 20 10

Quantity demanded per year Qx 5 7 10 15 20 30

According to this demand schedule, an individual buys 5 shirts at Rs.100 per shirt and 30 shirts

at Rs.10 per shirt in a year.

Demand Curve/Diagram:

Demand curve is a graphic representation of the demand schedule.

In figure (4.1), the quantity demanded of shirts is plotted on X-axis price is measured on Y-axis.

Each price-quantity combination is plotted as a point on this graph. If we join the price quantity

points a, b, c, d, e and f, we get the individual demand curve for shirts.

Assumptions of Law of Demand:

There should not be any change in the tastes of the consumers for goods

The purchasing power of the typical consumer must remain constant

The price of all other commodities should not vary

Limitations/Exceptions of Law of Demand:

Prestige goods: There are certain commodities like diamond, sports cars etc., which are

purchased as a mark of distinction in society. If the price of these goods rises, the demand

for them may increase instead of falling.

Price expectations: If people expect further rise in price of a particular commodity, they

may buy more in spite of rise in price. The violation of the law here is only temporary.

Ignorance of the consumer: If the consumer is ignorant about the rise in price of goods,

he may buy more at a higher price.

Giffen goods: If the prices of basic goods, (potatoes, sugar, etc) on which poor spend a

large part of their incomes declines, they increase demand for superior goods. Hence

when the price of giffen good falls, its demand also falls.

Market Demand for a Commodity:

The market demand for a commodity is obtained by adding up the total quantity demanded at

various prices by all the individuals over a specified period of time in the market. It is described

as the horizontal summation of the individuals demand for a commodity at various possible

prices in market.

In the schedule given below, the amount of commodity demanded by four buyers (which we

assume constitute the entire market) differs for each price. When the price of a commodity is Rs.

10, the total quantity demanded is 40 thousand units per week. At price of Rs. 2, the total

quantity demanded increases to 180 thousand units.

A market Demand Schedule in a Four Consumer Market:

Price

(Rs.)

Quantity

Demanded

Quantity

Demanded

Quantity

Demanded

Quantity

Demanded

Total Quantity

Demanded Per Week

(in thousands)

First Buyer

Second Buyer Third Buyer Fourth Buyer

10

8

6

4

2

10

15

25

40

60

13

20

30

35

50

6

9

10

15

30

11

16

20

30

40

40

60

85

120

180

.

Market Demand Curve:

The market demand curve DD/ for a commodity, like the individual demand curve is negatively

sloped, (figure 4.2). It shows that, other things remaining the same, there is an inverse

relationship between the quantity demanded and its price.

At price of Rs. 10, the quantity demanded in the market is 40 thousand units. At price of Rs. 20,

it increases to 180 thousand units. In. other words, the lower the price of the good X, the greater

is the demand for it.

Movement Vs Shifts of Demand Curve:

Demand is a multivariable function. If income and other determinants of demand such as tastes

of the consumers, changes in prices of related goods, income etc., remain constant and there is a

change only in price of the commodity, then we move along the same demand curve. In this case,

the demand curve remains unchanged. When, as a result of change in price, the quantity

demanded increases or decreases, it is technically called extension and contraction in demand.

The demand curve, which represents various price-quantities, has a negative slope. Whenever

there is a change in the quantity demanded of a good due to change in its price, there is a

movement from one point price-quantity combination to another on the same demand curve.

Such a movement from one point price quantity combination to another along the same demand

curve is shown in figure (4.3).

Diagram/Figure:

Here the price of a commodity falls from Rs. 8 to Rs. 2. As a result, the quantity demanded

increases from 100 units to 400 units per unit of time. There is extension in demand by 300 units.

This movement is from one point price quantity combination (a) to another point (b) along a

given demand curve. On the other hand, if the price of a good rises from Rs. 2 to Rs. 8, there is

contraction in demand by 300 units. We, thus, see that as a result of change in the price of a

good, the consumer moves along the given demand curve. The demand curve remains the same

and does not change its position. The movement along the demand curve is designated as change

in quantity demanded.

When there is a change in demand due to one or more than one factors other than price, it results

in the shift of demand curve. For example, if the level of income in community rises, other

factors remaining the same, the demand for the goods increases. Consumers demand more goods

at each price per period of time (Increase in demand). The demand curve shifts upward from the

original demand curve indicating that consumers at each price purchase more units of

commodity per unit of time.

If there is a fall in the disposable income of the consumers or rise in the prices of close substitute

of a good or decline in consumer taste or non-availability of good on credit, etc, etc., there is a

reduction in demand (fall or decrease in demand). The fall or decrease in demand shifts the

demand curve from the original demand curve to the left. The lower demand curve shows that

consumers are able and willing to buy less of the good at each price than before.

Schedule:

Px

(Rs.) Qx Rise in Q

x Fall in Q

x

12 100 300 50

6 250 500 200

4 500 600 300

In figure (4.4), the original demand curve is DD/. At a price of Rs. 12 per unit, consumers

purchase 100 units. When price falls to Rs. 4 per unit, the quantity demanded increases to 500

units. Let us assume now that level of income increases in a community. Now consumers

demand 300 units of the commodity at price of Rs. 12 per unit and 600 at price of Rs. 4 per unit.

Diagram/Figure:

As a result, there is an upward shift of the demand curve DD

2. In case the community income

falls, there is then decrease in demand at price of Rs. 12 per unit. The quantity demanded of a

good falls to 50 units. It is 300 units at price of Rs. 4 unit per period of time. There is a

downward shift of the demand to the left of the original demand curve.

Determinants of Demand:

The law of demand states that, other things remaining the same, demand for a commodity varies

inversely with price per unit of time. The other things have an important bearing on the demand

for a commodity. They bring about changes in demand independently of changes in price. These

non-price factors or shift factors or determinants which influence demand are as follow:

1) Changes in population: If population of a country increases, demand for various kinds of

goods will increase even if prices remain same. The demand curve will shift upward to

the right. The nature of commodities demanded will depend on the taste of consumers. If

percentage of children to the total population increases in a country, there will be greater

demand for toys, children food, etc. Similarly, if the percentage of old people to the total

population increases, demand for walking sticks, artificial teeth, etc. will increase.

2) Changes in tastes: Demand for a commodity may change due to changes in tastes and

fashions e.g., people develop a taste for coffee. There is then a decrease in the demand for

tea. The demand curve for tea shifts to the left of the original demand curve. Similarly

women's fashions are usually ever changing. So, whenever there is a change in their hair

style (say), the demand for hairpins, hair nets, etc. is greatly affected.

3) Changes in income: Increase in the income of consumers generally leads to an increase

in demand for some commodities and a decrease in demand for other commodities. For

example, when income of people increases, they begin to spend money on those which

were previously regarded by them as luxuries, or semi-luxuries and reduce the

expenditure on inferior goods. Take the case of a man whose income has increased from

Rs. 5000 to Rs. 50,000 per month. His consumption of wheat will go down because he

now spends more money on superior food such as cake, fish, daily products, fruits, etc.

4) Changes in the distributions of wealth: If an equal distribution of wealth is brought

about in a country, then there will be less demand for expensive luxuries goods. There

will be more demand for necessaries and comfort items.

5) Changes in the price of substitutes: If the price of a particular commodity rises, people

may stop further purchase of that commodity and spend money on its substitute which is

available at a lower price. Thus we find, a change in demand can also be brought about

by a change in the price of the substitute.

6) Changes in the state of trade: The total quantity of goods demanded is also affected by

the cyclical fluctuations in economic activities. If the trade is prosperous, the demand for

raw material, machinery, etc., increases. If on the other hand, the trade is dull, demand for

producer goods will fail sharply as compared to the demand for consumer goods.

7) Climate and weather conditions: The climate and weather conditions have an important

bearing on the demand of a commodity. For instance, the consumer's demand for woolen

clothes increases in winter and decreases in summer.

Why Demand Curves Slope Downwards?

Law of diminishing marginal utility: The law of demand is based on the law of

diminishing marginal utility. According to the cardinal utility approach, when a consumer

purchases more units of a commodity, its marginal utility declines. The consumer,

therefore, will purchase more units of that commodity only if its price falls. Thus a

decrease in price brings about an increase, in demand. The demand curve, therefore, is

downward sloping.

Income effect: Other things being equal, when the price of a commodity decreases, the

real income or the purchasing power of the household increases. The consumer is now in

a position to purchase more commodities with the same income. The demand for a

commodity thus increases not only from the existing buyers but also from the new buyers

who were earlier unable to purchase at higher price. When at a lower price, there is a

greater demand for a commodity by the households; the demand curve is bound to slope

downward from left to right.

Substitution effect: The demand curve slopes downward from left to right also because

of the substitution effect. For instance, the price of meat falls and the prices of other

substitutes say poultry remain constant. Then the households would prefer to purchase

meat because it is now relatively cheaper. The increase in demand with a fall in the price

of meat will move the demand curve downward from left to right.

The demand for any commodity at a given price is the quantity of it which will be bought per

unit of time at the price. Conceptually, the term ‘demand’ implies a desire for a commodity

backed by ability and willingness to pay for it. Then, it becomes effective demand which only

figures in economic analysis and business decisions.

Elasticity of Demand

What is Price Elasticity of Demand?

The law of demand tells us when the price of a good rises, its quantity demanded will fall, all

other things held constant. The law however, does not indicate as to how much the quantity

demanded will fall with the rise in price or how much responsive the demand is to a price rise.

The economists here use the concept of elasticity of demand.

Price elasticity of demand measures the degree of responsiveness of the quantity demanded of a

good to a change in its price. It is also defined as: "Proportionate change in quantity demanded

caused by a given proportionate change in price". Symbolically price elasticity of demand is

expressed as:

Ed = (∆Q/Q) / (∆P/P)

Where Ed stands for price elasticity of demand

Q stands for original quantity

P stands for original price

∆ stands for a small change.

The price elasticity of demand tells us the relative amount by which the quantity demanded will

change in response to a change in the price of a particular good. For example, if there is a 10%

rise in the price of a tea and it leads to reduction in its demand by 20%, the price elasticity of

demand will be:

Ed = -20 / +10 = -2.0

Degrees of Elasticity of Demand:

The variation in demand is, however, not uniform with a change in price. In case of some

products, a small change in price leads to a relatively larger change in quantity demanded. For

example, a decline of 1% in price leads to 8% increase in the quantity demanded of a

commodity. In such a case, the demand is said to be elastic. There are other products where the

quantity demanded is relatively unresponsive to price changes. A decline of 8% in price, for

example, gives rise to 1% increase in quantity demanded. Demand here is said to be inelastic.

The economists group various degrees of elasticity of demand into five categories.

(1) Perfectly Elastic Demand (Ed = ∞):

A demand is perfectly elastic when a small increase in the price of a good brings its quantity

demanded to zero. Perfect elasticity implies that individual producers can sell all they want at a

ruling price but cannot charge a higher price. If any producer tries to charge even one penny

more, no one would buy his product. People would prefer to buy from another producer who

sells the good at the prevailing market price.

A perfect elastic demand curve is illustrated in fig. 6.1.

The demand curve DD/ is a horizontal line which indicates that the quantity demanded is

extremely (infinitely) responsive to price. Even a slight rise in price (say Rs. 4.02), drops the

quantity demanded of a good to zero. The curve DD/ is infinitely elastic.

(2) Perfectly Inelastic Demand (Ed = 0):

When the quantity demanded of a good dose not change at all to whatever change in price, the

demand is said to be perfectly inelastic or the elasticity of demand is zero. For example, a 30%

rise or fall in price leads to no change in the quantity demanded of a good.

In figure 6.2 a rise in price from OA to OC or fall in price from OC to OA causes no change

(zero responsiveness) in the amount demanded.

(3) Unitary Elasticity of Demand (Ed = 1):

When the quantity demanded of a good change by exactly the same percentage as price, the

demand is said to have a unitary elasticity. For example, a 30% change in price leads to 30%

change quantity demanded.

In figure (6.3) DD/ demand curve with unitary elasticity shows that as the price falls from OA to

OC, the quantity demanded increases from OB to OD. On DD/ demand curve, the percentage

change in price brings about an exactly equal percentage in quantity at all points a, b. The

demand curve of elasticity is, therefore, a rectangular hyperbola.

(4) Elastic Demand:

If a one percent change in price causes greater than a one percent change in quantity demanded

of a good, the demand is said to be elastic. Alternatively, we can say that the elasticity of demand

is greater than 1. For example, if price of a good change by 10% and it brings a 20% change in

demand, the price elasticity is greater than one.

In figure (6.4) DD

/ curve is relatively elastic along its entire length. As the price falls from OA to

OC, the demand of the good extends from OB to ON i.e., the increase in quantity demanded is

more than proportionate to the fall in price.

(5) Inelastic Demand:

When a change in price causes a less than a proportionate change in quantity demanded, demand

is said to be inelastic. The elasticity of a good is here less than 1. For example, a 30% change in

price leads to 10% change in quantity demanded of a good, then Ed = 1/3

In figure (6.5), DD

/ demand curve is relatively inelastic. As the price fall from OA to OC, the

quantity demanded of the good increases from OB to ON units. The increase in the quantity

demanded is here less than proportionate to the fall in price.

Point Elasticity Method:

"The measurement of elasticity at a point on the demand curve is called point elasticity". The

point elasticity of demand is defined as: "The proportionate change in the quantity demanded

resulting from a very small proportionate change in price".

The price elasticity of demand can also be measured at any point on the demand curve. If the

demand curve is linear (straight line), it has a unitary elasticity at the mid point. The total

revenue is maximum at this point. Any point above the midpoint has elasticity greater than 1.

Here, price reduction leads to an increase in the total revenue. Below the midpoint elasticity is

less than 1. Price reduction leads to reduction in the total revenue of the firm.

Graph/Diagram:

(1) Elasticity of demand at point D = DG/DA = 400/400 = 1 (Unity).

(2) Elasticity of demand at point E = GE/EA = 200/600 = 0.33 (<1).

(3) Elasticity of Demand at point C = GC/CA = 600/200 = 3 (>1).

(4) Elasticity of Demand at point A is infinity.

(5) At point G, the elasticity of demand is zero.

If the demand curve is non linear, then elasticity at a point can be measured by drawing a tangent

at the particular point. This is explained with the help of a figure given above. In figure 6.10, the

elasticity on DD/ demand curve is measured at point C by drawing a tangent at point C:

Ed = BM/MO = BC/CA = 400/200 = 2 (>1).

Here elasticity is greater than unity. Point C lies above the midpoint of the demand curve DD/. In

case the demand curve is a rectangular hyperbola, change in price will have no effect on the total

amount spent on the product. As such, the demand curve will have unitary elasticity at all points.

Arc Elasticity Method:

Normally the elasticity varies along the length of the demand curve. If we are to measure

elasticity between any two points on the demand curve, then the Arc Elasticity Method is used.

Arc elasticity is a measure of average elasticity between any two points on the demand curve. It

is defined as: "The average elasticity of a range of points on a demand curve". Arc elasticity is

calculated by using the following formula:

Ed = (∆q/ ∆p) X (p1 + p

2) / (q

1 + q

2)

Where, ∆q denotes change in quantity.

∆p denotes change in price.

q1

signifies initial quantity.

q2

denotes new quantity.

P1

stands for initial price

P2 denotes new price.

Graphical presentation of measuring Elasticity using the Arc Method:

In fig. (6.11), it is shown that at a price of Rs. 10, the quantity demanded of apples is 5 Kg. per

day. When its price falls from Rs. 10 to Rs. 5, the quantity demanded increases to 12 Kg. of

apples per day. The arc elasticity of AB part of demand curve DD/ can be calculated as under:

Ed = (7/5) X (10 + 5) / (12 + 5) = 1.23 The arc elasticity is more than unity.

Types of Elasticity of Demand:

The quantity of a commodity demanded per unit of time depends on various factors such as price

of a commodity, the money income, the prices of related goods, the tastes of the people, etc.

Whenever there is a change in any of the variables stated above, it brings about a change in the

quantity of the commodity purchased over a specified period of time. The elasticity of demand

measures the responsiveness of quantity demanded to a change in any one of the above factors

by keeping other factors constant.

The three main types of elasticity of demand are now discussed in brief.

Price Elasticity of Demand:

Price elasticity of demand is defined as: "The ratio of proportionate change in the quantity

demanded of a good caused by a given proportionate change in price".

Ed = (Δq / Δp) X (P / Q)

Let us suppose that price of a good falls from Rs. 10 per unit to Rs. 9 per unit in a day. The

decline in price causes the quantity of the good demanded to increase from 125 units to 150 units

per day. The price elasticity will be:

Ed = (Δq / Δp) X (P / Q)

Δq = 150 - 125 = 25

Δp = 10 - 9 = 1

Original Quantity = 125

Original Price = 10

Ed = 25 / 1 X 10 / 125 = 2

Income Elasticity of Demand:

Income is an important variable affecting the demand for a good. When there is a change in the

level of income of a consumer, there is a change in the quantity demanded of a good, other

factors remaining the same. The degree of change or responsiveness of quantity demanded of a

good to a change in the income of a consumer is called income elasticity of demand. Income

elasticity of demand can be defined as: "The ratio of percentage change in the quantity of a good

purchased, per unit of time to a percentage change in the income of a consumer".

Ey = Percentage change in quantity demanded / Percentage change in Income

Let us assume that the income of a person is Rs. 4000 per month and he purchases six CD's per

month. Let us assume that the monthly income of the consumer increase to Rs. 6000 and the

quantity demanded of CD's per month rises to eight. The elasticity of demand for CD's will be

calculated as under:

Δq = 8 - 6 = 2

Δp = Rs. 6000 – Rs. 4000 = Rs. 2000

Original quantity demanded = 6

Original income = Rs. 4000

Ey = 2 / 200 X 4000 / 6 = 0.66

Cross Elasticity of Demand:

Cross elasticity of demand is defined as: "The percentage change in the demand of one good as a

result of the percentage change in the price of another good".

Exy = % Change in Quantity Demanded of Good X / % Change in Price of Good Y

When two goods are substitute of each other, such as coke and Pepsi, an increase in the price of

one good will lead to an increase in demand for the other good. The numerical value of goods is

positive. Therefore, Coke and Pepsi are close substitutes. However, in case of complementary

goods such as car and petrol, cricket bat and ball, a rise in the price of one good say cricket bat

by 7% will bring a fall in the demand for the balls (say by 6%). The cross elasticity of demand

which are complementary to each other is, therefore, 6% / 7% = 0.85 (negative).

Factors Determining Price Elasticity of Demand:

The price elasticity of demand is not the same for all commodities. It may be high or low

depending upon number of factor. These factors which influence price elasticity of demand, in

brief, are as under:

Nature of the Commodities - In developing countries, per capital income of the people

is generally low. They spend a greater amount of their income on the purchase of

necessities of life such as wheat, milk, cloth etc. They have to purchase these

commodities whatever be their price. The demand for goods of necessities is, therefore,

less elastic or inelastic. The demand for luxury goods, on the other hand is greatly elastic

e.g., if the price of burger falls, its demand in the cities will go up.

Availability of Substitutes - If a good has greater number of close substitutes available

in the market, the demand for the good will be greatly elastic e.g., if the price of Coca

Cola rises in the market, people will switch over to the consumption of Pepsi Cola, which

is its close substitute. So the demand for Coca Cola is elastic.

Proportion of Income Spent on the Good - If proportion of income spent on the

purchase of a good is very small, the demand for such a good will be inelastic e.g., if the

price of a box of matches or salt rises by 50%, it will not affect the consumers’ demand

for these goods. The demand for those therefore will be inelastic. On the other hand, if

the price of a car rises from Rs. 6 lakhs to Rs. 9 lakhs and it takes a greater portion of the

income of the consumers, its demand would fall. The demand for car is, therefore, elastic.

The Period of Time – The period of time plays an important role in shaping the demand

curve. In short run, when the consumption of a good can’t be postponed, its demand will

be less elastic. In long run if the price rise persists, people will find out methods to reduce

the consumption of goods. So the demand for a good in long run is elastic, other things

remaining constant. For example if price of electricity goes up, it is very difficult to cut

back its consumption in short run. However, if the rise in price persists, people will plan

substituting with gas heater, fluorescent bulbs etc. so that they use less electricity. So the

elasticity of demand will be greater (Ed = > 1) in the long run than in the short run.

Number of Uses of a Good - If a good can be put to a number of uses, its demand is

greater elastic (Ed > 1) e.g., if price of coal falls, its quantity demanded will rise

considerably because demand will be coming from households, industries, railways etc.

Importance of Elasticity of Demand:

Important in taxation policy - When finance minister levies tax on certain commodities,

he has to see whether the demand for that commodity is elastic or inelastic. If the demand

is inelastic, he can increase the tax and thus can collect larger revenue. But if the demand

of a commodity is elastic, he is not in a position to increase the rate of a tax. If he does so,

the demand for that commodity will go down and hence, total revenue will reduce.

Price discrimination by monopolist - If the monopolist finds that the demand for his

commodities is inelastic, he will at once fix the price at a higher level in order to

maximize his net profit. In case of elastic demand, he will lower the price in order to

increase his sale and derive the maximum net profit.

Important to businessmen - The concept of elasticity is of great importance to

businessmen. When the demand of a good is elastic, they increases sale by towering its

price. In case the demand is inelastic, they are then in a position to charge higher price for

a commodity.

Help to trade unions - The trade unions can raise the wages of the labor in an industry

where the demand of the product is relatively inelastic. On the other hand, if the demand,

for product is relatively elastic, the trade unions can’t press for higher wages.

Determination of rate of foreign exchange - The rate of foreign exchange is also

considered on the elasticity of imports and exports of a country.

Guideline to the producers - The concept of elasticity provides a guideline to the

producers for the amount to be spent on advertisement. If the demand for a commodity is

elastic, the producers shall have to spend large sums of money on advertisements for

increasing sales.

Use in factor pricing - The factors of production which have inelastic demand can obtain

a higher price in the market then those which have elastic demand. This concept explains

the reason of variation in factor pricing.

Supply Analysis

Supply is of the scarce goods. It is the amount of a commodity that sellers are able and willing to

offer fore sale at different prices per unit of time.

Law of Supply:

There is direct relationship between the price of a commodity and its quantity offered fore sale

over a specified period of time. When the price of a goods rises, other things remaining the same,

its quantity increases and as price falls, the amount available for sale decreases. This relationship

between price and quantities which suppliers are prepared to offer for sale is called law of

supply. The law of supply thus states that ceteris paribus, sellers supply more goods at a higher

price than they are willing at a lower price.

The supply function can also be expressed in symbols.

QxS = Φ (Px, Tech, Si, X ...)

Where, Qxs = Quantity supplied of commodity x by the producers.

Px = Price of commodity x.

Tech = Technology.

S = Supplies of inputs.

X = Taxes/Subsidies.

The law of supply can be explained with the help of a schedule and a curve.

Market Supply Schedule of a Commodity (In Rupees)

Px 4 3 2 1

QxS 100 80 60 40

In the table above, the produce are able and willing to offer for sale 100 units of a commodity at

price of Rs. 4. As the price falls, the quantity offered for sale decreases. At price of Re. 1, the

quantity offered for sale is only 40 units.

Supply Curve/Diagram:

In figure (5.1), price is plotted on the vertical axis OY and the quantity supplied on the horizontal

axis OX. The four points d, c, b, and a show each price quantity combination. The supply curve

SS/ slopes upward from left to right indicating that less quantity is offered for sale at lower

price and more at higher prices. The supply curve is usually positively sloped.

Determinants of Supply:

Changes in Factor Price - The rise of fall in supply may take place due to changes in the

cost of production of a commodity. If prices of various factor of production increase of a

commodity, then total cost of production will rise. There will be reduction in supply of

that commodity at each price because the amount demanded decreases with rise in price.

Conversely, if the prices of the various factors of production fall down, it will result in

lowering the cost of production and so an increase in the supply.

Changes in Technique - The supply of a commodity may also be affected by progress in

technique. If an improvement in technique takes place in a particular industry, it will help

in reducing its cost of production. This will result in greater production and so an increase

in supply of commodity. The supply curve will shift to the right of original supply curve.

Improvement in the Means of Transport - The supply of commodity may also increase

due to improvement in the means of transport. If the means of transport are cheep and

fast, then supply of the commodity can be increased at a short notice at lower price.

Climatic Changes in case of Agricultural Products - The supply of agricultural products

is directly affected by the weather conditions and the use of the better methods of

production. If rain is timely, plentiful and well-distributed; and improved methods of

cultivation are employed then other things remaining the same, there will be bumper

crops. It would then be possible to increase the supply of the agriculture products.

Political Changes - The increase or decrease in supply may also take place due to

political disturbances in a country. In such situations, the channels of production are

disorganized. It results in the decrease of certain goods and the supply curve shifts to the

left of originals curve.

Taxation Policy - If a government levies heavy taxes on the import of particular

commodities, then the supply of these commodities is reduced at each price. The supply

curve shifts to the left. Conversely if the taxes on output in the country are low and

government encourages the import of foreign commodities, then the supply can be

increased easily. The supply curve shifts to the right of originals supply curve.

Difference between Shift and Movement in Supply Curve:

As price rises, the quantity supplied increases and as price falls the quantity supplied increases

provided other things remain the same. This change in the quantity supplied of a commodity is a

movement of one price quantity combination to another on the same supply curve. Such a

movement at varying prices is now illustrated with the help of supply curve given in figure 5.2.

In the figure (5.2) given below, at price "aT" (Rs. 3), 50 units of quantity is supplied. When price

rises to “dL” (Rs. 7), the quantity supplied by the producers increases to 110. The change in

quantity supplied at varying prices is referred to as movement along the same supply curve.

Diagram/Figure:

If due to one or a combination of non-price factors, less quantity is brought into the market for

sale at each price, the supply is said to have fallen. In case of fall in supply, the supply curve

shifts to the left of the original supply curve. The rise and fall of supply curve (shifts in supply

curve) is explained with the help of an imaginary schedule and a diagram.

