Introduction to Marginal Costing

Marginal Costing Problems

1Q. Breaking up semivariable cost into fixed and variable

The following are the maintenance costs incurred in a machine shop per six months with corresponding machine hours.

Month Machine Hours Maintenance Cost

Jan 2000 300

Feb 2200 320

March 1700 270

April 2400 340

May 1800 280

June 1900 290

Analyze the maintenance cost which is semi variable into fixed and variable elements.

2Q. Marginal cost statement and Break even analysis

A company is producing a single article sells it at Rs. 20/- each. The marginal cost of production is Rs 12/- each and the fixed cost is Rs. 800/- p.a. You are required to calculate:

1. The profit volume ratio2. Breakeven point or sales in value and volume3. The sales value required to earn a profit of Rs.1000/-4. The profit at sales of Rs. 60005. The margin of safety at3,4

3Q. The cost sheet of a steel box manufactured by Box and Roll Ltd., is as under:

Particulars Rs.

Sales Price 100

Materials 30

Labor (30% fixed) 30

Overheads ( 30% Variable) 30

Total Cost 90

Profit 10

The current production and sales level is 1000 boxes p.a. you are required to

a. Prepare a marginal cost statement for the above b. Ascertain

I. p/v ratioII. BES in volume and valueIII. MOS at current level of productionIV. Sales to earn a profit of Rs. 50000V. Profit at sales 1500000

c. If the marginal cost of the steel box is reassessed a Rs.90/-, what should be the revised selling price to retain the same pv ratio.

4Q. The following figures related to a company manufacturing a varied range of products

Particulars Total Sales Total Costs

Year ended 31-12-2009 20000 18000

Year ended 31-12-2010 30000 26000

Assuming stability in prices, with variable cost carefully controlled reflect predetermine relationships and on unvarying figure for fixed costs, calculate:

I. The pv ratioII. Fixed costsIII. BesIV. Profit at sales Rs.40000V. Sales to earn a profit of Rs. 5000

5Q. Sensitivity analysis

The following information is obtained from Uncertain Enterprises For the Year ending 2009.

Sales 100000

Variable costs 60000

Fixed costs 30000

Find the p/v ratio, BEP, MOS Calculate the effect of

20% increase in selling price 10% decrease in selling price 5% increase in sales volume 10% decrease in fixed costs 10% decrease in variable costs 20% increase in selling price accompanied with an increase of fixed

overheads by Rs.10000

6Q. Break even chart and profit graph

The selling price of an article is Rs.10/-

The marginal cost is Rs6/- each and the total fixed cost of the concern is Rs.400p.a.

Construct a break-even chart and a profit graph and show:

Break even pointMargin of safetyFixed costAngle of incidence

7Q. Combined break even point on an overall basis

Brando Ltd., manufactuers and sells four types of products under the brand names A, B, C, D. The sales mix in value comprises 33 1/3 , 41 2/3, 16 2/3, 8 1/3, of A, B, C and D respectively.

The total budgeted sales(100%) are Rs. 60000 per month.

The variable cost structure is as under:-

Product Variable cost as a percentage of selling price

A 60

B 68

C 80

D 40

Fixed costs are Rs. 14700 per month

Calculate the monthly overall sales required for the company to break even.

8. BREAK EVEN SALES ANLYSIS AFTER MERGER OF FACTORIES.

There are two similar plants under the same management. The management desires to merge these two plants. The following particulars are available.

Particulars Factory-I Factory-II

Capacity operation 100% 60%

Sales Rs. 300 lacs Rs. 120 lacs

Variable costs Rs. 220 lacs Rs. 90 lacs

Fixed costs Rs. 40 lacs Rs. 20 lacs

You are required to calculate

a) What would be the capacity of the merged plant obtained the purpose of break even ?

b) What would be the profitability on working at 75% of the merged capacity?c) At what capacity can be the merged factory make a profit of Rs. 18 lacs?d) What would be the breakeven point( capacity) or break even capacity as a

result of merger additional fixed expenses of Rs. 5 lacs has to be incurred?

