UNIT 13: MARGINAl COSTING - eGyanKosh

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UNIT 13: MARGINAl COSTING

Structure13.0 Objectives13.1 Introduction13.2 Segregation of Mixed Costs13.3 Concept of Marginal Cost and Marginal Costing13.4 Income Statement under Marginal Costing and Absorption Costing13.5 Marginal Costing Equation and Contribution Margin13.6 Profit-Volume Ratio13.7 Managerial Uses of Marginal Costing13.8 Limitations of Marginal Costing13.9 Summary13.10 Key Words13.11 Answers to Check Your Progress13.12 Terminal Questions13.13 Further Readings

13.0 OBJECTIVESThe aims of this unit are:

● to introduce you with the concept of marginal costing; ● to explain the income statement under marginal costing and how it

differs from absorption costing; and ● to discuss the merits and limitations of marginal costing along with

developing a marginal cost equation uses of marginal costing in managerial decisions.

13.1 INTRODUCTIONThe elements of costs can be divided into fixed and variable costs. You have learnt these elements of cost in detail under Unit 2. You have also learnt that there are certain costs which are a combination of fixed and variable costs. These costs are called semi-variable costs. It is necessary to segregate the mixed costs into fixed and variable costs for managerial decisions. In this unit you will study about different methods of segregating mixed costs, the concept of marginal cost and marginal costing and its managerial uses in decision making.

13.2 SEGREGATION OF MIXED COSTSThe elements of cost can be divided into two categories. Fixed and variable costs. Fixed costs are those costs which do not vary but remain constant within a given period of time in spite of fluctuations in production. variable costs changes in direct proportion to the change in output. There

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Marginal Costingare certain costs, which are a combination of fixed, and variable costs. It contains a fixed element as well as a unit cost for variable expenses. Such costs increase with production but the change is less than the proportionate change in production. These costs are called semi-variable or semi-fixed or mixed costs. Example of these costs are depreciation, power, telephone etc. Rent of the telephone is fixed in a given period and per unit call charges is a variable component. For decision making, it becomes necessary to segregate the mixed costs into fixed and variable costs.Methods of Segregating Mixed CostThe following methods are applied to segregate the mixed costs into fixed costs and variable costs:1) Analytical Method: A careful analysis of mixed cost is done to

determine how far it varies with production. Some semi-variable costs may have 60 percent variability while other have 40 percent variability. Accuracy of this method depends upon the knowledge, experience and judgement of the analyst. This method is simple but not scientific.

2) high low Method: This technique was developed by J.H. William. In this method, the difference in two production levels i.e. highest and lowest, are compared out of the various levels. Since the fixed cost component remains constant, any increase or decrease in total semi-variable cost must be attributed to the variable portion. The variable cost per unit can be determined by dividing difference in total semi-variable cost with the difference in production units at two levels.

Illustration 1From the following information, find out the fixed and variable components.

Production (in units) Semi-Variable CostsRs.

100 1500200 2000250 2250300 2500

Highest production is 300 units, then semi-variable costs is Rs. 2500. Lowest production is 100 units, then semi-variable costs is Rs. 1500.

Variable Cost Per unit = Difference in CostsDifference in Volume

= Rs. 2500 – Rs. 1500300 – 100

= Rs. 1000200

= Rs. 5

Total semi-variable costs = Fixed Cost + Variable costs per unit production 2500 = F + Rs. 5 × 300 units F = Rs. 1000

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Marginal Costing and Cost Volume Profit Analysis

High-low method is based on observations of extreme data, hence the result may not be very accurate as it is based on extreme points and may not be true for normal situation.Scatter Diagram MethodIn this method, production and semi-variable cost data are plotted on a graph paper and tentative line of best fit is drawn. The following steps are involved:

● Volume of production is plotted on x-axis and semi-variable costs on y-axis.

● Corresponding semi-variable costs of each volume of production are plotted on a graph.

● A line of best fit is drawn through the points plotted. The point where this line intersects with y-axis, depicts the fixed cost.

● Variable cost can be determined at any level by subtracting the fixed cost element. The slope of the total cost curve is the variable cost per unit

Total Semi-Variable Cost

Semi Variable Cost

Fixed Cost

Output

The accuracy of line of best fit, depends upon the judgement and experience of the analyst. One may draw slightly up or slightly down, the intercept on y-axis will change or two analyst may draw a line having different slopes. This method involves analyst’s subjectivity and may not give accurate results.Method of least Square:This method is based on econometric technique, in which line of best fit is drawn with the help of linear equations.The equation of a straight line is y = a + b xWhere ‘a’ is the intercept on y-axis and ‘b’ is the slope of the line. Hence ‘a’ is the fixed cost component and ‘b’ is the slope or tangent of the line or variable cost per unit. From the above equation, two equation can be drawn. ∑y = na + b ∑ x ∑ xy = a∑ x + b ∑ x2

Solving the equations, will give us the value of ‘a’ (fixed cost) and ‘b’ (variable cost per unit).

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Marginal CostingIllustration 2From the following semi-variable cost information, compute the fixed cost and variable cost components.

Production(Units)

Semi-variable(Rs.)

100 1200200 1350150 1250190 1380180 1375

Solution

Month Production X

Semi-variable y X2 Xy

April 100 1200 10000 120000May 200 1350 40000 270000June 150 1250 22500 187500July 190 1380 36100 262200August 180 1375 32400 247500Total ∑X = 820 ∑Y = 6555 ∑X2 141000 ∑XY = 1087200

∑y = na + b ∑ x ∑ xy = a∑ x + b ∑ x2

Solving these equations 6555 = 6 a + 820 b 1087200 = 820 a + 141000 b a = Rs. 1004.632 b = Rs. 1.868After segregating the mixed costs into fixed cost and variable costs, the fixed component is added to fixed costs and variable component to variable costs. Now we have only two costs i.e. fixed costs and variable costs.

13.3 CONCEPT OF MARGINAl COST AND MARGINAl COSTING

The term ‘Marginal Cost’ is defined as the amount at any given volume of output by which the aggregate costs are changed if the volume of output is increased or decreased by one unit. In this context a unit may be single article, a batch of articles or an order. It is the variable cost of one unit of a product or a service. For example, the cost of 100 articles is Rs. 50,000 and that of 101 articles is Rs. 50,450, the marginal cost is Rs. 450 (i.e., Rs. 50,450 –50,000).Thus, the total cost is the aggregate of fixed cost and variable cost and if production is increased by one more unit, its cost can be computed as follows:

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TCn = FC + vQ …(1) TCn + 1 = FC + v (Q +1) …(2) ∴ MC = v(Subtracting 1 from 2)Marginal costing may be defined as “the ascertainment of marginal costs and of the effect on profit of changes in volume or type of output by differentiating between fixed costs and variable costs”. The concept of marginal costing is based on the behaviour of costs that vary with the production level. In marginal costing, costs are classified into fixed and variable costs. Even semi-variable costs are analysed into fixed and variable. The stock of work-in-progress and finished goods are valued at marginal cost. Marginal cost is equal to the increase in total variable cost because within the existing production capacity, an increase in variable one unit of production will cause an increase in variable costs only. The fixed costs remain same. In marginal costing, only variable costs are considered in calculating the cost of product, while fixed costs are treated as period cost which will be charged against the revenue of the period. The revenue generated from the excess of sales over variable costs is called contribution. Mathematically, Total sales – Variable costs = Contribution Sales = Variable cost + Contribution Sales – Variable cost = Fixed cost ± profit/loss Contribution – Fixed costs = ProfitFor example, the selling price of a product is Rs. 30 per unit and its variable cost is Rs. 20, the contribution per unit is Rs. 10. Let us take the following illustration how the profit is determined by using marginal costing technique.Illustration 3From the following particulars find out the amount of profit earned during the year using the marginal costing technique :

Product A B COutput (units) 10,000 20,000 60,000Selling Price (per unit) Rs.10 Rs. 10 Rs.5Variable cost (per unit) Rs. 6 Rs. 7. 50 Rs. 4.5 0

Total Fixed Cost Rs. 80,000.Solution:

Statement of Cost and Profit (Marginal Costing)Product

ARs.

BRs.

CRs.

DRs.

Sales Revenue 100,000 200,000 300,000 600,000Marginal Costs 60,000 1,50,000 2,70,000 4,80,000Contribution 40,000 50,000 30,000 1,20,000Fixed Costs ---- ---- ---- 80,000Profit ---- ---- ---- 40,000

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Marginal CostingThus the technique of marginal costing assumes that the difference between the aggregate value of sales and the aggregate value of variable costs or marginal costs, provides a fund (called contribution) to meet the fixed costs and balance is the profit. The concept of contribution is a very useful tool to management in managerial decisions making.

13.4 INCOME STATEMENT UNDER MARGINAl COSTING AND ABSORPTION COSTING

In marginal costing, the stock of work-in-progress and finished goods are valued at marginal cost not including the fixed costs. Whereas under full costing or absorption costing, the cost of product is determined after considering both fixed and variable costs.Let us explain the difference in the two methods with the help of an illustration given below :Illustration 4Given Production = 100,000 units Sales 90,000 units @ Rs. 3 per unit Variable manufacturing costs = Rs. 2 per unit Fixed overheads = Rs. 50,000 Selling and distribution costs = Rs. 10,000 of which Rs. 4000 is

variable Prepare the income statement under absorption costing and marginal

costing.Solution:

Income Statement(Under Absorption Costing)

Rs. Rs.

Sales 90,000 units @ Rs. 3 2,70,000

Less: Manufacturing costs :

Variable costs100,000 units @ Rs. 2 200,000

Fixed overheads 50,000

2,50,000

Less : Closing stock 10,000 units2,50,000 × 10,000

1,00,000

25,000 2,25,000

Gross margin (Rs. 2,70,000 – Rs. 2,25,000) 45,000

Less : Selling and distribution costs 10,000

Profit (Rs. 45,000 – Rs. 10,000) 35,000

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Income Statement(Under Marginal Costing)

Rs. Rs.