Schedule of Supply Curve:

Price per shirt(Rupees) Original quantity supplied per Week Rise in supply Fall in supply

50 200 320 140

40 160 200 100

30 100 150 70

20 39 100 15

Figure of Shifts in Supply Curve:

In figures (5.3), SS/ is the original supply curve. S

2S

2 to the right of the original supply curve

shows an increase in the quantity supplied at each price. S3S

3 supply curve to the left of original

supply curve indicates a decrease in supply at each price over a specified period of time.

Equilibrium of Demand and Supply

In economic sense, market is a system in which buyers and sellers bargain for price of a product,

settle the price and transact their business. The determination of price of a commodity depends

on the number of sellers and a number of buyers. The number of sellers in a market determines

the nature and degree of competition i.e. structure of the market.

The market structure is broadly classified into the following four types:

Perfect competition – Large number of sellers selling a homogenous product.

Monopoly – Single seller of a product without a close substitute.

Oligopoly – Small number of big sellers selling the same product

Monopolistic competition – Fairly large number of sellers selling differentiated products.

Characteristics of perfect competition Large number of sellers and buyers – The number of sellers and buyers is so large that

share of each seller in total supply and share of each buyer in total demand is negligibly

small and hence the market price determined by the forces is acceptable to both.

Homogeneity of products – Products supplied by various firms are so identical in

appearance and use that buyers hardly can distinguish between them. No firm can gain

competitive advantage over other firms nor do the firms distinguish between the buyers.

Perfect mobility of factors of production – For a market to be perfectly competitive,

there should be perfect mobility of resources that is factors of production must move

freely into or out of an industry and from one firm to another.

Free entry and free exit of firms – There is no restriction, legal or otherwise on the

firm’s entry into or exit from the industry.

Perfect knowledge – There is perfect dissemination of information about the market

conditions and both buyers and sellers are fully aware of the nature of product, its

availability and the price prevailing in the market.

Absence of collusion or artificial restraint – There is no collusion between sellers like

sellers’ unions nor is there any kind of collusion between buyers like consumer forum.

Sellers and buyers act independently and firms enjoy freedom of independent decisions.

Price Determination under Perfect Competition:

Demand for a commodity is "The total quantity of that commodity which buyers will take at

different prices per unit of time" while supply of a commodity refers to "That quantity of the

commodity which sellers are willing to offer for sale at different prices per unit of time".

Under perfect competition, there is a single ruling market price – the equilibrium price

determined by the interaction of forces of total demand (of all the buyers) and total supply (of all

the sellers) in the market. Thus, both the market or equilibrium price and the volume of

production in a market under perfect competition are determined by the intersection of total

demand and total supply.

In the market, there are large number of buyers and sellers. It is the desire of every buyer in the

market to purchase a commodity at the lowest possible price while the sellers wish to sell it at the

highest possible price. When buyers compete among themselves for the purchase of particular

commodity, the price of that commodity goes up and when there is competition amongst the

sellers, the price comes down. The price of a commodity tends to settle at a point where the

quantity demanded is exactly equal to the quantity supplied. The price at which the buyers and

sellers are willing to buy and sell an equal amount of commodity is called the, equilibrium price.

Let’s illustrate the above proposition with the help of a schedule and a curve.

Schedule:

Quantity Supplied (Cooking Oil Kg)

Per Week

Price (Rupees) Quantity Demanded

(Cooking Oil Kg) Per Week

800

600

500

450

19

18

17

16

100

250

400

450

350

100

15

14

500

700

When the price of cooking oil is Rs. 16 per Kg, the total quantity demanded in a week is exactly

equal to the total quantity supplied. So Rs. 16 is the equilibrium price for the period and the

equilibrium amount, i.e. the quantity demanded and offered for sale is 450 Kgs. of cooking oil is:

Qd

= Qs

If the conditions assumed above remain the same, then there can be no equilibrium price other

than Rs. 16 e.g., if the price of cooking oil happens to rise to Rs. 18 per Kg. At this price, the

sellers are anxious to sell 600 Kgs. of ghee but the buyers are willing to buy only 250 Kgs. The

sellers will compete with one another to dispose off this surplus stock. The competition among

the sellers will result in lowering the price. When the price comes down to Rs. 16 (i.e. the

equilibrium price), then the whole of the stock will be sold. Conversely, if the price happens to

fall to Rs. 14 per kilogram, the buyers would like to buy 700 Kgs. of cooking oil, but the sellers

are willing to sell only 100 Kgs. The buyers, in order to buy more cooking oil at a lower price

will compete among themselves. This competition among the buyers will increase the price of

ghee. Finally, the price will be reestablished at the equilibrium price which is Rs. 16.

In the figure (8.1) DD/ is the demand curve which, represents the different amount of .the

commodity that are purchased in the market at different prices, SS/ is the supply curve which

indicates the amount of the commodity that is offered for sale at different prices per unit of time.

MN is the equilibrium price i.e., Rs. 16 and ON 450 kg. is the equilibrium amounts. If the price

is below the equilibrium price (Rs. 16), there is upward pressure on price due to the resulting

shortage of good. In case, the price is above the equilibrium, there is a downward pressure on

price caused by the resulting surplus of good. If is only at price MN, the buyers take of the

market exactly what sellers place on the market.

Diagram/Figure:

Alfred Marshall was the first economist who pointed out that the pricing problem should be

studied from the view point of time. He distinguished three fundamental time periods in the

determination of price:

(1) Market period price.

(2) Short run normal price.

(3) Long run normal price.

Market Period Price:

The market period is very short period during which it is practically impossible to alter output or

increase stock. Thus, supply of a commodity tends to be perfectly inelastic. The market period

price is determined by interaction of market period demand and supply as shown in fig. 15.13.

Schedule:

Price (in Rs.) Per Kg. Amount Supplied Per Day Quantity in Kg. Demanded Per Day

50 50 1

40 50 10

30 50 15

20 50 23

10 50 50

As in a perfect market, there can be only one price for a particular commodity, so the buyers who

are willing to buy at higher price, enjoy consumer's surplus. In the graph (15.13), quantity is

measured along OX axis and price along OY axis. As the supply of a commodity is fixed and

cannot be held back, hence, the market period supply curve, SS will be a vertical straight line.

The market demand curve DD' intersects the market supply curve at point M. MS (Rs. 10) is the

market price at which the total quantity of the commodity is sold in the market. If demand for the

commodity rises, the new demand curve D1D

1 intersects the market supply curve at point LLS

which is equal to Rs. 50 will be new market price. If the demand falls, the new demand curve

D2D

2 cuts the supply curve at point R, Rs. 30 which is the new equilibrium price.

Short Period Price:

In the short run, the size of a firm and the number of firms comprising an industry remain the

same. The time is considered to be so short that if demand for product increases, the old firm can

use their existing equipments more intensively and increase the supply to a limited extent, but

new firms cannot enter into the industry. As such the supply curves will tend to be relatively

inelastic. The short run normal price is established at a point where the short period supply curve

and the demand curve intersect each other.

The short run supply curve of the industry is the lateral summation of the short period marginal

cost curves of all the firms. The market demand curve is a falling curve. The determination of

price and output in the short run can be explained with the help of the above diagrams.

In fig. 15.15(a), the short run supply curve (SRSC) of the industry intersects the market demand

curve at point E. The price will be OL and the quantity supplied OT. Suppose the demand for the

commodity has gone up. The new demand curve D1D

1 intersects the market supply curve (MSC)

at point F. The price rises from OL to OR without affecting the output which remains OT as

before. The entrepreneur lured by higher prices will use the fixed capital equipment more

intensively. The old machines will also be repaired and the production expanded. The new

demand curve then intersects the short period supply curve SRSC at point Q.

In fig 15.15(b), ON will be the short run normal price which is higher than the original market

price OL but lower than the raised market price OR. ON thus is the short run normal price of an

industry. This price cannot be changed by the action of an individual firm as it produces an

insignificant portion of the total supply of the output. It will have to adjust its product

accordingly. At price ON, the firm is earning abnormal profits because the price is higher than

the normal price OL.

If the market demand falls, the new demand curve D2D

2 intersects the market period supply

curve at point G. OZ then is the new equilibrium market price which is lower than the original

OL market price. The fall in the market price will affect the supply of the commodity. The firms

will reduce their output by decreasing the variable factors.

Long Period Price:

Long run is the period in which the factors of production can be adjusted to changes in demand.

Thus, in long-run, the supply curve of an industry tends to become relatively elastic. In long run,

the price will be determined at a point where demand curve and the long run supply curve

intersect each other.

In fig. 15.16, market supply curve (MSC), short period supply curve (SPC), long period supply

curve (LPSC), pass through the point P. The market price, short period price and the long run

normal price thus is equal to ON.

Let us suppose that there is an increase in the market demand. The new demand curve D1D

1

intersects the market supply cure, short period supply curve, and long period supply curve at

points Z, R, A, respectively. The new market price will be equal to OD, the short period price

equal to OC and long period price equal to OE. The market price OD is higher than short period

normal price and long run normal price. The short period normal price OC is lower than the

market price but higher than long run normal price. The long run normal price OE is the lower of

the two but is higher than the original market price ON. How much the long run price will differ

from the market price depends upon the supply condition in a particular industry.

In long-run, as compared to the demand force, the supply force becomes a dominant factor in

determining the equilibrium price.

Changes in Equilibrium Price:

Any change in the demand condition or the supply condition or simultaneous change in the

conditions of both demand and supply would lead to change in equilibrium price.

Effects of Changes in Demand on Equilibrium Price:

It is assumed that no change takes place in the supply schedule, i.e., it remains fixed. This can

also be illustrated in the following diagram.

In the figure (8.2) DD

/ is the original demand curve. PM is the equilibrium price and OM the

equilibrium amount. When demand rises, supply remaining the same, the equilibrium amount

increases from OM to OG and the equilibrium price rises from PM to FG. In case of fall in

demand, which is indicated by D2D

2 curve, the quantity demanded decreases from OM to OK

and the equilibrium price falls from PM to LK.

If the supply is perfectly elastic, a rise in demand will increase the quantity but will not affect the

price. If the supply is perfectly inelastic, then a rise in demand will affect the price but not the

quantity. This can be shown with the help of the fig. 8.3. When demand rises, the supply

increases from OK to OI with further rise in demand D2D

2 the supply increases from OI to ON.

In fig. 8.4, supply is perfectly inelastic. A rise in demand affects the price which rises from RM

to KM and with the further rise in demand to LM. The quantity supplied remains the same OM.

If elasticity of supply is equal to unity, the quantity and price change in equal proportion with a

rise in demand as is clear in fig. 8.5.

If elasticity of supply greater than unity, a rise in demand will affect the supply which will

change in greater proportion than the price as is obvious from the following fig. 8.6. When

demand rises, KL quantity supplied is greater in proportion than PN price.

If the elasticity of supply is less than unity, a rise in demand will change the price in greater

proportion than the quantity as shown in fig. 8.7.The proportionate change in quantity demanded

KL is less than the change in price RN.

Effects of Shifts in Supply on Equilibrium Price:

Here the demand curve remains fixed and a change takes place in the supply of a commodity.

In the diagram (8.8) the demand curve DD

/ is assumed as fixed and change takes place only in

supply curve. PM is the initial position of the equilibrium price and OM the initial equilibrium

amount. When supply increases, OK becomes the new equilibrium amount and NK the new

equilibrium price. When supply falls, OD is the new equilibrium amount and FD the new

equilibrium price.

If demand is perfectly elastic, as in fig. (8.9), the price will not be affected and quantity

demanded will, however, increase with the increase in supply. The price remains unaltered OD.

If the demand is perfectly inelastic, then with a fall in supply, the quantity demanded will remain

unaffected and the price will go up.

With inelastic demand curve, when supply decreases there is no change in the quantity. It

remains OM (figure 8.10). The price, on the other hand, rises from ML to MK and then with

further fall in supply, it increases to MZ. In practice, the elasticity of demand is neither perfectly

elastic nor perfectly inelastic. It is either equal to unity, greater than unity or less than unity.

Effect of Shift in Both Supply & Demand on Equilibrium Price and Quantity:

In the figure (8.11), DD/and SS

/ are the original demand and supply curves. When demand rises,

the demand curve DD1 shifts upward and it intersects the old supply curve SS

/ at point F. The

new equilibrium price is now equal to FK. But if supply also increases with the rise in demand,

the new equilibrium price will be established at a point where the new supply curve intersects the

new demand curve. When changes in both supply and demand take place, the new equilibrium

price is established at point N. NT becomes new equilibrium price and OT the new equilibrium

amount.

If the rise in supply is greater than the rise in demand, the price will be lower than the original

price. In Fig. (8.12), the price has fallen from EQ to E/Q

/.

If the change in demand is relatively higher than that of supply, the new equilibrium price will be

higher than the original price as is shown in fig. 8.13. The equilibrium price has increased from

EQ to E/Q

/.

Theory of Production Production of goods requires resources or inputs. These inputs are called factors of production

named as land, labor, capital and organization. A rational producer is always interested to get the

maximum output from the set of resources or inputs available to him. He would like to combine

these inputs in a technical efficient manner so that he obtains maximum desired output of goods.

The relationship between the inputs and the resulting output is described as production function.

A production function shows the relationship between the amounts of factors used and the

amount of output generated per period of time.

Q = f (x1, x

2... x

n)

Q is the maximum quantity of output and x1, x

2, x

n are quantities of various inputs. The

functional relationship between inputs and output is governed by the laws of returns.

The analysis of production function is generally carried with reference to time period which is

called short period and long period. In short run, production function is explained with one

variable factor and other factors of productions are held constant. This production function is

called as the Law of Variable Proportions or the Law of Diminishing returns. In long run,

production function is explained by assuming all factors of production variables. There are no

fixed inputs in the long run. Here the production function is called the Law of Returns to Scale.

As it is difficult to handle more than two variables in graph, the Law of Returns is explained by

assuming only two inputs i.e., capital and labor and study how output responds to their use.

Law of Variable Proportion/Law of Diminishing Returns:

The short run is a period of time in which only one input (say labor) is allowed to vary while

other inputs land and capital are held fixed. In the short run, therefore, production can be

increased with one variable factor and other factors remaining constant. In the short run, the law

of variable proportion governs the production behavior of a firm. The law shows the direction

and rate of change in the output of firm when the amount of only one factor of production is

varied while other factors of production are held constant.

The law states that when more and more units of a variable input are applied to a given quantity

of fixed inputs, the total output may initially increase at an increasing rate and then at a constant

rate but it will eventually increase at diminishing rates. That is, the marginal increase in the total

output eventually decreases when additional units of variable factors are applied to a given

quantity of fixed factors.

This law holds good under the following assumptions:

(i) Short run

(ii) Constant technology

(iii) Homogeneous factors

The law of variable proportions is, now explained with the help of table and graph.

Schedule:

Fixed Inputs

(Land &

Capital)

Variable

Resource

(labor)

Total Produce (TP

Quintals)

Marginal Product

(MP Quintals)

Average

Product (AP

Quintals)

30

30

1

2

10

25

10

15

Increasing marginal

return

10

12.5

30

30

30

30

30

3

4

5

6

7

37

47

55

60

63

12

10

8

5

3

Diminishing

marginal returns

12.3

11.8

11.0

10.0

9.0

30

30

8

9

63

62

0

-1

Negative marginal

returns

7.9

6.8

In the table above, it is assumed that a farmer has only 30 acres of land for cultivation. The

investment on it in the form of tube wells, machinery etc., and (capital) is also fixed. Thus land

and capital with the farmer is fixed and labor is the variable resource.

As the farmer increases units of labor from one to two to the amount of other fixed resources

(land and capital), the marginal as well as average product increases. The total product (TP) also

increases at an increasing rate from 10 to 25 quintals. It is the stage of increasing returns. This

stage of course, does not last long. With the employment of 3rd labor at the farm, the marginal

product (MP) and the average product (AP) both fall but MP falls more speedily than the AP.

The fall in MP and AP continues as more men are put on the farm. The decrease, however,

remains positive up to the 7th labor employed. On the employment of 7th worker, TP remains

constant at 63 quintals. The MP is zero. If more men are employed, MP becomes negative. It is

the stage of negative returns. The behavior of MP is shown in three stages. In the first stage, it

increases, in the 2nd it continues to fall and in the 3rd stage it becomes negative.

These stages can be explained with the help of graph below:

(i) Stage of Increasing Returns - The first stage of the law of variable proportions is generally

called the stage of increasing returns. In this stage as a variable resource (labor) is added to fixed

inputs of other resources, the total product increases up to a point at an increasing rate as is

shown in figure 11.1. The total product from the origin to the point K on the slope of the total

product curve increases at an increasing rate. From point K onward, during the stage II, the total

product no doubt goes on rising but its slope is declining. This means that from point K onward,

the total product increases at a diminishing rate. In the first stage, marginal product curve of a

variable factor rises in a part and then falls. The average product curve rises throughout .and

remains below the MP curve.

The phase of increasing returns starts when the quantity of a fixed factor is abundant relative to

the quantity of the variable factor. As more and more units of the variable factor are added to the

constant quantity of the fixed factor, it is more intensively and effectively used. This causes the

production to increase at a rapid rate. Another reason of increasing returns is that the fixed factor

initially taken is indivisible. As more units of the variable factor are employed to work on it,

output increases greatly due to fuller and effective utilization of the variable factor.

(ii) Stage of Diminishing Returns. This is the most important stage in the production function.

In stage 2, the total production continues to increase at a diminishing rate until it reaches its

maximum point (H) where the 2nd stage ends. In this stage both the marginal product and

average product of the variable factor are diminishing but are positive.

The 2nd phase of the law occurs when the fixed factor becomes inadequate relative to the

quantity of the variable factor. As more and more units of a variable factor are employed, the

marginal and average product decline. Another reason of diminishing returns in the production

function is that the fixed indivisible factor is being worked too hard. It is being used in non-

optimal proportion with the variable factor.

(iii) Stage of Negative Returns. In the 3rd stage, the total production declines. The TP curve

slopes downward (From point H onward). The MP curve falls to zero at point M and then is

negative. It goes below the X axis with the increase in the use of variable factor (labor). The 3rd

phase of the law starts when the number of a variable, factor becomes too excessive relative to

the fixed factors. A producer cannot operate in this stage because total production declines with

the employment of additional labor.

A rational producer will always seek to produce in stage 2 where MP and AP of the variable

factor are diminishing. At which particular point, the producer will decide to produce depends

upon the price of the factor he has to pay. The producer will employ the variable factor (say

labor) up to the point where the marginal product of the labor equals the given wage rate in the

labor market.

Production function establishes a physical relationship between output and inputs. It describes

what is technically feasible when the firm uses each combination of input. The firm can obtain a

given level of output by using more labor and less capital or more capital and less labor.

Production function describes the maximum output feasible for a given set of inputs in technical

efficient manner.

Long Run Production with Variable Inputs:

The long run is the lengthy period of time during with all inputs can vary. There is no fixed

output in the long run. All factors of production are variable inputs.

We now analyze production function by allowing two factors say labor and capital to vary while

all others are held constant. With both factors variable, a firm can produce a given level of output

by using more labor and less capital or more capital and less labor. A firm continues to substitute

one input for another while continuing to produce same level of output. If two inputs say labor

and capital are allowed to vary, resulting production function can be illustrated in figure 12(a).

In this figure each curve (called an Isoquant) represents a different level of output. The curves

which lie higher and to the right represent greater output levels than curves which are lower and

to the left. For example, point D represents a higher output level of 250 units than point A or B

which shows output level of 150 units.

The curve isoquant which represents 150 units of output illustrate that the same level of output

(150 units) can be produced with different combinations of labor and capital. Combination of

labor and capital represented by A can employ OL1 quantity of labor and OC

1 units of capital to

produce 150 units of output. The combination of labor and capital represented by point B will

use only OL2 units of labor and OC

1 of capital to produce the same level of output. The isoquant

through points A and B shows all different combinations of labor and capital that can be used to

produce 150 units of output.

The concept of isoquant or equal product curve can be better explained with the help of schedule

given below:

Combinations Factor X Factor Y Total Output

A 1 14 100 METERS

B 2 10 100 METERS

C 3 7 100 METERS

D 4 5 100 METERS

E 5 4 100 METERS

In the table given above, it is shown that a producer employs two factors of production X and Y

for producing an output of 100 meters of cloth. There are five combinations which produce the

same level of output (100 meters of cloth). The factor combination A using 1 unit of factor X and

14 units of factor Y produces 100 meters of cloth. The combination B using 2 units of factor X

and 10 units of factor Y produces 100 meters of cloth. Similarly combinations C, U and E,

produce 100 units of output, each. The producer, here, is indifferent as to which combination of

inputs he uses for producing the same amount of output.

The alternative techniques for producing a given level of output can be plotted on a graph.

The figure 12.1 shows the five factor combinations of X and Y plotted and shown by points a, b,

c, d and e. if we join these points, it forms an 'isoquant'.

An isoquant therefore, is the graphic representation of an iso-product schedule. All the factor

combinations of X and Y on an iso-product curve are technically efficient combinations. The

producer is indifferent as to which combination he uses for producing the same level of output.

In the figure 12.1, iso-product curve represents the various combinations of the two inputs which

produce the same level of output (100 meters of cloth).

Properties of Isoquants:

An isoquant slopes downward from left to right

An isoquant that lies above and to the right of another represents a higher output level

Isoquants cannot cut each other

Isoquants are convex to the origin

Iso-cost Lines:

A firm can produce a given level of output using efficiently different combinations of two inputs.

For choosing efficient combination of the inputs, the producer selects that combination of factors

which has the lower cost of production. The information about the cost can be obtained from the

iso-cost lines.

An iso-cost line shows all the combinations of labor and capital that are available for a given

total cost to the producer. Just as there are infinite numbers of isoquants, there are infinite

numbers of iso-cost lines, one for every possible level of a given total cost. The greater the total

cost, the further from origin is the iso-cost line.

The iso-cost line can be explained easily by taking a simple example.

Let us examine a firm which wishes to spend Rs. 100 on a combination of two factors labor and

capital for producing a given level of output. We suppose further that the price of one unit of

labor is Rs. 5 per day. This means that the firm can hire 20 units of labor. On the other hand if

the price of capital is Rs. 10 per unit, the firm will purchase 10 units of capital. In fig. 12.7, the

point A shows 10 units of capital used whereas point T shows 20 units of labor hired at the given

price. If we join points A and T, we get a line AT, called iso-cost line.

Let us assume now that there is no change in the market prices of the two factors labor and

capital, but the firm increases the total outlay to Rs. 150. The new price line BK shows that with

an outlay of Rs. 150, the producer can purchase 15 units of capital or 30 units of labor. The new

price line BK Shifts upward to right. In case the firm reduces the outlay to Rs. 50 only, the iso-

cost line CD shifts downward to the left of original iso-cost line and remains parallel to the

original price line.

Marginal Rate of Technical Substitution (MRTS):

MRTS is "The rate at which one factor can be substituted for another while holding the level of

output constant". The slope of an isoquant shows the ability of a firm to replace one factor with

another while holding the output constant. For example, if 2 units of factor capital (K) can be

replaced by 1 unit of labor (L), marginal rate of technical substitution will be thus:

MRS = ΔK / ΔL = 2 / 2 = 1

The concept of MRTS can be explained easily with the help of the table and the graph, below:

Factor

Combinations

Units of

Labor

Units of

Capital

Units of Output of

Commodity X

MRTS of Labor for

Capital

A 1 15 150 -

B 2 11 150 4:1

C 3 8 150 3:1

D 4 6 150 2:1

E 5 5 150 1:1

It is clear from the above table that all the five different combinations of labor and capital that is

A, B, C, D and E yield the same level of output of 150 units of commodity X. As we move down

from factor A to factor B, then 4 units of capital are required for obtaining 1 unit of labor without

affecting the total level of output (150 units of commodity X). The MRTS is 4:1. As we step

down from factor combination B to factors C to D to E, then MRTS decreases.

In figure 12.8, all the five combinations of labor and capital which are A, B, C, D and E are

plotted on a graph. The points A, B, C, D and E are joined to form an isoquant.

The decline in MRTS along an isoquant for producing the same level of output is named as

diminishing marginal rates of technical substitution.

Optimum Factor Combination:

In the long run, all factors of production can vary. The profit maximization firm will choose the

least cost combination of factors to produce at any given output level. The least cost combination

or the optimum factor combination refers to the combination of factors with which a firm can

produce a specific quantity of output at the lowest possible cost. The least cost combination of

factors for any level of output is that where the iso-product curve is tangent to an iso-cost curve.

The least cost combination of factors is now explained with the help of figure 12.9.

Here the iso-cost line CD is tangent to the iso-product curve 400 units at point Q. The firm

employs OC units of factor Y and OD units of factor X to produce 400 units of output. This is

the optimum output which the firm can get from the cost outlay of Q. In this figure, any point

below Q on the price line AB is desirable as it shows lower cost, but it is not attainable for

producing 400 units of output. As regards points RS above Q on iso-cost lines GH, EF, they

show higher cost. These are beyond the reach of the producer with CD outlay. Hence point Q is

the least cost point.

Law of Returns to Scale:

The law of returns to scale operates in the long period, explains the production behavior of the

firm with all variable factors. There is no fixed factor of production in the long run. The law

describes the relationship between variable inputs and output when all the inputs or factors are

increased in the same proportion. The law analyzes the effects of scale on the level of output.

It has been observed that when there is a proportionate change in the amounts of inputs, the

behavior of output varies. The output may increase by a great proportion, by in the same

proportion or in a smaller proportion to its inputs. This behavior of output with the increase in

scale of operation is termed as increasing returns to scale, constant returns to scale and

diminishing returns to scale.

(1) Increasing Returns to Scale:

If the output of a firm increases more than proportionate increase in all inputs, the production is

said to exhibit increasing returns to scale. For example, if the amount of inputs are doubled and

the output increases by more than double, it is said to be an increasing returns to scale. When

there is an increase in the scale of production, it leads to lower average cost per unit produced as

the firm enjoys economies of scale.

(2) Constant Returns to Scale:

When all inputs are increased by a certain percentage, and the output increases by the same

percentage, the production function is said to exhibit constant returns to scale. For example, if a

firm doubles inputs, it doubles output. The constant scale of production has no effect on average

cost per unit produced.