9Q. problems on decisions bases on Key factors..( limiting factors)

The following particulars are obtained from the records of a company engaged on manufacturing two products A and B from a certain raw materials:-

Particulars Product A Product B

Rs. Per unit Rs. Per unit

Sales 100 200

Materials (Rs. 10 per Kg.) 20 50

Wages(Rs. 6 per hour) 30 60

Variable overheads 10 20

The total fixed overheads Rs. 10000

Comment on the profitability of each product when:

The total sales potential in units is limited Total sales potential in value is limited Raw material is in short supply Production capacity is limiting factor When the total availability of raw material is 4000kgs. And maximum

sales potential of each product is 1000 units., find the product mix to yield maximum profit.

10Q. Decision to discontinue a department / product / product line

The following are obtained from the accounts of departmental stores having four -departments:-

Particulars Dept A Dept B Dept C Dept D Total

Rs. Rs. Rs. Rs. Rs.

Sales 5000 8000 6000 7000 26000

Marginal Cost 5500 6000 2000 2000 15500

Fixed cost(apportioned) 500 4000 1000 1000 6500

Total Cost 6000 10000 3000 3000 22000

Profit/(loss) (1000) (2000) 3000 4000 4000

a) On the basis of the above information, management wants to discard dept B immediately as the loss show I maximum after the dept A will be discarded. What is your advice?

b) On the above information fixed cost is ascertained as follows:a. Dept A Nilb. Dept B Rs. 2500c. Dept C Rs.500d. Dept D Rs. 1000

And the balance of 2500 is treated as general overhead, will your advice under (a) differ? How?

11Q. Make or buy decisions

Spare Parts Ltd., has an annual production of 90000 units for a motor component whose cost structure is as under:

Particulars Rs. Per unit

Materials 270

Labour (25% fixed) 180

Variable expenses 90

Fixed expenses 135

Total 675

i. The purchase manager has an offer from a supplier who is willing to supply at Rs. 540. Should the component be purchased and production stopped?

ii. Assume the resources now used for the manufacturing of this component are used to produce another new product for which selling price is Rs. 485.

In the later case material price will be Rs. 200 per unit. 90000 units of this product can be produced at the same cost basis as the above for labor and expenses. Discuss whether it would be advisable to divert he resources to manufacture that new product, on the footing that the component is presently being produced , would , instead of being produced, be purchased from the market .

12Q. Exploring New Markets

Ice Cold Ltd., manufactures and sells direct to consumers 10000 containers of snow per month at Rs. 125/- per container, the factory’s normal production capacity is 20000 containers of snow per month. An analysis of cost for 10000 containers show:

Particulars Amount Rs.

Direct materials 100000

Direct labor 247500

Power 14000

Misc. Supplies 43000

Containers 60000

Fixed Expenses 795500

Total costs 1260000

a. The company has received an offer for the export of 120000 containers P.A. at 10000 containers per month. If the export price is Rs. 75 per container can the company accept the offer?

b. Keeping in mind the principles of marginal costing what is the minimum export price (per container) which the company can quote?

c. If the export price is Rs. 42 per container can the company accept the offer/d. Will the answer to C will change if

a. Cash subsidy @ 10% on the F.O.B value of exports is to be received from Government of India..

Marginal Costing Study Material

There are two main techniques for estimating product cost and profit. They are: (a) Absorption Costing, and (b) Marginal Costing. CONCEPT OF ABSORPTION COSTING

Cost is the base for ascertaining of profit or fixing selling price or valuating inventory. Different bases are used for classifying costs for different purposes. In this chapter the terms product cost and period cost are most important for understanding the terms absorption costing and marginal costing.

Product costs are associated with unit of output. They are the costs ‘absorbed by’ or ‘attached to’ the units produced. These costs go into the determination of inventory valuation (finished goods and partly completed goods) hence are called inventoriable cost.

They consist of direct materials, direct labor and factory overheads (partly or fully). The extent of inclusion of factory costs depends on the type of costing system in force-absorption and marginal costing. Where the absorption costing method is adopted factory overheads both fixed and variable costs are included as part of product cost. Where the marginal costing method is adopted only variable factory overheads are included as part of inventoriable cost.