Sales 90,000 units @ Rs. 3 per unit 2,70,000

Less : Marginal Costs Variable manufacturing costs :100,000 units @ Rs. 2 per unitLess : Closing inventory of 10,000 units @ Rs. 2

200,000

20,000

1,80,000

Add : Variable selling and distribution costs 4,000 1,84,000

Contribution(Sales Rs. 2,70,000 – Variable Cost Rs. 1,84,000)

86,000

Less Fixed Costs : Fixed overheads Fixed selling and distribution

50,0006,000 56,000

Profit (Rs. 86,000 – Rs. 56,000) 30,000

The profit computed under marginal costing is Rs. 5000 less in comparison to full costing. The closing stock under absorption costing is valued at Rs. 2.50 per unit (fixed and variable cost) whereas under marginal costing it is Rs. 2 per unit (only variable cost). The difference is of Rs. 0.50 per unit on a closing inventory of 10,000 units which amounts to Rs. 5,000.We can draw the following inferences:1) When all costs are variable costs, then both the methods will report

the same net income.2) When sales and production are in balance (no opening or closing

stock) both the methods will again report the same profit.3) When there is a closing stock (and no opening stock) the net income

reported under absorption costing will be higher than that reported under marginal costing. Thus the technique of absorption costing may lead to odd results particularly for seasonal business in which stock level fluctuates widely from one period to another.

4) When there is a opening stock (and no closing stock), the profit under marginal costing will be more than the profit reported under absorption costing.

5) When the closing stock is more than the opening stock (presuming that both opening and closing stocks are valued at same price), profit reported under marginal costing will be less than the profit reported under full costing or absorption costing.

The technique of absorption costing may also lead to rejection of a profitable business. An order at a price which is less than the total cost may be refused, though this order may be profitable. Look at the following illustration:

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Marginal CostingIllustration 5XYZ Ltd. has a capacity to production 100,000 units and company is presently operating at 70% capacity. The company is selling its product at Rs. 120 each. The cost information is as follows.

Per Unit TotalVariable Cost Rs. 60 Rs. 42,00,000Fixed Costs Rs. 30 Rs. 21,00,000Total Rs. 90 Rs. 63,00,000

The company has received an order for 20,000 units at Rs. 70 per unit. Should the order be accepted or rejected.SolutionUnder absorption costing, cost includes both fixed as well as variable cost. Thus the cost per unit is Rs. 90 and the order at Rs. 70 per unit be rejected. Under marginal costing, only variable costs are considered. When company will supply extra 20,000 units, only variable cost will increase and fixed cost will remain same.The fixed cost of Rs. 21,00,000 is already recovered by operating at 70% installed capacity. Thus the order will increase the profit.

Before Order Rs.

Order Rs. After Order Rs.

Sales 70,000 @ Rs. 120

84,00,000 14,00,000(20,000 × Rs. 70)

98,00,000

Variable costs @ Rs. 60

42,00,000 12,00,000 54,00,000

Contributions 42,00,000 200,000 44,00,000

Fixed costs 21,00,000 — 21,00,000

Profit 21,00,000 200,000 23,00,000

Accepting the order enhances the profit by Rs. 200,000.The difference between absorption costing and marginal costing arises mainly due to recovery of fixed overheads and valuation of inventory.Valuation of StocksIn absorption costing, stocks of work-in-progress and finished goods are valued at works cost or cost of production, which includes fixed costs also. Where as in marginal costing, stocks are valued at marginal cost or variable cost only. This method does not result in carrying over of fixed cost of one period to another, as it happens in the case of absorption costing. In other words, valuation of stock is done at a lower price in marginal costing, thus profit will differ under two methods of costing.Absorption of OverheadsIn absorption costing, both fixed and variable overheads are charged to production while in marginal costing only variable overheads are charged to production. Thus under absorption costing, there will be either over-

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absorption or under absorption of fixed overheads, where as in marginal costing, the actual amount of fixed overheads is wholly charged to contribution. Hence profit will differ.Let us see following illustration how the profit fluctuates under both these methods when there is opening and closing stock of inventory:Illustration 6XYZ Ltd. produces one product. Its quarterly budget of sales, cost of sales and production is as follows:

quarterly Budget Total Rs.

Per Unit Rs.

Sales 40,000 units @ Rs. 3 1,20,000 3Cost of Sales : Rs.Variable Manufacturing Costs 60 ,000 1.50Fixed Manufacturing Costs 12 ,000 0.30

Total Cost72,000 1.80

Gross Profit 48,000 1.20 Less Selling and Distribution Costs (Fixed) 28,000 0.70 Net Operating Profit 20,000 0.50

The actual production and sales on a quarterly basis is as follows: (units)

quarter I quarter II quarter III quarter IVOpening Inventory 0 0 9,000 2,000Production 40,000 45,000 35,000 38,000Sales 40,000 36,000 42,000 40,000Closing Inventory 0 9,000 2,000 0

Prepare quarterly income statement under absorption costing and marginal costing.Solution

Income Statement (under Absorption Costing)

quarter I Rs.

quarter II Rs.

quarter III Rs.

quarter IV Rs.

Sales 1,20,000 1,08,000 1,26,000 1,20,000

Manufacturing Costs :Opening inventory* 0 0 16,200 3,600 Variable Costs 60,000 67,500 52,500 57,000 (Rs. 1.50 per unit) Fixed overheads 12,000 12,000 12,000 12,000 Cost of goods 72,000 79,500 80,700 72,600Less Closing Stock* 0 16,200 3,600 0Cost of Sales 72,000 63,300 77,100 72,600Gross Profit (Sales – Cost of Sales) 48,000 44,700 48,900 47,400Less Fixed Selling Costs 28,000 28,000 28,000 28,000Profit 20,000 16,700 20,900 19,400

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Marginal Costing*Opening and closing stock is valued at full cost i.e. fixed and variable which is 0.30 + 1.50 respectively = Rs. 1.80.

Income Statement (Under Marginal Costing)

quarter I

quarter II

quarter III

quarter IV

Sales 1,20,000 1,08,000 1,26,000 1,20,000Costs of Sales : Cost of opening inventory* 0 0 13,500 3,000 Variable Mfg. Exp. 60,000 67,500 52,500 57,000 Cost of good available for sale 60,000 67,500 66,000 60,000 Less Closing Stock* 0 13,500 3,000 0Cost of Sales : 60,000 54,000 63,000 60,000 Contribution (Sales – Cost of Sales) 60,000 54,000 63,000 60,000Less Fixed Costs : Fixed Mfg. Cost 12,000 12,000 12,000 12,000 Fixed Selling Exp. 28,000 28,000 28,000 28,000Net Profit 20,000 14,000 23,000 20,000

*Opening stock and closing stock is valued at marginal cost i.e. Rs. 1.50 per unit.The main features of marginal costing are:1) All costs are classified in fixed and variable costs. Variable cost per

unit remains same and fixed costs remain same in total regardless of the changes in production.

2) Fixed costs are considered period costs and variable costs are considered as product costs. Hence fixed costs are not included in product cost.

3) Stock of work-in progress and finished goods are valued at marginal costs or variable costs.

4) The difference in the value of opening stock and closing stock does not affect the unit cost of production as all the product costs are variable costs.

Direct Costing and Marginal Costing are used inter-changeably. As both the techniques are more or less same. In direct costing, costs are classified into direct and indirect costs. Direct costs are those which can be directly allocated to cost unit or cost centre while indirect costs can not be allocated to cost unit or costs centre directly. The only difference between the two is that some fixed cost could be considered to be direct costs under certain circumstances.

13.5 MARGINAl COSTING EqUATION AND CONTRIBUTION MARGIN

In full costing or absorption costing, all costs are classified into three broad classes- manufacturing, administrative and selling. In the income statement, manufacturing costs are deducted from the sales revenue to get the gross margin or gross profit then administrative and selling expenses are deducted from gross margin to arrive at net operating income. Under

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marginal costing, costs are clarified into fixed and variable expense. All variable costs, whether they are manufacturing, administrative or selling are deducted from sales revenue. The difference is called contribution margin or marginal income. All fixed costs are recovered from the contribution and balance is profit or loss.Illustration 7Two companies A Ltd. and B Ltd. sell the same type of product. Their income statement are as follows:

A ltd.Rs.

B ltd.Rs.

Sales 2,40,000 2,40,000Less Variable Cost 96,000 1,20,000Fixed Costs 64,000 40,000Profit 80,000 80,000

State which company is likely to earn greater profit if there is: (i) heavy demand, (ii ) poor demand for its products.Solution

A ltd.Rs.

B ltd.Rs.

Sales 2,40,000 2,40,000Variable Cost 96,000 1,20,000Contribution 1,44,000 1,20,000P/V Ratio (Contribution ÷ Sales) 0.60 0.50

In case of A Ltd., every sale of Rs. 100 gives a contribution of Rs. 60 whereas in case of B Ltd. every sale of Rs. 100 provides a contribution of Rs. 50. In case of heavy demand, profit of A Ltd. will rise much faster in comparison to B Ltd. During poor demand or decline in sales of Rs. 100 will lead to decline in contribution in A Ltd. and B Ltd. by Rs. 60 and Rs. 50 respectively.Mathematically, Sales = Variable cost = + Fixed cost ± Profit. Sales – Variable cost = Fixed Cost ± Profit Sales – Variable cost = Contribution Contribution – Fixed Cost ± Profit.To make profit, contribution should be greater than fixed cost. Further, to maximize profit, contribution should be maximized. When contribution is equal to fixed cost, then a firm is at ‘no profit no loss point’ called break even point which you will study in detail under Unit 14.

13.6 PROFIT-VOlUME RATIOProfit volume ratio or contribution to sales ratio is a relationship between contribution and sales. It is the ratio between contribution per product to turnover of the product. Mathematically,

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Marginal Costing P/V Ratio = Sales – Variable Cost

Sales

= ContributionSales

= 1 – Variable CostSales

= Fixed Cost + ProfitSales

= Change in contributionChange in sales

= Change in ProfitChange in sales

Profit-volume ratio depicts the soundness of the company’s product. Profit volume analysis is used to determine break even for a product, a group of products and to know how the profit changes if changes are made in price, volume, costs or any combination of these. But P/V graph does not show how cost varies with the change in the level of production. The profit volume ratio and contribution has a direct relationship. The profit volume ratio can be improved by improving the contribution and contribution can be improved by :i) increasing the selling priceii) decreasing the marginal or variable costs.iii) putting more emphasis on those products which have higher profit

volume ratio.Profit Volume GraphFor preparing the profit volume graph, following steps are involved :

● Sales are depicted on x-axis and profit and loss on y-axis. ● X-axis divides the graph into two parts. The lower area of the x-axis

depicts loss and upper area depicts the profit. When sales is zero, loss is equal to fixed cost.