(3) Diminishing Returns to Scale:

The term 'diminishing' returns to scale refers to scale where output increases in a smaller

proportion than the increase in all inputs. For example, if a firm increases inputs by 100%, but

the output decreases by less than 100%, the firm is said to exhibit decreasing returns to scale. In

case of decreasing returns to scale, the firm faces diseconomies of scale. The firm's scale of

production leads to higher average cost per unit produced.

The three laws of returns to scale are now explained with the help of a graph below:

The figure 11.6 shows that when a firm uses one unit of labor and one unit of capital (point a), it

produces 1 unit of quantity. When the firm doubles its outputs by using 2 units of labor and 2

units of capital, it produces more than double from q = 1 to q = 3. So the production function has

increasing returns to scale in this range. Another output from quantity 3 to quantity 6. At last,

doubling point c to point d, the production function has decreasing returns to scale. The doubling

of output from 4 units of input causes output to increase from 6 to 8 units increases of two units.

Internal Economics of Scales:

These arise within the firm as a result of increasing the scale of output of the firm. A firm secures

these economies from the growth of the firm independently. The main scale economies are:

Technical Economies - When production is carried on a large scale, a firm can afford to

install up to date and costly machinery and can have its own repairing arrangements. As

the cost of machinery will be spread over a very large volume of output, the cost of

production per unit will therefore, be low. A large firm can also secure the services of

experienced entrepreneurs and workers which a small firm cannot afford. In a large

establishment there is much scope for specialization of work, so the division of labor can

be easily secured.

Managerial Economies - When production is carried on a large scale, the task of manager

can be split up into different departments and each department can be placed under the

supervision of a specialist of that branch. The difficult task can be taken up by the

entrepreneur himself. Due to these functional specializations, the total return can be

increased at a lower cost.

Financial Economies - Financial economies arise from the fact that a big establishment

can raise loans at a lower rate of interest than a small establishment.

Risk Bearing Economies - A big firm can undertake risk bearing economies by spreading

the risk. In certain cases the risk is eliminated altogether. A big establishment produces a

variety of goods in order to cater the needs of different tastes of people. If demand for a

certain type of commodity slackens, it is counter balanced by increasing demand of other

commodities produced by the firm.

Economies of Scale - As a firm grows in size, it is possible for it to reduce its cost. The

reduction in costs, as a result of increasing production is called economies of scale.

Internal Diseconomies of Scale:

The extensive use of machinery, division of labor, increased specialization and larger plant size

etc., no doubt entail lower cost per unit of output but the fall in cost per unit is up to a certain

limit. As the firm goes beyond the optimum size, the efficiency of the firm begins to decline. The

average cost of production begins to rise.

The main factors causing diseconomies eventually leading to higher per unit cost are as follows:

Lack of co-ordination - As a firm becomes large scale producer, it faces difficulty in

coordinating the various departments of production. The lack of co-ordination in the

production, planning, marketing personnel, account, etc., lowers efficiency of the factors

of production. The average cost of production begins to rise.

Loose control - As the size of plant increases, the management loses control over the

productive activities. The misuse of delegation of authority, the redtapism bring

diseconomies and lead to higher average cost of production.

Lack of proper communication - The lack of proper communication between top

management and the supervisory staff and little feedback from subordinate staff causes

diseconomies of scale and results in the average cost to go up.

Lack of identification - In a large organizational structure, there is no close liaison

between the top management and the thousands of workers employed in the firm. The

lack of identification of interest with the firm results in per unit cost to go up.

External Economies of Scale:

These economies are not specially availed by any firm. The main external economies are:

Economies of localization - When an industry is concentrated in a particular area, all the

firms situated in that locality avail some common economies such as skilled labor,

transportation facilities, banking and insurance facilities etc.

Economies of vertical disintegration - The vertical disintegration implies the splitting up

the production process in such a manner that some jobs are assigned to specialized firms

e.g., when an industry expands, repair work of the various parts of the machinery is taken

up by the various firms specialists in repairs.

Economies of information - As the industry expands, it can set up research institutes. The

research institutes provide market information, technical information etc for the benefit of

alt the firms in the industry.

Economies of by products - All the firms can lower the costs of production by making use

of waste materials.

External Diseconomies:

The diseconomies of large scale production are (i) Diseconomies of pollution, (ii) Excessive

pressure on transport facilities, (iii) Rise in the prices of the factors of production, (iv) Scarcity of

funds, (v) Marketing problems of the products, (vi) Increase in risks etc.

Optimum firm is that firm which fully utilizes its scale of operation and produces optimum

output with the minimum cost per unit production.

Cost of Production & Cost Curves "Production costs are those which must be received by resource owners in order to assume that

they will continue to supply them in a particular time of production".

Analysis of Short Run Cost of Production:

Short run is a period of time over which at least one factor must remain fixed. For most of the

firms, the fixed factors which can’t be increased to meet the rising demand of the good is capital

i.e., plant and machinery. Short run, then, is a period of time over which output can be changed

by adjusting the quantities of resources such as labor, raw material, fuel but the size or scale of

the firm remains fixed.

In long run there is no fixed resource. All the factors of production are variable. The length of the

long run differs from industry to industry depending upon the nature of production e.g., a balloon

making firm can change the size of firm more quickly than a car manufacturing firm.

Total Costs:

The total cost of a firm in the short run is divided into two categories:

(1) Total Fixed Cost (TFC): TFC occur only in short run. It is the cost of firm's fixed resources.

Fixed cost remains the same in short run regardless of how many units of output produced. We

can say that fixed cost of a firm is that part of total cost which does not vary with changes in

output per period of time. Fixed cost is to be incurred even if the output of the firm is zero. For

example, the firm's resources which remain fixed in the short run are building, machinery and

even staff employed on contract for work over a particular period.

(2) Total Variable Cost (TVC): TVC is the cost of variable resources of a firm that are used

along with the firm's existing fixed resources. Total variable cost is linked with the level of

output. When output is zero, variable cost is zero. When output increases, variable cost also

increases and it decreases with the decrease in output. For example, wages paid to the labor

engaged in production, prices of raw material which a firm incurs on the production of output are

variable costs. A firm can reduce its variable cost by lowering output but it cannot decrease its

fixed cost. These expenses remain fixed in the short run. In the long run there are no fixed

resources. All resources are variable. Therefore, a firm has no fixed cost in the long run. All long

run costs are variable costs.

(3) Total Cost (TC): It is the sum of fixed cost and variable cost incurred at each level of output.

TC = TFC + TVC

Where, TC = Total cost

TFC = Total fixed cost

TVC = Total variable cost

Short run costs of a firm are now explained with the help of a schedule and diagrams.

Schedule :( in Rupees)

Units of Output (in Hundred) Total Fixed Cost Total Variable Cost Total Cost

0 1000 0 1000

1 1000 60 1060

2 1000 100 1100

3 1000 150 1150

4 1000 200 1200

5 1000 400 1400

6 1000 700 1700

7 1000 1100 2100

The short run cost data of the firm shows that total fixed cost TFC, column (2) remains constant

at Rs. 1000 regardless of the level of output. The column (3) indicates variable cost which is

associated with the level of output. Total variable cost is zero when production is zero. Total

variable cost increases with the increase in output. The variable cost does not increase by the

same amount for each increase in output. Initially the variable cost increases by a smaller amount

up to 3rd

unit of output and after which it increases by larger amounts. Column (4) indicates total

cost which is the sum of TFC and TVC. The total cost increases for each level of output. The rise

in total cost is sharper after the 4th

level of output. The concepts of costs, i.e., (1) total fixed cost

(2) total variable cost and (3) total cost can be illustrated graphically.

Total Fixed Cost Curve/Diagram:

In diagram (13.1), the total fixed cost of a firm is assumed to be Rs. 1000 at various levels of

output. It remains the same even if the firm's output is zero.

Total Variable Cost Curve/Diagram:

In figure (13.2), the total variable cost curve (TVC) increases with the higher level of output. It

starts from the origin, and then increases at a diminishing rate up to the 4th units of output. It

then begins to rise at an increasing rate.

Total Cost Curve Curve/Diagram:

In figure (13.3), total cost curve which is the sum of the total fixed cost and variable cost at

various levels of output has nearly the same shape. The difference between the two is by only a

fixed amount of Rs. 1,000. The total variable cost curve and the total cost curve begin to rise

more rapidly as production is increased. The reason for this is that after certain output, the

business has passed its most efficient use of its fixed costs in the form of machinery, building

etc., and its diminishing return begins to set in.

Average Costs:

The entrepreneurs are no doubt interested in the total costs but they are equally concerned in

knowing the cost per unit of the product. The unit cost figures can be derived from the total fixed

cost, total variable cost and total cost by dividing each of them with corresponding output.

(1) Average Fixed Cost (AFC): It is found out by dividing total fixed cost by the corresponding

output.

AFC = TFC / Q

For instance, if the total fixed cost of a shoes factory is Rs. 5,000 and it produces 500 pairs of

shoes, then the average fixed cost is equal to Rs. 10 per unit. If it produces 1,000 pairs of shoes,

the average fixed cost is Rs. 5 and if the total output is 5,000 pairs of shoes, then the average

fixed cost is Re. 1 pair of shoe.

The concept of average fixed cost can be explained with the help of the curve. In the diagram

(13.4), the AFC curve gradually falls from left to right showing the level of output. The larger

the level of output, the lower is the AFC and smaller the level of output, greater is the AFC. The

AFC never becomes zero.

(2) Average Variable Cost (AVC): It is obtained by dividing the TVC by the total output.

AVC = TVC / Q For instance, if the total variable cost for producing 100 meters of cloth is Rs. 800, the average

variable cost will be Rs. 8 per meter.

When a firm increases its output, the average variable cost decreases in the beginning, reaches a

minimum and then increases. In the beginning, a firm is not producing to its full capacity and

hence various factors of production employed for the manufacture of a particular commodity

remain partially absorbed. As the output of the firm increases, they are used to its fullest extent.

So the AVC begins to decrease. When the plant works to its full capacity, the AVC is at its

minimum. If the production is pushed further from the plant capacity, then less efficient

machinery and less efficient labor may have to be employed. This results in the rise of AVC. The

AVC can also be represented in the form of a curve.

The shape of the AVC curve (Fig. 13.5) is like a flat U-shaped curve. It shows that when the

output increases, there is a steady fall in the AVC due to increasing returns to variable factor. It

reaches its minimum when 500 meters of cloth are produced. When production is increased to

600 meters of cloth or more, AVC begins to rise due to diminishing returns to the variable factor.

(3) Average Total Cost (ATC): It is obtained by dividing the total cost by the total number of

commodities produced by the firm.

ATC = TC / Q

As the output of a firm increases, ATC like the AVC decreases in the beginning reaches a

minimum and then it increases. AFC and AVC have both the tendency to fall as output increases.

ATC will continue to fall so long as AVC does not rise. Even if AVC continues to rise, it is not

necessary that the ATC will rise. It can be due to the fact that the increase in AVC is less than the

fall in AFC. The increase in AVC is counter balanced by a rapid fall of AFC. If the rise in the

AVC is greater than the fall in AFC, then the ATC will rise.

The tendency to rise on the part of average total cost in the beginning is slow, after a certain

point it begins to increase rapidly.

Diagram/Curve:

The average total cost is represented here by a U-shaped curve in Fig. (13.6). The average total

cost curve is also like a U-shaped curve. It shows that as production increases from 100 meters to

200 meters of cloth, the cost falls rapidly, reaches a minimum but then with higher level of

output, the average fixed cost begins to increase.

Short Run and Long Run Average Cost Curves:

In the long run, all costs of a firm are variable. The factors of production can be used in varying

proportions to deal with an increased output. The firm having time period long enough can build

larger scale or type of plant to produce the anticipated output. The shape of the long run average

cost curve is also U-shaped but is flatter than that of the short run curve as is illustrated in the

following diagram:

In diagram 13.7 given above, there are five alternative scales of plant SAC

1, SAC

2, SAC

3, SAC

4

and, SAC5. In the long run, the firm will operate in the scale of plant which is most profitable to

it. For example, if the anticipated rate of output is 200 units per unit of time, the firm will

choose the smallest plant. It will build the scale of plant given by SAC1 and operate it at point A.

This is because of the fact that at the output of 200 units, the cost per unit is lowest with the plant

size 1 which is the smallest of all the four plants. In case, the volume of sales expands to 400

units, the size of the plant will increase and the desired output will be attained by the scale of

plant represented by SAC2 at point B. If the anticipated output rate is 600 units, the firm will

build the size of plant given by SAC3 and operate it at point C where the average cost is Rs. 26

and also the lowest. The optimum output of the firm is obtained at point C on the medium size

plant SAC3. If the anticipated output rate is 1000 per unit of time, the firm would build the scale

of plant given by SAC5 and operate it at point E. If we draw a tangent to each of the short run

cost curves, we get the long-run average cost (LAC) curve. The LAC is U-shaped but is flatter

than the short run cost curves.

Marginal Cost (MC):

Marginal Cost is governed only by variable cost which changes with changes in output.

Marginal Cost = Change in Total Cost = ΔTC

Change in Output Δq

The various types of costs and their relationship can be shown in the table given below:

Units of Output TFC TVC ATC AFC AVC MC

Rs. Rs. Rs. Rs. Rs. Rs.

1 30 15 45 30 15 15

2 30 16.9 23.4 15 8.4 1.9

3 30 18.4 16.1 10.1 6.1 1.5

4 30 19.4 12.3 7.5 4.8 1

5 30 20 10 6 4.0 0.6

6 30 22 8.7 5 3.7 2

7 30 25 7.8 4.3 3.6 3

8 30 30 7.5 3.7 3.7 5

9 30 36 7.3 3.3 4 6

10 30 43 7.3 3 4.3 7

11 30 60 8.2 2.7 5.5 17

12 30 90 10 2.5 7.5 30

13 30 125 11.9 2.3 9.6 35

14 30 165 13.9 2.1 11.8 40

15 30 210 16 2 14.8 45

16 30 270 18.7 1.9 16.7 60

As production increases, the average total cost and the marginal cost both begin to decrease. The

average total cost goes on decreasing up to the 9th

unit and then after 10th

unit, it begins to rise.

The marginal cost goes on falling up to 5th unit and then it begins to increase. So long as the

average total cost does not rise, the marginal cost remains below it. When average total cost

begins to increase, the marginal cost rises more than the average total cost.

In fig.13.10, AVC goes on falling up to the 7th unit, and then it steadily moves upwards. On the

other hand the MC falls up to the 5th unit and then rises more rapidly than average variable cost.

Diagram/Figure:

Time Value of Money The value / purchasing power of money at a particular time is called time value of money. A

rupee today is worth more than a rupee to be received tomorrow. The time value of money is a

tool to understand the effective rates on business loans or true return on an investment by helping

the manager determine the actual value of money now and in the future based on interest rates,

discount rates, expected costs and expected sales. Through targeted analysis, organizations are

able to use this information to decide whether projects, big or small, simple or complex, are

going to be beneficial to the company. By observing various tools and indicators such as future

value, present value, future/present value of an annuity, companies can determine the expected

return on an investment to ensure that it will result in increased profits. The time value of money

demonstrates that it may be better to have money now rather than later.

A rupee is worth more today than tomorrow for the following reasons:

An invested rupee can earn interest over time

The future always involves uncertainty and receiving a rupee in future involves risk

A rupee is subject to inflation thus lessening its purchasing power

The notations used in various interest formulas calculations are as follows:

P = principal amount

n = No. of interest periods

i = interest rate (It may be compounded monthly, quarterly, semiannually or annually)

F = Future amount at the end of year n

A = equal amount deposited at the end of every interest period (Annuity)

G = uniform amount which will be added/subtracted period after period to/ from the amount

of deposit at the end of period 1

Interest is the cost of borrowing money. An interest rate is the cost stated as a percentage of

the amount borrowed per period of time, usually one year.

SIMPLE INTEREST:

Simple interest is calculated on the original principal only. Accumulated interest from prior

periods is not used in calculations for the following periods.

S.I. = P x i x n

Ex: A man borrowed Rs. 10,000 at 12% p.a. for 3 years. How much he has to pay after 3

years?

Sol: Here, P = Rs. 10,000

i = 12% = 0.12

n = 3 years

S.I. = 10,000 x 0.12 x 3 = Rs. 3,600

Amount to be paid after 3 years = 8,500 + 3,600 = Rs. 12,100

COMPOUND INTEREST:

Compound interest is calculated each period on the original principal and all interest

accumulated during past periods. Although the interest may be stated as a yearly rate, the

compounding periods can be yearly, semiannually, quarterly, or even continuously. In this case,

the interest earned in each period is added to the principal of the previous period to become the

principal for the next period.

C.I. = P {(1 + i) n – 1}

Ex: If Rs. 50,000 is invested for 10 years at 10% interest compounded annually, calculate the

amount to be received after 10 years.

Sol: Here, P = Rs.50, 000

i = 10% = 0.10

n = 10 years

The amount to be received after 10 years = 50,000 (1.1) 10

= Rs. 1, 29, 700

NOMINAL and EFFECTIVE INTEREST RATES:

The annual rate of interest is called Nominal Interest Rate. When the interest is compounded

more than once in a year e.g. monthly, quarterly or semi-annually; the corresponding annual rate

of interest is called Effective Interest Rate. The formula used to calculate effective interest rate

from given nominal interest rate is:

i eff = {(1 + r/m) m

– 1}

Where, r = nominal interest rate

m = number of compounding in a year

Ex: What is effective interest rate of nominal interest rate of 18% compounded semi-annually

Sol: i eff = {(1 + r/m) m

– 1} = {(1 + 0.18/2) 2 – 1} = 18.8%

CONTINUOUS COMPOUNDING:

The ultimate limit for the number of compounding periods in one year is called continuous

compounding. The effective interest rate under such situations is calculated as follows:

i ∞ = lim {(1 + r/m) m

– 1} = lim [{(1 + r/m) m/r

} r – 1]

m → ∞ m → ∞

= [lim {(1 + r/m) m/r

} r] – 1 = e

r - 1

m → ∞

Ex: Calculate the effective interest rate of nominal interest rate of 18.23% if the interest is

compounded continuously.

Sol: i ∞ = e r – 1 = e

0.1823 – 1 = 20%

Time-Value Equivalence:

Two things are equivalent when the produce the same effect. The comparison of various

alternative projects necessitates the use of equivalence principle, wherein receipts and payments

occurring at different time periods are expressed on an equivalent basis. In fact, equivalence is

the heart of making engineering economic decisions.

Ex: i) Rs 100 today is equivalent to Rs. 108 after 1 year at 10% interest compounded annually

ii) Rs. 100 today is equivalent to Rs. 23.74 received at the end of each year for the next 5

years.

iii) Rs. 23.74 received at the end of each year for the next 5 years is equivalent to a lump

sum of Rs. 179.1 received 10 years from now.

iv) Rs. 23.74 received at the end of each year for the next 5 years is equivalent to Rs.

31.77 at the end of years 6, 7, 8, 9 and 10.

Cash Flow Diagrams

A cash flow diagram is a pictorial representation of all cash inflows and outflows along a time

line. The time line is the horizontal scale, which is divided into time periods, usually in years.

Cash inflows and cash outflows are then located on the time-line in adherence to problem

specifications by drawing vertical lines above the axis and below the axis respectively.

Compound Interest Factors:

Single-Payment Compound Amount / Future value of an amount:

Here, the objective is to find the-single future-sum (F) of the initial payment (P) made at time 0

after n periods at an interest rate i compounded every period.

Fig 1: Cash flow diagram of single-payment compound amount

The formula to obtain the single-payment compound amount is:

F = P (1+i) n

= P (F/P, i, n)

Where, (F/P, i, n) is called as single-payment compound amount factor

Ex: A person deposits a sum of Rs. 20,000 at the interest rate 18% compounded annually for

10 years. Find the maturity value after 10 year.

Sol: P = Rs. 20,000

i = 18% compounded annually

n = 10 years F

P

0 A

1 2 3 4 - - n

F

i%

F = P (1 + i) n = P (F/P, i, n) = 20,000 (F/P, 18%, 10)

= 20,000 x 5.234 = Rs. 1, 04, 680

The maturity value of Rs. 20,000 invested now at 18% compounded yearly is equal to

Rs.1, 04, 680 after 10 years.

Single Payment present worth amount:

Here, the objective is to find the present worth amount (P) of a single future (F) which will be

received after n periods at an interest rate of compound at the end of every interest period.

Fig 2: Cash flow diagram of single-payment present worth amount

The formula to obtain the present worth is:

P = F / (1+i) n

= F (P/F, i, n)

Where, (P/F, i, n) is called as single-payment present worth factor

Ex: A person wishes to have a future sum of Rs. 1, 00, 000 for his son’s education after 10

years from now. What is the single-payment that the deposit now so that he gets the

desired amount after 10 years? The bank gives 15% interest rate compounded annually.

Sol: F = Rs.1.00.000

i = 15%, compounded annually

n = 10 years

P = F/ (1+i) n

= F (P/F, i, n) = 1, 00, 000 (P/F, 15%, 10)

= 1, 00, 000 x 0.2472 = Rs. 24,720

The person has to invest Rs.24, 720 now so that he will get a sum of Rs.10, 000 after 10

years at 15% interest rate compounded annually.

Equal-Payment Series Compound Amount / Future value of an annuity:

The objective is to find the future worth of n equal payments which are made at the end of every

interest period till the end of the nth

interest period at an interest rate of compounded at the end of

each period.

Fig 3: Cash flow diagram of equal-payment series compound amount.

P

0 1 2 3 4 A

-

-

3

1

2

4

1

%

A

-

- n

F

i%

A A A A - - A

F

1 2 3 4 n 0

i %

The formula to get F is:

F = A [(1+i) n

– 1] / i = A (F/A, i, n)

Where, (F/A, i, n) is termed as equal-payment series compound amount factor.

Ex: A person who is not 35 years old is planning for his retired life. He plans to invest an

equal sum of Rs.10, 000 at the end of every year for the next 25 years starting from the

end of the next year. The bank gives 20% interest rate, compounded annually. Find the

maturity value of his account when he is 60 years old.

Sol: A = Rs. 10,000

n = 25 years

i = 20%

F = A [(1+i) n

– 1] / i = A (F/A, i, n) = 10,000 (F/A, 20%, 25)

= 10,000 x 471.981 = Rs. 47, 19, 810

The future sum of the annual equal payments after 25 years is equal to Rs. 47, 19,810.

Sinking Fund Amount:

In this type of investment mode, the objective is to find the equivalent amount (A) that should be

deposited at the end of every interest period for n interest periods to realize a future sum (F) at

the end of the nth interest period at an interest rate of i.

Fig 4: Cash flow diagram of equal payment series sinking fund

The formula to get F is:

A = F [i / {(1+i) n

– 1}] = F (A/F, i, n)

Where, (A/F, i, n) is called sinking fund factor.

Ex: A company has to replace a present facility after 15 years at an outlay of

Rs.5, 00, 000. It plans to deposit an equal amount at the end of every year for the next 15

years at an interest rate of 18% compounded annually. Find the equivalent amount that

must be deposited at the end of every year for the next 15 years.

Sol: F = Rs. 5, 00, 000

n = 15 years

i = 18%

A = F [i / {(1+i) n

– 1}] = F (A/F, i, n) = 5, 00, 000 (A/F, 18%, 15)

= 5, 00, 000 X 0.0164 = Rs.8, 200

The annual equal amount which must be deposited for 15 years is Rs.8, 200.

A A A A - - A

F

1 2 3 4 n 0

i %

Equal Payment Series Present worth amount:

The objective is to find the present worth of an equal payment made at the end of every interest

period for n interest periods at interest rate of i compounded at the end of every interest period.

The formula to compute P is:

P = A [(1+i) n

– 1] / i (1+i) n

= A (P/A, i, n)

Where, (P/A, i, n) is called equal-payment series present worth factor.

Fig 5: Cash flow diagram of equal-payment series present worth amount.

Ex: A company wants to set up a reserve which will help company to have an annual

equivalent amount of Rs. 10, 00, 000 for the next 20 years towards its employees’ welfare

measures. The reserve is assumed to grow the rate of 15% annually. Find the single-

payment that must be made now the reserve amount.

Sol: A = Rs.10, 00, 000

i = 15%

n = 20 years

P = A [(1+i) n

– 1] / i (1+i) n = A (P/A, i, n) = 10, 00, 000 x (P/A, 15%, 20)

= 10, 00, 000 X 6.2593 = Rs. 62, 59, 300

The amount of reserve which must be set-up now is equal to Rs. 62, 59, 300

Equal-Payment Series Capital Recovery Amount:

The objective is to find the annual equivalent amount (A) which is to be recovered at the end of

every interest period for n interest periods for a loan (P) which is sanctioned now at an interest

rate of i compounded at the end of every interest period.

Fig. 6: Cash flow diagram of equal-payment series capital recovery amount.

The formula to compute P is as follows:

A = P [i (1+i) n

/ {(1+i) n

– 1}] = A (P/A, i, n) Where, (A/P, i, n) is called capital recovery factor.

A A A A - - A

n 1 2 3 4

P i %

A

-

-

3

1

2

4

1

%

A

-

A

1 A A

-

-

3

1

2

4

1

%

A

-

A

-

-

3

1

2

4

1

%

A

-

A

-

-

3

1

2

4

1

%

A

-

A

n A

-

-

3

1

2

4

1

%

A

-

A

-

-

3

1

2

4

1

%

A

-

A

-

-

3

1

2

4

1

%

A

-

A

-

-

3

1

2

4

1

%

A

-

A

-

-

3

1

2

4

1

A

-

P

Ex: A bank gives a loan to a company to purchase an equipment worth Rs. 10, 00, 000 at an

interest rate of 18% compounded annually. This amount should be repaid in 15 yearly

equal installments. Find the installment amount that the company has to pay to the bank.

Sol: P = Rs. 10, 00, 000

i = 18%

n = 15 years

A = P [i (1+i) n

/ {(1+i) n

– 1}] = A (P/A, i, n) = 10, 00, 000 x {AIP, 18%, 15)

= 10, 00, 000 x (0.1964) = Rs. 1, 96, 400

The annual equivalent installment to be paid by the company to bank is Rs. 1, 96, 400.