Period costs are costs associated with time period rather than the unit of output or manufacturing activity. These costs are not treated as part of inventory and hence are treated as expenses in the period in which they are incurred. Administrative, selling and distribution costs are treated as period costs and are deducted as an expense for the determination of income and are not regarded as a part of inventory.Absorption Costing

Absorption costing is a cost accounting method of charging all direct costs and all production costs of an organization to specific units of production. Absorption costing is also known as Total Cost method, Traditional method, Conventional method and Cost Plus method. Absorption costing is an approach to product costing, wherein the total cost is considered. The production cost of product, process or operation consists of manufacturing cost, both fixed and variable cost, as well as direct and indirect cost. In absorption costing most of the fixed cost is treated as part of product cost and inventory values are arrived at accordingly. It is the simpler and oldest method, in practice. Accounting Standards (AS-2) recommend the use of absorption costing for the valuation of stock and work-in-progress. MERITS OF ABSORPTION COSTING The following are the merits of absorption costing:

a. Under absorption costing all costs should be charged to units manufactured. Thus, price based on absorption costing ensures that all costs are covered.

b. It helps to confirm accrual and matching concepts which require matching costs with revenue for a particular period.

c. It makes calculation of gross profit and net profit separately in income statement possible.

d. It discloses the efficient or inefficient utilization of production resources by indicating underabsorption or overabsorption of factory overheads.

e. This method has been recognized by various bodies like, FASB (USA), ASC (UK), ASB (India) for the purpose of preparing external reports and valuation of inventory.

Table 1: Ascertainment of Profit Under Absorption Costing

Particulars Amount (Rs.)

Amount (Rs.)

Sales Less: Cost of Goods Manufactured – Direct Material – Direct Labor Factory Overheads – Variable – Fixed (at actual production basis)

Add: Value of Opening Stock

Less: Value of Closing

xxx xxx

xxx xxx

xxxx

xxxx

xxx xxx xxx xxx xxx

xxx


Amount (Rs.)

Stock

Add: Underabsorption of fixed overhead (or) Less: Overabsorption of fixed overhead

xxx xxx

xxxx

xxxx xxxx

LIMITATIONS OF ABSORPTION COSTING

a. Comparison and control of cost is difficult because it depends on the level of output. An increase in the level of production reduces the unit cost and a decrease in the production level or output increases the unit cost. For different levels of output different unit costs are available.

b. Managerial decisions such as make or buy a product, choice of alternatives, fixation of price, number of units to be produced to earn desired profit etc., cannot be taken with the help of absorption costing because it considers the total cost and not the variable cost which is important for taking such decision.

c. In absorption costing, closing stock is valued at cost of production (fixed cost and variable cost), which means a portion of fixed cost is carried forward to the next period.

d. It lacks accuracy in determining the selling price of a product or service as it considers the total cost for its calculation.

e. It is considered to be an unsound practice, in the sense all the costs incurred in the year are not charged to revenue

Figure 1: Absorption Costing

MARGINAL COSTING

It is also known as variable costing or direct costing. This technique takes into consideration only the variable cost as product cost. Under this method, the fixed manufacturing costs are considered as period costs and charged directly to Profit and Loss Account.

As per CIMA, London, Marginal Costing is, “the ascertainment of marginal costs and the effect on profit of changes in volume or type of output by differentiating between fixed cost and variable cost”. Meaning of Marginal Cost and Contribution MARGINAL COST It is the cost incurred on producing an additional unit of production. In other words, it is the total variable cost. The marginal cost includes all the direct costs and variable overheads. According to CIMA London, the marginal cost is, ‘the amount at any given volume of output by which aggregate costs are changed, if volume of output is increased or decreased by one unit’. Per unit marginal cost will remain same irrespective of the level of production. CONTRIBUTION In marginal costing technique, contribution is the difference between the sales value and the marginal or variable cost of the product. This contribution covers the fixed cost and generates the profit. Contribution minus fixed expenses equals profit. A detailed study based on the contribution made by each product or department helps in analyzing the relative profitability of that product or department. Mathematically, contribution can be expressed as follows:

Contribution = Selling Price – Marginal Cost (or)

Contribution = Fixed Cost + Profit (or)

Contribution – Fixed Cost = Profit.