● At a particular level of sales volume, the profit is depicted on y-axis. Both the points are joined by a straight line called profit line.

● The point where profit line inter-sects the x-axis is called the break even point.

● The angle between sales line and profit line is called angle of incidence.Illustration 8Construct profit volume graph with the help of the following data: XYZ Ltd. reports the following results on 31st March, 2004 : Sales @ Rs. 3 each Rs. 3,00,000/- Variable cost Rs. 2 each Rs. 2,00,000/- Fixed cost Rs. 50,000/-Construct the P/V chart.

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Solution P/V ratio = Contribution

Sales Contribution = Sales – Variable Cost = Rs. 3,00,000 – Rs. 2,00,000 = Rs. 1,00,000.

–50,000 Fixed cost

Contribution line

Loss area BEP 200,000

+50,000

Y

0 Sales volume

Profit-Volume Graph

Profit

Cos

t/Rev

enue

On X-axis, OX represents sales volume, on Y-axis OY represents profit while OY’ loss. OFC represents fixed cost. The line FCP represents Fixed cost and profit as well as total contribution. BE is the break-even point. The area BEX represents margin of safety while XBEP profit area. PBEX is the angle of incidence. You will be acquainted with all these terms in detail in Unit 14.Where a company is manufacturing more than one product of varying profitability, the profit-volume graph can be constructed as follows :Illustration 9XYZ ltd. produces three products X, Y and Z. The cost data is as follows:

Fixed Cost Rs. 25,000X y Z

Rs. Rs. Rs.Sales 50,000 25,000 30,000Variable Costs 20,000 20,000 18,000You are required to

i) Calculate the Profit- Volume ratio of each products, andii) Prepare a profit- volume ratio chart.

SolutionX

Rs.y

Rs.Z

Rs.Total Rs.

Sales 50,000 25,000 30,000 105,000Variable Costs 20,000 20,000 18,000 58,000Contribution 30,000 5,000 12,000 47,000Profit - volume ratio 3/5 or

0.605/25 or

0.2012/30 or

0.4047/105 or

0.45

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Marginal CostingThe sequence should be X, Z and Y. (Descending order of P/V Ratio)Product Sales Variable

CostContribution Cumulative

ContributionFixed Costs

Cumulative Profit

Cumulative Sales

X 50,000 20,000 30,000 30,000 25,000 5,000 50,000

Z 30,000 18, 000 12,000 42,000 25,000 17,000 80,000

Y 25,000 20,000 5,000 47,000 25,000 22,000 105,000

Profit-Volume Graph (Multi-products)

Profi

t (R

s. ‘0

00)

120

–30

–20

–10

10

20

30

Y

Y

z

x

20 40 60 80 100 Sales (Rs. ‘000)

13.7 MANAGERIAl USES OF MARGINAl COSTING

Marginal Costing is a useful tool to management in taking various policy decisions, profit planning and cost control. Following are a few of the managerial problem where marginal costing is helpful in decision making:1) Price Fixation2) Accepting Special Order and Exploring Additional Markets3) Profit Planning4) Key Factors or Limiting Factor5) Sales Mix Decisions6) Make or Buy Decisions7) Adding or Dropping Decisions8) Suspension of Activities1) Price FixationUnder marginal costing, fixed costs are ignored and price is determined on the basis of variable costs (marginal). In normal business conditions, the price fixed must cover full costs otherwise firm will incur losses. In certain circumstances like trade depression, dumping, seasonal fluctuation in demand, highly competitive market etc. pricing is fixed with the help of marginal costing rather than full costing.

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During trade depression, the price may go down even below the full cost of the product. In such case, the management has to decide whether to close down the production activities until the recession is over or continue the production activities. In case, the production activities are closed down, the firm will incur loss equal to its fixedcost or un-escapable costs. The main emphasis of management is to minimise its losses. The firm should continue its production activities so long as the selling price is more than the marginal costs because any contribution earned will help in recovery of the fixed costs which results in reduction of loss.Dumping means selling the product in foreign market at a price less than its total cost. The firm recover its fixed cost from the domestic market and marginal cost of the product becomes the basis for price fixation. Similarly if the firm produces product of seasonal demand or perishable goods marginal costing is more useful technique than full costing.Suppose the marginal cost of a product is Rs. 50 per unit and fixed cost is Rs. 200,000 per annum. Selling price of the product is Rs. 55 per unit and 10,000 units can be sold at this price.

Per Unit TotalRs. Rs.

Marginal Cost 50.00 500,000

Fixed Cost 20.00 200,000

Total Cost 70.00 700,000

The selling price is less than the total cost of the product, yet is beneficial to continue the production activity. The contribution earned is Rs. 5 per unit and total contribution is Rs. 50,000. This will reduce the loss by Rs. 50,000. If the firm discontinue production activity, then loss will be Rs. 200,000 (Fixed Cost). Hence the firm should continue production activity.If the selling price is less than marginal cost, loss will be more than the fixed costs. Hence the firm should fix the price equal to or above the marginal cost in special circumstances. Production should be discontinued if the price obtained is below the marginal cost so that the loss may not be more than fixed costs.2) Accepting Special Order and Exploring Additional MarketsIn case of spare capacity, a firm can increase its total profits by accepting an special order above the marginal cost and at a price lower than its regular selling price. The additional contribution earned from the special order will be the additional profit to the firm. When additional order is accepted at a price below prevailing price to utilise idle capacity, it should be carefully seen that it will not affect the normal market and goodwill of the company. The special order from a local dealer should not be accepted as it will affect the relationship with other dealers.Illustration 10The company is operating at 60% of the installed capacity (total capacity of 10,000 units per month). Its monthly fixed expenses is Rs. 6 lakhs per month. The other costs are:

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Marginal CostingDirect Material Rs. 55 per unitDirect Labour Rs. 10 per unitVariable Expenses Rs. 25 per unit

The company has invested Rs. 1 crore in the business and is currently earning a return of 7.2 per cent per annum before taxes. The managing director is prepared to accept new business at any price which will raise the return on investment to 20 per cent before taxes. A special offer was received for 4000 units every month if the product is supplied at Rs. 120 per unit. Would you advise the company to accept the offer?Solution

Total Capacity = 10,000 units per monthPresent Production = 6000 units per monthFixed Cost = Rs. 6 lakhs per monthMarginal Cost = Rs. 90 per unitReturn on Investment = 7.2 per centAnnual Profit = Rs. 7,20,000Profit per month = Rs. 60,000

The selling price per unit will be

Output 6000 unitsPer Unit (Rs.) Total (Rs.)

Direct Cost 90 5,40,000

Fixed Cost 100 6,00,000Total Cost 190 11,40,000Profit 10 60,000Selling Price 200 12,00,000

The total cost of the product is Rs. 190 per unit. The company has received the offer at Rs. 120 per unit. It appears that if the offer is accepted, the company will loose Rs. 70 per unit. Hence the offer be rejected. But this analysis is fallacious as fixed cost will not change when production is increased. Here only variable cost which changes. Thus the selling price should be compared with the marginal cost which is Rs. 90 per unit. If the order is accepted each unit will provide Rs. 30 contribution towards profit. If the order is accepted then the profit position will be as follows:

Output Present 6000 units Order 4000 units 10,000 units Total Rs.

Per Unit Rs.

Total Rs.

Per Unit Rs.

Total Rs.

Sales 200 12,00,000 120 4,80,000 16,80,000 Variable Cost 90 5,40,000 90 3,60,000 9,00,000 Contribution 110 6,60,000 30 1,20,000 7,80,000 Fixed Costs 100 6,00,000 — — 6,00,000 Profit 10 60,000 30 1,20,000 1,80,000

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Marginal Costing and Cost Volume Profit Analysis Return on Investment = 1,80,000 × 12 × 100

1 crore = 21.6%

The above statement provides that if the company accepts the offer, it will earn additional Rs. 1,20,000 per month. The return on investment is enhanced from 7.2 per cent to 21.6%. Before accepting the offer, following factors must be evaluated :

● The lower selling price for this offer, should not affect adversely the regular customers and goodwill of the company.

● Decrease in price should not create a doubt in the customer’s mind about the quality of the product.

● No possibility of any other more profitable use of unutilised capacity.3) Profit PlanningMarginal costing is very helpful in determining the level of activity to achieve the planned profits. The separation of costs in to fixed and variable aid management further in planning and evaluating the profit resulting from a change in volume, a change in selling price, a change in fixed costs and variable costs.Illustration 11XYZ Ltd. is manufacturing and selling a product whose cost data is as follows:

Per Unit TotalRs. Rs.

Current Sale (20,000 units) 20 400,000Variable Cost (20,000 units) 10 200,000Fixed Cost 100,000Profit 100,000

It is proposed to reduce the selling price due to competition by 10 per cent. How many units are to be sold to maintain the present profit level ?SolutionNew selling price after 10% reduction = Rs. 18 Contribution = Selling price – Variable Cost = Rs.18 – Rs.10 = Rs. 8 per unit Desired Contribution = Fixed Cost + Profit = Rs. 100,000 + Rs.100,000 = Rs. 200,000

Sales required to earn desired profit (units) = Desired ContributionContribution Per Unit

= Rs. 2,00,000Rs. 8

= 25,000 units

Desired Sales (Value) = Fixed Cost + Desired profit P/V ratio

= Rs. 2,00,000 × Rs. 18Rs. 8

= Rs. 4,50,000

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Marginal Costing4) key Factors or limiting FactorThe marginal costing technique provides that the product with highest contribution per unit is preferred. This inference holds true so long as it is possible to sell as much as it can produce. But sometimes an organisation can sell all it produces but production is limited due to scarcity of raw material, labour, electricity, plant capacity or capital.These are called key factors or limiting factors. A key factor or limiting factor puts a limit on production and profit of the firm. In such situation, management has to take a decision whose production is to be increased, decreased or stopped. In such cases,selection of the product is done on the basis of contribution per unit of scarce factor of production. The key factor or scarce factor should be utilized in such a manner that contribution per unit of scarce resource is the maximum.

