CHAPTER 3 - Owais Husain PhD.€¦ · Web viewBreak even point is the level of sales at which profit is zero. According to this definition, at break even point sales are equal to

Managerial Accounting Cost Behavior & CVP Analysis

CHAPTER 3COST BEHAVIOUR AND CVP ANALYSIS

Topics covered

Introduction Cost Behavior Patterns

- Variable cost behavior - Fixed cost behavior- Semi variable & mixed costs

Importance of CVP analysis - Assumptions underlying CVP analysis

Contribution Margin Interrelation of cost-volume and Profit

- Change in fixed cost and sales volume-Change in variable cost and sales volume - Change in fixed cost, sales price and sales volume - Change in variable cost, fixed cost and sales volume -Change in regular sales price

Breakeven Analysis - Target Net Profit Analysis - Margin of Safety - Sales Mix and CVP

Introduction:

Cost behavior as meaning how a cost will react or changes as changes take place in the level of business activity. An understanding of cost behavior is the key to many decisions in an organization in that by understanding how costs behave; a manager is better able to predict what costs will be under various operating circumstances.

CVP Analysis has a number of purposes such as: to provide information to the management about cost behavior for routine Planning and one-off

Decision Making; to determine what volume of sales is needed at any given budgeted sales price in order to Break

Even stage; to identify the ‘risk’ in the budget by measuring the Margin of Safety; to calculate the effects on profit of change in variable costs, sales prices, fixed costs and so on.

Managers must understand the interrelationship between Cost, Volume, and Profit for planning and decision making. Many questions are related to Cost, Volume and profit in business such as: Car Sale in automobile business, Passengers required in airline business. In other ward what effects does a change in volume have on profits? Managers of all organizations must understand the fundamental

Faculty: Dr. Uvesh Husain Mazoon University College1


relationships of Sales (revenues), Costs (expenses) and Net income (profit). This interrelationship is very important for sound decision making.

Cost-Volume-Profit (CVP) analysisCost-Volume-Profit (CVP) analysis helps mangers to predict the outcome of their decisions by expressing the relationships among a business’s costs, volume and profit or loss. Its relationship is on relatively short-term decisions, although it may be applied to longer-term and strategic decisions. An especially important aspect of cost-volume-profit analysis is its use in answering “what if” questions, such as “what if sales decline?”, “What if cost increase?”, “What if we introduce new products?” CVP analysis is a tool for answering such questions. The use of CVP analysis is an integral part of the management decision process. Managers at varying levels of responsibility rely on cost-volume-profit analysis to make both major and minor decisions concerning individual products as well as overall performance. Managers usually have a variety of decision models, or formal frameworks involving quantitative analysis, at hand for making a choice among alternatives. Cost-volume-profit analysis is one of the most useful decision models the management accountant can prepare for the management.

COST CLASSIFICATIONS TO DESCRIBE COST BEHAVIOR

Before venturing into CVP analysis as such, we shall refurbish our understanding of some of the aspects of Costs. In general, costs behave differently at different stages in a business environment. The understanding of Cost Behavior is essential. The study of Cost Behavior describes how costs change-indeed, if they change-in response to a shift in activity levels or a cost driver. A Cost Driver is a factor that causes, or “drives” an activity’s costs. Managers need to know how costs behave to make informed decisions about products, to plan and to evaluate performance. Fundamentally managers need to know the cost behavior of the following categories of costs viz., fixed, variable and mixed.

Cost Behavior: The way in which a cost will react or respond to changes in the level of business activity or cost driver.

RELEVANT RANGE

The distinction between fixed and variable costs is only valid within a certain range of activity. For example, the manager of a Turkish restaurant increased the capacity from 150-250 seats, requiring an increase in rent costs, utilities and many other costs. Although these costs are usually thought of as fixed, they change when activity moves beyond a certain range. This range within which the fixed costs do not change is referred to as the Relevant Range. So, Relevant Range is the Activity Levels within which a given fixed cost will be unchanged even though volume changes. Relevant range consists of the activity levels over which the CVP calculations hold. Relevant range is the band of volume in which a specific relationship between cost and volume is valid. For example, the fixed cost could be $50,000 for a production range of 0-10,000 units and could be $80,000 for a production range of 10,000-20,000.