Table 2: Ascertainment of Profit Under Marginal Costing


Amount (Rs.)

Sales

Less: Variable Cost

Direct Material

xxx xxx

xxxx

Direct Labor

Variable Manufacturing Overheads

Add: Value of Opening Stock

Less: Value of Closing Stock

Add: Variable Administration Overheads

Variable Selling Overheads

Contribution

Less: Fixed expenses

Factory

Administration

Selling & Distribution

Net Income or Profit

xxx

xxxx

xxx xxx

xxx xxx

xxx xxx xxx

xxx xxx xxx

xxxx

xxxx

xxxx

Illustration 1 From the information given below, you are required to prepare profit statements for the year based on (i) Absorption Costing (ii) Marginal Costing.

CMR Ltd. produces a single product, which is bottled and sold in cases. The normal annual level of operations, on which the production fixed overhead absorption is based is 18,000 cases. Data for the last accounting year were as follows:

Production 20,000 cases; sales 16,000 cases.

.

Rs. per case

Selling price Production costs: – Direct material – Direct labor – Variable overhead Fixed overhead (budgeted and incurred) Selling and Administration costs Fixed Variable

30 7 6 4

54,000

Rs.25,000 15% on sales revenue.

There was no opening stock of finished goods and the work-in-progress stock may be assumed the same at the end of the year as it was at the beginning of the year. Solution

Profit Statement (under Absorption Costing Method)

Particulars Amount (Rs.) Amount (Rs.)

Sales 16,000 units @ Rs.30 per case Less: Production cost 20,000 cases @ Rs.20 Less: Closing stock 4,000 cases @ Rs.20 Less: Rectification of over absorption of 2000 units @ Rs.3 per unit Less: Selling & Administrative cost Fixed Variable @ 15% on sales Profit

4,00,000 80,000

4,80,000

3,14,000 3,20,000 6,000 25,000 72,000

1,66,000 97,000

69,000

Note: Fixed cost per unit =

= Rs.3

Production cost per unit = Rs.7 + Rs.6 + Rs.4 + Rs.3

= Rs.20

Profit Statement (under Marginal Costing Method)

Particulars Amount

(Rs.) Amount

(Rs.)

Sales 16,000 cases @ Rs.30 per case Less: Variable Cost 20,000 @ Rs.17 (Rs.7 + Rs.6 + Rs.4) Less: Closing Stock 4,000 @ Rs.17 Add: Variable Selling & Administrative Cost Contribution Less: Fixed Cost: Production Selling and Administration Profit

4,80,000

3,44,000

3,40,000 68,000

2,72,000 72,000

54,000 25,000

1,36,000

79,000

57,000

FEATURES OF MARGINAL COSTING i. All the costs are classified into fixed and variable cost. Variable cost varies

according to the level of activity but per unit variable cost remains fixed. Fixed cost is fixed in absolute value at any level of activity.

ii. Under marginal costing, the fixed cost is treated as period cost and variable cost is treated as product cost.

iii. Inventories are valued at marginal cost. iv. When marginal costing is used in process costing, the products are transferred from

process to process at marginal cost. v. The product is priced on the basis of marginal cost and contribution. vi. The profitability of products and divisions are determined on the basis of

contribution margin. vii. Under marginal costing, the importance is given to total contribution and

contribution from each product while presenting the data. viii. There is no effect of differences in the amount of opening stock and closing stock on

unit cost of production in marginal costing.

Figure 2: Marginal Costing

Difference between Absorption Costing and Marginal Costing The following are the main points of difference between the absorption costing and marginal costing:

a. Under marginal costing, the distinction between the period cost and product cost determines when costs are matched with revenues. Direct or variable or product costs are assigned to products and matched with revenues when they are recognized, while period costs are matched with revenues in the period in which the costs are incurred. But in absorption costing, fixed costs are treated as part of production cost and accordingly inventory is valued.

b. In absorption costing, arbitrary apportionment of fixed costs over the products results in underabsorption or overabsorption of such cost, whereas, in marginal costing since fixed costs are excluded, there is no underabsorption or overabsorption of overheads.

c. In absorption costing, managerial decision-making is based on profit, which is the difference between the sales value and the total cost of the product. But in marginal costing, the managerial decisions are based on contribution and not profit.