Mathematically, Profitability = ContributionKey Factor

For example, if raw material is the limiting factor, the profitability of each product is determined by contribution per Kg of raw material. If machine capacity is a limiting factor then contribution per machine hour is calculated. It electricity is the limiting factor, then contribution per unit of electricity of each product is calculated.Illustration 12A company produces two products X and Y. The cost information is as follows:

Product X ySale Price Rs. 20 Rs. 15Variable Cost Rs. 10 Rs. 8Required Machine hours per unit 2 1Sales Potential (Units) 1000 1200Available production hours 2000

Calculate and find the best product mix.Solution

Product X ySale Price Rs. 20 Rs. 15

Variable Cost Rs. 10 Rs. 8

Contribution Rs. 10 Rs. 7

Required machine hours per unit 2 1

Contribution per machine hour Rs. 5 Rs. 7Product Y gives the highest contribution per machine hours. The best solution would be to produce Y to the maximum extent that can be sold and remaining hours should be devoted for production of X. Hence 1200 units of Y be produced and remaining 800 hours be devoted to product X which means 400 units of X. Thus the optimum mix is 400 units of X and 1200 units of Y.

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5) Sales Mix DecisionIn marginal costing, profit is calculated by subtracting fixed cost from contribution. It means management should try to maximise the contribution. When a business firm produces variety of product lines, then problem of best sales mix arises. The best sales mix is that which yields the maximum contribution. The products which gives the maximum contribution are to be retained and their production should be increased keeping in view the demand. The products, which yield less contribution, should be reduced or closed down depending upon the situation.Illustration 13State which of the following sales mix you would recommend to the management?

Elements of cost XRs.

yRs.

Sale Price 200 150

Direct Material 100 80

Direct Labour 40 30

Variable Overheads 20 20

Fixed Overheads : Rs. 100,000 Alternative Sales Mix :a) 2000 units of X and 2000 units of Yb) 3000 units of X and 1000 units of Yc) 4000 units of X and Nil units of YSolution

Product X yRs. Rs.

Sale Price 200 150Direct Material 100 80Direct Labour 40 30Variable Overheads 20 20Contribution per unit 40 20

Choice of Sales Mix :

Sales Mix (1) : Contribution on Rs.2000 units of X @ Rs. 40 per units = 80,0002000 units of Y @ Rs. 20 per units = 40,000

Total Contribution = Rs. 120,000Sales Mix (2) : Contribution on Rs.

3000 units of X @ Rs. 40 per unit = 120,0001000 units of Y @ Rs. 20 per unit = 20,000

= Rs. 140,000Sales Mix (3) : Contribution on

4000 units of X @ Rs. 40 per unit = Rs. 1,60,000

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Marginal CostingSales mix 3 gives the highest contribution and is the best mix among the above alternatives.6) Make or Buy DecisionA particular component used in the main product may be purchased or may be manufactured in its own factory by utilising the idle capacity of the existing facilities. In such make or buy decision, the marginal cost of manufacturing in the unit is compared with the purchase price from the market. If marginal cost is less than the purchase price, then the component should be manufactured in its own unit, otherwise it should be purchased from the market. Fixed expenses are not taken in the cost of manufacturing on the assumption that they have been already incurred, the additional cost involved is only variable cost.Illustration 14XYZ Ltd. produces a variety of products and components. Their cost information and purchase prices are as follows:

X y Z

Rs. Rs. Rs.

Direct Material 12 4 2

Direct Labour 4 16 6

Variable Overhead 2 4 4

Fixed Cost 6 20 10

Bought out price 15 45 25

One of these products can be produced in the factory and rest two are to be bought from outside. Select the component which should be bought from outside ?Solution

Comparative Cost Sheet

XRs.

yRs.

ZRs.

Direct Material 12 4 2Direct Labour 4 16 6Variable Overhead 2 4 4Marginal Cost 18 24 12Bought out price 15 45 25Saving (–) or increase (+) –3 +21 +13

It is clear from the above statement that Y should be produced in its own unit as its marginal cost is much lower than the purchase price and other two components i.e., X and Z be purchased from the market.7) Adding and DroppingAn organisation may have a number of product lines or departments. Certain product lines or departments may turn out to be unprofitable with the passage

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of time or due to technological developments. Production of such products or departments can be discontinued. The marginal costing approach assist in these situations to take a decision. It helps in the introduction of a new product line and work as a good guide for deciding the optimum mix keeping in mind the available resources and demand of the product. The contribution of different products or departments is to be compared and the product or department whose P/V ratio is the lowest is to be dropped out. The following illustration explains how marginal costing technique helps the management in decision making.Illustration 15A company manufactures three products whose cost data is given below.

Product X(Rs.)

y(Rs.)

Z(Rs.)

Selling Price 100 80 90Direct Material 20 12 16Direct Labour 16 16 16Variable Overhead 16 12 15

The management wants to drop out Product Y as it is not profitable. What advice would you like to give the management ?Solution

Comparative Cost Statement

Product X(Rs.)

y(Rs.)

Z(Rs.)

Selling Price 10 0 80 90

Less Marginal Cost :Direct Material 20 12 16Direct Labour 16 16 16Variable Overhead 16 52 12 40 15 47

Contribution 48 40 43

P/v ratio 48 % 50% 47.77%

Product Y is the most profitable product line as its P/V ratio is the highest when compared to products X and Z.8) Suspension of ActivitiesDuring trade recession and cut throat competition the demand of the product is not adequate to cover the fixed costs, management may consider to suspend the operations for the time being. If certain portion of fixed expenses is escapable e.g. salary of temporary staff then size of contribution should exceed the escapable fixed costs. In some units when production is restarted after suspension, some additional or special costs are incurred like overhauling of the plant and machinery. These costs are called additional costs of shut down. These costs are deducted from the escapable fixed costs and amount of contribution is compared with the net escapable fixed costs. If the contribution is greater than the net escapable fixed cost, the production should be continued and vice versa.

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Marginal Costing Shut down point = Net Escapable Fixed Costs

Contribution per unit Net escapable fixed cost = Total fixed cost for the period – unescapable

fixed costs + additional costs of shut down.Illustration 16XYZ Ltd. is manufacturing 200,000 boxes per annum when working at normal capacity. The cost information is as follows :

Rs.Direct Material = 8.00Direct Labour = 2.00Variable Overheads = 3.00Fixed Overheads = 3.00Total Cost = 16.00

The selling price is Rs. 20 per unit. It is estimated that in the next quarter only 10,000 units can be produced and sold. Management plans to shut down the plant and estimating that fixed cost can be reduced to Rs. 80,000 for the quarter. The fixed overheads are incurred uniformly throughout the year. Additional cost of plant shut down is Rs. 10,000.From the above information you are requested to decide the following:a) Whether the plant should be shut down for a period of three monthb) Calculate the shut down point for three months.SolutionRs.a) Sale Price 16 Marginal Costs : Rs. Direct Material 8 Direct Labour 2 Variable Overheads 3 13 Contribution : Rs. 3 per unit. Fixed Overhead = Rs. 3 × 200,000 = Rs. 600,000 per annum

Fixed overheads for quarter = Rs. 600,0004 = Rs. 1,50,000

If plant is operated, the loss is : Rs.

Total contribution on 10,000 units (10,000 units × Rs. 3) = 30,000Fixed Cost = 150,000Loss (Fixed cost – Contribution) = 120,000If plant is closed, then loss will be :Unescapable fixed cost = Rs. 80,000Addition shut down cost = Rs. 10,000Total Loss = Rs. 90,000

As is evident from the above calculations that the plant should be closed down for the quarter, so that the loss will be reduced by Rs. 30,000.

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b) Shut down point Net Escapable Fixed Cost = Total Fixed Cost for the period – Shut

down costs + additional costs. = Rs. 150,000 – Rs. 80,000 + Rs. 10,000 = Rs. 80,000

Shut down point = Net Escapable Fixed CostContribution Per Unit

= Rs. 80,000Rs. 3

= 26,667 units per quarter

For suspension of business activity, only costs should not be taken into consideration, there are other factors also like, employees interest, fear of plant obsolescence, loss of customers in future, government action, perishable raw material and company is having a huge stock of material, etc.Check your ProgressA) Fill in the blanks: i) The technique of marginal costing is based on classification of

costs in to _________ and _________. ii) Contribution is the sum of _________ and _________. iii) In marginal costing, closing stock is valued at _________. iv) Profit-volume ratio is the relationship between _________ and

_________. v) In absorption costing, closing stock is valued at _________ .B) State whether each of the following statement is True or False. i) Fixed cost per unit remains constant. ii) Variable cost per unit remains constant iii) Absorption costing is not as suitable for decision making as

marginal costing is iv) Semi-variable costs consists of fixed costs and factory costs v) Fixed costs are not taken in to consideration in valuation of

work-in-progress in marginal costing C) From the following choose the most appropriate answer 1) Contribution margin is also known as a) Gross profit b) Net profit c) Earning before tax d) Marginal income 2) Contribution is the difference between a) Sales and variable cost b) Sales and fixed cost c) Sales and total cost

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Marginal Costing d) Factory cost and profit 3) When fixed cost is Rs. 20,000 and Profit volume ratio is 25 per

cent, then break even point will occur at a) Rs. 5000 b) 5000 units c) Rs. 80,000 d) 80,000 units 4) Period cost means a) Variable cost b) Fixed costs c) Prime cost d) Factory cost 5) If profit-volume ratio is 25 per cent and sales is Rs. 100,000, the

variable cost will be a) Rs. 25,000 b) Rs. 50,000 c) Rs. 75,000 d) None of the above 6) The valuation of stock in marginal costing as compared to

absorption costing is a) Higher b) Lower c) Same d) None of the above

13.8 lIMITATIONS OF MARGINAl COSTINGThe marginal costing has the following limitations :1) Difficulty in cost Analysis : Separation of costs into fixed and

variable becomes very difficult under certain circumstances and in certain business situations. The accuracy of marginal costing results depends upon how accurately costs are classified.

2) Inappropriate basis of pricing : In marginal costing, there is a danger of too many sales being made at marginal cost or marginal cost plus some contribution, resulting in under recovery of fixed overheads. This situation will arise during depression or increasing competition.

3) Under valuation of inventory : In marginal costing, inventories are valued at variable costs. It may create problems in inter firm transfer of goods at marginal costs resulting in higher profits. Employees may demand higher salaries and other benefits. Exclusion of fixed costs from inventory cost seems to be against the accepted accounting procedure.

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4) Same marginal cost per unit : This assumption is partly true within a limited range of activity. Scarcity of labour and material brings change in price, trade discount of bulk purchases, changes in the productivity of men etc. will influence the marginal cost per unit.