Uniform gradient series factor (A/G, i, N):

In some cases, the periodic payments don't occur at an equal series. They may increase or

decrease by a constant amount. For example a series of payments would be uniformly increasing

in Rs. 200, 250, 300 and 350 occurring at the end of the first, second, third and fourth years.

Similarly a uniformly decreasing series will be Rs. 200, 150, 100, 50 occurring at the end of first,

second, third and fourth years. In each case, an equal payment series provides the base with a

constant annual increase or decrease at the end of the second year.

The pattern of an arithmetic gradient is then A', A' + G, A' + 2G ... A' + (N-l) G where N is the

duration of the series. The calculation can be made simple by converting the series to an

equivalent annuity of equal payments A. The formula for the translation is developed by

separating the series in two parts:

1) First for base annually designated A

2) Second for an arithmetic gradient series increasing by G each period.

(1)

End of year

(2)

Gradient series

(3)

Set of series equivalent

to gradient series

(4)

Annual series

0 0 0 0

1 0 0 A

2 G G A

3 2G G+G A

: : :

: : :

n-1 (n-2) G G+G+G…+G A

n (n-1) G G+G+G….+G+G A

0

200

250

300

1 2 3 4

G 2G 3G

Fig 7

350

F = G (F/A, i, n – 1) + (F/A, i, n-2) + G (F/A, i, 2) + (F/A, i, 1)

= 111....11221

niiiii

G nn

i

nGiiii

i

G nn

111...11

221

The bracket terms constitute the equal payment series compound amount factor for n years.

Therefore,

i

nG

i

i

i

GF

n

11 = G (A/G, i, n)

Thus, A = A’ + G (A/G, i, n)

Annuity with an unknown: Annuity is characterized by:

(1) Equal payments (A)

(2) Equal periods between payment N and

(3) The first payment occurring at the end of the first period.

Ex: We purchased a machine by paying Rs 10,000 to reduce the cost of production. The

machine's life time is 5 years and has no resale value and the machine reduces the cost of

production by Rs. 3000. Find out what rate of return will be earned on the investment.

Sol: A = 2000

N = 5

P = 10,000

P = A (P/A, i, 5)

3333.33000

000,10/ AP

For i = 15, (P/A 15, 5) = 3.3572

For i = 16, (P/A, 16, 5) = 3.2743

By interpolation:

i = 753.0152743.33522.3

2743.33333.3115

= 15.75%.

Annuity due: A series of payment made at the beginning instead of the end of each period is referred as

annuity due. In this case, calculation will be as follows:

1. The series should be divided in to two equal parts.

2. First payment should be treated separately

3. Remaining payment should follow the rule of general annuity calculation.

Ex: What is the present worth of a series of 10 years end payments of Rs 1000 each, when the

first payment is due today and the interest rate is 5%?

Sol: A = Rs 1000

P = A + A (P/A, 5, 9) = 1000 +1000 (7.1078)

= 1000 + 7107.8 = Rs. 8107.8

Deferred annuity:

In case of deferred annuity the first payment doesn't begin until some date later than the end of

the first period.

Procedure: i) Divide the series in to two equal parts.

ii) One part is number of payment paid which follow the general annuity calculation

iii) Second part is the number of period

iv) Find out present worth of annuity, and then discount these values through pre-annuity

period.

Evaluation of Engineering Projects Project can be defined as a temporary endeavor to create a unique product or service e.g.

designing a new product, building a plant etc. Project contains a combination of organizational

resources pulled together to create something which did not previously exist. All projects involve

capital expenditure which is nothing but an initial fund requirement at present, mostly, and

resulting in expected future benefit patterns.

Capital budgeting is a process used to determine whether a firm’s proposed investments or

projects are worth undertaking or not. This is a strategic asset allocation process and

management needs to use capital budgeting techniques to determine which project will yield

more return over a period of time.

A Project whose cash flows have no impact on the acceptance/rejection of other projects is

termed as Independent Project. A set of projects from which at most one will be accepted is

termed as Mutually Exclusive Projects.

Following are the capital budgeting techniques:

Present worth method / Net Present Value method

Future worth method

Equivalent Annual Worth method

Internal Rate of Return method

Profitability Index

Payback Period

Capital budgeting techniques give same acceptance or rejection decisions regarding independent

projects but conflict may arise in case of mutually exclusive projects. In such cases, net present

value method should be given priority due to its more conservative or realistic reinvestment rate

assumption. The Net Present Value and Internal Rate of Return, both methods are superior to the

payback period, but Net present Value is superior to even Internal Rate of Return.

Present Worth Method (PW):

Under this method, the present worth of all cash inflows (revenues) is compared against the

present worth of all cash outflows (costs) associated with an investment project. The cash flow of

each alternative will be reduced to time zero at discount rate i. Then, depending on the type of

decision, the best alternative will be selected by comparing present worth amounts of the

alternatives. The difference between the present worth of the cash flows (inflows – outflows)

referred to as Net Present Worth (NPW) determines whether or not the project will be accepted.

For Independent Projects: If PW > 0, then select the proposal

If PW < 0, then reject the investment project.

If PW = 0, remain indifferent to the investment.

For mutually exclusive alternatives, PW of cash flows can be calculated by either revenue

based present worth method or cost based present worth

In a revenue dominated cash flow diagram, the profit, revenue, salvage value (all inflows) will

be assigned with positive sign. The costs (out flows) will be assigned with negative sign. In a

cost dominated cash flow diagram, the costs (out flows) will be assigned with positive sign and

the profit, revenue; salvage value (all inflows) will be assigned with negative sign. In case the

decision is to select the alternative with maximum profit, then the alternative with the maximum

PW will be selected. If the decision is to select the alternative with the minimum cost, then the

alternative with the least PW will be selected.

S

Revenue dominated cash flow diagram R 1 R 2 R 3 R n

0 1 2 3 n

P

Where, P is the initial investment

R n is the net revenue at the end of nth year.

i is the interest rate compounded annually

S is the salvage value at the end of the nth year.

The present worth expression is:

PW (i) = -P + R1 (P/F, i, 1) + R2 (P/F, i, 2) + ……. + R n (P/F, i, n) + S (P/F, i, n)

If it is a uniform series or equal payment series then the formula will be

PW (i) = -P + R (P/F, i, n) + S (P/F, i, n)

Cost dominated cash flow diagram S

0 1 2 3 4 5 n

P C1 C2 C3 C4 C5 C n

Where, P is the initial investment

C n is the net cost of operation and maintenance at the end of the nth year

S is the salvage value at the end of the nth year

C n is the discounted rate of interest

The present worth expression is:

PW (i) = P + C1 (P/F, i, 1) + C2 (P/F, i, 2) + ……. + C n (P/F, i, n) - S (P/F, i, n)

If it is a uniform series or equal payment series then the formula will be

PW (i) = P + C (P/F, i, n) - S (P/F, i, n)

Ex: Given the following information, suggest which technology should be selected based on

present worth method, assuming 15% interest rate compounded annually.

Technology Initial Cost (Rs.) Service Life Annual O & M Cost

A

B

4,00,000

5,00,000

15 Years

15 Years

25,000

29,000

Sol: The cash flow diagram of technology A is:

0 1 2 3 ……. 14 15

Rs. 25,000

Rs. 4, 00, 000

PW (15%) A = 400000 + 25000 (P/A, 15, 15) = Rs. 400000 + Rs. 25,000 (5.8474)

= Rs. 4, 00, 000 + Rs. 1, 46, 185 = Rs. 5, 46, 185

The cash flow diagram for technology B is:

0 1 2 3 …………. 14 15

Rs. 29,000

Rs. 5, 00, 000

PW (15%) B = Rs. 500000 + Rs. 29000 (P/A, 15, 15) = Rs. 500000 + Rs. 29,000 (5.8474)

= Rs. 5, 00, 000 + Rs. 1, 69, 575 = Rs. 6, 69, 575

Since PW amount of technology A is lower, hence technology A is to be selected.

Comparison of Projects having Unequal Lives:

In order that projects are comparable, they must be made co-terminated i.e. their termination

point be made same. Projects are made co-terminated by using either Common Multiple Method

or Study Period Method.

In common multiple method, LCM of lives of various projects is calculated and projects are

repeated as many times till their LCM is reached. Suppose, three projects have lives respectively

2, 3 and 4 years, then their LCM is 12 which means the 1st project would be repeated 5 more

times, 2nd

for 3 more times and the 3rd

for 2 more times to make all projects co-terminated.

In study period method, a limited period which is same for both projects is selected and cash

flows during the period are considered while all cash flows beyond the period are ignored.

Ex: The data of two lease options (A & B) are given below:

A B

First Cost (Rs.)

Annual Lease Cost (Rs.)

Annual Returns (Rs.)

Lease Term (years)

-150, 000

-35, 000

10, 000

6

-1, 80, 000

-31, 000

20, 000

9

(a) Determine which lease option should be selected if the interest rate is 15%?

(b) If the study period of 5 years is used, which option should be selected?

Sol: (a) LCM of the lives of two lease options i.e. of 6 and 9 is 18.

PW A = -1, 50,000 [1 + (P/F, 15, 6) + (P/F, 15, 12)] – 35,000 (P/A, 15, 18)

+ 10,000 [(P/F, 15, 6) + (P/F, 15, 12) + (P/F, 15, 18)]

= Rs. – 4, 50, 360

PW B = -1, 80,000 [1 + (P/F, 15, 9)] – 31,000 (P/A, 15, 18)

+ 20,000 [(P/F, 15, 9) + (P/F, 15, 18)]

= Rs. – 4, 13, 840

Since PW B > PW A, Option B is selected.

(b) For 5-year study period:

PW A = -1, 50,000 – 35,000 (P/A, 15, 5) + 10,000 (P/F, 15, 5) = -2, 62, 360

PW B = -1, 80,000 – 31,000 (P/A, 15, 5) + 20,000 (P/F, 15, 5) = -2, 73, 970

Since PW B < PW A, Option A is selected.

Comparisons of Projects having Infinite Lives:

There are some projects like dams, bridges, rail roads etc. whose life is very difficult to

determine. In such cases, projects are compared by finding their capitalized costs. Capitalized

Cost is the sum of first cost and the present worth of disbursements assumed to last forever.

Capitalized cost = P + A (P/A, i, n), n→∞ = P + A / i

A is the difference between annual receipts and annual disbursements

Ex: A grant of Rs. 6, 00,000 was given for the construction of a dam. Annual maintenance

cost is estimated at Rs. 20,000. In addition, Rs. 30,000 will be required in every 10 years

for major repairs. Find out the initial cost if annual rate of interest is 5%.

Sol: First cost = Capitalized cost – Annual disbursement / i

= 6, 00,000 – [20,000 + 30,000 (A/F, 5, 10)] / 0.05

= 6, 00,000 – 4, 47,700 = Rs. 1, 52,300

Advantages of PW Method:

It recognizes time value of money and suitable to apply even to uneven cash flow streams

It takes into account the earning over the entire life of the project

It considers the objective of maximum profitability

Disadvantages of PW Method:

It is very difficult to determine appropriate discount rate

PW calculation is very sensitive to discount rate

It wholly excludes the value of any real options that may exist within the investment

Future Worth Method (FW):

Future worth method is particularly useful in an investment situation where we need to compute

the equivalent worth of a project at the end of its investment period rather than at its beginning.

For a single project:

If FW > 0, accept the project

If FW < 0, reject the investment proposal

If FW = 0, remain indifferent to the investment.

For a mutually exclusive alternatives future worth cash flows can be calculated by

i) Revenue based future worth - alternative with the maximum future worth amount should

be selected as the best alternative.

ii) Cost based future worth - alternative with the minimum future worth amount should be

selected as the best alternative.

The formula for the future worth for a given interest rate i is

FW(i) = - P (F/P, i, n) + R1 (F/P, i, n-1) + R2 (F/P, i, n-2) + ………. + R n + S

If it is equal payment series then the formula will be

FW (i) = - P (F/P, i, n) + R (F/P, i, n) + S

If the cash flow stream is cost-based, then the future worth is given by

FW (i) = P (1 + i)n + C1 (1 + i)

n-1 + C2 (1 + i)

n-2 + ………..+ C n – S

= P (F/P, i, n) + C1 (F/P, i, n-1) + C2 (F/P, i, n-2) + ………. + C n - S

In equal payment series the formula will be

FW (i) = P (F/P, i, n) + C (F/P, i, n) - S

Ex: Given the following particulars, which machine should be selected based on future worth

method, assuming 20% interest rate, compounded annually?

Particulars Machine A Machine B

Initial cost (Rs.)

Life (years)

Annual O & M cost (Rs.)

Salvage value (Rs.)

80,00,000

12.0

8,00,000

5,00,000

70,00,000

12.0

9,00,000

4,00,000

Sol: Cash flow diagram of machine A is:

S = Rs. 5, 00, 000

i = 20%

0 1 2 3 4 ……………… … 12

Rs. 8, 00, 000

Rs. 80, 00, 000

FW (20%) A = 80, 00,000 (F/P, 20, 12) + 8, 00,000 (F/A, 20, 12) -5, 00,000

= Rs. 10, 24, 92, 800

Cash flow diagram of machine B is:

S = Rs. 4, 00, 000

i = 20%

0 1 2 3 4 ……………… … 12

Rs. 9, 00, 000

Rs. 70, 00, 000

FW (20%) B = 70, 00, 000 (F/P, 20, 12) + 9, 00, 000 (F/A, 20, 12) - 4, 00, 000

= Rs. 9, 76, 34, 900

The future worth (cost) of machine B is less than that of machine A. So machine B

should be selected.

Ex: Which alternative from the following should be selected based on future worth method of

comparison assuming 12% interest rate compounded annually.

Alternative A Alternative B

Initial cost (Rs.)

Useful life (year)

Salvage value (Rs.)

Annual cost (Rs.)

4,00,000

4.0

2,00,000

40,000

8,00,000

4.0

5,50,000

- Nil -

Sol: Cash flow diagram of alternative A is:

S = Rs. 2, 00, 000

i = 12%

0 1 2 3 4

Rs. 40, 000

Rs. 4, 00, 000

FW (12%) A = Rs. 4, 00, 000 (F/P, 12%, 4) + Rs. 40, 000 (F/A, 12%, 4) - Rs. 2, 00, 000

= Rs. 6, 20, 760

Cash flow diagram of alternative B is:

S = Rs. 5, 50, 000

i = 12%

0 1 2 3 4

Rs. 8, 00, 000

FW (12%) B = Rs. 8, 00, 000 (F/P, 12%, 4) - Rs. 5, 50, 000 = Rs. 7, 09, 200

The alternative A should be selected as it involves less future worth (cost).

Equivalent Annual Worth Method (EAW):

In this method, all the receipts and disbursements occurring over a period are converted to an

equivalent uniform yearly amount. A large number of engineering economic decisions are based

on annual comparison like cost accounting procedures, depreciation charges, tax calculations etc.

Diagram of EAW

0 1 2 3

The term equivalent annual worth (EAW) is used when costs and receipts are both present.

Diagram of EAC

The term equivalent annual cost (EAC) is used to designate comparison involving only costs.

For single alternatives if

EAW > 0, Accept the investment proposal

EAQ < 0, Reject the investment proposal

EAW = 0, Remain indifferent to the investment.

For multiple alternatives or mutually exclusive alternatives if all the alternatives are revenue

dominated, the alternative with higher EAW will be selected. If all the alternatives are cost

based, the alternative with least EAW will be accepted.

R 1 R 2 R 3 R n

C 1 C 2 C 3 C n

Cost

R

ecei

pt

n

0

C 1

Cost

s R

ecei

pt

s

C 2 C 3 C 4 C n

1 2 3 4 n

…….

……

…. ……

….

3, 00, 000

1 0 3

2, 00, 000

2

6, 00, 000

2 1 3 4 0

3, 00, 000

4

Ex: Consider a machine that costs Rs.40, 000 and a 10 year useful life. At the end of 10 years,

it can be sold for Rs.5, 000 after tax adjustment. If the firm could earn after-tax revenue

of Rs.10, 000 per year with this machine, should it be purchased at interest rate of 15%,

compounded annually?

Sol: Initial cost (P) = Rs.40, 000/-

Useful life (n) = 10 years

Salvage value = Rs. 5, 000/-

Revenue = Rs.10, 000/-

i = 15%, compound annually

Case I: PW (15%) = -P + R (P/A, i, n) + S (P/F, i, n)

= - 40, 000 + 10, 000 (P/A, 15%, 10) + 5, 000 (P/F, 15%, 10)

= - 40,000 + 10, 000 (5.0188) + 5000 (0.2472) = Rs. 11, 424

Case II: EAW (15%) = PW (i) (A/P, i, n) = Rs. 11424 (A/P, 15%, 10)

= Rs. 11424 (0.1993) = Rs. 2277

Since EAW (15%) > 0, so the project is accepted.

Ex: Suggest which machine should be purchased at 15% interest rate based on annual

equivalent worth method.

Machine A Machine B

First Cost Rs.3,00,000 Rs.6,00,000

Life period 4 years 4 years

Salvage value Rs.2,00,000 Rs.3,00,000

O & M Cost Rs.30,000 Rs.0

Sol: The cash flow diagram of machine A is shown below.

EAC (15%) A = P (A/P, i, n) + C – S (A/F, i, n)

= 3, 00, 000 (A/P, 15%, 4) + 30, 000- 2, 00, 000 (A/F, 15%, 4)

= Rs. 95, 033

The cash flow diagram of machine B is shown below.

30, 000

EAC (15%) B = P (A/P, i, n) – S (A/F, i, n)

= 6, 00, 000 (A/P, 15%, 4) – 3, 00, 000 (A/F, 15%, 4))

= Rs. 1, 50, 090

Since the equivalent annual cost of Machine A is less than that of Machine B, it is

advisable to purchase Machine A.

Rate of Return Method:

The rate of return is a percentage that indicates the relative yield on different uses of capital.

Three rates of return appear frequently in engineering economy studies:

The minimum acceptable rate of return (MARR) is the rate set by an organization to

designate the lowest level of return that makes an investment acceptable.

Internal rate of return (IRR) is the rate on the unrecovered balance of the investment in a

situation where the terminal balance is zero. It is a discount rate at which NPV = 0.

External rate of return (ERR) is the rate of return that is possible to obtain for an

investment under current economic conditions. For example, suppose analysis of an

investment shows that it will realize an IRR of 50 percent. Rationally, it is not reasonable

to expect that we can invest in the external market and get that high a rate. In engineering

economy studies, the external interest rate most often set to the MARR.

Minimum Acceptable Rate of Return (MARR):

The minimum acceptable rate of return, also known as the minimum attractive rate of return, is a

lower limit for investment acceptability set by organizations or individuals. It is a device

designed to make the best possible use of a limited resource. Rates vary widely according to the

type of organization, and they vary even within the organization. Historically, government

agencies and regulated public utilities have utilized lower required rates of return than have

competitive industrial enterprises. Within a given enterprise, the required rate may be different

for various divisions or activities. These variations usually reflect the risk involved. For instance,

the rate of return required for cost reduction proposals may be lower than that required for

research and development projects in which there is less certainty about prospective cash flows.

Internal Rate of Return Method (IRR):

The internal rate of return, represented by i in the traditional interpretation of interest rates, is the

rate of interest earned by an alternative investment on the unrecovered balance of an investment.

The internal rate of return can be calculated by equating the annual, present, or future worth of

cash flow to zero and solving for the interest rate (IRR) that allows the equality. While solving

for the interest rate, it may result in a polynomial equation which may result in multiple roots of

the equation. In such cases the IRR may or may not be one of the equation roots.

Calculation of IRR:

IRR is “The Discount rate at which the costs of investment equal to the benefits of the

investment. Or in other words IRR is the Required Rate that equates the NPV of an investment

zero. The ascertainment of IRR involves trial and error method and if IRR falls between two

interest rates, then it is found out using interpolation.

If IRR exceeds firm’s MARR, then the project is accepted, otherwise, it is rejected. For mutually

exclusive projects, project with highest IRR is selected.

Ex: A person is planning a new business. The initial outlay and cash flow pattern for the new

business are as listed below. The expected life of the business is five years. Find the rate

of return for the new business.

Period 0 1 2 3 4 5

Cash flow (Rs.) -1,00,000 30,000 30,000 30,000 30,000 30,000

Sol: Initial investment = Rs. 1, 00, 000

Annual equal revenue = Rs. 30, 000

Life = 5 years

PW(i) = -1, 00, 000 + 30, 000 (P/A, i, 5)

When i = 10%, PW (10%) = -1, 00, 000 + 30, 000 (P/A, 10%, 5)

= -1, 00, 000 + 30, 000(3.7908) = Rs. 13, 724

When i = 15%, PW (15%) = -1, 00, 000 + 30, 000 (P/A, 15%, 5)

= -1, 00, 000 + 30, 000 (3.3522) = Rs. 566

When i =18%, PW (18%) = -1, 00, 000 + 30, 000 (P/A, 18%, 5)

= -1, 00, 000 + 30, 000 (3.1272) = Rs. -6, 184

= 15% + 0.252% = 15.252%

Therefore, the IRR for the new business is 15.252%.

Ex: A firm has identified three mutually exclusive investment proposals whose details are

given below. The life of all the three alternatives is estimated to be five years with

negligible salvage value. The minimum attractive rate of return for the firm is 12%.

Alternative

A1 A2 A3

Investment Rs. 1,50,000 Rs. 2,10,000 Rs. 2,55,000

Annual net income Rs. 45,570 Rs. 58,260 Rs. 69,000

Find the best alternative based on the rate-of return method of comparison.

Sol: Alternative A1

Initial outlay = Rs. 1, 50, 000

Annual profit = Rs. 45, 570

Life = 5 years

PW (i) = -1, 50, 000 + 45, 570 (P/A, i, 5)

PW (12%) = -1, 50, 000 + 45, 570 (P/A, 12%, 5)

= -1, 50, 000 + 45, 570 (3.6048) = Rs. 14, 270.74

PW (15%) = -1, 50, 000 + 45, 570 (P/A, 15%, 5)

= -1, 50, 000 + 45, 570 (3.3522) = Rs. 2, 759.75

PW (18%) = -1, 50, 000 + 45, 570 (P/A, 18%, 5)

= -1, 50, 000 + 45, 570 (3.1272) = Rs. -7, 493.50

Therefore, IRR of the alternative A1 is

= 15.81%

Alternative A2

Initial outlay = Rs. 2, 10, 000

Annual profit = Rs. 58, 260

Life of alternative A2 = 5 years

PW (i) = -2, 10, 000 + 58, 260 (P/A, i, 5)

PW (12%) = -2, 10, 000 + 58, 260 (P/A, 12%, 5)

= -2, 10, 000 + 58, 260 (3.6048) = Rs. 15.65

PW (13%) = -2, 10, 000 + 58, 260 (P/A, 13%, 5)

= -2, 10, 000 + 58, 260 (3.5172) = Rs. -5, 087.93

Therefore, IRR of alternative A2 is

= 12%

Alternative A3

Initial outlay = Rs. 2, 55, 000

Annual profit = Rs. 69,000

Life of alternative A3 = 5 years

PW (i) = -2, 55, 000 + 69, 000 (P/A, i, 5)

PW (12%) = -2, 55, 000 + 69, 000 (P/A, 12%, 5)

= -2, 55, 000 + 69, 000 (3.6048) = Rs. -6, 268.80

PW (11%) = -2, 55, 000 + 69, 000 (P/A, 11%, 5)

= -2, 55, 000 + 69, 000 (3.6959) = Rs. 17.1

Therefore, IRR of alternative A3 is

= 11%

From the above data, it is clear that the rate of return for alternative A3 is less than the

minimum attractive rate of return of 12%. So, it should not be considered for comparison.

The remaining two alternatives are qualified for consideration. Among the alternatives

A1 and A2, the rate of return of alternative A1 is greater than that of alternative A2.

Hence, alternative A1 should be selected.

IRR Misconceptions:

IRR method for project evaluation leads to conflicting results under following conditions:

(i) The pattern of cash inflows plays an important role in project evaluation while using IRR

method. i.e. the cash flows of one project may increase over time, while those of others

may decrease and vice versa. The major drawback with the IRR method is that for

mutually exclusive projects, it can give contradictory investment decision when

compared with NPV. Consider the following example.

In the above example A and B are mutually exclusive projects. Both projects require an

initial outlay of $ 1,000,000 but the pattern of cash inflows is different. Cash inflows for

Project A are increasing over the period of time while for Project B these are declining.

IRR decision rule leads to select Project A as Project A IRR > Project B IRR. But

decision on the basis of NPV evaluation implies that project B is more viable. Thus on

the basis of mere IRR the company may select less profitable project.

(ii) The cash outflow of the projects may differ. i.e. a project may need capital outlay not

only at the time of investment but after regular intervals during its expected life.

Consider the following example:

Project A requires an initial outlay at the beginning of the project while Project B needs

cash outflow in year 2 and year 4 also. Decision based on IRR method leads to select

project B but NPV of project B is less than of Project A. again under such circumstances

IRR method plays a deceive role.

Summarizing the above discussion the timings and pattern of cash flows can produce

conflicting results in the NPV and IRR methods of project evaluation.

Public Projects and Cost-Benefit Analysis:

Public projects are undertaken by the Government to enhance the standard of living and welfare

of citizens. Activities such as police forces, health care services, education system belong to

public projects. While evaluating the private projects, the focus is on maximizing profit, in case

of public projects, the objective might be providing goods/services to public at minimum cost

The basic measure of accepting a public project is a benefit-cost (B/C) ratio.

B/C ratio = PW of Benefits / PW of Costs

= FW of Benefits / FW of Costs

= EAW of Benefits / EAW of Costs

Like private projects, cash flows in public projects are also discounted at a suitable rate known as

Social Discount Rate.

For Independent Projects,

If B/C ratio > 1, Accept the project

B/C ratio < 1, Reject the project

B/C ratio = 1, Depends on the Govt.