Contribution is the difference between the sales value and the marginal cost of the product.

VALUE OF MARGINAL COSTING TO MANAGEMENT Marginal costing is very useful to the managers because of the following reasons:

i. Marginal costing by separating the costs into fixed and variable cost, exercises effective control over it and also facilitates responsibility-oriented control.

ii. Marginal costing, by analyzing the cost data, showing the variable cost and contribution for each product and product line aids the management in taking appropriate decisions.

iii. Marginal costing leads to greater accuracies in calculation of profits as the valuation of closing stock of finished goods and work-in-progress are easy and simple.

iv. The data presented is more reliable and more acceptable, as it excludes the fixed costs and also avoids allocation and apportionment. Usually the fixed costs are not allocated and apportioned on scientific basis.

v. The cost information presented under marginal costing is simpler, meaningful, and an effective aid to the management in decision-making.

LIMITATIONS OF MARGINAL COSTING

Some of the important limitations of marginal costing are as follows:

Separation of all expenses into fixed and variable is practically difficult, because neither the variable cost is absolutely variable nor the fixed expenses are absolutely fixed. This problem of classification becomes more complicated with the presence of semi-variable and semi-fixed expenses.

Time factor is not given due importance in marginal costing and all those expenses connected to time are excluded. Therefore, the pricing decision based on marginal costing is useful in short run but not in the long run. The long run decisions are based only on total cost and not on variable cost.

Marginal cost understates the stock of finished goods and work-in-progress because of which the Balance Sheet does not exhibit the true and fair view.

As the closing stock is valued at variable cost under marginal costing technique, the full loss on account of goods destroyed cannot be recovered from the insurance company.

The other cost techniques such as budgetary control and standard costing can achieve better control when compared to marginal costing, as marginal costing deals with cost behavior but does not provide any standard for evaluation of performance.

It fails to reveal the impact of change of manufacturing practice, for example, replacement of labor force by machine.

Difference between Marginal Costing and Direct Costing

In case of direct costing, only direct costs are considered in the calculation of the cost of a product. All indirect expenses or costs are met from the total margin available from all products. Most people tend to think that direct costing and marginal costing are one and the same. But they are different, because, all direct costs may not be variable. A direct cost can be identified with the product directly. So it can be fixed or variable in nature. If any such cost is included in the product, the cost calculated under direct costing and marginal costing will be different.

Effects of absorption costing and marginal costing on income statements

Alternatives Absorptio

n costing Net income

Marginal costing net income

PV > SV High Low

PV = SV Equal

PV < SV Low High

SV (Constant),

PV (fluctuating)

Uneven income

Constant income

PV (Constant) Income changes in proportion to change in SV

Low change Greater Change

Change in net income over a long period

Both the results becomes almost similar

RG Company furnished the following data. Ascertain net income of the company under

1. Absorption Costing Method.2. Marginal Costing Method.


Direct Material cost per unit 3 Direct Labor cost per unit 5 Variable manufacturing OH cost per unit 2

Total fixed manufacturing OH per year 60,000

Number of units produced per year - 20,000 unitsClosing stock - 5,000 unitsSales price per unit - Rs. 30 Variable selling expenses - Rs. 2 per unit Fixed selling expenses - Rs. 40,000

Solution : Cost per unit under marginal costingParticulars Amount

(Rs)Direct Materials 3

Direct Labor 5

Variable manufacturing cost 2

Per unit cost 10

Cost per unit under absorption costing

Particulars Amount (Rs)

Direct Materials 3

Direct Labor 5

Variable manufacturing cost

2

Fixed manufacturing cost (60000/20000)

3

Per unit cost 13

Marginal Costing Income statement Particulars Amount

(Rs.)Amount (Rs.)