5) Not suitable to all concerns : This technique may not be suitable in those industries which have large stock of work-in-progress e.g. contact and ship building industry. If fixed expenses are not included in valuation of work-in- progress losses may occur in the initial years till the contract is completed. On completion of the contract, huge profit will be depicted.

6) New Technology : With the development of science and technology, new cost efficient machines are available resulting in reduction in labour costs and increased fixed costs. The system of costing, which ignores significant portion of cost i.e. fixed cost, can not be very effective.

13.9 lET US SUM UPThe elements of costs are material, labour and expenses. These elements of costs are broadly put into two categories: fixed and variable costs. The cost of product or process can be ascertained by absorption costing and marginal costing. In absorption costing or full costing, cost of a product is determined after considering both fixed and variable cost. Whereas in marginal costing only variable costs are considered in calculating the cost of product and fixed costs are charged against the revenue (consideration) of the period. Marginal costing is a definite improvement over the absorption costing.Marginal costing involves computation of marginal cost. The marginal cost is also called variable costs. It comprises of direct material, direct labour and variable overheads. Marginal costing helps the management in taking various managerial decisions like price fixation, profit planning, add and drop decisions, make or buy decision, sales mix decision, etc.Marginal costing technique has some limitations. The categorisation of expenses into fixed and variable elements is tedious and complex task. The behaviour of per unit variable and total fixed cost is questionable as assumed in marginal costing. Inspite of these limitations, marginal costing is a useful technique for decisions making in several business decisions.

13.10 kEy WORDSAbsorption costing or full costing: A technique where all costs, fixed and variable, are allocated to cost unit.Break Even Point: A level of production activity, where sales revenue is equal to variable cost and fixed cost or contribution equal to fixed cost. It is also called ‘no profit, no loss’ point.Contribution: The difference between sale price and variable costs is called contribution.Marginal Cost: It comprises of direct material, direct labour and variable overheads or cost of producing one additional unit.

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Marginal CostingMarginal Costing: It is a technique where only variable costs are considered while computing the cost of product. The fixed costs are met against the total contribution of all the products taken together.

13.11 ANSWERS TO ChECk yOUR PROGRESSA) i) Fixed and Variable, ii) Fixed Cost and Profit, iii) variable cost, iv) Contribution and sales, v) full costB) i) F, ii) T, iii) T, iv) F, v) TC) 1) D, 2) A, 3) C, 4) B, 5) C, 6) D

13.12 TERMINAl qUESTIONS1) Under what conditions, the income statement prepared under full

costing or absorption costing and marginal costing will give similar results.

2) State the conditions, the income statement prepared with absorption costing and marginal costing will give different results.

3) Explain the application of marginal costing in managerial decision making.

4) How semi-variable costs or mixed costs can be segregated into fixed and variable components.

5) ‘The profit is the product of the P/V ratio and the margin of safety’. Comment.

6) What are the limitations of marginal costing techniques?7) A manufacturer produces a car component. The cost sheet of the

component is as follows:

Material 4.00

Direct Labour 2.00

Variable Overheads 1.50

Fixed Overheads 2.50

10.00

A foreign manufacturer who uses this car component offers to purchase 20,000 units at Rs. 13 per component against the usual price of Rs. 15 per unit. If this offer is accepted the fixed expenses will go up by Rs. 40,000 annually.

Would you accept this offer? Are there any other considerations, which may affect your decision?

(Yes, profit increases by Rs. 70,000)8) The management of company worried about the performance of

Department X and wants to close the department. The following data is supplied by the cost accountant.

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Marginal Costing and Cost Volume Profit Analysis Department

XRs.

yRs.

ZRs.

Sales 40,000 60,000 1,00,000

Variable Costs 36,000 48,000 60,000

Fixed costs (apportioned on the basis of sales)

6,000 9,000 15,000

Total Cost 42,000 57,000 75,000

Profit or Loss –2000 +3000 +2500

a) You are required to advise management in respect of closure of department X.

b) On the above, the specific fixed costs are ascertained as follows: X Rs. 2000; Y Rs. 13000; and Z Rs. 5000 and the balance of Rs. 10,000 is treated as general fixed overheads.

(Ans. : (a) Continue X (b) Close Y, Total Profit Rs. 26,000)9) A Company manufacturers and markets three products X, Y and Z. All

the three products are manufactured from the same set of machines. Production is limited by machine capacity. From the data given below, indicate the priorities for product X, Y and Z with a view to maximising profits.

X y Z

Raw Material per unit 11.00 16.25 21.00

Direct Labour per unit 2.50 2.50 2.50

Variable Overheads 1.50 2.25 3.50

Selling Price 25.00 30.00 35.00

Machine time required per unit in minutes 40 20 20

(Ans. : Y, Z and X. Contribution per unit : 0.225, 0.45, 0.4 respectively.)10) XYZ Ltd. produces three products and cost data is as follows:

X y ZRs. Rs. Rs.

Selling price per unit 100 75 50P/V Ratio 0.10 0.20 0.40Maximum sales potential (in units) 40,000 25,000 10,000Raw material content as % of variable costs

50.00 50.00 50.00

The fixed expenses are estimated at Rs. 6,80,000. The company uses a single raw material in all the products. Raw material is in short supply and the company has a quota for the supply of raw materials to the extent of Rs. 18,00,000 per annum for the manufacture of its products to meet its sales demand.

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Marginal Costing a) Calculate the product mix which will give the maximum overall profits keeping the short supply of raw materials.

b) Compute the maximum profit. [Ans. : (a) Product mix of X, Y and Z are 10,000, 25,000 and 10,000

units respectively; (b) Profit Rs. 95,000 ]

13.13 FURThER READINGSKishore, Ravi M., Management Accounting with Problems and Solutions, Taxmann Allied Services Pvt. Ltd. New Delhi, 2000.Horngren, C.T., Gary L. Sundem and Frank H. Selto, “Management Accounting”, Prentice Hall of India, New Delhi, 1994.Kaplan, R.S., “Advanced Management Accounting”, Engle Wood Cliffs, NJ., Prentice Hall Inc.

Note : These questions will help you to understand the unit better. Try to write answers for them. But do not submit your answers to the University. These are for your practice only.

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UNIT 14: COST VOlUME PROFIT ANAlySIS

Structure14.0 Objectives 14.1 Introduction 14.2 Break Even Analysis14.3 Break Even Point14.4 Impact of Changes in Sales Price, Volume, Variable Costs and Fixed

Costs on Profits14.5 Required Sales for Desired Profit14.6 Sales Volume Required to Earn a Desired Profit Per Unit 14.7 Sales Required to Maintain Present Profit 14.8 Margin of Safety 14.9 Angle of Incidence 14.10 Break Even Charts 14.11 Profit Volume Graph14.12 Assumption in Break Even Analysis14.13 Let Us Sum Up 14.14 Key Words 14.15 Answers to Check Your Progress 1.16 Terminal Questions 14.17 Further Readings

14.0 OBJECTIVESAfter studying this unit you should be able to:

● understand the concept of break even analysis, impact of change in sales volume, price, variable cost, fixed costs on profits;

● apply cost-volume profit relationship for profit planning; ● understand the concept of margin of safety, angle of incidence, and

profit volume ratio in decision making; and ● examine the assumptions and limitations of the break even analysis.

14.1 INTRODUCTIONIn this unit you will learn about the concept of break-event point and finding out of break even point through mathematical equation and graphic representation. You will be acquainted with the relationship between Cost, Volume and Profit and its impact on planning and evaluation of business operations. You will also study the concepts of margin of safety, angle of incidence, limiting factor and profit volume ratio in decision making. The unit also deals with the underlying assumptions of break even analysis.

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Cost Volume Profit Analysis14.2 BREAk EVEN ANAlySISThe analysis of cost behaviour is necessary for planning, control and decision making. Analysis of cost behaviour means analysis of variability of each cost element in relation to the level of output. Every cost follows some definite behaviour pattern. For example total variable costs varies in direct proportion to the volume of output but per unit variable cost remains same. Examples of such costs are direct material, direct labour, packaging expenses, selling commission, etc. These costs are called product costs and are controllable, as they incur only when production takes place. Whereas fixed costs remains same irrespective to the level of output but per unit fixed cost goes on decreasing with the increasing level of out put as fixed cost scattered over a large number of units. Examples of such expenses are rent, rates and insurance, executives’ salary, audit fees, etc. These costs are also called period costs and are uncontrollable. The mixed costs or semi-variable costs have both the elements variable and fixed. These costs also change in the same direction in which volume of output changes but this change is less than proportionate change in output. Examples of such costs are power, telephone, depreciation, etc. Thus the concept of break even analysis is a logical extension of marginal costing. It is based on the same principle of classifying the costs into fixed and variable.Semi-variable costs are segregated in fixed and variable components as discussed in the earlier chapter. Fixed component is added in fixed costs and variable component with variable cost. Thus the costs are classified into two water tight compartments i.e. fixed and variable.The cost behaviour play a significant role in decision making. The relationships in volume, cost and profit shows that if volume increase by 10 per cent (say), then cost will not increase by 10 per cent. Because only variable cost will increase and fixed costs remain same and unit fixed cost declines. Consequently, profit will not increase by 10 per cent but more than that and vice versa. The level of production changes due to many reasons, such as recession or boom, competition, introduction of new product, increase in demand, scarce raw material, etc. The management wants to know the effect of these changes on profit. The break-even analysis helps the management in decision making in these situations.The study of cost-volume-profit relationship is some time called as “break even analysis.” In the opinion of some, it is a misnomer as break even analysis depicts a point where costs and total sales revenue is same. Beyond this point, it is called cost- volume-profit relationship. Some hold the view, that break even analysis can be interpreted in two senses – narrow and broad sense. In narrow sense, it refers to determine the level of output where total costs equal to total revenue i.e. no profit, no loss. In the broad sense, it is used to determine the probable profit at any level of output.

14.3 BREAk EVEN POINTIt is a point where sales revenue equals the costs to make and sell the product and no profit or loss is reported. In the words of Keller and Ferrara, “the break even point of a company or a unit of a company is the level of sales

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income which will equal to the sum of its fixed costs and variable costs.” Charles T. Horngren define it, “the break even point is that point of activity (sales volume) where total revenues and total expenses are equal, it is the point of zero profit and zero loss.”There are two methods of calculating break even point. Mathematical method and Graphical method.