The relevant range is the range of activity within which the assumptions that have been made about variable and fixed costs are valid

FIXED COST BEHAVIOR

Fixed cost behavior can be summarized as follows:

Fixed Cost BehaviorIn Total Per Unit

Total fixed cost is not affected by changes in activity (i.e., total fixed cost remains constant even if activity changes).

Fixed cost per unit decreases as the activity level rises and increases as the activity level falls.

EXAMPLE: Assume that a company manufactures microwave ovens. The company pays $9,000 per month to rent its factory building. The total cost and the cost per unit of rent at various levels of activity would be:

Number ofRent Cost Ovens Rent Costper Month Produced per Oven

$9,000 1 $9,000$9,000 10 $900$9,000 100 $90$9,000 200 $45

As we know, Fixed Costs are those that are unchanged as volume changes within the relevant range of activity. Note that it is the total fixed cost that does not change at various activity levels. But, fixed cost per unit, changes with each change of activity level. For example, Microwave oven manufacturing firm with $9,000 total fixed cost in the relevant range of 1-200 ovens has the same total fixed cost at any level of the relevant range. But, the unit fixed cost will vary, at each activity level in the relevant range. I.e., at 100 units the fixed cost per unit is $ 90 ($ 9,000 ÷ 100) and at the activity level of 400 units the unit fixed cost is $45 ($9000 ÷ 200).

If activity changes enough, fixed costs may change. For example, if microwave production were doubled, another factory building might have to be rented.

The relevant range is the range of activity within which the assumptions that have been made about variable and fixed costs are valid. For example, the relevant range within which total fixed factory rent is $9,000 per month might be 1 to 200 microwaves produced per month.



VARIABLE COST BEHAVIOR

Variable cost behavior can be summarized as follows:

Variable Cost BehaviorIn Total Per Unit

Total variable cost increases and decreases in proportion

to changes in activity.

Variable cost per unit is constant.

EXAMPLE: A company manufactures microwave ovens. Each oven requires a timing device that costs $30. The cost per unit and the total cost of the timing device at various levels of activity (i.e., number of ovens produced) would be:

Cost per Number of Total VariableTiming Ovens Cost—TimingDevice Produced Devices

$30 1 $30$30 10 $300$30 100 $3,000$30 200 $6,000

A GRAPHIC VIEW OF COST BEHAVIOR

Not all variable costs have exactly the same behavior pattern. Some variable costs behave in a true variable or proportionately variable pattern. Other variable costs behave in a step-variable pattern.

True variable or proportionately variable pattern :

Direct materials would be a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of production activity. Moreover, any amounts purchased but not used can be stored up and carried forward to the next period as inventory.



Step-variable pattern

A cost (such as cost of a maintenance worker) that is obtainable only in large pieces and that increases and decreases only in response to fairly wide changes in the activity level.

As an example, let us consider the labor cost of maintenance workers, which would be part of indirect labor. Unlike, direct materials, the time of maintenance workers is obtainable only in large chunks, rather than in exact quantities. Moreover, any maintenance time not utilized cannot be stored up as inventory and carried forward to the next period. Furthermore, the utilization of indirect labor time can be quite flexible, whereas the utilization of direct materials is usually quite set.

MIXED COSTS

Not all costs are strictly Fixed or strictly Variable. These costs are known as Mixed Costs are those which are partly fixed and partly variable. A classic example is the Electricity Utility costs. These costs may be partly fixed and partly variable. The Electricity Utility charges may be based on a fixed minimum monthly charge plus a variable cost for each kilowatt-hour in excess of the specified minimum usage. Mixed costs are also called Semi Variable Costs. A Mixed cost has characteristics of both a variable and a fixed cost. Mixed costs are sometimes called semi-variable or semi-fixed costs.