For Mutually exclusive projects, one involving higher B/C ratio is selected. Here, incremental

analysis can also be used to compare carious alternative projects.

Benefits of a public project can be of two types:

i) Primary benefits – availability of water, electricity, irrigation etc.

ii) Secondary benefits – recreational benefits, other benefits.

For example, benefits from a dam include:

a) water supply for domestic as well as industrial use

b) flood control

c) hydro-power generation

d) recreation

Costs in a public project are all resources required to achieve stated objectives which are:

i) Imputed costs of existing assets employed on another project besides the current use of it.

ii) Preliminary costs of investigation and technical services required to start a project.

iii) Spillover costs which constitute all significant adverse effects caused by the project.

Ex: In a particular locality of a state, the vehicle users take a roundabout route to reach

certain places because of the presence of a river. This results in excessive travel time and

increased fuel cost. So, the state government is planning to construct a bridge across the

river. The estimated initial investment for constructing the bridge is Rs. 40, 00, 000. The

estimated life of the bridge is 15 years. The annual operation and maintenance cost is Rs.

1, 50, 000. The value of fuel savings due to the construction of the bridge is Rs. 6, 00,

000 in the first year and it increases by Rs. 50, 000 every year thereafter till the end of the

life of the bridge. Check whether the project is justified based on BC ratio by assuming

an interest rate of 12%, compounded annually.

Sol: Initial investment = Rs. 40, 00, 000

Annual operation and maintenance = Rs. 1, 50, 000

Annual fuel savings during the first year = Rs. 6, 00, 000

Equal increment in fuel savings in the following years = Rs. 50, 000

Life of the project = 15 years

Interest rate = 12%

Total present worth of costs

= Initial investment (P) + Present worth of annual operating and maintenance cost (CP)

= Rs. 40, 00, 000 + 1, 50, 000 (P/A, 12%, 15)

= Rs. 40, 00, 000 + 1, 50, 000 x 6.8109 = Rs. 50, 21, 635

Present worth of fuel savings (BP):

A1 = Rs. 6, 00, 000

G = Rs. 50, 000

n = 15 years

i = 12%

Present worth of the fuel savings (BP)

= [A1 + G (A/G, 12%, 15)] (P/A, 12%, 15)

= [6, 00, 000 + 50, 000 (4.9803)] (6.8109) = Rs. 57, 82, 556

BC Ratio = Bp / (P + Cp) = 57, 82, 556 / 50, 21, 635 = 1.1515

Since the B/C ratio > 1, the construction of the bridge across the river is justified.

Ex: Two mutually exclusive projects are being considered for investment. Project Al requires

an initial outlay of Rs. 30, 00, 000 with net receipts estimated as Rs. 9, 00, 000 per year

for the next 5 years. The initial outlay for the project A2 is Rs. 60, 00, 000, and net

receipts have been estimated at Rs. 15, 00, 000 per year for the next seven years. There is

no salvage value associated with either of the projects. Using the benefit cost ratio, which

project would you select? Assume an interest rate of 10%.

Sol: Alternative A1

Initial cost (P) = Rs. 30, 00, 000

Net benefits / year (B) = Rs. 9, 00, 000

Life (n) = 5 years

Annual equivalent of initial cost

= P x (A/P, 10%, 5) = 30, 00, 000 x 0.2638 = Rs. 7, 91, 400

B/C ratio =

= 9, 00, 000 / 7, 91, 400 = 1.137

Alternative A2

Initial cost (P) = Rs. 60, 00, 000

Net benefits / year (B) = Rs. 15, 00, 000

Life (n) = 7 years

Annual equivalent of initial cost

= P x (A/P, 10%, 7) = 60, 00, 000 x 0.2054 = Rs. 12, 32, 400

= 15, 00, 000 / 12, 32, 400 = 1.217

The B/C ratio of alternative A2 is more than that of alternative A1 and hence, alternative

A2 is selected.

Limitations of Cost-benefit analysis:

Difficulties in benefit assessment

Arbitrary social discount rate

Ignores opportunity cost

Difficulties in cost assessment

Payback Period Method (PBP):

It is defined as the time period required for a project to return back the capital employed in it. For

example, an investment of Rs. 50,000 which returns Rs. 10,000 per year will have a five year

payback period. Shorter PBPs are more desirable for investors than longer PBPs.

Thus, PBP = First Cost / Net Annual Savings

Discounted Payback Period:

One of the limitations in using payback period is that it does not take into account the time value

of money. However, the discounted payback period solves this problem. This technique is

somewhat similar to payback period except that the expected future cash flows are discounted for

computing payback period. If discounted payback period is smaller than some pre-determined

number of years then an investment is worth undertaking.

For example an initial investment of Rs. 10,000 (Year 0) generates cash flows from Years 1-6 as

given below:

Year Cash Flows PV of Cash Flows Cumulative Cash Flows

0 -$10,000 -$10,000 $-10,000

1 1500 1389 -8611

2 2500 2143 -6468

3 4000 3175 -3293

4 3000 2205 -1088

5 3000 2042 +954

6 3000 1891 +2845

The Payback Period occurs in Year 4, when the cash flow turns from a Negative (-1088) to a

Positive (+954).

Thus, Discounted Payback Period = 4 Years + (1088 / 2042) = 4.53 Years

Depreciation Analysis Depreciation is the decrease in value of physical properties with the passage of time and use.

Production equipment gradually becomes less valuable through wear and tear. This lessening in

value is recognized in accounting practices as an operating expense. Instead of charging the full

purchase price of a new asset as one time expense, the outlay is spread over the life of the asset

in the accounting records. Annual depreciation deductions are intended to match the yearly

fraction of value used by an asset in the production of income over the assets actual economic

life. The actual amount of depreciation can never be established until the asset is retired.

Fixed assets are assets having long-term perspective such as plant, building, machinery etc.

Depreciation is a permanent continuing and gradual shrinkage in book value of a fixed asset.

Current assets are never depreciated. Moreover, depreciation is always charged on book value of

the asset and not on market value of it.

Causes of Depreciation:

1. Physical depreciation: It is caused mainly from wear and tear when the asset is in use

and from corrosion, rust, rot and decay from being exposed to wind, rain, sun and other

elements of nature.

2. Economic Factors: These cause the asset to be put out of use even though it is in good

physical condition. These arise due to obsolescence (Assets become outdated as a result

of introduction of new model of it) and inadequacy (termination of the use of an asset

because of growth and change in size of the firm).

3. Time factors: There are some assets, which loses its values after a particular time period.

Assets having lease, copyrights and patents right loses its value after the time is over.

4. Depletion: Consumption of exhaustible natural resources to produce product or services

is termed as depletion. Removal of oil, timber, rock or minerals from a site decreases the

value of the holding.

5. Accident: Sometimes due to accident or sudden failure the asset loses its technological

characteristic inherent in it.

Need For Providing Depreciation:

To know the true profits: As depreciation is an expense, it is desirable to charge

depreciation on fixed assets for earning purposes. Depreciation amount must be deducted

out of the income earned in order to calculate true net profit/loss of business enterprises.

To show true financial position: Financial position can be studied from the balance

sheet which contains assets and liabilities of a business. If depreciation is not charged on

fixed assets, then their values are overstated which will not show the true financial

position of a business.

To make provisions for replacement of assets: If depreciation is not provided, profits

are overstated and are distributed as dividends to the shareholders. Provision for

depreciation is a charge to P/L account and the accumulated amount provides additional

working capital besides providing sum for replacement of the asset.

Depreciation Methods:

Terminologies:

P = Purchase price (unadjusted basis) of assets.

S = Salvage value or future value at end of asset’s life. It is the expected selling price of a

property when the asset can no longer be used by its owner.

N = useful (tax) life of asset. This is the expected period of time that a property will be used

in a trade or business or to produce income.

N = number of years of depreciation

D t (n) = Annual depreciation charges.

B t (n) = Book value shown on accounting records at end of year.

B t (0) = p

Straight line method (SL):

The most widely used and simplest method for the calculation of depreciation is straight line

method. The straight line method assumes that the value of an asset decreases at a constant rate.

Thus if an asset has a first cost of Rs.5, 000 and an estimated salvage value of Rs. 500, the total

depreciation over its life will be Rs. 4, 500. If the estimated life in 5 years, the depreciation per

year will be 4, 500 5 = 900. This is equivalent to a depreciation rate of 1/5 = 20% per year.

The depreciation in any year is n

FPDT

The book value is

n

FPtPBT

And the depreciation rate per year isn

1

Ex: Initial cost of the asset = Rs. 5000

Life time = 5 years

Salvage value = 0

From the following data find out

a) The depreciation charge during year 1

b) The depreciation charge during year 2

c) The depreciation reserve accumulated by the end of year 3

d) The book value at the end of year 3

Sol: (a) & (b): In case of straight line method as the depreciation charge is constant, the

depreciation charges for year 1 and 2 is constant.

5

5000)2()1(

n

FPDD TT = 1000 per year

(c) The depreciation reserve at the end of the third year is the sum of the annual

depreciation charges for the first three years and is equal to 3 (1000) = Rs. 3000

(d) The book value at the end of third year is 20005

500035000

Declining balance Method (DB):

Value of an asset diminishes at a decreasing rate. The declining balance depreciation assumes

that an asset decreases in value faster early rather than in the latter portion of its service life. By

this method a fixed percentage is multiplied times the book value of the asset at the beginning of

the year to determine the depreciation charge for that year. Thus as the book value of the asset

decreases through time, so does the size of the depreciation charge. For example,

First cost = Rs. 5, 000

Salvage value = Rs. 1, 000

Life of the asset = 5 years and

Depreciation rate is 30% per year.

Declining Balance method

End of year Depreciation charge during year Book value at end of year

0 5000

1 (0.30) (50000) = 1,500 3,1500

2 (0.30) (3,500) = 1,050 2,450

3 (0.30) (2,450) = 735 1,715

4 (0.30) (1,7115) = 515 1,200

5 (0.30) (1,200) = 360 840

For a depreciation rate a, the general relationship expressing the depreciation charge in any year

for declining balance depreciation is:

D (t) = a. BV (t-1)

BV (t) = BV t-1 – D t

Therefore, declining-balance depreciation

BV (t) = BV t-1 – a. BV t-1

Thus, D (t) = a (1-a) t-1

P

And BV (t) = (1 - R) P = P (1-a) t

Double Declining Balance method (DDB):

If the declining balance method of depreciation is used for income tax purposes the maximum

rate that may be used is double the straight line rate that would be allowed to a particular asset

being depreciated. Thus for an asset with an estimated life of N years, the maximum rate that

may be used with this method is R = 2/N. Many firms and individuals choose to depreciate their

assets using declining balance depreciation with maximum allowable rate. Such a depreciation

method is commonly known as the Double Declining Balance method of depreciation.

Ex: Initial cost = 5000

N = 5 years

S = 0.

Find D t (1), D t (2) and depreciation reserves at the end of year 3, and B t (3).

Sol: The depreciation rate 4.05/22

N

a

D t (1) = [B t (0)] (0.4) = 5000 (0.4) = 2000

D t (2) = [B t (l)] (0.4) = (5000 - 2000) (0.4) = 1200

The depreciation reserve at the end of year 3 is

D t (l) + D t (2) + [B t (2) (0.4)] = 2000 + 1200 + 720 = 3920

B t (3) = P - depreciation reserve = 5000 - 3920 = 1080

Switch From DB/DDB to SL depreciation

A difficulty may arise with the use of declining balance depreciation because in the above

example salvage value is zero. After the end of life time or at the end of year 5, we find that:

B t (5) = P (1 – R) N = 5000 (0.6)

5 = 388.88

It is not uncommon for the book value with DB/DDB depreciation to exceed the asset’s value at

the end of its life. It is allowable under the tax law to depreciate an asset over the early portion of

its life using DB depreciation and then switching to SL depreciation for the remainder of the

asset’s life. The switch usually occurs when the next period’s SL depreciation amount on

undepriciated balance of the asset exceeds the next period’s DB depreciation charge.

Suppose, an asset has first cost of 5000, a five year useful life and no salvage value. Determine

an accelerated depreciation schedule. Applying the double declining balance method as was done

for Rs. 5000 and N values.

We know book value B t (5) = 388.8 is higher than the zero salvage value. Therefore to make

book-value zero, we have to switch to straight line method.

End of year DDB

charges

Book value

with DDB

SL depreciation on

undepreciated balance

Book value

DDB SL

0 5000 5000

1 2000 3000 5000/5 = 100 3000

2 1200 1800 3000/4 = 750 18000

3 720 1080 1800/3 = 600 1080

4 432 648 1080/2 = 540 540

5 259.2 388.8 540 0

At the end of year 2, the book value resulting from DDB depreciation is 1800 which equal the

undepreciated balance because S = 0.

Then the SL charges for the last 3 years would be = 1800/3 = 600

Since this annual charge is less than DDB charge for 3rd

year, (720), accelerated depreciation is

continued another year. Thus B t (3) = 1080 and the SL depreciation charge for each of the last 2

years 1080/2 = 540. This is larger than the DDB depreciation charge for year 4 (432) and signals

the time to switch.

Sum - of – the - years - Digits Method:

To compute the depreciation deduction by the SYD method, the digits corresponding to the

number for each permissible year of life are first listed in reverse order. The sum of these digits

is then determined. The depreciation factor for any year is a number from the reverse ordered

listing for that year divided by the sum of the digits. For example for a property having a

depreciable life of five years, SYD depreciation factors are as follows:

Year Number of the year in Reverse order SYD Depreciation Factor

1. 5 5/15

2. 4 4/15

3. 3 3/15

4. 2 2/15

5. 1 1/15

The depreciation for any year is the product of the SYD depreciation factor for that year and the

difference between the cost basis (B) and the estimated final SV.

Ex: The cost of a vehicle is Rs. 1, 00,000 and the salvage value after 4 years of its useful life

is Rs. 20,000. Calculate the depreciation charges and book value of the asset every year

using sum-of-years-digit method.

Sol: SYD = 1 + 2 + 3 + 4 = 10

Depreciable Amount = 1, 00,000 – 20,000 = Rs. 80,000

End of Year SYD depreciation rate Depreciation Charge Book Value

1 4/10 32,000 68,000

2 3/10 24,000 44,000

3 2/10 16,000 28,000

4 1/10 8,000 20,000

Modified Accelerated Cost Recovery System (MACRS):

To determine depreciation schedule appropriate for depreciable property, MACRS has defined

various property classes (life of the asset) and all assets fall into any of the categories. Assets

having life more than or equal to 15 years are depreciated at 150%/N and assets below 15 years

life are depreciated at 200%/N where N is the asset’s property class.

Procedure for calculation of MACRS Declining balance depreciation

1. Divide the appropriate percentage (either 200 or 150 per cent) by the number of years in

the recovery period to calculate MACRS depreciation rate.

2. Divide the result from step 1 by 2 to convert the percentage to the half year convention

for the first year of services.

3. The percentage for the second year of service is calculated by multiplying the remaining

basis (the current book value) by the base rate.

4. The procedure is continued until a switch to the straight line methods allowed in order to

reach the terminal salvage value. Since the mid-year convention is used in MACRS, the

remaining life at the end of the year is determined by N – K + 0.5 for K = 1, 2 …..N,

Straight line depreciation for the remaining year is calculated as

D (k) = BV (k) / (N – k + 0.5)

Ex: Switch from declining balance to straight line Depreciation in MACRS of a 7-year

property class asset having purchase price of Rs. 10,000 with no salvage value

Sol: The base rate is 200% / 7 = 28.57

Depreciation charges and book values for different periods are presented below:

MACRS to Straight line

End of

year

MACRS

Depreciation rate

Declining

balance

deduction

Straight line

deduction

Book value

after

depreciation

0 10,000

1 14.29 1429 1333 8571

2 24.29 2429 1319 6122

3 17.49 1749 1113 4373

4 12.49 1249 972 3124

5 8.93 893 893 2231

6 8.93 637 893 1338

7 8.93 455 893 445

8 4.45 325 445 0

In the above table up to 4th

year, straight line depreciation is less than declining balance

deduction. In the fifth year straight line deduction is equal to dealing balance deduction.

From that year we will switch over to straight line deduction such that book value is zero.

After-tax Economic Evaluations:

Most of the firms pay different types of taxes and one of the most important taxes is income tax

which is levied on the net income of the person. But tax most of the time influences a decision. A

simple adjustment of rate of return calculated without regard for taxes gives an approximation to

the after tax rate of return.

IRR after tax = IRR before tax (1 - effective income tax rate)

For after tax comparisons, following table can be prepared.

Column heading Column number Arithmetic computation in column

Investment year 1

Before tax operating cash flow 2

Book value before depreciation 3

MACRS depreciation rate 4

Depreciation charge 5 4 x original basis

Book value after depreciation 6 (3) – (5)

Cash flow for debt 7

Cash flow for debt interest 8

Taxable Income 9 (2) – (5) – (8)

Cash flow for taxes 10 Tax rate x (9)

After – tax cash flow 11 (2) – (7) – (10)

After tax comparison can be made by any comparison methods like PW, EAW or IRR.

Ex: Initial investment on a machine is 60, 000, i = 15% (After taxes). The Machine is 5 years

MACRS recovery property. Over six years, investment estimated to save 25,000/year.

Annual operating cost is 5,000. It will be depreciated by MACRS method and will have

no salvage value. Income tax rate is 40%. Does the proposal to invest on the machine

satisfy the firm’s new minimum acceptable rate of return?

Sol: Let’s find out IRR before tax

PW = - 60,000 + (20,000) (P/A, i, 6) = 0

PW (25%) = - 60, 000 + (20, 000) (2.9514) = - 60, 000 + 59, 028 = -972

PW (23%) = - 60, 000 + 61, 846 = 1, 846

Using interpolation,

IRR = %2)972(1846

1846%23

= 23% + [0.655] 0.02 = 23.14

Thus, IRR after tax = (23.14%) (1 - 0.40) = 13.84%

It will be rejected as if it is below 15%

After - tax flows (After depreciation)

Investment

year

Before tax

cash flow

Depreciation

charge

Taxable

loan

Taxes 40% After taxes

cash flow

0 -60,000 -60,000

1 20,000 12,000 8,000 3,200 16,800

2 20,000 19,200 800 320 19,680

3 27,000 11,520 8480 3392 16608

4 20,000 6912 13088 5235.2 14764.8

5 20,000 6912 13088 5235.2 14764.8

6 20,000 3456 19,644 7857.6 12142.4

IRR after-tax = 15.87 %

As it is more than 15%, investment can be made on the machine.

Costing

The cost accounting consists of two words: Cost and Accounting. Cost means the resources

sacrificed for the production of a commodity and accounting refers to the financial information

system. Cost accounting system can be described as measurement and reporting of resources

used in monetary terms. Cost accounting is the branch of accounting dealing with the

classification, recording, allocation, summarization and reporting of current and prospective cost.

Costing and cost accounting

We use costing and cost accounting interchangeably. But they should not be. Costing refers to

the technique and process of ascertaining cost. The technique consists of the principles and rules

for the determining the costs of products and services.

Cost accounting on the other hand, is defined as the process of accounting for cost from the point

at which expenditure is incurred. It is that specialized branch of accounting which involves

classification, accumulation, allocation, absorption and control of costs.

According to CIMA, cost accounting is the application of costing and cost accounting principles,

methods and techniques to the science, art and practice of cost control. It includes the

presentation of information derived those from for the purpose of managerial decision making:

a) Cost Ascertainment: Ascertaining the cost of goods produced and services rendered has

been the chief function of cost accounting. This purpose is some times referred to as

product costing or cost accumulation.

b) Cost Analysis: Cost analysis is one of the important functions of cost accounting as it

helps in decision making. While making decision, we require information about cost,

revenue and other information. So we have to analyze the cost.

c) Cost Control: To control the cost is chief motive of every management. Cost information

shows the performance of the organization. There are two types of cost control method:

Standard Costing and Budgetary Control. Actual costs are compared to the budgeted cost.

This help in controlling the cost.

Objectives of cost accounting

1. The cost accounting helps in ascertaining the cost of production of every units, job,

operation process, department and service.

2. It indicates management any inefficiency and extent of various forms of waste, whether

in material, time, expense or in the use of machine, equipment and tools.

3. It provides actual figures of cost for comparison with estimates and to assist the

management in their price fixing policy.

4. It present comparative cost data for different periods and different volumes of production

and assist the management in budgetary control.

5. It record and report to the concerned manager how actual costs compare with standard

cost and possible causes of differences between them.

6. It indicates exact cause of increase/decrease in profit/loss shown by financial accounts.

7. It provides data for comparison cost within firm and also between similar firms

Cost Centre vs. Cost Unit:

A cost centre is a location (department), person (salesman) or item of equipment (machine) in

relation to which cost may be ascertained. The main purpose of ascertaining cost of a cost centre

is control of cost. For example, in the functional area of marketing, it may become necessary to

distinguish between selling costs which become the responsibility of one area sales manager with

those for which another area manager is responsible. Therefore, in order to relate costs to the

managers concerned and compare the profitability of different areas, a sales territory may be

constituted as a cost centre.

The ascertainment of cost necessitates the determination of unit in terms of which costs are

ascertained. The unit of product/service chosen for the purpose is called a cost unit. The choice

of a cost unit depends on what is being produced, whether goods or services and what is relevant

to the purpose of cost ascertainment. Some of the examples of cost units are given below:

Industry Cost Unit

Cement Tonne

Bricks 1000 bricks

Nursing home Bed per day

Electricity Kilowatt hour

Transport Passenger kilometer

Printing press Thousand copies

Carpets Square foot

Hotel Room per day

Elements of Cost:

Following are the three broad elements of cost:

MATERIAL - The substance from which a product is made is known as material. It can be

direct as well as indirect. The material which becomes an integral part of a finished product and

which can be conveniently assigned to specific physical unit is termed as direct material. Some

of the examples of direct material are components specifically purchased, primary packing

materials, partly produced components etc. The material which is used for purposes ancillary to

the business and which cannot be conveniently assigned to specific physical units is termed as

indirect material. Consumable stores, oil and waste, printing and stationery material etc. are

some of the examples of indirect material.

LABOR - For conversion of materials into finished goods, human effort is needed and such

human effort is called labor. Labor can be direct as well as indirect. The labor which actively and

directly takes part in the production of a particular commodity is called direct labor. Direct labor

costs are, therefore, specifically and conveniently traceable to specific products. The labor

employed for the purpose of carrying out tasks incidental to goods produced/services provided, is

indirect labor. It cannot be practically traced to specific units of output. Wages of storekeepers,

foremen, Directors’ fees, salaries of salesmen etc, are examples of indirect labor costs.

EXPENSES – All costs other than materials and labor are termed as expenses. These may be

direct or indirect. Direct expenses can be directly, conveniently and wholly allocated to specific

cost centers/cost units. Examples of such expenses are hire purchase of machinery, cost of

defective work etc. Indirect Expenses are those which can’t be directly, conveniently and wholly

allocated to cost centers or cost units. Examples of such expenses are rent, lighting, insurance

charges etc.

Overhead - The term overhead includes indirect material, indirect labor and indirect expenses.

Thus, all indirect costs are overheads. Overheads may be incurred in a factory or office or selling

and distribution divisions. Thus, overheads may be of three types:

Factory Overheads: They include the following things:

Indirect material used in a factory such as lubricants, oil, consumable stores etc.

Indirect labor such as gatekeeper, timekeeper, works manager’s salary etc.

Indirect expenses such as factory rent, factory insurance, factory lighting etc.

Office and Administration Overheads: They include the following things:

Indirect materials used in an office such as printing and stationery material, brooms etc.

Indirect labor such as salaries payable to office manager, office accountant, clerks, etc.

Indirect expenses such as rent, insurance, lighting of the office

Selling and Distribution Overheads: They include the following things:

Indirect materials used such as packing material, printing and stationery material etc.

Indirect labor such as salaries of salesmen and sales manager etc.

Indirect expenses such as rent, insurance, advertising expenses etc.

Various components of total cost can be depicted with the help of the table below:

Direct material plus Direct labor plus

Direct expenses Prime cost or direct cost or first cost

Prime cost plus works overheads Works or factory cost or manufacturing cost

Works cost plus office and

administration overheads Office cost or total cost of production

Office cost plus selling and

distribution overheads Cost of sales or total cost

Cost Sheet: Cost sheet is a document that provides for the assembly of an estimated detailed cost in respect

of cost centers and cost units. It analyzes and classifies in a tabular form the expenses on

different items for a particular period.

Example: Following information has been obtained from the records of XYZ Ltd. for the period

from June 1 to June 30, 1998. Prepare a statement of cost.

Cost of raw materials on June 1,1998 30,000

Purchase of raw materials during the month 4,50,000

Wages paid 2,30,000

Factory overheads 92,000

Cost of work in progress on June 1, 1998 12,000

Cost of raw materials on June 30, 1998 15,000

Cost of stock of finished goods on June 1, 1998 60,000

Cost of stock of finished goods on June 30, 1998 55,000

Selling and distribution overheads 20,000

Sales 9,00,000

Administration overheads 30,000

Solution:

Statement of cost sheet of XYZ Ltd. for the period ending on June 30, 1998.

Opening stock of raw materials

Add-- purchase

30,000

4,50,000

------------

4,80,000

15,000

Less-- closing stock of raw material

Value of raw materials consumed

Wages

Prime cost Factory overheads

Add-- opening stock of work in progress

Less-- closing stock of work in progress

Factory cost Add-- Administration overhead

Cost of production of goods manufactured

Add--opening stock of finished goods

4,65,000

2,30,000

6,59,000

92,000

7,87,000

12,000

7,99,000

---

7,99,000

30,000

8,29,000

60,000

8,89,000

Less-- closing stock of finished goods

Cost of production of goods sold Add-- selling and distribution overheads

Cost of sales

Profit

Sales

55,000

8,34,000

20,000

8,54,000

46,000

9,00,000

Classification of Cost:

Cost may be classified into different categories as follows:

1. Fixed, Variable and Semi-Variable Costs:

The cost which varies directly in proportion with every increase or decrease in the volume of

output or production is known as variable cost (Direct cost). For example wages of laborers, cost

of direct material, power etc. The cost which does not vary but remains constant within a given

period of time and a range of activity in spite of the fluctuations in production is known as fixed

cost (Indirect cost). Some of its examples are rent, insurance charges, manager’s salary etc. The

cost which does not vary proportionately but simultaneously does not remain stationary at all

times is known as semi-variable cost. Some of its examples are depreciation, repairs etc.