14.3.1 Mathematical MethodThe break even point through mathematical method can be found out either byi) Equation Method, orii) Contribution Margin Technique.Equation MethodWe know,Sales – Variable costs – Fixed cost = Profit (S – VC – FC = P) Sales – Variable costs = Fixed costs + Profit (S – VC = FC + P)Sales minus variable costs is called Contribution. (S – VC = C) Contribution = Fixed costs + Profit (C = FC + P)At break even point, profit is zero.∴ Contribution = Fixed Costs (at break even point) Or (SP – VC) Q = FWhere, SP is selling price, VC is the variable costs, F is a fixed costs and Q is the number of units produced and sold. Look at the following illustration how the break even point is to be calculated:Illustration 1Calculate the break even point from the following information : Selling price = Rs. 3 per unit Variable cost = Rs. 2 per unit Fixed cost = Rs. 90,000 Estimated sales for the period = 100,000 units or Rs. 300,000 Suppose the units to be produced and sold at break even point is Q, then Sales – Variable Costs = Contribution = Fixed Costs 3 Q – 2 Q = 90,000 Q = 90,000 unitsWhen we produce and sell 90,000 units, then total sales revenue is Rs. 2,70,000 (90,000 units Rs. 3 ) and total cost is Rs. 2,70,000, (VC Rs. 2 × 90000 units = 1,80,000 + F C Rs. 90,000)Contribution Margins TechniqueContribution per unit means difference between selling price and variable costs

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Cost Volume Profit Analysisor Contribution per unit = Selling price per unit – Variable Cost per unit Total Contribution = Sales Revenue – Total Variable CostsBreak even point can be expressed in terms of units to be produced and sold or in terms of value of goods. At break even point, we knowBreak Even Point in Units Sales – Variable Costs = Fixed Costs or (SP – VC) Q = Fixed Costs or BEP (in units) = Fixed Costs

SP per unit – VC per unit

or

Q = Fixed CostsContribution per unit

Break Even Point in ValueMultiplying both sides by selling price (SP),

SP × Q = BEP (in Value)= Fixed Costs × SP per unitContribution per unit

or

BEP (in Value) = Fixed Costs × SalesTotal Sales – Total Variable Costs

= Fixed Costs × SalesTotal Contribution

Let us calculate the break-even point with the help of above equations by using the information given in illustration 1

BEP (in units) = Fixed CostsSP – VC

= Rs. 90,000Rs. 3 – Rs. 2

= 90,000 units

BEP (in Value) = Fixed Costs × Selling PriceSP – VC

= Fixed Costs × Selling PriceContribution per unit

= Rs. 90,000 × Rs. 3Rs. 3 – Rs. 2

= Rs. 2,70,000

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Marginal Costing and Cost Volume Profit Analysis BEP (in Value) = Fixed Costs × Total Sales

Total Sales – Variable Costs

= Rs. 90,000 × Rs. 3,00,000Rs. 3,00,000 – Rs. 2,00,000

= Rs. 2,70,000It shows that a firm will be at a break even point when it is producing and selling 90,000 units or having a sale of Rs. 2,70,000.Profit / Volume Ratio (P/V ratio)Total contribution divided by total sales is called profit-volume ratio or contribution ratio (P/V ratio). Break-even point can be determined with the help of P/V ratio. P/V ratio = Contribution

Sales

= Sales – Variable CostSales

= 1 – Variable CostSales

or

P/V ratio = Fixed Cost + ProfitSales

+ F + PS

BEP (in Value) = Fixed Costs × Total SalesTotal Sales –Variable Costs

= Fixed Costs × Total SalesTotal Contribution

= Fixed CostsTotal Contribution ÷ Total Sales

= Fixed CostsP/V ratio

Variable Costs to Sales is called Variable Cost Ratio

∴ BEP (in value) = Fixed Costs

Variable CostsSales

1 –

It should be noted that firms producing one product line only, the calculation of break- even point is preferred in units and firms having a variety of product lines, calculation of break even point is preferred in value. P/V ratio can also be expressed in the form of percentage by multiplying by 100. Look at the following illustration.Illustration 2XYZ Ltd. is manufacturing and selling four types of products A, B, C and D. The sales mix and variable costs are as follows:

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Cost Volume Profit AnalysisProduct Sales per month Variable Cost RatioA 2,00,000 50%B 1,50,000 50%C 1,00,000 75%D 2,50,000 40%

The fixed costs are Rs. 1,50,000 per month. Calculate break even point.SolutionFirstly calculate the variable costs and contribution.

Particular A B C D TotalSales (Rs.) 2,00,000 1,50,000 1,00,000 2,50,000 7,00,000Variable Costs (Rs.) 1,00,000 75,000 75,000 1,00,000 3,50,000Contribution (Rs.) 1,00,000 75,000 25,000 1,50,000 3,50,000Fixed Costs (Rs.) — — — — 1,50,000Profit (Rs.) 2,00,000

P/V ratio = Total ContributionTotal Sales

= Rs. 3,50,000Rs. 7,00,000

= 0.50 (i.e., 50%)

Break Even Point (in value) = Rs. 1,50,0000.50

= Rs. 3,00,000

Variable Cost Ratio = Variable CostsTotal Costs

= Rs. 3,50,000Rs. 7,00,000

= 0.50 (i.e., 50%)

∴ BEP (in value) = Fixed Costs

Variable CostsSales

1 – = Rs. 1,50,000

0.50

= Rs. 3,00,000

Break-even point as percentage of estimated capacity utilisation : Break-even point can also be calculated as a percentage of estimated sales or capacity utilisation by dividing the break-even sales by the estimated capacity sales/utilisation.Illustration 3The ratio of variable costs to sales is 70 percent. The break even point occurs at 60 percent of the capacity. Find the break even point sales when fixed costs are Rs. 90,000. Also compute profit at 75% of the capacity sales.SolutionAs the variable cost to sales ratio = 70% We know P/V ratio or Contribution ratio = 1 – VC

Sales = 1 – 0.70

= 0.30

∴ BEP (in value) = Fixed CostP/V ratio

= Rs. 90,00030

= Rs. 3,00,000

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BEP occurs at 60 per cent of the capacity utilisation

Capacity Utilisation Sales60% Rs. 3,00,00075%

We can apply unitary method or proportion method

X = Rs. 3,00,000 × 7560

= Rs. 3,75,000

Now we can compute, contribution earned when sales is Rs. 3,75,000. Sales multiplied by P/V ratio gives the contribution. Contribution = Sales × P/V Ratio = Rs. 3,75,000 × 30% = Rs. 1,12,500 ∴ Profit = Contribution – Fixed Costs = Rs. 1,12,500 – Rs. 90, 000 = Rs. 22,500

14.3.2 Graphical MethodThe break-even point can also be shown graphically. The BEP chart shows the relationships between cost, volume and profit at various levels of output. Fixed costs, variable costs and sales revenues are shown on Y-axis and volume of out on X-axis. The break-even point is that point at which the total cost line and total sales line intersect each other. This point represents “no profit, no loss”.The following steps are involved in construction of break even chart:

● Sales volume is plotted on x-axis. Sales volume may be expressed in terms of value (rupee), units or as percentage of capacity.

● Cost and Revenue are depicted in y-axis. Fixed costs remains constant irrespective to the sales volume. Hence it is parallel to the x-axis and starts from Rs. 90,000. (Data of illustration 1) Variable cost starts from (0,0) because no sales volume, no variable cost and as the volume increases variable cost also increases. When a parallel line of variable cost drawn from the fixed cost line in y - axis, it depicts the total cost line. The sales revenue curve also starts from (0,0).

● The point of intersection of sales revenue line and total cost line depicts, break even point. It occurs at a point of 90,000 units on x-axis and Rs. 2,70,000 (in terms of value) on y-axis.

● The area to the left side of break even point depicts loss zone as cost curve is at a higher level and sale revenue line is at a lower level. The area to the right hand side of break even point is called profit zone as sale revenue line lies at a higher level than the total cost line.

● The angle formed by the intersection of sale value line and total cost line is known as angle of incidence. Larger the angle, lower is the break even point and vice versa.

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Cost Volume Profit AnalysisLet us draw a break even chart with the help of the following illustration.Illustration 4Let us draw a break-even chart with the help of data given below at different production levels of 0, 80,000, 90,000, 1,00,000 1,10,000, and 1,20,000 units.Sale Price = Rs. 3 per unit Variable Cost = Rs. 2 per unit Fixed Cost = Rs. 90,000SolutionThe costs and profits and different levels of output is computed as follows :

Output Variable Cost Rs. Fixed Cost Rs. Total Cost Rs. Sale Rev. Rs.

Profit Rs.

0 0 90,000 90,000 0 –90,000

80,000 1,60,000 90,000 2,50,000 2,40,000 –10,000

90,000 1,80,000 90,000 2,70,000 2,70,000 0

1,00,000 2,00,000 90,000 2,90,000 3,00,000 10,000

1,10,000 2,20,000 90,000 3,10,000 3,30,000 20,000

1,20,000 2,40,000 90,000 3,30,000 3,60,000 30,000

The above data if presented on a graph, it appears as follows :Break Even Chart

Angle of incidence

Break even point

Profit Z

one

Sales revenue

Cos

ts/s

ales

Rev

enue

s (in

’000

rupe

es)

Output (in ’000 units)

Fixed cost

Profit

Margin of Safety

Variable cost

Loss Area

290


Contribution break even chartFrom this chart we can ascertain the contribution earned at different levels of activity. Under this method, total cost line is not drawn instead the contribution line is drawn from the (0.0) point or origin. Intersection of cost line and sales line does not arises in this case as break even point occurs at where contribution is equal to fixed cost. When contribution is greater than fixed cost it is profit and vice versa. The contribution break even chart shows the contribution at different levels of activity and any level of activity below the BEP will not cover the fixed cost.Let us represent the data as given in illustration 4 by means of contribution break-even Chart.Solution :

Output Variable Cost (Rs.)

Fixed Cost (Rs.)

Total Cost (Rs.)

Sale Rev. (Rs.)

Contribution (Rs.)