Examples of mixed costs include electricity, heat, repairs, telephone and maintenance ect.

To illustrate, assume that Global manufacturers using rented machinery. The rental charges are $25,000 per year plus $ 1 for each machine hour used. If the machinery is used $20,000 hours, the total rental charge is $ 45,000 [$25,000 + (20,000 x $ 1)]. If the machinery is used 30,000 hours, the total rental charge is $ 55,000 [$ 25,000 + (30,000 x $ 1)] and so on.

In this illustration, a rental cost of $25,000 will be incurred, even if the machinery is not used. The $25,000 is constant over all levels of production and represents the fixed cost component of the mixed cost. The rental charge of $ 1 per hour represents the variable cost component of the mixed cost. It causes the total mixed cost to increase as machine hours are used.

How do we separate the Mixed Costs into Fixed and Variable Components?

(1) High-low method(2) Scatter graph method(3) Least – squares method

Most straightforward approach to determining the variable cost element of mix costs is used “High-Low method”.



The High-Low Method:

The High-Low method estimates a cost function on the basis of only the highest volume and lowest-volume points within the relevant range of sample. In this method two costs are selected, one at the high side and another at the low side of the relevant range and transferred to a graph scaled for cost and units of production. If these points are representative of activity in the relevant range, a line connecting them should be a close estimate of the cost pattern for the entire relevant range of activity.

The High-Low method is easy to use, but it has a major defect. It uses only two data observations, regardless of the number of observations available. Because these two points may not represent the normal relationship between the cost and the cost driver and because better estimation methods are available, the high low-method is only recommended when very few observations of past results are available.

To illustrate assume that maintenance costs for Arco company have observed as follows within the relevant range of 5,000 to 8,000 direct labor hours (DLH)

Month DLH Maintenance costs incurredJan 5500 $ 745Feb 7000 850Mar 5000 700Apr 6500 820May 7500 960June 8000 1,000July 6000 825

Month DLH Maintenance costs incurredHigh point observed 8,000 $ 1, 000Low point observed 5,000 700Change observed 3,000 $ 300

Variable cost per unit = Change in cost/Change in activity= $ 300/ 3000 = $ 0.10 per direct labor hour

Fixed cost element = Total cost – Variable cost element= $ 1,000 – (0.10 X 8,000 labor hours)= $ 200

Cost formula for maintenance-over the relevant range of 5000 to 8000 DLH =$ 200 fixed cost + $0.10 per DLH



CVP Analysis:

CVP analysis is the study of the interrelationship between costs, output volume and profit at various levels of activity. To assist planning and decision making, management should know not only the budgeted profit, but also; the output and sales level at which there would be neither profit nor loss (break even point) and the amount by which actual sales can fall below the budgeted sales level, without a loss being incurred (the margin of safety).

Cost-volume-profit (CVP) analysis is a study of the effects of changes in costs and volume on a company’s profits.

Cost-volume-profit (CVP) analysis a study of the interrelationship between the following factors:

• Unit selling prices

• Sales volume or level of activity

• Unit variable costs.

• Total fixed costs.

• Sales mix

IMPORTANCE OF CVP ANALYSIS

CVP analysis is important in profit planning

It is also having a critical factor in such management decisions such as setting selling price, determining the best product mix and making maximum use of production facilities.

ASSUMPTIONS UNDERLYING CVP ANALYSIS

Cost – Volume – Profit analysis is based on the following assumptions:

1. Selling price is constant. The price does not change as volume changes.

2. Costs are linear and can be accurately split into fixed and variable elements. The total fixed cost is constant and the variable cost per unit is constant.