2. Product Costs and Period Costs: The costs which are a part of the cost of a product rather than an expense of the period in which

they are incurred are called as product costs. They become an expense at that time. These costs

may be fixed as well as variable, e.g., cost of raw materials and direct wages, depreciation on

plant and equipment etc.

The costs which are not associated with production are called period costs. They are treated as an

expense of the period in which they are incurred. They may also be fixed as well as variable.

Such costs include general administration costs, salaries salesmen and commission, depreciation

on office facilities etc.

3. Decision-Making Costs and Accounting Costs: Decision-making costs (future costs) are special purpose costs that are applicable only in the

situation in which they are compiled. They have no universal application. Accounting costs

(historical costs) are compiled primarily from financial statements. They have to be altered

before they can be used for decision-making.

4. Relevant and Irrelevant Costs: Relevant costs are those which change by managerial decision. Irrelevant costs are those which

do not get affected by the decision. For example, if a manufacturer is planning to close down an

unprofitable retail sales shop, this will affect the wages payable to the workers of a shop. This is

relevant in this connection since they will disappear on closing down of a shop. But prepaid rent

of a shop is irrelevant costs which should be ignored.

5. Shutdown and Sunk Costs: A manufacturer or an organization may have to suspend its operations for a period on account of

some temporary difficulties, e.g., shortage of raw material, non-availability of requisite labor etc.

During this period, though no work is done yet certain fixed costs, such as rent and insurance of

buildings, depreciation, maintenance etc., for the entire plant will have to be incurred. Such costs

of the idle plant are known as shutdown costs. Sunk costs are the past costs which have been

created by a decision that was made in the past and can’t be changed by any decision that will be

made in future. Investments in plant and machinery, buildings etc. are examples of such costs.

6. Out-of-Pocket Costs Out-of-pocket cost means the present or future cash expenditure regarding a certain decision that

will vary depending upon the nature of the decision made. For example, a company has its own

trucks for transporting raw materials and finished products from one place to another. It seeks to

replace these trucks by keeping public carriers. In making this decision, of course, the

depreciation of the trucks is not to be considered but the management should take into account

the present expenditure on fuel, salary to driver and maintenance. Such costs are termed as out-

of-pocket costs.

7. Opportunity Cost Opportunity cost refers to an advantage in measurable terms that have foregone on account of

not using the facilities in the manner originally planned. For example, if a building is proposed to

be utilized for housing a new project plant, the likely revenue which the building could fetch, if

rented out, is the opportunity cost which should be taken into account while evaluating the

profitability of the project.

8. Cost Estimation and Cost Ascertainment Cost estimation is the process of pre-determining the cost of a certain product job or order. Such

pre-determination may be required for several purposes such as budgeting, measurement of

performance efficiency, preparation of financial statements, make or buy decisions etc. Cost

ascertainment is the process of determining costs on the basis of actual data. Hence, the

computation of historical cost is cost ascertainment while the computation of future costs is cost

estimation.

9. Cost Allocation and Cost Apportionment Cost allocation refers to the allotment of all the items of cost to cost centers or cost units whereas

cost apportionment refers to the allotment of proportions of items of cost to cost centers or cost

units Thus, the former involves the process of charging direct expenditure to cost centers/cost

units whereas the latter involves the process of charging indirect expenditure to cost centers/cost

units. For example, the cost of labor engaged in a service department can be charged wholly and

directly but the canteen expenses of the factory can’t be charged directly and wholly. Its

proportionate share will have to be found out. Charging of costs in the former case will be

termed as allocation of costs whereas in the latter, it will be termed as apportionment of costs.

10. Cost Reduction and Cost Control Cost reduction and cost control are two different concepts. Cost control is achieving the cost

target as its objective whereas cost reduction is directed to explore the possibilities of improving

the targets. Thus, cost control ends when targets are achieved whereas cost reduction has no

visible end. It is a continuous process.

11. Marginal Costing and Absorption Costing

Marginal costing is formally defined as the accounting system in which variable costs are

charged to cost units and the fixed costs of the period are written-off in full against the aggregate

contribution. Absorption costing on the other hand, charges all costs, both variable and fixed, to

the cost centers/cost units.

Marginal Costing:

The ascertainment of marginal cost is based on the classification and segregation of cost into

fixed and variable cost. Marginal cost is the cost of the marginal or last unit produced. In this

connection, a unit may mean a single commodity, a dozen, or any other measure of goods. For

example, if a manufacturing firm produces X unit at a cost of Rs. 300 and (X + 1) units at a cost

of Rs. 320, the cost of an additional unit will be Rs. 20 which is marginal cost. The marginal cost

varies directly with the volume of production and marginal cost per unit remains the same. It

consists of prime cost, i.e. cost of direct materials, direct labor and all variable overheads. It does

not contain any element of fixed cost which is kept separate under marginal cost technique.

Marginal costing may be defined as the technique of presenting cost data wherein variable costs

and fixed costs are shown separately for managerial decision-making. Marginal costing

technique has given birth to a very useful concept of contribution where contribution is given by:

Contribution = Sales revenue less variable cost (marginal cost)

Contribution may be defined as the profit before the recovery of fixed costs. Thus, contribution

goes toward recovery of fixed cost and profit, and is equal to fixed cost plus profit. In case a firm

neither makes profit nor suffers loss, contribution will be just equal to fixed cost. This is known

as break even point.

Break-even Analysis:

The break-even analysis (BEA) also known as Cost-Volume-Profit (CVP) analysis has

considerable significance for economic research, business decision-making, investment analysis

etc. This technique traces relationship between costs, revenue and profit at varying levels of

output. In BEA, the break-even point (BEP) is located at the level of output at which the net

income or profit is zero. At this point, total cost is equal to the total revenue. Hence, BEP is the

no-profit-no-loss point.

The term ‘marginal cost’ is usually applied to the variable cost of a unit of product/service

Marginal costing is a form of management accounting based on the distinction between:

a) the marginal costs of making selling goods or services, and

b) fixed costs, which should be the same for a given period of time, regardless of the level

of activity in the period.

Suppose that a firm makes and sells a single product that has a marginal cost of Rs. 5 per unit

and that sells for Rs. 8 per unit. For every additional unit of the product that is made and sold, the

firm will incur an extra cost of Rs. 5 and receive income of Rs. 8. The net gain will be Rs. 3 per

additional unit. This net gain per unit, the difference between the sales price per unit and the

marginal cost per unit, is called contribution. Contribution means ‘making a contribution towards

covering fixed costs and making a profit’. Before a firm can make a profit in any period, it must

first of all cover its fixed costs.

Cost-Volume-Profit (C-V-P) Relationship:

In marginal costing, marginal cost varies directly with the volume of production or output. On

the other hand, fixed cost remains unaltered regardless of the volume of output. If volume is

changed, variable cost varies as per the change in volume. Apart from profit projection, the

concept of C-V-P is relevant to virtually all decision-making areas, particularly in the short run.

The relationship among cost, revenue and profit at different levels may be expressed in graphs

such as breakeven charts, profit volume graphs, or in various statement forms. Profit depends on

a large number of factors, most important of which are the cost of manufacturing and the volume

of sales. Both these factors are interdependent. Volume of sales depends upon the volume of

production and market forces which in turn is related to costs. Management has no control over

market. In order to achieve certain level of profitability, it has to exercise control and

management of costs, mainly variable cost. This is because fixed cost, a non-controllable cost is

dependent on such factors as Volume of production, Product mix, Productivity of the factors of

production, Technology, Size of plant etc.

Thus, the cost-volume-profit analysis furnishes the complete picture of the profit structure. This

enables management to distinguish among the effect of sales, fluctuations in volume and the

results of changes in price of product/services.

Assumptions:

Following are the assumptions on which the theory of CVP is based:

The changes in the level of various revenue and costs arise only because of the changes in

the number of product (or service) units produced and sold.

Total costs can be divided into a fixed component and a component that is variable with

respect to the level of output.

There is linear relationship between revenue and cost.

The unit selling price, unit variable costs and fixed costs are constant.

The analysis either covers a single product or assumes that the sales mix sold in case of

multiple products will remain constant as the level of total units sold changes.

Limitations of break even analysis:

Selling costs are especially difficult to handle in break-even analysis. This is because the

changes in selling costs are a cause and not a result of changes in output and sales.

Costs in a particular period may not be caused entirely by the output in that period. For

example, maintenance expenses may be the result of past output

Break-even analysis assumes that profits are a function of output ignoring the fact that

they are also caused by other factors such as technological change, improved

management, changes in the scale of the fixed factors of production, etc.

A basic assumption in break-even analysis is that the cost-revenue-volume relationship is

linear. This is realistic only over narrow ranges of output

Break-even analysis is not an effective tool for long-range use and its use should be

restricted to the short run only.

Marginal Cost Equations and Breakeven Analysis:

Sales – Marginal cost = Fixed cost + Profit = Contribution

1. Contribution Contribution is the difference between sales and marginal or variable costs. It contributes toward

fixed cost and profit. The concept of contribution helps in deciding breakeven point, profitability

of products, departments etc.

2. Profit Volume Ratio (P/V Ratio), its Improvement and Application The ratio of contribution to sales is P/V ratio. It is the contribution per rupee of sales and since

the fixed cost remains constant in short-run, P/V ratio will also measure the rate of change of

profit due to change in volume of sales. The P/V ratio may be expressed as follows:

P/V Ratio = Contribution = Change in Contribution = Change in Profit

Sales Change in Sales Change in Sales

A fundamental property of marginal costing system is that P/V ratio remains constant at different

levels of activity. A change in fixed cost does not affect P/V ratio.

3. Breakeven Point Breakeven point is the volume of sales or production where there is neither profit nor loss.

S (sales) – V (variable cost) = F (fixed cost) + P (profit)

At BEP P = 0

Thus, Break-even point (BEP) = F / (S -V) = Fixed cost / (Sales – Variable cost)

= Fixed cost / Contribution per unit

Break-even Sales = Fixed cost

P/V Ratio

4. Margin of Safety (MOS) Margin of safety is calculated as the difference between the total sales (actual or projected) and

the breakeven sales. It may be expressed in monetary terms (value) or as a number of units

(volume). A large margin of safety indicates the soundness and financial strength of business.

Margin of safety can be improved by lowering fixed and variable costs, increasing volume of

sales or selling price and changing product mix.

Margin of safety = Sales at selected activity – Sales at BEP = Profit

P/V Ratio

Problem: A company producing a single article sells it at Rs. 10 each. The marginal cost of production is

Rs. 6 each and fixed cost is Rs. 400 per annum. You are required to calculate the following:

P/V ratio

Breakeven sales

Sales to earn a profit of Rs. 500

Profit at sales of Rs. 3,000

New breakeven point if sales price is reduced by 10%

Margin of safety at sales of 400 units

Particulars Amount Amount Amount Amount

Units produced 1 50 100 400

Sales (units * 10) 10 500 1000 4000

Variable cost 6 300 600 2400

Contribution (sales- VC) 4 200 400 1600

Fixed cost 400 400 400 400

P/V Ratio = (Contribution / Sales) x 100 = 0.4 or 40%

Breakeven sales (Rs.) = Fixed cost / (P/V Ratio) = 400/ 0.4 = Rs. 1,000

Sales at BEP = Contribution at BEP/ (P/V Ratio) = 100 units

Contribution at profit Rs. 500 = Fixed cost + Profit = Rs. 900

Sales to earn a profit of Rs. 500 = Contribution / (P/V Ratio) = 900/.4 = Rs. 2,250 (or 225 units)

Contribution at sales Rs. 3,000 = Sales x P/V Ratio = 3000 x 0.4 = Rs. 1,200

Profit at sales of Rs. 3,000 = Contribution – Fixed cost = Rs. 1200 – Rs. 400 = Rs. 800

New P/V ratio when sales price is reduced by 10% = Rs. 9 – Rs. 6 / Rs. 9 = 1/3

Sales at BEP = Fixed cost/PV ratio = Rs. 400 / (1/3) = Rs. 1200

Margin of safety (at 400 units) = (4000 – 1000) / 4000 x 100 = 75 %

(Actual sales – BEP sales/Actual sales x 100)

Problem:

The sales and profits during two years are as follows:

Year Sales Profit

2006 1, 00,000 15,000

2007 1, 20,000 23,000

You are required to find out:

a) P/V ratio

b) Fixed cost

c) Profit at an estimated sales of Rs. 1, 25,000

d) Sales required to earn a profit of Rs. 20,000

Solution:

a) P/V ratio = Change in profit x 100 = 8,000 x 100 = 40%

Change in sales 20,000

b) Since contribution is 40% of sales, Variable cost = 60% of sales = Rs. 60,000

Fixed cost = 1, 00,000 – 60,000 – 15,000 = Rs. 25,000

c) Contribution, when sales is Rs. 1, 25,000 = 1, 25,000 x 0.4 = Rs. 50,000

Profit = 50,000 – 25,000 = Rs. 25,000

d) Sales required to earn a profit of Rs. 20,000 = (Fixed cost + Desired profit) / (P/V ratio)

= (25,000 + 20,000) / 0.40 = Rs. 1, 12,500

Breakeven Analysis - Graphical Presentation

Breakeven chart is a device which shows the relationship between sales volume, marginal costs

and fixed costs, and profit or loss at different levels of activity. Such a chart also shows the effect

of change of one factor on other factors and exhibits the rate of profit and margin of safety at

different levels. A breakeven chart contains total sales line, total cost line and the point of

intersection called breakeven point.

Construction of a Breakeven Chart 1. Select a scale for sales on horizontal axis and a scale for cost and revenue on vertical axis

2. Plot fixed cost on vertical axis and draw fixed cost line passing through this point parallel

to horizontal axis

3. Plot variable costs for some activity levels starting from the fixed cost line and join these

points. This will give total cost line. Alternatively, obtain total cost at different levels;

plot the points starting from horizontal axis and draw total cost line.

4. Plot the maximum or any other sales volume and draw sales line by joining zero and the

point so obtained.

The following Figure shows a typical break even chart.

Limitations and Uses of Breakeven Charts A simple breakeven chart gives correct result as long as variable cost per unit, total fixed cost

and sales price remain constant. In practice, all these factors may change and the original

breakeven chart may give misleading results. But then, if a company sells different products

having different percentages of profit to turnover, the original combined breakeven chart fails to

give a clear picture when the sales mix changes. In this case, it may be necessary to draw up a

breakeven chart for each product or a group of products. A breakeven chart does not take into

account capital employed which is a very important factor to measure the overall efficiency of

business. Fixed costs may increase at some level whereas variable costs may sometimes start to

decline. For example, with the help of quantity discount on materials purchased, the sales price

may be reduced to sell the additional units produced etc. These changes may result in more than

one breakeven point, or may indicate higher profit at lower volumes or lower profit at still higher

levels of sales.

Nevertheless, a breakeven chart is used by management as an efficient tool in marginal costing,

i.e. in forecasting, decision-making, long term profit planning and maintaining profitability. The

margin of safety shows the soundness of business whereas the fixed cost line shows the degree of

mechanization. The angle of incidence is an indicator of plant efficiency and profitability of the

product or division under consideration.

Multiple Product Situations:

In real life, most of the firms turn out many products. Here, there is no problem with regard to

the calculation of break-even point. However, the assumption has to be made that the sales mix

remains constant. This is defined as the relative proportion of each product’s sale to total sales. It

could be expressed as a ratio such as 2:4:6, or as a percentage as 20%, 40%, and 60%.

The calculation of breakeven point in a multi-product firm follows the same pattern as in a single

product firm. While the numerator will be the same fixed costs, the denominator now will be

weighted average contribution margin. The modified formula is as follows:

Breakeven point (in units) = Fixed costs / Weighted average contribution margin per unit

B.E. point (in revenue) = Fixed cost / Weighted average P/V ratio

The weights are assigned in proportion to the relative sales of all products. Here, it will be the

contribution margin of each product multiplied by its quantity.

Example: A furniture manufacture produces and sells the cabinets, office tables and chairs. The various

details regarding his business are given below:

Product Selling price per

unit Rs.

Variable cost per

unit Rs.

% of rupee sales

volume

File cabinet 1000 900 20

Office tables 500 400 30

Chairs 200 125 50

Capacity of the firm = Rs 1, 50, 000 of total sale volume

Annual fixed cost = Rs 20, 000

Calculate

1) S BEP and 2) Profit if firm works at 80% of capacity

Solution:

The contribution towards fixed cost in each case is

a) File cabinet - Rs 1000 - Rs 900 = Rs 100

b) Office tables - Rs 500 - Rs 400 = Rs 100

c) Chairs - Rs 200 - Rs 125 = Rs 75

Now there contributions are to be converted into percentages of sell prices and the formula is

contribution percentage

100Pr

Prx

iceSelling

CostVariableiceSelling

Therefore, the contribution percentage for individual items is

File cabinet %101001000

100100

1000

900100

xx

Office tables %20100500

100100

500

400500

xx

Chairs %5.37100200

75100

200

125200

xx

To get the total contribution per rupee sales volume for the file cabinet, office tables and chairs,

we multiply the contribution percentage of each of the products by the percentage of sales

volume for that particular product and add the figures so obtained.

Furniture (a) Contribution % (b) % of sales in Rs (c) b x c/100

File cabinet 10 20 2000/100=2.00

Office tables 20 30 600/100 = 6.00

Chairs 37.5 50 1875/100=18.7

26.75 or 27%

27% is the total contribution per rupee of overall sales given the present product sales mix.

1) 74074.10027

20000

%27

20000

argRsx

ratioinMonContributi

CostsFixedBEP

2) Profit = Total revenue – Total costs

Here Total revenue = 80% of the total capacity of the firm (given data in the problem)

Therefore, Profit

= 80% of Rs 1, 50, 000 - (Total fixed cost + Total variable cost)

= 1, 20, 000 - (20,000 + 73% of 1, 20, 000)

= Rs 12, 400

Managerial Uses of Break-even Analysis

Break-even analysis not only highlights the areas of economic strength and weaknesses in the

firm but also sharpens the focus on certain leverages which can be operated upon to enhance its

profitability. Through break-even analysis, it is possible to devise managerial actions to enhance

profitability of the firm. The break-even analysis can be used for the following purposes:

Safety Margin: The break-even chart can help the manager to get a fast idea about the

profits generated at the various levels of sales. But while deciding upon the volume at

which the firm would operate, apart from the demand, manager should consider the

‘Safety Margin’ associated with the proposed volume. The safety margin refers to the

extent to which the firm can afford a decline in sales before it starts incurring losses. If

the safety margin is dropping over a period of time, it would mean that the firm’s

resistance capacity to avoid losses has become poorer. A margin of safety can be negative

as well. In that case, it reveals the percentage increase in sales necessary to reach the BEP

so as at least to avoid losses.

Volume Needed to Attain Target Profit: Break-even analysis may be utilized for the

purpose of determining the volume of sales necessary to achieve a target profit.

Target sales volume = unitinmonContributi

etprofitTtFixed

arg

argcos

Change in Price: The manager is often faced with a problem of whether to reduce price

or not. Before deciding on this question the manager must consider a number of points. A

reduction in price leads to a reduction in the contribution margin. This means that the

volume of sales will have to be increased to maintain the previous level of profit. The

higher the reduction in the contribution margin, the higher is the increase in sales needed

to ensure the previous profit. However, reduction in price may not always lead to a

proportionate increase in the volume of sales. Assuming that the present conditions

continue, break-even analysis will help the manager to know the required volume of sales

to maintain the previous level of profit. And on the basis of its knowledge and

experience, it will be much easier for the management to judge whether the required

increase in sales will be feasible. The formula for determining the new volume of sales to

maintain the same profit, given a reduction in price, is:

New volume of sales = Fixed cost + Profit______

Variable cost – New Selling price

Change in Costs:

If Variable Costs Change An increase in variable costs leads to a reduction in the contribution margin. Therefore,

when increases in costs are expected or is unavoidable, a common question which arises

is what total sales volume we need to maintain our present profits without any increase in

price or, in the alternative, what price should be fixed for the product to maintain our

present profit without any change in sales volume. The formula to determine the new

quantity (Q n) when there is a change in variable costs is:

New quantity = Fixed cost + Profit______

New selling price – Variable cost

If Fixed Costs Change

An increase in fixed costs of a firm may be caused either by external circumstances (e.g.,

an increase in machinery costs, taxes, etc) or by a managerial decision (e.g., an increase

in salaries). Then a question arises on what total sales volume do we need to maintain to

have our present profits without any increase in price or in the alternative, what price

should be set if there is no change in sales volume? The formula to determine the new

quantity (Q n) or the new price (SP n3) given a change in fixed costs would be:

VCSP

FCFCQQ n

n

COMMERCIAL BANKING

A bank is an institution which deals with money and credit. It accepts deposits from the public,

makes the funds available to those who need them, and helps in the remittance of money from

one place to another.

According to the Indian Companies Act, 1949, banking means “the accepting for the purpose of

Indian Companies lending or investment, of deposits of money from the public, repayable on

demand or otherwise, and withdrawal by cheques, draft or otherwise.”

FUNCTIONS OF COMMERCIAL BANKS OR MODERN BANKS

In the modern world, banks perform such a variety of functions that it is not possible to make an

all-inclusive list of their functions and services. However, some basic functions performed by the

banks are discussed below.

a. Accepting Deposits: The first important function of a bank is to accept deposits from those who can save but

cannot profitably utilize this saving themselves. People consider it more rational to

deposit their savings in a bank because by doing so they, on the one hand, earn interest,

and on the other, avoid the danger of theft. To attract savings from all sorts of

individuals, the banks maintain different types of accounts:

(i) Fixed Deposit Account (Time deposits) - Money in these accounts is deposited

for fixed period of time (say one, two, or five years) and cannot be withdrawn

before the expiry of that period. The rate of interest on this account is higher than

that on other types of deposits. Longer the period, higher will be rate of interest.

(ii) Current Deposit Account (Demand deposits) - These accounts are generally

maintained by the traders and businessmen who have to make a number of

payments every day. Money from these accounts can be withdrawn in as many

times and in as much amount as desired by the depositors. Normally, no interest is

paid on these accounts.

(iii) Saving Deposit Account - The aim of these accounts is to encourage and

mobilize small savings of the public. Certain restrictions are imposed on the

depositors regarding the number of withdrawals and amount to be withdrawn in a

given period. Cheques facility is provided to the depositors. Rate of interest paid

on these deposits is low as compared to that on fixed deposits.

(iv) Recurring Deposit Account - The purpose of these accounts is to encourage

regular savings by the public, particularly by the fixed income group. Generally

money in these accounts is deposited in monthly installments for a fixed period

and is repaid to the depositors along with interest on maturity.

b. Advancing of loans:

The second important function of a bank is advancing of loans to the public. After

keeping certain cash reserves, the banks lend their deposits to the needy borrowers.

Before advancing loans, the banks satisfy themselves about the creditworthiness of the

borrowers. Various types of loans granted by the banks are discussed below:

(i) Money at Call - Such loans are very short period loans and can be called back by

the bank at a very short notice of say one day to fourteen days. These loans are

generally made to other banks or financial institutions.

(ii) Cash Credit - It is a type of loan which is given to the borrower against his

current assets, such as shares, stocks, bonds, etc. The bank opens the account in

the name of the borrowers and allows him to withdraw borrowed money from

time to time up to a certain limit as determined by the value of his current assets.

Interest is charged only on amount actually withdrawn from the account.

(iii) Overdraft - Sometimes, the bank provides .overdraft facilities to its customers

though which they are allowed to withdraw more than their deposits. Interest is

charged from the customers on the overdrawn amount.

(iv) Discounting of Bills of Exchange - This is another popular type of lending by the

modern banks. In a bill of exchange the debtor accepts the bill drawn upon him by

the creditor and agrees to pay. After making some marginal deductions (in the

form of commission), the bank pays the value of the bill to the holder. When the

bill of exchange matures, the bank gets its payment from the party which had

accepted the bill. Thus, such a loan is self-liquidating.

(v) Term Loans - The banks have also started advancing medium-term and long-

term loans. The maturity period for such loans is more than one year. The amount

sanctioned is either paid or credited to the account of the borrower. The interest is

charged on the entire amount of the loan and the loan is repaid either on maturity

or in installments.

c. Credit Creation: A unique function of the bank is to create credit. In fact, credit creation is the natural

outcome of the process of advancing loan as adopted by the banks. When a bank

advances a loan to its customer, it does not lend cash but opens an account in the

borrower’s name and credits the amount of loan to this account. Thus, whenever a bank

grants a loan, it creates an equal amount of bank deposit. Creation of such deposits is

called credit creation which results in a net increase in the money stock of the economy.

d. Promoting Cheques System:

Banks also render a very useful medium of exchange in the form of cheques. Through a

cheque, the depositor directs the bankers to make payment to the payee. Cheque is the

most developed credit instrument in the money market. In the modern business

transactions, cheques have become much more convenient method of settling debts than

the use of cash.

e. Agency Functions: Banks also perform certain agency functions for and on behalf of their customers:

(i) Remittance of Funds - Banks help their customers in transferring funds from one

place to another through cheques, drafts, etc.

(ii) Collection and Payment of Credit Instruments - Banks collect and pay various

credit instruments like cheques, bills of exchange, promissory notes.

(iii) Execution of Standing Orders - Banks execute the standing instructions of their

customers for making various periodic payments. They pay subscriptions, rents,

insurance premium etc. on behalf of their customers.

(iv) Purchasing and Sale of Securities - Banks undertake purchase and sale of

various securities like shares, stocks, bonds, debentures etc. on behalf of their

customers.

(v) Collection of Dividends on Shares - Banks collect dividends, interest on shares

and debentures of their customers.