0 0 90,000 90,000 0 0

80,000 1,60,000 90,000 2,50,000 2,40,000 80,000

90,000 1,80,000 90,000 2,70,000 2,70,000 90,000

1,00,000 2,00,000 90,000 2,90,000 3,00,000 1,00,000

1,10,000 2,20,000 90,000 3,10,000 3,30,000 1,10,000

1,20,000 2,40,000 90,000 3,30,000 3,60,000 1,20,000

Contribution Break Even Chart

Variable costs

Cos

t/Rev

enue

Sales curve

Contribution curve

Fixed costProfit area

Loss Area

OutputO X

Y

BEP

14.4 IMPACT OF ChANGES IN SAlES PRICE, VOlUME, VARIABlE COSTS AND FIXED COSTS ON PROFITS

14.4.1 Impact of Sale Price Changes on ProfitSuppose the normal sales volume of X Y Z Ltd. is 1,00,000 units, selling

291

Cost Volume Profit Analysisat a price of Rs. 3 per unit. The variable cost is Rs. 2 per unit, fixed cost is Rs. 90,000. The capital investment is Rs. 1,00,000. Let us study the impact of change in price on profit under two conditions i.e. increase in price by 5 per cent and 10 per cent and decrease in price by 5 per cent and 10 per cent

Impact of Change in Sales Prices on Profit

Sl. No.

Particulars Decrease in Price Normal Volume

Increase in Price10% 5% 5 % 10%

1. Outputs (units) 1,00,000 1,00,000 1,00,000 1,00,000 1,00,0002. Sales ( Rs.) 2,70,000 2,85,000 3,00,000 3,15,000 3,30,0003. Variable Costs ( Rs.) 2,00,000 2,00,000 2,00,000 2,00,000 2,00,0004. Marginal Income or

Contribution (2-3) ( Rs.)70,000 85,000 1,00,000 1,15,000 1,30,000

5. Fixed Costs (Rs.) 90,000 90,000 90,000 90,000 90,0006. Operating Profit / Loss

(4-5) (Rs.)–20,000 –5,000 10,000 25,000 40,000

7. % Change in Profit –300% –150% — 150% 300%8. Break even point (units) 1,28,571 1,05,882 90,000 78,261 69,2319. P/V Ratio 0.2592 0.2982 0.3333 0.3651 0.393910. Return on Investment % –20% –5% 10.00 25.00 40.00

From the above table, we can draw the following inferences:1) A small change in price brings wide fluctuations in operating profit.

For example 5 per cent decrease in price brings 150 per cent decrease in profit and vice versa. The change is 30 times.

The change can be computed as follows:

= % Change in Profit% Change in Price

When price declines by 5 percent, then change in profit is

= 150%5%

= 30 times

There is an inverse relationship in change in price and change in break even point. When price increase other factors remains same, the break-even point declines.

Increase in sale price leads to higher contribution resulting in lower break even point and vice versa. A lower number of units have to be sold in order to recover the fixed cost.

2) Profit-Volume Ratio: There is a direct relationship in change in price and change in profit volume ratio. With change in price, the contribution also changes consequently P/V ratio also changes.

3) Return of Investment: Like in operating profits, the change in price has a magnified impact on return on investment.

14.4.2 Impact of Volume Changes on ProfitLet us study the impact of change in volume on profit in the above-mentioned example.

292


Sl. No.

Particulars Decrease in Price Normal Volume

Increase in Price10% 5% 5% 10%

1. Outputs (units) 80,000 90,000 1,00,000 1,10,000 1,20,0002. Sales ( Rs.) 2,40,000 2,70,000 3,00,000 3,30,000 3,60,0003. Variable Costs (Rs.) 1,60,000 1,80,000 2,00,000 2,20,000 2,40,0004. Contribution (Rs.) (2-3) 80,000 90,000 1,00,000 1,10,000 1,20,0005. Fixed Costs (Rs.) 90,000 90,000 90,000 90,000 90,0006. Operating Profit

(4-5) ( Rs.)- 10,000 0 10,000 20,000 30,000

7. % Change in Profit -200 -100 - 100 2008. Break even point (units) 90,000 90,000 90,000 90,000 90,0009. P/V Ratio Percentage 0.3333

or 33.33%

0.3333 or

33.33%

0.3333 or

33.33%

0.3333 or

33.33%

0.3333 or

33.33%10. Return on Investment (%) -10.00 0 10.00 20.00 30.00

From above table, the following inferences can be drawn:1) Percentage Change in Profit: A small change in sales volume brings

a wide fluctuation in profit. For example, a 10 per cent change in sales volume leads to a 100 per cent change in profit. It is called operating leverage or operating elasticity. Mathematically, it is

OL or OE = % Change in Profit% Change in Price

The operating leverage or operating elasticity is the degree of responsiveness or sensitivity of operating profit to change in sales. In the above example, operating leverage or operating elasticity is

OL or OE = % Change in Profit% Change in Prince

= 100 %10 %

= 10 times

It depicts that 1 percent change in sales leads to 10 times change in operating profit i.e. 10 per cent.

2) Break Even Point: There is no impact on the break-even point. Because contribution per unit (Sale Price – Variable Costs) and fixed costs are not influenced by the change in volume. Thus break even point is unaffected when there is a change in sales volume.

3) P/V Ratio: Like break even point, there is no impact on profit volume ratio as contribution per unit and sale price per unit is same as at normal level.

4) Return on Investment: Like in operating profit, the impact of change in sale volume has a magnified impact on return on investment.

14.4.3 Impact of Change in Price and Volume on Profit

Sl. No. Particulars

Decrease in PriceNormal Volume

Increase in Price10% 5 % 5 % 10%

Increase in Volume Decrease in Volume20% 10% 10% 20%

1. Outputs (units) 1,20,000 1,10,000 1,00,000 90,000 80,0002. Sales ( Rs.) 3,24,000 3,13,500 3,00,000 2,83,500 2,64,000

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Cost Volume Profit Analysis3. Variable Costs ( Rs.) 2,40,000 2,20,000 2,00,000 1,80,000 1,60,0004. Contribution ( 3-2) 84,000 93,500 1,00,000 1,03,500 1,04,0005. Fixed Costs ( Rs.) 90,000 90,000 90,000 90,000 90,0006. Operating Profit -6,000 3,500 10,000 13,500 14,0007. % Change in Profit –160.00 –65.00 - 35.00 40.008. Break even point

(units)1,28,571 1,05,882 90,000 78,261 69,231

9. P/V Ratio Percentage 0.2592 or

25.92

0.2982 or

29.82

0.3333 or

33.33

0.3651 or

36.51

0.3939 or

39.3910. Return on Investment

(%)6.00 3.5 10.00 13.50 40.00

Activity: 1 Try to draw the inferences from the above table and also prepare the similar tables for increasing and decreasing the fixed costs and variable cost and study the impact on profit, break even profit, P/V ratio etc.

14.5 REqUIRED SAlES FOR DESIRED PROFITBreak even point equation can be extended to estimate the profit and loss at different levels of production. At break even point, profit is zero but for calculating the sales volume required to earn a desired profit, the profit value is put as desired profit. The following equations can be derived for this purpose. Sales – Variable Costs = Fixed Costs + Desired Profit

or Contribution = Fixed Costs + Desired Profit

Sales Volume Required (in Units) = Fixed Costs + Desired ProfitSP – VC (per unit)

= Fixed Costs + Desired ProfitContribution Per Unit

Sales Volume Required (in Value) = (Fixed Costs + Desired Profit) SalesSales – Variable Costs

= (Fixed Costs + Desired Profit) SalesTotal Contribution

= Fixed Costs + Desired ProfitP/V Ratio

= Fixed Costs + Desired Profit1 – Varilable Costs/Sales

Illustration 5A company producing a single product and sells it at Rs. 10 per unit. Variable cost is Rs. 6 per unit and fixed cost is Rs. 40,000 per annum. Calculate (a) Break even point, (b) Sales volume required to earn a profit of Rs. 60,000 per annum

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Solution Contribution = SP – VC = Rs. 10 – Rs. 6 = Rs. 4 per unit

BEP (in units) = Fixed Costs Contribution Per Unit

= Rs. 40,000Rs. 4

= 10,000 units

BEP (in Value) = Fixed CostsP/V Ratio

P/V Ratio = Total ContributionTotal Sales

= Rs. 4,00,000Rs. 1,00,000

= 0.40

BEP = Rs. 40,0000.40

= 1,00,000

Sales volume required to earn a desired profit (in units)

= Fixed Costs + Desired ProfitContribution Per Unti

= Rs, 40,000 + Rs. 60,000Rs. 4

= Rs, 1,00,000Rs. 4

= 25,000 units

Sales volume required to earn a desired profit (in Value)

= Fixed Costs + Desired ProfitP/V Ratio

= Rs, 40,000 + Rs. 60,000Rs. 40

= Rs. 2,50,000

14.6 SAlES VOlUME REqUIRED TO EARN A DESIRED PROFIT PER UNIT

If we add the desired profit per unit with variable cost and apply the same equations, the result will provide us the sales volume required to earn a desired profit per unit.In Units Sales Volume Required (in units) = Fixed Costs

SP – (VC + DP)where DP is desired profit per unit.In value Sales volume required (in Value)

295

Cost Volume Profit Analysis = Fixed CostsVC + P

Selling Price1 –

= Fixed Costs

(VC + Desired Percentage of Profit on SalesSP

1 –

Illustration 6The cost information computed by the cost accountant is as follows :

Sales = 1,00,000 unitsSelling Price = Rs. 10 per unitVariable cost or out of pocket-costs = Rs. 6 per unitFixed costs or burden = Rs. 60,000 per annumCompute the following :a) Break even points in units and valueb) Make a profit of Rs. 40,000c) Make a profit of Rs. 2 per unitd) Make a profit of 30% on salesSolutiona) Break Even Point (in units) Contribution per unit = SP – VC = Rs.10 – Rs. 6 = Rs. 4 per unit

BEP (in units) = Fixed CostsContribution Per Unit

= Rs. 60,000Rs. 4

= 15,000 units

In Value

P/V Ratio or Contribution Ratio = SP – VCSP

= Rs. 10 – Rs. 6Rs. 10

= 0.40

BEP (in Value) = Fixed CostsP/V Ratio

= Rs. 60,0000.40

= Rs. 1,50,000

b) Sales volume required to earn a profit of Rs. 40,000 In Units =

Fixed Costs + Desired ProfitContribution Per Unit

= Rs. 60,000 + Rs. 40,000

Rs. 4 = Rs. 25000 units

296

Marginal Costing and Cost Volume Profit Analysis =

Fixed Costs + Desired ProfitP/V Ratio

= Rs. 60,000 + Rs. 40,000

Rs. 0.40

= Rs. 250,000 units

c) Sales volume required to earn a profit of Rs. 2 per unit In Unit =

Fixed CostsSP – (VC + P)