3. The sales mix is constant in multi-product companies.

4. In manufacturing companies, inventories do not change. The number of units produced equals the number of units sold.

CONTRIBUTION MARGIN :

One of the key relationships in CVP analysis is contribution margin (CM).

Contribution margin is the amount of revenue remaining after deducting variable costs. (OR)

Contribution margin is the excess of sales revenue over variable costs.



The amount that sales (net of variable expenses) contributes toward covering fixed expenses and then toward profits.

The unit contribution margin remains constant so long as the selling price and the unit variable cost do not change

The contribution margin is especially useful in short term planning.

Formula for and computation of contribution margin:

Sales - Variable costs = Contribution Margin

CONTRIBUTION MARGIN PER UNIT

The contribution margin per unit is useful in analyzing the profit potential of proposed projects.

Formula for contribution margin per unit :

Unit Selling Price - Unit variable costs = Contribution Margin per unit

CONTRIBUTION MARGIN RATIO

The contribution Margin can also be expressed as a percentage. Contribution Margin Ratio is also called Profit-Volume ratio.

The contribution margin (CM) ratio is the ratio of contribution margin to total sales.

The contribution margin ratio is also useful in setting business policy.

If the company has only one product, the CM ratio can also be computed using per unit data:

THE CONTRIBUTION APPROACH

A contribution format income statement is very useful in CVP analysis because it highlights cost behavior.

EXAMPLE: Last month’s contribution income statement for Nord Corporation, a manufacturer of exercise bicycles, follows:



Total Per UnitSales (500 bikes)........................ $250,000 $500Variable expenses...................... 150,000 300 Contribution margin................... 100,000 $200Fixed expenses........................... 80,000 Net operating income................. $ 20,000

The contribution margin of $ 100,000 is available to cover the fixed costs of 80,000, once the fixed costs are covered, any remaining C.M adds directly to the operating income of the company. The fixed costs can be thought of as a bucket, while the contribution margin is water filling. Once the bucket is filled, the over flowing represents operating income. Up until the point of overflows.

EXAMPLE: For Nord Corporation, the CM ratio is 40%, computed as follows:

or

The CM ratio shows how the contribution margin will be affected by a given change in total sales.

EXAMPLE: Assume that Nord Corporation’s sales increase by $150,000 next month. What will be the effect on (1) the contribution margin and (2) net operating income?

(1) Effect on contribution margin:

(2) Effect on net operating income:

If fixed expenses do not change, the net operating income for the month will also increase by $60,000.

Present Expected ChangeSales (in units)............................. 500 800 300Sales (in dollars).......................... $250,000 $400,000 $150,000Variable expenses........................ 150,000 240,000 90,000



Contribution margin.................... 100,000 160,000 60,000Fixed expenses............................. 80,000 80,000 0 Net operating income................... $ 20,000 $ 80,000 $ 60,000

BREAK-EVEN ANALYSIS

A Second key relationship in CVP analysis is the level of activity at which total revenues equal total costs, both fixed and variable. This level of activity is called the break-even point. At this volume of sales, the company will realize no income and suffer no loss. Since no income is involved when the break-even point is the objective, the analysis is often referred to simply as break-even analysis.

Knowledge of the break-even point is useful to management in deciding whether to introduce new product lines, change sales prices on established products, or enter new market areas. Thus this analysis will help the manager to assess the riskiness of a project.

Break even point is the level of sales at which profit is zero. According to this definition, at break even point sales are equal to fixed cost plus variable cost .