(vi) Acting as Representative and Correspondent - Sometimes the banks act as

representatives and correspondents of their customers. They get passports,

travelers’ tickets, book vehicles, plots for their customers and receive letters on

their behalf.

f. General Utility Function:

In addition to agency services, the modern banks provide many general utility services as

given below:

(i) Locker Facility - Banks provide locker facility to their customers. The customers

can keep their valuables and important documents in these lockers for safe

custody.

(ii) Travelers’ Cheques - Banks issue travelers’ cheques to help their customers to

travel without the fear of theft or loss of money. With this facility, the customers

need not take the risk of carrying cash with them during their travels.

(iii) Letters of Credit - Letters of credit are issued by the banks to their customers

certifying their creditworthiness. Letters of credit are very useful in foreign trade.

(iv) Collection of Statistics - Banks collect statistics giving important information

relating to industry, trade and commerce, money and banking. They also publish

journals and bulletins containing research articles on economic and financial

matters.

(v) Underwriting Securities - Banks underwrite the securities issued by the

government, public or private bodies. Because of its full faith in banks, the public

will not hesitate in buying securities carrying the signatures of a bank.

(vi) Gift Cheques - Some banks issue cheques of various denominations (say of

Rs.11, 21, 31, 51.101, etc.) to be used on auspicious occasions.

(vii) Foreign Exchange Business - Banks also deal in the business of foreign

currencies. Again, they may finance foreign trade by discounting foreign bills of

exchange.

BANKS AND ECONOMIC DEVELOPMENT

In a modern economy, banks are to be considered not merely as dealers in money but also the

leaders in development. They are not only the store houses of the country’s wealth but also are

the reservoirs of resources necessary for economic development. It is the growth of commercial

banking in the 18th and 19th centuries that facilitated the occurrence of industrial revolution in

Europe. Similarly, the economic progress in the present day developing economies largely

depends upon the growth of sound banking system in these economies.

Commercial banks can contribute to country’s economic development in following ways:

1. Capital Formation:

Capital formation is the most important determinant of economic development and banks

promote capital formation. Capital formation has three well-defined stages:

(a) Generation of saving - They stimulate savings by providing a number of

incentives to the savers, such as, interest on deposits, free and cheap remittance of

funds, safe custody of valuables, etc.

(b) Mobilization of saving - By expanding branches in different areas and giving

various incentives, they succeed in mobilizing savings generated in the economy.

(c) Canalization of saving in productive uses - They not only mobilize resources

from those who have excess of them, but also make the resources so mobilized

available to those who have the opportunities of productive investment.

2. Encouragement to Entrepreneurial Innovations:

In underdeveloped countries, entrepreneurs generally hesitate to invest in new ventures

and undertake innovations largely due to lack of funds. Facilities of bank loans enable the

entrepreneurs to step up investment and innovational activities, adopt new methods of

production and increase productive capacity of economy.

3. Monetization of Economy:

Monetization of the economy is essential for accelerating trade and economic activity.

Banks, which are creators and distributors of money, allow money to play active role in

the economy.

4. Influencing Economic Activity: Banks can directly influence economic activity, and hence, the pace of economic

development through its influence on:

(a) Variations in Interest Rates - A reduction in the interest rates makes the

investment more profitable and stimulates economic activity. An increase in the

interest rate, on the other hand, discourages investment and economic activity.

(b) Availability of Credit - Bankers can also influence economic activity by the

availability of credit. Through their credit creation activity the banks increase the

supply of purchasing power and hence the aggregate demand. This, in turn,

increases investment, production and trade in the economy.

5. Implementation of Monetary Policy:

Economic development needs an appropriate monetary policy. But, a well-developed

banking system is a necessary pre-condition for the effective implementation of the

monetary policy. Control and regulation of credit by the monetary authority is not

possible without the active cooperation of the baking system in the country.

6. Promotion of Trade and Industry:

Economic progress in the industrially advanced countries in the last two hundred years or

so is mainly due to expansion in trade and industrialization which could not have been

made possible without the development of banking system. The use of bank cheque, the

bank draft and the bill of exchange has revolutionized the internal and international trade.

7. Encouragement to Right Type of Industries:

By granting loans (particularly medium-term and long-term), the banks can provide

financial resources to the right type of industries to secure necessary material, machines

and other inputs. In a planned economy, it is necessary that the banks should formulate

their loan policies in accordance with the broad objectives and strategy of

industrialization as adopted in the plan. This will promote right type of industrialization

in the economy.

8. Regional Development:

Banks can also play an important role in achieving balanced development in different

regions of the economy. They can transfer surplus capital from the developed regions to

the less-developed regions where it is scarce and most needed. This reallocation of funds

between regions will promote economic development in underdeveloped areas of the

economy.

9. Development of Agriculture and Other Neglected Sectors:

Underdeveloped economies are primarily agricultural economies and majority of the

population in these economies live in rural areas. Therefore, economic development in

these economies requires the development of agriculture and small-scale industries in

rural areas. So far, banks, in underdeveloped countries have been paying more attention

to trade and commerce and have almost neglected agriculture and industry. Thus,

necessary structural and functional reforms in the banking system of the underdeveloped

countries should be made in older to encourage the banks to play developmental role in

these economics.

TYPES OF BANKS

Banks can be classified into various types on the basis of their functions, ownership, domiciles

etc. The following are the various types of banks:

1. Commercial Banks: The banks which perform all kinds of banking business and generally finance trade and

commerce are called commercial banks. Since their deposits are for a short period, these

banks normally advance short-term loans to the businessmen and traders. However,

recently, the commercial banks have also extended their areas of operation to medium-

term and long-term finance. Majority of the commercial banks are in the public sector.

But, there are certain private sector banks operating as joint stock companies. Hence, the

commercial banks are also called joint stock banks.

2. Industrial Banks: Industrial banks also known as investment banks, mainly meet the medium-term and

long-term financial needs of the industries.

The main functions of the industrial banks are:

(a) They accept long-term deposits

(b) They grant long-term loans to the industrialists to enable them to purchase land,

construct factory building, purchase heavy machinery, etc.

(c) They help selling or even underwrite the debentures and shares of industrial firms

(d) They can also provide information regarding the general economic position of the

economy.

In India, industrial banks, like Industrial Development Bank of India, Industrial Finance

Corporation of India, State Finance Corporations, are playing significant role in the

industrial development of the country.

3. Agricultural Banks: Agricultural credit needs are different from those of industry and trade. Industrial and

commercial banks normally do not deal with agricultural finance.

The agriculturists require:

(a) Short-term credit to buy seeds, fertilizers and other inputs, and

(b) Long-term credit to purchase land, to make permanent improvements on land, to

purchase agricultural machinery and equipment, etc.

In India, agricultural finance is generally provided by co-operative institutions.

4. Exchange Banks:

Exchange banks deal in foreign exchange and specialize in financing foreign trade. They

facilitate international payments through the sale and purchase of bills of exchange and

thus play an important role in promoting foreign trade.

5. Saving Banks:

The main purpose of saving banks is to promote saving habits among he general public

and mobilize their small savings. In India, postal saving banks do this job. They open

accounts and issue postal cash certificates.

6. Central Bank:

Central bank is the apex institution which controls, regulates and supervises the monetary

and credit system of the country.

Important functions of the central bank are:

(a) It has the monopoly of note issue

(b) It acts as the banker, agent and financial adviser to the slate

(c) It is the custodian of member banks reserves

(d) It is the custodian of nation’s reserves of international currency

(e) It serves as the lender of the last resort

(f) It functions as the bank of central clearance, settlement and transfer and

(g) It acts as the controller of credit.

7. Classification on the Basis of Ownership:

(a) Public Sector Banks - These are owned and controlled by the government. In

India, the nationalized banks and the regional rural banks come under these

categories

(b) Private Sector Banks - These banks are owned by the private individuals or

corporations and not by the government or cooperative societies

(c) Cooperative Banks - Cooperative banks arc operated on the cooperative lines. In

India, cooperative credit institutions are organized under the cooperative

societies’ law and play an important role in meeting financial needs in the rural

areas.

8. Classification on the Basis of Domicile:

(a) Domestic Banks - These are registered and incorporated within the country

(b) Foreign Banks - These are foreign in origin and have their head offices in the

country of origin.

9. Scheduled and Non-Scheduled Banks:

In India, banks have been broadly classified into scheduled and non-scheduled banks. A

Scheduled Bank is that which has been included in the Second Schedule of the Reserve

Bank of India Act, 1934 and fulfills the three conditions:

(a) It has paid-up capital and reserves of at least Rs. 5 lakhs

(b) It ensures the Reserve Bank that its operations are not detrimental to the interest

of the depositors

(c) It is a corporation/cooperative society and not a partnership or single owner firm.

The banks which are not included in the Second Schedule of the Reserve Bank of India

Act are non-scheduled banks.

BALANCE SHEET OF A BANK

The balance sheet of a bank is a statement of its liabilities and assets at a particular time.

Liabilities refer to all debit items representing the obligations of the bank or others’ claims on the

bank. In other words, all those items because of which the bank is liable to pay to others form the

liabilities of the bank. Assets, on the other hand, refer to all credit items representing the bank’s

claims on others and its ownership of wealth.

Table 1: Balance Sheet of a bank

Liabilities Assets

1. Share Capital 1. Cash

2. Reserve fund (a) Cash in hand

3. Deposits: (b) Cash with central bank

(a) Demand deposits (c) Cash with other banks

(b) Time deposits 2. Money at call and shot notice

(c) Saving deposits 3. Bills purchased or discounted

4. Borrowings from other banks 4. Investments

5. Acceptance and endorsements. 5. Loans and advances

6. Other liabilities 6. Acceptance and endorsements

7. Buildings and other fixed assets

Total Total

Thus, the balance sheet shows how a bank raises funds and how it invests them. It is customary

that the liabilities are mentioned on the left side and the assets on the right side of the balance

sheet. The totals on the two sides (i.e., the total liabilities and the total assets) are always equal.

Liabilities of the Bank:

1. Share Capital:

A joint stock bank initially raises its funds by issuing share capital. In other words, share

capital is the contributions made by the shareholders. Share capital is in the form of:

(a) Authorized capital - the maximum amount of capital the bank is authorized to

raise in the form of shares

(b) Issued capital - the part of the authorized capital issued in the form of shares for

public subscription

(c) Subscribed capital - the part of the issued capital actually subscribed by the

public and part of the subscribed capital actually paid by the subscribers.

(d) Paid-up capital - It is the actually paid-up share capital which constitutes the

liability of the bank.

2. Reserve Fund:

Reserve fund is the amount accumulated over the years out of undistributed profits.

Normally, all the profits of the bank are not distributed among the shareholders; some

part is retained undistributed for meeting contingencies. This reserve fund actually

belongs to the shareholders.

3. Deposits: Deposits from the public constitute the major portion of the banks’ working capital.

Various types of deposits accepted by the bank are:

(a) Demand deposits - the deposits which can be withdrawn at any time and on

which no interest is paid

(b) Time deposits - the deposits which can be withdrawn after a fixed period of time

and on which high rate of interest is paid and

(c) Saving deposits - the deposits which can be withdrawn to the limited extent in a

given period and on which some interest is paid.

4. Borrowings from Banks: Sometimes, the bank borrows loans from other banks on temporary basis to meet the

increased demand for money. Central bank is the lender of the last resort and provides

loan facilities to the banks in special circumstances. All these borrowings form the

liability of the borrower bank.

5. Other Liabilities: Certain other miscellaneous liabilities are incurred by the bank. For example, by acting as

an agent the bank makes collections on behalf of its customers and thus creates liability.

Again, the profits earned by the bank represent the liability because they arc payable to

the shareholders.

Assets of the Bank:

The asset side of the balance sheet shows the manner in which the funds of the bank are utilized.

Given below are various assets of the bank arranged in an ascending order of profitability and

descending order of liquidity:

1. Cash:

Cash is the most liquid but non-earning asset and is considered as the first line of defense.

Every bank keeps certain amount of cash in order to meet the cash requirements of its

depositors.

2. Money at Call and Short Notice: Money at call and short notice refers to loans which are recoverable by the bank on

demand or at a very short notice. These loans are for a maximum period of 15 days. Such

loans are earning as well as highly liquid assets which can be converted into cash quickly

and without loss.

3. Bills purchased or discounted: The bank utilizes its funds in trade bills and treasury bills which it discounts. The amount

of the bills is collected by the bank on maturity. The bills discounted are short-term

(normally of 90 days) self-liquidating assets. They are self-liquidating because, at the end

of the commercial transaction, the money will be repaid.

4. Investments:

Some funds are invested in profit-yielding assets, mainly the government securities.

Government securities arc relatively safe because there is certainty of repayment after

maturity. Moreover, the banks can borrow from the central bank against these securities.

5. Loans and Advances:

Loans and advances are the most profitable and the least liquid assets of the bank. Banks

provide loans and advances to the businessmen either through overdraft or by discounting

of bills of exchange. The difference between loans and advances is that the advances are

for short period and loans are for relatively longer period. Loans and advances earn high

rate of interest, carry greater risk and are generally non-shiftable.

6. Building and other Fixed Assets: Bank’s assets also include the value of the movable and immovable properties of the

bank, such as office buildings, furniture etc. These assets do not contribute to the income

of the bank and constitute very small properties of the assets of the bank.

The importance of the balance sheet of a bank clearly brings out the following points:

i) It represents the complete functioning of the bank. It tells how the bank raises money and

how it invests it.

ii) It throws light on the financial position (i.e., liquidity and solvency position) of the bank

because it contains all information about the liabilities and assets of the bank.

iii) The progress of the bank over time can be determined by comparing the balance sheet of

different periods

iv) A comparison of balance sheet of different banks gives comparative picture of financial

position of a bank vis a vis that of others.

v) It gives an estimate of the confidence of the public in the bank. Increasing saving or time

deposits of bank represent that the confidence of the people in the bank is also increasing.

vi) It shows the loans and investment policy of the bank.

vii) It provides information about the interest of various persons, such as shareholders,

debtors, creditors, etc.

NEW TRENDS IN COMMERCIAL BANKING

Drastic changes have been experienced in both theory and practice of commercial banking the

world over especially in the post-war period. Major changes are discussed below:

1. New Developments in Banking Theory:

Traditional commercial loan theory has now been completely discarded and has given

place to the modern shiftability and anticipated income theories. All these theories

attempt to resolve the liquidity-earning problem of the bank, i.e., how a bank can achieve

the two conflicting objectives of liquidity as well as profitability simultaneously.

According to commercial loan theory, the banks can ensure sufficient liquidity by

granting only short-term self- liquidating loans secured by goods in the process of

production or goods in transit. The shiftability theory requires the banks to solve their

liquidity problem by purchasing highly liquid assets which can be easily shifted to other

banks in times of need for liquidity. According to the recent anticipated income theory,

the banks can solve their liquidity problem even by advancing long-term loans if the

borrowers repay the loans in series of continuous installments.

2. Term Lending: Term loans not only increase earnings of the banks, but also improve their liquidity

because such loans are almost always repaid on an installment basis. The term loans are

also beneficial to the borrowers. They are used to purchase machinery and equipment for

the industries where the expected income flow from the investment will not be sufficient

to repay a short-term loan.

3. Hire Purchase Finance: Hire purchase finance, which refers to the credit facilities for the purchase of durable

goods on installment basis, is another post-war development in commercial banking. The

dealers selling on hire-purchase get advances from the banks by hypotheticating their

goods to the banks. Hire purchase facilities help the small entrepreneurs to start new

business and the existing small producers to purchase new tools and equipment. The

commercial banks entered into this highly profitable business by acquiring the direct

ownership of, or a partnership in the established hire-purchased finance companies.

4. Personal Loans:

Another departure from the traditional banking practice is the advancing of personal

loans by commercial banks. This is a direct consequence of post-war policy of

redistribution of income in favor of the working class which was instrumental in

stimulating consumer credit by the banks. Commercial banks started granting personal

loans for meeting expenditures to purchase motor cars, household appliances,

professional equipment, house repairs and decorations, etc.

CHANGING PATTERNS OF COMMERCIAL BANKING IN

DEVELOPING COUNTRIES Quite recently, the commercial banking has undergone a number of structural and functional

changes in developing countries like India. The major changes are mentioned below:

i) The commercial banks in the developing countries are slowly departing from the

traditional strict self-financing rules favoring risk free self-liquidating loans. They have

now started adhering to the shiftability theory which maintains that as long as the assets

of the commercial banks can be shifted or sold for liquidity, the banks can extend the

period of lending.

ii) The Indian commercial banks have recently started providing hire-purchase finance.

These banks advance loans for purchasing consumer durables (mainly motor cars) and

producers’ equipment.

iii) Some Indian banks grant personal loans to their customers for purchasing consumer

durable, like motor cars, scooters, electric fans, professional equipment, agricultural

equipment, etc. Such loans are made available to the individuals with stable and

continuous income, particularly to the government servants, employees of statutory

bodies and of established industrial, financial, and commercial institutions.

iv) The structure of commercial bank lending in the developing countries (e.g., India, Ghana,

and Libya) has changes from commerce to industry.

v) In India, after the nationalization of major commercial banks in 1969, direct lending to

agriculture by the commercial banks has shown notable increases.

RESERVE BANK OF INDIA The Reserve Bank of India is India’s central bank. It is the apex monetary institution which

supervises, regulates controls and develops the monetary and financial system of the country.

The Reserve bank was established on April 1, 1935 under the Reserve Bank of India Act, 1934.

Initially, it was constituted as a private shareholders’ bank with a fully paid-up capital of Rs. 5

crore. But, it was nationalized on January 1, 1949.

Organization:

1. Issue Department - Its main function is to issue, and distribute the paper currency.

2. Banking Department - This department deals with government transactions, manages

public debt and arranges for the transfer of government funds, maintains the cash reserves

3. Department of Banking Development - It aims at expanding banking facilities in

unbanked and rural areas.

4. Department of Banking Operations - Its function is to supervise, regulate and control

the working of the banking institutions in the country.

5. Agricultural Credit Department - It deals with the problems of agricultural credit and

provides facilities of rural credit to state governments and state cooperatives.

6. Industrial Finance Department - Its main objective is to provide financial help to the

small and medium scale industries.

7. Non-Banking Companies Department - It supervises the activities of non-banking

companies and financial institutions in the country

8. Exchange Control Department - It conducts the business of sale and purchase of

foreign exchange.

9. Legal Department - It provides advice to various departments on legal issues. It also

gives legal advice on the implementation of banking laws in the country.

10. Department of Research and Statistics. It conducts research on problems relating to

money, credit, finance, production, collect important statistics relating to various aspects

of the economy; and publish these statistics.

11. Department of Planning and Reorganization - It deals with the formulation of new

plans or reorganization of existing policies for making them more effective.

12. Economic Department - It is concerned with framing proper banking policies for better

implementation of economic policies of the government.

13. Inspection Department - It undertakes the function of inspecting various offices of the

commercial banks.

14. Department of Accounts and Expenditure - It keeps proper records of all receipts and

expenditures of the Reserve Bank.

15. RBI Services Board - It deals with the selection of new employees, for different posts in

the Reserve Bank.

Management:

The management of the Reserve Bank is under the control of Central Board of Directors

consisting of 20 members:

(a) The executive head of the Bank is called Governor who is assisted by four Deputy

Governors. They are appointed by the Government of India for a period of five years.

The head office of the Reserve Bank is at Bombay

(b) There are four local boards at Delhi, Calcutta, Madras and Bombay representing four

regional areas, i.e., northern, eastern, southern and western respectively. These local

boards are advisory in nature and the Government of India nominates one member each

from these boards to the Central Board

(c) There are ten directors from various fields and one government official from the Ministry

of Finance.

FUNCTIONS OF RESERVE BANK

The Reserve Bank of India performs various traditional central banking functions as well as

undertakes different promotional and developmental measures to meet the dynamic requirements

of the country.

The broad objectives of the Reserve Bank are:

(a) Regulating the issue of currency in India

(b) Keeping the foreign exchange reserves of the country

(c) Establishing the monetary stability in the country and

(d) Developing the financial structure of the country on sound lines consistent with the

national socio-economic objectives and policies.

Main functions of the Reserve Bank are described below:

1. Note Issue:

The Reserve Bank has the monopoly of note issue in the country. It has the sole right to

issue currency notes of all denominations except one rupee notes. One rupee notes are

issued by the Ministry of Finance of the Government of India. The Reserve Bank acts as

the only source of legal tender because even the one rupee notes are circulated through it.

2. Banker to Government:

The Reserve Bank acts as the banker, agent and adviser to Government of India:

(a) It maintains and operates government deposits

(b) It collects and makes payments on behalf of the government

(c) It helps the government to float new loans and manages the public debt

(d) It provides development finance to the government for carrying out 5- year plans

(e) It undertakes foreign exchange transactions on behalf of the Central Government

(f) It acts as the agent of the Government of India in the latter’s dealings with the

IMF, the World Bank, and other international financial institutions

3. Banker’s Bank:

The Reserve Bank acts as the banker’s bank in the following respects:

(a) Every Bank is under the statutory obligation to keep a certain minimum of cash

reserves with the Reserve Bank. The purpose of these reserves is to enable the

Reserve Bank to extend financial assistance to the scheduled banks in times of

emergency and thus to act as the lender of the last resort.

(b) The Reserve Bank provide financial assistance to scheduled banks by discounting

their eligible bills and through loans and advances against approved securities

(c) Under the Banking Regulation Act, 1949 and its various amendments, the

Reserve Bank has been given extensive powers of supervision and control over

the banking system. These regulatory powers relate to the licensing of banks and

their branch expansion; liquidity of assets of the banks; management and methods

of working of the banks; reconstruction and liquidation of banks etc.

4. Custodian of Exchange Reserves:

The Reserve Bank is the custodian of India’s foreign exchange reserves. It maintains and

stabilizes the external value of the rupee, administers exchange controls and other

restrictions imposed by the government, and manages the foreign exchange reserves. The

Reserve Bank sells and buys foreign currencies in order to achieve the objective of

exchange stability.

5. Controller of Credit: As the central bank of the country, the Reserve Bank undertakes the responsibility of

controlling credit in order to ensure internal price stability and promote economic growth.

Through this function, the Reserve Bank attempts to achieve price stability in the country

and avoids inflationary and deflationary tendencies in the country. The Reserve Bank

regulates money supply in accordance with the changing requirements of the economy.

6. Ordinary Banking Functions: The Reserve Bank also performs various ordinary banking functions:

(a) It accepts deposits from the central government, state governments and even

private individuals without interest

(b) It grants loans and advances to the central government, state governments, local

authorities, scheduled banks and state cooperative banks repayable within 90 days

(c) It buys and sells securities of the Government of India and foreign securities

(d) It can borrow from any scheduled bank in India or from any foreign bank

(e) It can open an account in the World Bank or in some foreign central bank

(f) It buys and sells gold and silver.

7. Promotional and Developmental Functions:

The Reserve Bank also performs a variety of promotional and developmental functions:

(a) By encouraging the commercial banks to expand their branches in the semi-urban

and rural areas

(b) By establishing the Deposit Insurance Corporation, the Reserve Bank helps to

develop the banking system of the country, instills confidence of the depositors

and avoids bank failures

(c) Through the institutions like Unit Trust of India, the Reserve Bank helps to

mobilize savings in the country

(d) Since its inception, the Reserve Bank has been making efforts to promote

institutional agricultural credit by developing cooperative credit institutions

(e) The Reserve Bank also helps to promote the process of industrialization in the

country by selling up specialized institutions for industrial finance

MONETARY POLICY OF THE RESERVE BANK

Monetary policy refers to the policy of the central bank of a country to regulate and control the

volume, cost and allocation of money and credit with the aim of achieving the objectives of

optimum levels of output and employment, price stability, balance of payment equilibrium, or

any other goal set by the government.

Monetary and fiscal policies are closely interrelated and therefore should be pursued in

coordination with each other. Fiscal policy generally brings about changes in money supply

through the budget deficit. An excessive budget deficit, for example, shifts the burden of control

of inflation to monetary policy. This requires a restrictive credit policy. On the contrary, a fiscal

policy, which keeps the budget deficit at a very low level, frees the monetary authority from the

burden of adopting an anti-inflationary monetary policy.

In a developing economy like India, appropriate monetary policy can play a positive role in

creating conditions necessary for rapid economic growth. Moreover, since these economies are

highly sensitive to inflationary pressures, the monetary policy should also serve to control

inflationary tendencies by increasing savings by the people, checking credit expansion by the

banking system and discouraging deficit financing by the government

In India, during the planning period, the aim of the monetary policy of the Reserve Bank has

been to meet the needs of the planned development of the economy. With this broad aim, the

monetary policy has been pursued to achieve the twin objectives of the economic policy of the

government:

(a) To accelerate process of economic growth with a view to raise national income,

(b) To control and reduce the inflationary pressures in the economy.

Policy of Credit Expansion:

The overall trend in the economy during planning period has been that of continuous expansion

of currency and credit with an objective of meeting the developmental needs of the economy.

This expansion has been achieved by adopting the following measures:

1. Revision of Open Market Operations:

The Reserve Bank revised its open operations policy in October 1956, according to which

it started giving discriminatory support to the sale and purchase of government securities.

2. Liberalization of the Bill Market Scheme:

Through the bill market scheme, the commercial banks receive additional funds from the

Reserve Bank to meet the increasing credit requirements of their borrowers.

3. Facilities to Priority Sectors: The Reserve Bank continues to provide credit facilities to priority sectors such as small-

scale industries and cooperatives, even though the general policy of the Bank is to control

credit expansion.

4. Credit Facilities through Financial Institutions:

The Reserve Bank has also been instrumental in the establishment of various financial

institutions like Industrial Development Bank of India, Industrial Finance Corporation of

India, Industrial Credit and Investment Corporation of India, State Finance Corporations,

and National Bank for Agriculture and Rural Development.

5. Deficit Financing: Continuous increase in money supply in the country has been caused by adopting the

method of deficit financing to finance the budgetary deficit of the government. This has

been made possible through changes in the reserve requirements of the Reserve Bank.

6. Anti-Inflationary Fiscal Policy: The Seventh Five Year Plan prefers an anti-inflationary fiscal policy to an anti-

inflationary monetary policy and emphasizes a positive, promotional and expansionary

role for monetary policy.