Sales 4,50,000Less Variable costs Variable cost of goods sold Opening inventory 0 Cost of goods produced( 20,000 units @ Rs. 10 )

2,00,000

Cost of goods available for sale 2,00,000 Closing stock (5000 units @ Rs. 10) 50,000 Variable cost of goods sold 1,50,000 Variable selling expenses(15000 units @ Rs. 2)

30,000

Total variable cost of good sold 1,80,000Contribution 2,70,000Less: Fixed costs Manufacturing OH 60,000 Fixed selling expense 40,000 1,00,000Net Income 1,70,000

Income statement under Absorption Costing


Amount (Rs.)

Sales 4,50,000Less Cost of goods sold Variable cost of goods sold Opening inventory 0 Cost of goods produced( 20,000 units @ Rs. 13 )

2,60,000

Cost of goods available for sale 2,60,000 Closing stock (5000 units @ Rs. 13) 65,000 1,95,000 1,95,000

Gross Margin 2,55,000Less Fixed costs 40,000 Variable selling expenses (15,000 @ 2)

30,000 70,000

Net Income 1,85,000

COST-VOLUME-PROFIT ANALYSIS

Cost-Volume-Profit (CVP) Analysis studies the relationship of cost, volume and profit. These three factors are interrelated. The cost of the product determines its selling price and selling price determines the profit. Selling price affects the volume of sales, which directly affects the volume of production and volume of production influences the cost. In brief, variations in volume of production result in changes in cost and profit. According to CIMA, London, “CVP analysis is the study of the effects on future profits of changes in fixed cost, variable cost, sales price, quantity and mix”. This is the most important technique, which is used in managerial decision-making and profit planning.

In Management Accounting it is very important to find out how costs and profits vary in relation to changes in volume, i.e., quantity of the product manufactured and sold.

All the above linear relationships hold good under three assumptions, namely,

a. Every cost can be classified as fixed cost or variable cost. Fixed costs remain the same even if the volume (i.e., quantity of product manufactured and sold) changes. A cost like factory rent would be an example of a fixed cost.

On the other hand, variable costs vary in proportion to changes in activity. An example of a variable cost is raw material. If volume of production increases by say 10%, then we can expect raw material costs also to increase by 10%.

b. The selling price of the product remains the same even if volume varies.

c. There is only one product. If there is more than one product, the product mix is assumed to be constant.

Mathematical relationship between cost-volume-profit requires the understanding of marginal cost equation.

Marginal Cost Equation:

Sales = Variable Cost + Fixed Expenses + Profit /Loss [S = V + F + P] (or)

Sales = Variable Cost + Contribution [S = V + C ] (or)

Sales – Variable Cost = Fixed Expenses + Profit/Loss [S – V = F + P] (or)

Sales – Variable cost = Contribution [S – V = C]

In order to understand the mathematical relationship between cost, volume and profit, it is desirable to understand the following concepts, their calculation and application.

a. Contribution/Sales (C/S) or Profit Volume (P/V) Ratio. b. Break Even Point. c. Margin of Safety

Contribution/Sales Ratio or P/V Ratio The profitability of the operation of a business can be known with the help of profit/volume ratio. Profit/volume ratio establishes the relationship between contribution and sales. Any increase in contribution leads to increase in profit because fixed cost is assumed to be constant for all the levels of production. Profitability of the product can be ascertained by comparing the P/V ratios for the different products. Higher the P/V ratio higher the profit and lower the P/V ratio lower is the profit. A higher P/V ratio is an indicator of sound financial health of the company’s product.

The profit/volume ratio is expressed in percentage. It is expressed in the following ways:

P/V Ratio = (or)

= (or)

= x 100 (or)

= x 100

Desired sales, variable cost and contribution can be found out with the help of P/V ratio. The formulae are as follows:

Desired Sales = Desired Contribution/P/V Ratio (or)

= (Fixed Cost + Desired Profit) / P/V Ratio

Variable Cost = Sales (1 – P/V ratio)

Contribution = Sales x P/V Ratio Improving P/V Ratio P/V ratio shows the profitability of the organization. Hence, organizations can improve their P/V ratio without an increase in fixed cost. P/V ratio can be increased or improved by taking any of the following steps:

By increasing the sales price or selling price per unit.