Assumption of (BEP)

The Break-even Analysis depends on three key assumptions:

Average per-unit sales price (per-unit revenue)

Average per-unit cost

Monthly fixed costs

The break even point can be :

1. Computed from a mathematical equation

2. Computed by using contribution margin

3. Derived from a cost-volume-profit (CVP) graph

The break-even point can be expressed either in sales dollars or sales units

BREAK-EVEN ANALYSIS

Summary of Nord Corporation Data:Per Bike Percent Per Month



Selling price........................................ $500 100%Variable expenses............................... 300 60% Contribution margin............................ $200 40% Fixed expenses.................................... $80,000

Break-Even point (Mathematical Equation Method)

Q = Break-even quantity in bikes

Profits = Sales – (Variable expenses + Fixed expenses)

Sales =Variable expenses + Fixed expenses + Profits

$500Q = $300Q + $80,000 + $0

$200Q = $80,000

Q = $80,000 ÷ $200 per bike

Q = 400 bikes

X = Break-even point in sales dollars

Sales =Variable expenses + Fixed expenses + Profits

X = 0.60X + $80,000 + $0

0.40X = $80,000

X = $80,000 ÷ 0.40

X = $200,000

Break-Even point (Contribution Margin Method)

At the break-even point, contribution margin must equal total fixed costs. On the basis of this relationship, the break-even point can be computed by using either the contribution margin per unit or the contribution margin ratio.

When the contribution margin per unit is used, the formula to compute break-even point in units is as follows:

Break-even point in units = Fixed costs / Contribution Margin per unit

When the contribution margin ratio is used, the formula to compute break-even point in dollars is :

Break-even point in dollars = Fixed costs / Contribution Margin Ratio

Example:



VOLUME CHANGES AND NET OPERATING INCOME

Contribution income statements are given on this and the following page for monthly sales of 1, 2, 400, and 401 bikes.

Total Per UnitSales (1 bike)....................................... $ 500 $500Variable expenses............................... 300 300 Contribution margin............................ 200 $200Fixed expenses.................................... 80,000 Net operating income (loss)................ $(79,800)

Total Per UnitSales (2 bikes)..................................... $ 1,000 $500Variable expenses............................... 600 300 Contribution margin............................ 400 $200Fixed expenses.................................... 80,000 Net operating income (loss)................ $(79,600)

Note the following points:

1. The contribution margin must first cover the fixed expenses. If it doesn’t, there is a loss.

2. As additional units are sold, fixed expenses are whittled down until they have all been covered.

Total Per UnitSales (400 bikes).................................... $200,000 $500Variable expenses.................................. 120,000 300 Contribution margin............................... 80,000 $200Fixed expenses....................................... 80,000 Net operating income (loss)................... $ 0

Total Per Unit

Sales (401 bikes).................................... $200,500 $500Variable expenses.................................. 120,300 300



Contribution margin............................... 80,200 $200Fixed expenses....................................... 80,000 Net operating income (loss)................... $ 200

Note the following points:

1. If the company sells exactly 400 bikes a month, it will just break even (no profit or loss).

2. The break-even point is:

• The point where total sales revenue equals total expenses (variable and fixed).

• The point where total contribution margin equals total fixed expenses.

3. Each additional unit sold increases net operating income by the amount of the unit contribution margin.

GRAPHIC PRESENTATION

Cost-Volume-Profit (Break-Even) Chart

Cost-volume-profit analysis can be presented graphically as well as in equation form. Many managers prefer the graphic format because the operating profit or loss for any given level of sales can be visually determined.

A Cost-Volume-Profit chat, sometimes called a break-even chart, may assist management in understanding relationships among costs, sales and operating profit or loss.

An effective way to derive the break-even point is to prepare a break-even graph. Because this graph also shows costs, volume, and profits, it is referred to as the cost-volume-profit (CVP) graph.

PREPARING A CVP GRAPH

.

$200

$100

$300

Dol

lars

(000

)

Number of bikes200 400 600

80

Break-even point:400 bikes or

$200,000 in sales

TotalSales

TotalExpenses



1. Volume expressed in units of sales is indicating along the horizontal axis. The range of volume shown on the horizontal axis should reflect the relevant range in which the enterprise expects to operate. Dollar amounts representing total sales and costs are indicated along the vertical axis.