Policy of Credit Control:

The Reserve Bank has adopted a number of credit control measures to check the inflationary

tendencies in the country:

1. Bank Rate:

The bank rate is the rate at which the Reserve Bank advances to the member banks

against approved securities. Bank rate is considered as a pace-setter in the money market.

Changes in the bank rate influence the entire interest rate structure.

2. Net Liquidity Ratio:

In order to check excessive borrowings from the Reserve Bank by the commercial banks,

the Reserve Bank introduced the system of net liquidity ratio in September 1964.

According to this system, a commercial bank can borrow from the Reserve Bank at the

bank rate only if it maintains a minimum net liquidity ratio to its total demand and time

liabilities, and it will have to pay a penal rate of interest to the Reserve Bank, if the net

liquidity ratio falls below the minimum ratio fixed by the Reserve Bank.

3. Open Market Operations: Through the technique of open market operations, the central bank seeks to influence the

excess reserves position of the banks by purchasing and selling of government securities.

When the central bank purchases securities from the banks, it increases their cash reserve

position and hence their credit creation capacity. On the other hand, when central bank

sells securities to the banks, it reduces their cash reserves and the credit creation capacity.

4. Cash-Reserve Requirement (CRR):

The central bank of a country can change the cash-reserve requirement of the bank in

order to affect their credit creation capacity. An increase in the cash- reserve ratio reduces

the excess reserve of the bank and a decrease in the cash-reserve ratio increases their

excess reserves.

5. Statutory Liquidity Ratio (SLR):

Under the original Banking Regulation Act 1949, banks were required to maintain liquid

assets in the form of cash, gold and unencumbered approved securities equal to not less

than 25% of their total demand and time deposits liabilities.

FINANCIAL MARKET

Financial markets arc functionally classified into:

(a) Money market and

(b) Capital market.

This classification is on the basis of term of credit, i.e., whether the credit is supplied for a short

period or long period. Money market refers to institutional arrangements which deal with short-

term funds. Capital market, on the other hand, deals in long-term funds.

CHART 1

STRUCTURE OF INDIAN MONEY MARKET

Indian Money Market

Organized Sector Unorganized Sector

Indigenous Bankers

Money Lenders Reserve Bank

of India Commercial

banks P.O. Saving

Banks Non-banking Companies

Cooperative Banks

Scheduled Commercial

Banks

Non-scheduled Banks

Public Sector Banks

Indian Banks

Foreign Banks

Regional Rural Banks

State Bank Group

Nationalized banks

STRUCTURE OF INDIAN MONEY MARKET

i) Broadly speaking the money market in India comprises two sectors – organized and

unorganized sectors. The organized sector consists of the Reserve Bank of India, the

State Bank of India with its seven associates, twenty nationalized commercial banks,

other schedule and non-scheduled commercial banks, foreign banks, and Regional Rural

Banks. It is called organized because its parts are systematically coordinated by the RBI.

ii) Non-bank financial institutions such as the LIC, the GIC and subsidiaries. The UTI also

operate in this market, but only indirectly through banks, and not directly.

iii) Quasi-government bodies and large companies also make their short term surplus funds

available to the organized marker through banks.

iv) Cooperative credit instructions occupy the intermediary position between organized and

unorganized parts of the Indian money market. These institutions have a three-tier

structure. At the top there are state cooperative banks. At the local level, there are

primary credit societies and urban cooperative banks.

Unorganized Sector of the Indian Money Market

The unorganized segment of the Indian money market is composed of unregulated non-bank

financial intermediaries, indigenous bankers and money lenders which exist even in the small

towns and big cities. Their lending activities are mostly restricted to small towns and villages.

The persons who normally borrow from this unorganized sector include farmers, artisans, small

traders and small scale producers who do not have any access to modern banks. The following

are some of the constituents of unorganized money market in India.

1. Indigenous Bankers:

Indigenous bankers include those individuals and private firms which are engaged in

receiving deposits and giving loans and thereby act like a mini bank. Their activities are

not at all regulated. During the ancient and medieval periods, those indigenous bankers

were very active. But with the growth of modern banking, particularly after the advent of

British, the business of the indigenous bankers received a set back. Moreover, with the

growth of commercial banks and Co-operative banks the area of operations of indigenous

bankers has again contracted further.

2. Unregulated non-bank financial intermediaries:

There are different types of unregulated non-bank financial intermediaries in India. They

are mostly constituted by loan or finance companies, chit funds etc. A good number of

finance companies in India are engaged in collecting substantial amount of funds in the

form of deposits, borrowings and other receipts. They normally give loans to wholesale

traders, retailers, artisans, and different self-employed persons at a rate of interest ranging

between 36 to 48%.

3. Money Lenders: Money lenders are advancing loans to small borrowers like marginal and small farmers,

agricultural laborers, artisans, factory and mine workers, low paid staffs, small traders

etc. at a very high rate of interest and also adopt various malpractices for manipulating

loan records of these poor borrowers. The money lending operation of the money lenders

is totally unregulated and unsupervised which leads to worst exploitation of the small

borrowers.

Organized Sector of Indian Money Market:

The organized segments of the Indian money market is composed of the Reserve bank of India,

the State Bank of India, Commercial banks, Co-operative banks, foreign banks, finance

corporations and the Discount of Finance House of India Limited. Mumbai, Calcutta, Chennai,

Delhi, Bangalore and Ahmedabad are the leading centers of the organized sector of the Indian

money market. The Mumbai money market is a well organized one, having the head offices of

the RBI and different commercial banks, well developed stock exchange, the bullion exchange

and fairly organized market for Government securities.

The main constituents of the organized sector of Indian money market include:

(i) The Call Money Market:

The call money market in a most common form of developed money market. The call

money market in India is very much centered at Mumbai, Chennai and Calcutta and out

of which the Mumbai is the most important one. In such market, lending and borrowing

operations are carried out for one day. Normally, scheduled commercial banks, Co-

operative banks and the Discount and Finance House of India operate in this market

ii) The Treasury bill Market: Treasury bill markets are markets for treasury bills. In India such treasury bills are short

term liability of the Central Government which is of 91 day and 364 day duration.

Normally, the treasury bills should be issued so as to meet temporary revenue deficit over

expenditure of a Government at some point of time. But, in India, the treasury bills are,

now a day, considered as a permanent source of funds for the Central Government. In

India, the RBI is the major holders of the treasury bills, which is around 90 % of the total.

(ii) The Commercial Bill Market:

The Commercial bill market is a kind of sub-market which normally deals with trade bills

or the commercial bills. It is a kind of bill which is normally drawn by one merchant firm

on the other and they arise out of commercial transactions. The purpose for issuing a

commercial bill is simply to reimburse the seller as and when the buyer delays payment.

But, in India, the commercial bill market is not so developed. This is mainly due to

popularity of the cash credit system in bank lending.

(iii) The Certificate of Deposit (CD) Market: The certificate of Deposit (CD) was introduced in India by the RBI in, March 1989 with

the sole objective of widening the range of money market instruments and also to attain

higher flexibility in the development of short term surplus funds for the investors. In

India, six financial institutions, viz,, IDBI, ICICI, IFCI, IRBI, SIDBI and Export and

Import Bank of India were permitted in 1993 to issue for period varying between 1 to 3

years. Banks normally pay high rates of interest on CDs.

(iv) The Commercial Paper Market: In India, the Commercial Paper (CP) was introduced in the money market in January

1990. A listed company having working capital not less than Rs. 5 crore can issue CP.

(v) Money Market Mutual Funds: In India, the RBI has introduced a scheme of Money Market Mutual Funds (MMMFs) in

April 1992. The main objective of this scheme was to arrange an additional short term

revenue for the individual investors. This scheme has failed to receive much response as

the initial guidelines were not attractive. Thus, in November, 1995, the RBI introduced

some relaxations in order to make the scheme more attractive and flexible. As per the

exiting guidelines, the banks, public financial institutions and the private financial

institutions are allowed to set up MMMFs.

The Indian money market has its distinctive characteristics as it suffers from various defects. The

following are some of its characteristics:

1. Lack of adequate integration:

There is lack of adequate integration in the Indian money market. The organized and the

unorganized sector of Indian money market are totally separate from each other and they

have independent financial operations of their own. Therefore, activities of one sector

have no impact on the activities of the other sector. It is very difficult to establish a

national money market under such a background. Moreover, the various constituents of

the Indian money market viz., commercial banks, Co-operative banks and foreign banks

are competing among themselves and the competition is much in the countryside.

2. Shortage of funds:

Another important feature of Indian money market is the shortage of funds. Therefore,

the demand for loanable funds in the money market is much higher than that of its

supply. In recent years, the development of rural banking structure, with the opening rural

branches of commercial banks and with the expansion of Co-operative banks, has

improved the fund position of the Indian money market, to some extent.

3. Lack of adequate banking facilities:

Indian money market is also characterized by lack of adequate banking facilities. Rural

banking network in the country is still inadequate. In the rural areas, a substantial number

of populations, having small saving potential, have no access to facilities. Under such a

system, a huge amount of small savings are not mobilized which needs to be mobilized.

4. Lack of rational interest rate structure:

There is lack of rational interest structure which is mostly resulted from lack of co-

ordination among different banking institutions. Recently, there in some improvement in

this regard, particularly after the introduction of standardization of interest rates by the

RBI for its rationalization.

5. Absence of Organized Bill Market: There is absence of organized bill market in India although the commercial banks

purchase and discount both inland and foreign bills to a limited extent. Although, the RBI

has introduced its limited bill market under its scheme of 1952 and 1970, but the same

scheme has failed to popularize the bill finance in India.

6. Existence of Unorganized Money Market:

Another important feature of Indian money market is the existence of its unorganized

character, where one of its segments is constituted by the indigenous bankers and money

lenders. Although the RBI has tried to bring the indigenous bankers under its direct

control but the attempts have failed. Thus, as the indigenous bankers remained outside

the organized money market, therefore, RBI’s control over the money market is quite

limited.

7. Seasonal stringency of money and fluctuations in interest rates:

Another important feature of Indian money market is its seasonal stringency of money

and the volatile fluctuation of interest rates. India, being a agricultural country has to face

huge demand for funds during the period of October to June every year so as to meet its

requirement for farm operations and also for trading in agricultural produce. But the

money market is not having sufficient elasticity. Thus it creates seasonal stringency of

funds leading to a rise in the rate of interest. But in the rainy and slack season the demand

for fund slumps down leading to an automatic fall in the rate of interest. Such regular

fluctuations in interest rates are not at all conducive to developmental activities of the

country.

UNDERDEVELOPMENT OF INDIAN MONEY MARKET

Considering the various defects of Indian money market it can be observed that the money

market in India is relatively under-developed. Moreover, in respect of resources, organization

stability and elasticity, the said market cannot be compared with the developed money markets

of London and New York. But among the third world countries India has been maintaining the

most developed banking system. Even then the organization of the money market is still

underdeveloped. The under development nature of Indian money market is mostly determined by

the following shortcomings.

Firstly, Indian money market fails to possess an adequate and continuous supply of short term

assets such as treasury bills, bills of exchange, short term Government bonds etc.

Secondly, this market is lacking the highly organized banking system, so important for the

successful working of a money market.

Thirdly, the sub-markets like acceptance market and the commercial bill market are non-existent

in Indian money market.

Fourthly, Indian money market has totally failed to develop market for short term assets and

accordingly there are no dealers of short term assets who act as intermediaries between the

Government and the entire banking system.

Fifthly, Indian money market in suffering from lack of co-ordination between its different

constituents.

Sixthly, Indian money market again fails to attract any foreign funds.

Finally, Indian money market cannot be termed as a developed one considering its supply of

fund and the liquidity position.

In recent years, serious efforts have been made by the Government and the RBI to remove the

shortcomings of Indian money market. RBI, in the mean time has reduced considerably the

differences between the various constituents of money market. Differences in the interest rates

have also been reduced by the RBI and the monetary stringency has also been reduced by the

RBI through open market operations and bill market scheme.

Even then Indian money market is still very much dependent on the call money market which is

again characterized by high volatility. In the mean time, the RBI has introduced various

measures to reform the money market. The following are some of the important reform measures

introduced to strengthen the Indian money market:

(i) Remission of Stamp Duty:

In order to remove the major administrative constraint in the use of bill system, the

Government has remitted the stamp duty in August 1989.

(ii) Deregulation of interest rates: Another important step to strengthen the money market was to deregulate the money

market interest rates since May, 1989. This will bring interest rate flexibility and

transparency in money market transactions.

(iii) Introduction of new instruments: The RBI has introduced certain money market instruments for strengthening the market

conditions. These instruments are 182 days treasury bills, longer maturity treasury bills,

certificates of Deposits (CDs), Commercial Paper (CP) and dated Government securities.

Discount and Finance House of India (DFHI) promoted the 182-day treasury bills

systematically and these bills were the first security sold by auction for financing the

fiscal deficit of the Central Government.

(iv) DFHI: The Discount and Finance House of India (DFHI) was setup in April 25, 1988 as a part of

the reform package for strengthening money market. The main function of DFHI is do

bring the entire financial system consisting of the scheduled commercial banks, co-

operative banks, foreign banks and all India financial institutions, both in the public and

private sector, within the fold of the Indian money market. This House will normally buy

bills and short term papers from different banks and financial institutions in order to

invest all of their idle funds for short periods.

v) Money Market Mutual Funds (MMMFs):

The Government announced the establishment of Money Market Mutual Funds

(MMMFs) in April 1992 with the sole objective to bring money market instruments

within the reach of individuals. The MMMFs have been set up by different scheduled

commercial banks and public financial institutions. The shares or units of MMMFs have

been issued only to individuals.

Thus the aforesaid measures to reform Indian money market have helped it to become more

advanced, solvent and vibrant. With the introduction of new instruments, the secondary market

has also been developed considerably. Moreover, with the setting up of DFHI and MMMFs, the

lot of Indian money market has also achieved considerable progress in recent times and is also

expected to achieve further progress in the years to come.

INDIAN CAPITAL MARKET

By the term Capital market we mean a market for long term funds, whereas the money market

constitutes the market for short term funds. Capital market includes all existing facilities and

institutional arrangements developed for borrowing and lending medium and long term funds

available in the market. This is not a market for capital goods; rather it is a market for raising and

advancing money capital for investment purposes. In a capital market, the demand for long term

funds mostly arises from private sector manufacturing industries, agricultural sector and also

from the Government, which are again largely utilized for the economic development of the

country. Even the consumer goods industries usually need a considerable support from the

capital market.

Similarly, both the State and Central Governments, which are engaged in developing infra-

structural facilities viz., transport, power, irrigation, and communications etc. along with the

development of basic industries also, need a considerable support from the capital market. In a

capital market, the supply of funds usually comes from individual savers, corporate savings

various banks, insurance companies’ specialized financial agencies and also the Government.

The following are some of the institutions supplying funds to the Indian Capital market:

i) Commercial banks in India, which are interested in government securities and on

debentures of companies are considered as important investors;

ii) The insurance companies like LIC and GIC have also attained growing importance in the

Indian Capital market and are mostly investing in government securities;

iii) Various special institutions viz., the IDBI, IFCI, ICICI, UTI etc. are giving long form

capital to the private sector of the country, and

iv) Provident funds of employees which constitute a major volume of savings but their

investments are very much restricted in government securities.

After independence, the rapid growth and expansion of the corporate and public enterprises has

necessitated the development of the capital market in India. The capital market is composed of

the borrowers who demand fund and the lenders who supply fund in the market. A sound capital

market always tries to offer adequate quantity of capital to any industrial and business house at a

reasonable rate which is expected to result high prospective yield to make borrowing worth while

Structure of Development Banks of India

Development banks in India have developed in the post-independence period. The structure of

Indian development banks can be divided into two broad categories:

(a) Those which promote agricultural development and

(b) Those which promote industrial development.

1. Agricultural Development Banks

(i) At All-India Level: National Bank for Agriculture and Rural Development

(ii) At State Level: State Land Development Banks (SLDBs).

(iii) At Local Level: Primary Land Development Banks (PLDBs), and branches of

State Land Development banks (SLDBs).

2. Industrial Development Banks i) At All-India Level. Industrial Finance Corporation of India (IFCI), Industrial

ii) Development Bank of India (IDBI), Industrial Credit and Investment Corporation

of India (ICICI), Industrial reconstruction Bank of India (IRBI).

iii) At State Level. State Finance Corporations (SFCs) and State Industrial

Development Corporations (SIDs).

3. Industrial Finance Corporation of India (IFCI)

Industrial Finance Corporation is the first industrial development bank set up by the

Government of India in July 1948. It was established with a view to provide medium and

long-term credit to the eligible industrial units in the country. It extends financial

assistance to large and medium sized industrial units in both private and public sectors

and also to cooperatives.

Functions:

The IFCI provides assistance in the following forms:

i) It grants loans and advances to industrial concerns both in rupees and foreign

currency repayable within 25 years.

ii) It subscribes to the shares and debentures issued by the industrial concerns.

iii) It underwrites the issues of stocks, shares, bonds, (debentures of the industrial

concerns subject to the condition that such stocks, shares, etc. are disposed of by

the Corporation within a period of 7 years from the time of acquisition.

In recent years, the Corporation has started asking interest in the promotional activities

such as organizing techno-economic surveys, setting up of technical consultancy

organizations etc.

4. State Finance Corporations

The Industrial Finance Corporation provides financial assistance to large public limited

companies and cooperative societies and does not cover the small and medium-sized

industries. In order to meet the varied financial needs of small and medium sized

industries, the Government of India passed the State Finance Corporations Act in 1951,

which empowers the state governments to establish such Corporations in their states.

Functions:

Various functions of and types of financial assistance to be provided by the SFCs are

given below:

i) The SFCs have been established to provide long-term finance to small-scale and

medium-sized industrial concerns organized as public or private companies,

corporations, partnership or proprietary concerns.

ii) The SFCs extend loans and advances to the industrial concerns repayable within a

period of 20 years.

iii) The SFCs underwrite the issue of stocks, shares, bonds and debentures by

industrial concerns.

iv) The SFCs are prohibited from subscribing directly to the shares or stock of any

company having limited liability, except for under-writing purposes, and granting

any loan or advance on the security of own shares.

5. Industrial Development Bank of India (IDBI)

The IDBI is the apex financial institution in the field of development banking in the

country. It was established in July, 1964 with the twin objectives of:

(a) Meeting growing financial needs of rapid industrialization in the country

(b) Coordinating the activities and assisting the growth of all institutions engaged in

financing industries.

It is an organization with sufficiently large financial resources which not only provides

direct financial assistance to the large and medium-large industrial units, but also helps

the small and medium industries indirectly by extending refinancing and rediscounting

facilities to other industrial financing institutions.

Functions: Various types of assistance to be provided by the IDBI are as follows:

(i) Direct Financial Assistance - The IDBI provides direct financial assistance to

industrial concerns in the form of granting loans and advances, and subscribing to,

purchasing or underwriting the issues of stocks bonds or debentures

(ii) Indirect Financial Assistance - The IDBI provides indirect financial assistance

to the small and medium industrial concerns through other financial institution.

(iii) Development Assistance. The Development Assistance Fund is used to provide

assistance to those industries which are not able to obtain funds in the normal

course mainly because of heavy investment involved or low rate of returns.

(iv) Promotional Function. Besides providing financial assistance, the IDBI also

undertakes various promotional activities such as marketing and investment

research, techno- economic surveys.

6. Industrial Credit and Investment Corporation of India (ICICI)

The Industrial Credit and Investment Corporation of India was registered as a private

limited company in 1955. It was set up as a private sector development bank to assist and

promote private industrial concerns in the country.

Broad objectives of the ICICI are:

(a) To assist in the creation, expansion and modernization of private concerns

(b) To encourage participation of internal and external capital in the private concerns

(c) To encourage private ownership of industrial investment.

Functions:

The ICICI performs the following functions:

i) It provides long-term and medium-term loans in rupees and foreign currencies.

ii) It participates in the equity capital of the industrial concerns.

iii) It underwrites new issues of shares and debentures.

iv) It guarantees loans raised by private concerns from other sources.

v) It provides technical, managerial & administrative assistance to industrial

concerns

7. Unit Trust of India (UTI)

The Unit Trust of India was established in 1964 as a public sector investment institution.

The main objective of the UTI is to mobilize the savings of the small and medium income

groups and channeling them into productive investment. It thus, the one hand, contributes

to the industrial development and diversification of the economy, on and the other hand,

provides the small savers the opportunity for sharing the benefits of industrial

development by utilizing their savings in profitable and less risky investments.

Functions: (a) It sells its units to the investors in small and medium income groups

(b) It invests the funds so collected through the sale of units in industrial and

corporate securities

(c) It distributes the annual gross income among the unit-holders in the form of

dividends.

8. Industrial Reconstruction Corporation of India (IRCI)

Considering the seriousness of the problem of industrial sickness, the Government of

India established the Industrial Reconstruction Corporation of India in April 1973.The

main purpose of the IRCI was to prevent and cure the problem of industrial sickness. It

was expected to provide assistance to the sick units for their rehabilitation and

reconstruction. The IRCI was set up with an authorized capital of Rs. 25 crore, issued

capital of Rs.10 crore and paid-up capital of Rs. 2.5 crore.

The resources of the Corporation have been subscribed by Industrial Development Bank

of India (1DBI), Industrial Finance Corporation of India (IFC1), Industrial Credit and

Investment Corporation of India (1CICI), Life Insurance Corporation (LlC), State Bank

of India (SBI) and the nationalized banks. The Government of India has granted an

interest -free loan of Rs. 10 crore to the Corporation.

9. Industrial Reconstruction Bank of India (IRBI)

By a special Act passed in March 1985, the Government converted the IRCI into the

IRBI. The 1RB1 has been set up as a statutory corporation with the objective of

functioning as the principal institution for providing financial assistance needed for

rehabilitation of sick industrial concerns. The authorized capital of the IRBI is Rs. 200

crore and paid-up capital as on March, 31, 19S9 was Rs. 112.5 crore. During 1993-94 the

IRBI sanctioned financial assistance of Rs. 425.8 crore of which Rs. 188.6 crore

disbursed. At the end of June 1991, the cumulative financial assistance sanctioned and

disbursed stood at Rs, 1244 and Rs. 919 crore respectively.

IRBI has been converted into a full-fledged development financial institution with a new

name Industrial Investment Bank of India Ltd. (IIBI) with effect from March 27, 1997.

10. Export-Import (EXIM) Bank of India

The Export-Import (EXIM) Bank of India is the principal financial institution in India for

coordinating the working of institutions engaged in financing export and import trade. It

is a statutory corporation wholly owned by the Government of India. It was established

on January 1, 1982 for the purpose of financing, facilitating and promoting foreign trade.

Functions:

The main functions of the EXIM Bank are as follows:

i) Financing of exports and imports of goods and services, not only of India but also

of the third world countries;

ii) Financing of export & import of machinery and equipment on lease basis

iii) Financing of joint ventures in foreign countries;

iv) Providing loans to Indian parties to enable them to contribute to the share capital

of joint ventures in foreign countries;

v) To undertake limited merchant banking functions such as underwriting of stocks,

shares, bonds or debentures of Indian companies engaged in export or import; and

vi) To provide technical, administrative and financial assistance to parties in

connection with export and import.

10. Small Industries Development Bank of India (SIDBI)

Small Industries Development Bank of India (SIDBI) was established as wholly owned

subsidiary of Industrial Development Bank of India (IDBI) under the small Industries

Development of India Act 1989. It is the principal institution for promotion, financing

and development of industries in the small scale sector. It also coordinates the functions

of institutions engaged in similar activities. For this purpose, SIDBI has taken over the

responsibility of administrating Small Industries Development Fund and National Equity

Fund from IDBI.

Functions:

SIDBI provides assistance to the small scale industries sector in the country through the

existing banking and other financial institutions, such as, State Financial Corporations,

Stale Industrial Development Corporations, commercial banks, cooperative banks etc.

The major functions of SIDBI are given below:

i) It refinances loans and advances provided by the existing lending institutions to

the small scale units.

ii) It discounts and rediscounts bills arising from sale of machinery to and

manufactured by small scale industrial units.

iii) It grants direct assistance and refinance loans extended by primary lending

institutions for financing export of products manufactured by SSIs.

iv) It provides services like factoring, leasing, etc. to small units.

v) It provides financial support to National Small Industries Corporation for

providing; leasing, hire-purchase and marketing help to the small scale units.

11. Life Insurance Corporation (LIC) of India

Life Insurance Corporation of India (LIC) was established in 1956 to spread the massage

of life insurance in the country and to mobilize people’s savings for nation-building

activities. Main features of LIC are given below:

1. Saving Institution - Life insurance both promotes and mobilizes saving in the

country. The income tax concession provides further incentive to higher income

persons to save through LIC policies. The total volume of insurance business has

also been growing with the spread of insurance-consciousness in the country.

2. Term Financing Institution - LIC also functions as a large term financing

institution in the country. The annual net accrual of invested funds from life

insurance business and net income from its vast investment is quite large.

3. Investment Institutions - LIC is a big investor of funds in government securities.

Under the law, LIC is required to invest at least 50% of its accruals in the form of

premium income in government and other approved securities. LIC funds are also

made available directly to the private sector through investment in shares,

debentures, and loans.

4. Stabilizer in Share Market - LIC acts as a downward stabilizer in share market.

The continuous inflow of new funds enables LIC to buy shares when the market is

weak. But, the LIC does not usually sell shares when the market is overshot. This

is partly due to the continuous pressure for investing new funds and partly due to

the disincentive of capital gains tax.

12. General Insurance Corporation (GIC) of India

General Insurance companies sell insurance against specific risks, such as of loss from

fire and accident, to property of various kinds, such as motor vehicles, goods, machinery,

buildings, etc., and also against risk of personal accidents and sickness. The policies of

these companies do not involve saving feature. The purchaser of general insurance

simply buys a service and not any financial asset. In this way, general insurance

companies cannot be considered as financial intermediaries in the true sense. However,

they do accumulate large amounts of funds from premiums and investment income and

thus manage portfolios of assets like other financial institutions.