·By reducing the variable or marginal cost and ensuring the efficient utilization of men, material and machines.

By changing the sales mix. It means selling the products more, which is having a higher P/V ratio.

The Break Even Point A break even point is a point at which a firm earns no profit and does not bear any loss. It is a point at which the total sales are equal to total costs. In other words, contribution is sufficient to cover fixed cost only. At break even point, the income of the firm is equal to the expenditure. Every unit produced after break even point contributes to the profit of the organization.

Illustration 2 Monotonous Co., manufactures and sells a single variety of a product. For 2000-01, the Management Accountant estimated the following profit levels depending upon the different quantities of the product manufactured and sold:

Sales Quantity (’000

units)

Sales Value

Rs. lakh [Selling Price

= Rs.10]

Total Costs

Rs. lakh

Profit/(Loss)

Rs. lakh

20

25

30

35

40

45

50

2.0

2.5

3.0

3.5

4.0

4.5

5.0

3.6

3.7

3.8

3.9

4.0

4.1

4.2

(1.6)

(1.2)

(0.8)

(0.4)

—

0.4

0.8

Solution

As seen from above when 20,000 units are sold, there is a loss of Rs.1.6 lakh. However, as more and more units are sold the loss goes on decreasing. When sales are 40,000 units there is no loss. When sales increase beyond 40,000 units the firm earns a profit.

The above situation can be represented on a graph as follows:

The graph shows that when sales quantity is 40,000 units the Sales Value Line and the Total Cost Line intersect at a point BEP. This point is called the Break Even Point. On the X-axis the BEP indicates that when sales quantity is 40,000 units, Total Cost equals Sales Value. On the Y-axis BEP indicated that Total Cost equals Sales Value when each of these amounts is Rs.4 lakh.

The Break Even Point is a kind of borderline. If sales are less than break even sales, the company incurs a loss. If sales are more than break even sales the company earns a profit.

BREAK EVEN POINT ON P/V GRAPH We can plot profit against sales quantity on a Profit-Volume Graph using the figures given earlier. We get the following P/V graph:

Figure 4

Here, the Break Even Point BEP is the point at which the Profit Line intersects the X-axis.

As seen earlier it is the point at which sales quantity is 40,000 units.

A break even point is a point at which a firm earns no profit and does not bear any loss. It is a point at which the total sales are equal to total costs. In other words, contribution is sufficient to cover fixed cost only.

A break even point is a point at which a firm earns no profit and does not bear any loss. It is a point at which the total sales are equal to total costs. It can be ascertained arithmetically or graphically. Arithmetically, it is called break even analysis and graphically, it is termed as break even chart.

In the given graph, the sales line and variable line starts from the ‘0’ point indicating variable cost is dependent on the sales. Fixed cost line is parallel to the horizontal axis denoting its fixed nature irrespective of the amount of production. Total cost line has been derived after adding variable cost line with the fixed cost. The point at which the sales line intersects the total cost line represents the B.E. Point. Area between total cost line and sales line is situated to the right side of the B.E.P. This denotes profit. Left side area of B.E.P. denotes loss. Right side area of the B.E.P. denotes the margin of safety i.e. sales over the B.E.P. and the angle between sales line and total cost line is known as angle of incidence.

BREAK EVEN POINT FORMULA We can arrive at the break even point using a mathematical model as shown below:

Let s = Selling price per unit of the product.

v = Variable cost per unit of the product manufactured and sold.

Q = Quantity (units) of the product manufactured and sold.

F = Total fixed cost for the period under consideration.

P = Profit for the period under consideration.

Then we have,

Sales Revenue – Total Cost = Profit So, sQ – [vQ + F] = P So, (s – v) Q – F = P

We can use this equation to find the quantity QB of units to be manufactured and sold in order to break even.