2. A Sales line is plotted by beginning at zero on the left corner of the graph. A second point is determined by multiplying any units of sales on the horizontal axis by the unit sales price of $ 500. For example for 600 bikes of sales, the total sales would be $ 300,000 ( 600 bikes X $ 500). The sales line is drawn upward to the right from zero through the $ 300,000 point.

3. A cost or expenses line is plotted by beginning with total fixed costs, $ 80,000, on the vertical axis. A second point is determined by multiplying any units of sales on the horizontal axis by the unit variable costs and adding the fixed costs. For example 200 bikes, the total estimated costs would be (200 X $ 500 + $ 80,000) $180,000. The cost line is drawn upward to the right from $ 80,000 on the vertical axis through the $ 180,000 point.

4. Horizontal and vertical lines are drawn at the point of intersection of the sales and cost lines, which is the break-even point, and the areas representing operating profit and operating loss are identified.

In the above CVP graph, the dotted lines drawn from the point of intersection of the total sales line and total cost line identify the break-even point in total sales dollars and units. The break-even point is $ 200,000 of sales, which represents a sales volume of 400 bikes. Operating profits will be earned when sales levels are to the right of the break-even point (profit area/operating profit area), and operating losses will be incurred when sales are to the left of the break-even point ( loss area/operating loss area).

BEP & CHANGE OF VARIABLES

EFFECT OF CHANGES IN FIXED COSTS

The break-even point is affected by changes in the fixed costs, unit variable costs, and the unit selling price.

To illustrate assume that

Unit sales price : $ .50 Percentage : 100%

Unit variable cost : $ .40 80%

Unit contribution margin $ .10 20%

Fixed costs : $ 6,000

Changes in fixed expenses cause changes in the break-even point. For example, if we double the $ 1000 monthly rent of the vending machines, what would be the monthly break-even point in number of units and dollar sales?

The fixed expenses would increase from $ 6,000 to $ 7, 000, and the unit contribution margin is $ .10

Break-even sales (units) = Fixed costs / unit contribution margin

= $ 7,000/ $.10 = 70,000 units



Break-even sales (dollars) = Fixed costs / contribution margin ratio

= $ 7,000/ $.20 = $ 35,000

Note that a one-sixth increase in fixed expenses altered the break-even point by one sixth: from 60,000 units to 70,000 units and from $30,000 to $ 35,000. This type of relationship always exists between fixed expenses and the break-even point if everything else remains constant. Increases in fixed costs will raise the break-even point. Likewise, decreases in fixed costs will lower the break-even point.

Although fixed costs do not change in total with changes in the level of activity, they may change because of such factors as changes in property tax rates or salary increases given to factory supervisors.

EFFECTS OF CHANGES IN VARIABLE COSTS

Although unit variable costs do not change with changes in volume of activity, they may change because of such factors as changes in the price of direct materials and increases in wages for factory workers providing direct labor. Increases in unit variable costs will raise the break-even point. Likewise, decreases in unit variable costs will lower the break-even point.

To illustrate, assume that Park Co. is evaluating a proposal to pay an additional 2% commission to its sales representatives as an incentive to increase sales. Fixed costs are estimated at $ 840,000, and the unit selling price, unit variable cost, and unit contribution margin before the additional 2% commission are as follows

Unit selling price : $ 250

Unit variable cost : 145

Unit contribution margin 105

The break-even point is 8,000 units, computed as follows:

Break-even sales (units) = Fixed costs / Unit contribution Margin

= $ 840,000/ $ 105 = 8,000 units

If the sales commission proposal is adopted, variable costs will increase by $ 5 per unit ($ 250 X 2%) This increase in the variable costs will decrease the unit contribution margin by $ 5 (from $ 105 to $ 100). Thus the break even point computed as follows:


= $ 840,000/ $ 100 = 8,400 units

The additional 2% sales commission increases the break-even point by 400 units.

EFFECTS OF CHANGES IN THE UNIT SELLING PRICE



Increases in the unit selling price will lower the break-even point, while decreases in the unit selling price will raise the break-even point.

To illustrate, assume that Graham Co. is evaluating a proposal to increase the unit selling price of its product from $ 50 to $ 60. The following data have been gathered:

Current Proposed

Unit selling price $ 50 $ 60

Unit variable cost 30 30

Unit contribution margin 20 30

Total fixed costs $ 600,000 $ 600,000

The break-even point based on the current selling price is computed as follows:


= $ 600,000/ $ 20 = 30,000 units

If the selling price is increased by $ 10 per unit, the break-even point is computed as follows:


= $ 600,000/ $ 30 = 20,000 units

The $ 10 per unit increase in the selling price increases the unit contribution margin by $ 10. Thus, the break-even point decreases by 10,000 units ( from 30,000 units to 20,000 units)

SUMMARY OF EFFECTS OF VARIABLES ON BREAK-EVEN POINT

A summary of the impact of the equation variables on the break-even point in units is shown below:

Direction of change in variable Direction of change in

Break-even point in units

Unit sales price Increase Decrease

Decrease Increase

Variable cost per unit Increase Increase

Decrease Decrease

Fixed costs Increase Increase

Decrease Decrease

TARGET NET PROFIT ANALYSIS

Management usually sets an income objective for individual product lines. This objective called target net income is extremely useful to management because it indicates the sales necessary to achieve a specified level of income. The amount of sales necessary to achieve target net income can



be determined from each of the approaches used in determining break-even sales.

EXAMPLE: Assume that Nord Corporation’s target profit is $70,000 per month. How many exercise bikes must it sell to reach this goal?

EQUATION METHOD

Q = Number of bikes to attain the target profit

Sales = Variable Expenses + Fixed Expenses + Profits

$500Q = $300Q + $80,000 + $70,000

$200Q = $150,000

Q = $150,000 ÷ $200 per bike

Q = 750 Bikes

(or, in sales dollars, 750 bikes × $500 per bike = $375,000)X = Dollar sales to reach the target profit figure

Sales = Variable Expenses + Fixed Expenses + Profits

X = 0.60X + $80,000 + $70,000

0.40X = $150,000

X = $150,000 ÷ 0.40

X = $375,000

CONTRIBUTION MARGIN METHOD

Fixed expenses + Target profitUnit sales to attain=target profit Unit contribution margin$80,000+$70,000= =750 bikes$200 per bike

Fixed expenses + Target profitDollar sales to attain=target profit CM ratio$80,000+$70,000= =$375,0000.40

MARGIN OF SAFETY

The margin of safety is the excess of budgeted (or actual) sales over the break-even sales. The margin of safety can be expressed either in dollar or percentage form.



Managers use the margin of safety to evaluate current operations or to measure the risk of a new business plan.

The formulas are:

(in dollars)

Margin of Safety = Total budgeted or actual sales − Break even sales

The margin of safety can also be expressed in percentage form.

MOS = Margin of safety in dollars / Total budgeted or actual salesCompany X Company Y

Sales...................................................... $500,000 100% $500,000 100%Variable expenses................................. 350,000 70% 100,000 20% Contribution margin............................. 150,000 30% 400,000 80% Fixed expenses...................................... 90,0 00 340,000 Net operating income............................ $ 60,000 $ 60,000 Break-even point:

$90,000 ÷ 0.30.................................. $300,000$340,000 ÷ 0.80................................ $425,000

Margin of safety in dollars:$500,000 – $300,000......................... $200,000$500,000 – $425,000......................... $75,000

Margin of safety percentage:$200,000 ÷ $500,000........................ 40%$75,000 ÷ $500,000.......................... 15%

CVP Analysis with Multiple Products:

In real life situation, most of the business has more than one product. So far we were discussing the application of CVP analysis with one product. But, the real life situation is different. When we want to use CVP analysis, with multiple products, we assume a certain sales mix of the products. This sales mix is based on either historical data or an estimate of future activity. Once the Sales Mix is estimated, regardless of the level of activity, the ratio of each product in the total mix of the product is assumed to be constant, in the relevant range.