Note that at the break even point profit i.e., P = 0

So the above equation becomes,

(s – v) QB – F = 0

or QB =

Since s – v = Unit contribution

We have the formula,

Break Even (Quantity) =

We may be interested in the Break Even Sales value instead of the Break Even Sales quantity.

Break Even Sales (Value)

=

Break Even Sales Quantity x Selling price per unit.

=

The above can be written as:

Break Even Sales (value) =

is the C/S ratio (also called the P/V ratio or contribution margin)

Break Even Sales Value = or

USES OF BREAK EVEN ANALYSIS

Prediction: Break Even Analysis is useful in predicting what sales volume has to be achieved in order to start earning a profit.

For example, in the above case sales should be at least 40,000 units or Rs.4 lakh before the firm starts earning a profit.

Margin of Safety: Break Even Analysis can also be used to answer the question, “How low can the sales fall before the firm will begin to incur losses?”

In the example above, break even sales are Rs.4 lakh. Actual sales are expected to be Rs.5 lakh. Then if actual sales are lower by more than 10,000 units, Rs.1 lakh or 20%, the firm will incur losses.

10,000 units or Rs.1 lakh or 20% is called the Margin of Safety. It is the difference between actual sales and Break Even sales.

Figure 5

Scale of Operations: An important decision is to decide the scale of operations of a firm. In practical terms this would mean deciding upon the capacity of the firm to produce and sell its products.

Consider the three cases illustrated below:

Case I

Figure 6

Case II

Figure 7

Case III

Figure 8

In all the cases the firm has a capacity of 100%. This means that the company does not have the necessary infrastructure to produce more than 100 units in a year [capacity is usually specified as maximum possible production per year].

i. In Case I, once the sales quantity crosses 25 units or 25% of capacity, the firm begins to earn a profit. This is relatively a safe situation because the firm can start earning profit at a relatively low level of activity.

ii. In Case II, the firm begins to earn a profit once the sales quantity crosses 65 units or 65% of capacity. This is a riskier situation than Case I because the firm has to achieve a much higher level of activity before it can start earning profits.

iii. Case III is a disaster because the firm cannot earn a profit even when sales quantity equals the capacity of 100 which is the maximum possible production.

Changes in Underlying Factors: Break Even analysis can also be used to study the effect of changes in underlying factors on the Break Even Point and Margin of Safety.

Illustration 3

A manufacturing unit produces 750 units of products annually. The marginal cost of each product is Rs.480 and the product is sold for Rs.600. Fixed costs incurred by the company is Rs.24,000 annually. Calculate P/V ratio. What would be the break even point in terms of output and in terms of sales value?

Solution

Contribution per unit = Sales – Variable Cost = Rs.600 – Rs.480 = Rs.120P/V Ratio

= = = 20%

Break Even Point (in units) = Fixed cost/contribution per unit.

= 24,000/120 = 200 units.

Break Even Point (in Rs.) = Break Even point x Selling price per unit

= 200 x 600 = Rs.1,20,000,

or,

Break Even Point (in Rs.) = Fixed Cost/ P/V Ratio

= 24,000/ 20% = Rs.1,20,000.

Illustration 4

From the following figures, calculate

i. Break Even Point

ii. Sales to earn a profit of Rs.1,20,000.

Particulars Rs.

Sales

Fixed Cost

Variable Expenses

4,00,000

1,80,000

2,80,000

Solution

Contribution = Sales – Variable Cost = Rs.4,00,000 – Rs.2,80,000

= Rs.1,20,000

P/V Ratio = = =30%

i. Calculation of Break Even Point

Break Even Point (in Rupees)

=

ii. Sales to earn a profit of Rs.1,20,000

Break Even Point (Rs.) =

= Rs.10,00,000. Margin of Safety

Margin of safety is the difference between the actual sales and the sales at the break even point or, the excess of actual sales over the break even sales. At BEP, the margin of safety is nil because the actual sales and the break even sales are equal. Margin of safety is the excess of actual production over the production at the break even point because of marginal costing assumption that the production or output must coincide with the sales.

Margin of safety can also be expressed in percentage. The formula for calculating the margin of safety is,

Documents

Introduction to Marginal Costing