If a company sells multiple products, break even analysis is somewhat more complex .The reason is that the different products will have different selling prices, different costs, and different contribution margins. Consequently, the break even point will depend on the mix in which the various products are sold.

The term Sales Mix(Revenue mix) means the relative combination of quantities of products and services that constitutes total revenues. Managers try to achieve the combination or mix that will yield the greatest amount of profits.



Table of information of ABC company in August

Product 101 Product 102

Units produced and sold 12,000 8,000

Direct Material 22,000 32,000

Direct labor 15,000 12,000

Variable overhead cost 26,000 34,000

Selling price ( per unit) 34 40

total fixed costs 48,000

1. To calculate BEP in September?2. Units to be sold to obtain profit of $3o,ooo?3. To find X= 55% and Y= 45% ?

(1) Formula of BEP in multiple products: BEP=total FC/WAUCM UVC(X)=22,000+15,000+26,000/12,000=5.25 UVC(Y)=32,000+12,000+34,000/8,000=9.75 UCM= P-UVC UCM(X)= 34-5.25 =28.75 UCM(Y)=40-9.75 =30.25 WAUCM =UCM* % of total

WAUCM(X)= 28.75*60%=17.25 WAUCM(Y)=30.25*40%= 12.1 total of sales mix 29.35



BEP=total FC/WAUCM BEP=48,000/ 29.35=1635.5 X=1635.5 *0.6= 981 units Y=1635.5 *0.4= 654 units

(2) Units to be sold to obtain $3o,ooo? BEP=total FC+P/WAUCM BEP=48,000+ 30,000/ 29.35=2,657 X=2,675*0.6=1,605 units Y=2,675*0.4=1070 units (3) X= 55% and Y= 45% ? 28.75*55% =15.8 30.25*45%= 13.6 total of sales mix 29.4

BEP=total FC/WAUCM 48,000/29.4=1632

1632*55%=897 units 1632*45%=734 units

Summary:

Cost behavior analysis examines the relationship between costs and the activities or drivers that cause them. Knowledge of these relationships, which are called cost behavior pattern, is essential for evaluating operations and predicting future costs. To carry out CVP analysis, a clear understanding of Cost Behavior is needed. Costs need to be studied to determine whether they are fixed, variable or mixed.

The most basic use of CVP analysis is breakeven analysis. The contribution margin per unit is the selling price per unit minus the variable cost per unit. The breakeven point can then be found as the fixed costs divided by the contribution margin per unit. The CVP model can be extended to consider the activity level needed to reach target net income. The formula becomes; breakeven point equals the sum of total fixed costs plus target net income divided by the contribution margin per unit. There are two types of Break Even Charts, traditional and Contribution. The margin of safety shows how far above breakeven point a firm is operating. Operational gearing affects the amount of profit due to changes in sales volume. Activity level can be calculated for Target Profits. Another useful feature of the CVP model is that it allows management to assess how sensitive the breakeven point is to other considerations. One can raise or lower revenues or costs and recalculate the breakeven point. Another useful formulation involves the contribution margin ratio. It is the contribution margin per unit divided by the selling price per unit. Then the breakeven point in dollars-that is equal to the Fixed Cost divided by the contribution ratio or the break even point in units multiplied by the Selling Price per unit. Incremental analysis is the examination of only the revenues and costs that change from one



alternative to another. Often incremental decisions can be couched in terms of fixed and variable costs so that CVP analysis could be used to solve the problem. One danger of using CVP analysis is that managers might place too much emphasis on short term actions to improve profits. CVP analysis should be used to make decisions that are consistent with the overall strategy of the firm.


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CHAPTER 3 - Owais Husain PhD.€¦ · Web viewBreak even point is the level of sales at which profit is zero. According to this definition, at break even point sales are equal to