= 60,000

Rs. 10 – (Rs. 6 + Rs. 2) =30,000 units

In Value =

Fixed Costs1 – (VC + PD) / SP

= 60,000

1 – (6 + 2) / 10

= 60,0002/10 = Rs. 3,00,000

d) Sales volume required to earn a profit of 30% on sales In unit =

Fixed CostsSP – (VC + 30% of SP)

= 60,000

Rs. 10 – (6 + 3) = 60,000 units

In Value =

Fixed Costs1 – (VC + 30% of SP)/SP

= Rs. 60,000

1 – (6 + 3) / 10 = Rs. 6,00,000

Calculations of selling price per unit for a particular break even point. We know BEP Units =

Fixed CostsContribution Per Unit

∴ Contribution Per unit = Fixed CostsBEP Units

Selling price per unit – Variable cost per unit = Contribution per unitSelling price per unit = Contribution per unit + Variable Cost per unit Thus Selling Price Per Unit =

Fixed CostsDesired BEP + Variable Cost

297

Cost Volume Profit AnalysisIllustration 7Given Fixed costs = Rs. 40,000Selling price per unit = Rs. 40Variable Cost = Rs. 30The break even point in this case is

BEP Units = Rs. 40,000

Rs.40 – Rs. 30

= Rs. 40,000

Rs. 10

= 4000 unitsWhat should be selling price per unit, if management wants to reduce the break-even point from 4000 units to 2500 units?Solution Selling Price Per Unit =

Fixed CostsDesired BEP + VC

= Rs. 40,0002500 units + Rs. 30

= Rs. 16 + Rs. 30 = Rs. 46 per unit

14.7 SAlES REqUIRED TO MAINTAIN PRESENT PROFIT

Calculating the sales volume required to meet the proposed expenditureBecause of high competition in the market, the management plans an aggressive promotion policy to boost the sales, which requires an extra expenditure. In such cases, management wants to know the additional sales volume required to cover the expected increase in expenditure.Here the logic should be to cover the extra expenditure, how much additional units to be sold. Suppose contribution per unit is Rs. 10 per unit and a company spends Rs. 1,00,000 extra on advertisement, then logically company must sell 10,000 extra units to cover this expenditure. Thus the formula should beIn unitsAdditional Sales Volume Required =

Proposed ExpenditureContribution Per Unit

In valueAdditional Sales Volume Required =

Proposed ExpenditureP/V Ratio

Illustration 8Sales 10,000 unitsFixed Cost Rs.1,00,000Variable Cost Rs. 2,00,000The selling price is Rs. 36 per unit. The company is spending Rs. 100,000 on advertisement to promote its product. Find the sale volume required to earn the present profit.

298


SolutionExtra sales volume required to meet the additional publicity expenditure of Rs. 1,00,000 so as to maintain the present profit level is worked out as follows: Variable Cost Per Unit =

Rs. 2,00,00010,000 units = Rs. 20 per unit

Contribution Margin = Rs. 36 – Rs. 20 = Rs. 16 per unit

Additional Sales Required (in units) = Rs. 1,00,000

Rs. 16 = 6,250 units

When a company sells 6,250 unit extra, then present level of profit will be maintained. For example, before spending money the company was earning a profit of Rs. 60,000 which is as follows: Profit = Contribution – Fixed Cost = Rs. 16 × 10,000 – Rs. 1,00,000 = Rs. 1,60,000 – Rs. 1,00,000 = Rs. 60,000When sales volume increase to 16,250 units (i.e. 10,000 units + 6,250) then profit will be= Rs. 16 × 16,250 – Rs. 2,00,000 (F. C. Rs. 1,00,000 + Advertisement Rs.

1,00,000)= Rs. 2,60,000 – Rs. 2,00,000 = Rs. 60,000Calculating the sales volume required to offset price reductionSome time management wants to follow the policy of price reduction or increasing commission to dealers for increasing the sales or to face the competition. In these case new values are used for calculations and formula remains the same.Illustration 9ABC Ltd. manufactured and markets a product whose cost data is as follows:

Material Costs = Rs. 16 per unit Conversion (Variable Cost) Dealer’s Margin

= Rs. 12 per unit Rs. 4 per unit(10% of selling price)

Selling Price = Rs. 40 per unit

Fixed Cost = Rs. 5,00,000

Present Sales = 90,000 units

Capacity Utilisation = 60%

Management has following two suggestions, which alternative is better so as to maintain the present profit level?a) Reduction in Selling Price by 5%b) Increasing the dealer’s margin by 25% over the existing ratesSolution Total variable costs = Rs. 16 + Rs.12 + Rs. 4

299

Cost Volume Profit Analysis = Rs. 32 per unit Contribution per unit = Rs. 40 – Rs. 32 = Rs. 8 per unit Present Profit Level = Rs. 8 × Rs. 90,000 – Rs. 5,00,000 = Rs. 2,20,000a) First alternative : Price reduction by 5% New selling price = (Rs. 40 – Rs.2) = Rs. 38 per unit New Dealer’s Commission = 10% of Rs. 38 = Rs. 3.80 New Contribution = Rs. 38 – ( Rs. 16 + Rs. 12 + Rs. 3.80) = Rs. 6.20 per unit Sales volume requires to earn a desired profit (in units)

= FC + DP

Contribution per unit

Sales volume required (in units) = Rs. 5,00,000 + Rs. 2,20,000

Rs. 6.20

= Rs. 7,20,000

Rs. 6.20 = 1,16,129 units

b) Second Alternative : Increasing dealer’s commission by 25%

New Dealer’s Commission = Rs. 4+25% of Rs. 4 = Rs. 5 per unit

New Contribution = Rs. 40 – (Rs. 16 + Rs. 12 + Rs. 5)

= Rs. 7 per unit

Sales required (in units) = Rs. 5,00,000 + Rs. 2,20,000

Rs. 7

= 1,02,857 unitsIn the second alternative, lesser units are required to be sold as compared to the first alternative. Contribution margin is also high in second alternative. Hence second alternative is better in comparison to the first alternative.Calculating new sales volume or new selling price to offset the impact of change in variable costs and fixed costs.When a company introduces new production plans or improve the process, then generally variable costs and fixed costs also change. In such situation, there are two alternatives before the management to earn the same profits either to increase the sales volume or increase the selling price when costs increases and vice versa. The new sales volume needed to earn the same profit, when only variable costs changes, then new contribution is calculated by changing the variable cost and break even equation remains same. If management wants to change the selling price and volume remains the same, then new selling price is :New selling price = Old selling price + (new variable cost -old variable cost)

300


When fixed cost changes, then fixed costs is replaced by a new fixed cost in the equation and new volume of sales can be computed to earn the same profit. If management thinks that selling price be changed and volume remain the same, then new selling price is :

New Selling Price = Old Selling + New Fixed Cost – Old Fixed Costs

Volume of Production

The logic is change in selling price is incremental change in variable cost and / or fixed cost per unit is added in selling price so as to earn the same profit. Look at the following illustration how the new selling price is calculated when there is change in variable and fixed costs :Illustration 10The cost information supplied by the cost accountant is as follows: Sales 20,00 units @ Rs. 10 per unit Rs. 2,00,000 Variable cost Rs. 6 per unit Rs. 1,20,000Contribution Rs. 80,000Fixed Cost Rs. 30,000Profit Rs. 50,000Calculate the (a) new sales quantity and (b) new selling price to earn the same profit ifi) Variable cost increases by Rs. 2 per unitii) Fixed cost increase by Rs. 10,000iii) Variable cost increase by Re. 1 per unit and fixed cost reduces by Rs.

10,000Solutioni) Variable cost increases by Rs. 2

a) New Sales Quantity Required = F + DPSP – Vn

where Vn is the new variable cost

= Rs. 30,000 + Rs. 50,000

Rs. 10 – Rs. 8 = Rs. 80,000

Rs. 2 = 40,000 units

b) New selling price = Old selling price + change in variable cost per unit = Rs. 10 + Rs. 2 = Rs. 12 per unit To earn the same amount of profit, management should either increase

the production to 40,000 units or increase the selling price to Rs. 12 per unit

ii) Fixed costs increases by Rs. 10,000 a) Sales volume needed to earn a desired profit

= F + DPSP – Vc

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Cost Volume Profit Analysis Fn is the new fixed costs =

Rs. 40,000 + Rs. 50,000Rs.10 – Rs. 6 =22500 unit

b) New selling price

= SPO + Fn – Fo

Q

SPO is old selling price, Fn is new fixed cost and Fo is old fixed cost.

= 10 + Rs. 40,000 + Rs. 30,000

20,000 units = Re. 10.50

To earn the same amount of profit i.e. Rs. 50,000 management should either increase the sales volume to 22,500 units or increase the selling price to Rs. 10.50.

iii) Variable cost increase by Re. 1 per unit and fixed cost reduces by Rs. 10,000.

a) Sales volume required to earn a desired profit

= F + DPSP – Vn

= Rs. 20,000 + Rs. 50,000

Rs. 10 – Rs. 7 = Rs. 70,000

Rs. 3 = 23,333 units

b) New Selling price

= SPO + VCn – VCo

Q + Fn – Fo

= Rs. 10 + Rs. 20,000 – Rs. 30,000

20,000 units + Rs. 7 – Rs. 6

= Rs. 10 – Rs. 0.50 + Re. 1 = Rs. 10.50To earn the same profit i.e. Rs. 50,000 management should either increase the sales to 23,333 units or increase the selling price to Rs. 10.50.Illustration 11The Cost data of XYZ Ltd as follows:

Product X

Product y

Product Z

Total

Rs.Sales (40 : 50 : 10) (Rs.) 80,000 1,00,000 20,000 2,00,000Variable Costs (Rs.) 50,000 60,000 10,000 1,20,000Contribution (Rs.) 30,000 40,000 10,000 80,000Fixed (Rs.) ----- ----- ----- 50,000Profit ----- ----- ----- 30,000Calculate :

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i) Break Even Point, andii) Break even point if sales mix ratio is changed to 30:50:20Solutioni) Break Even Point When company is producing multi products, then for computing

break even equation in terms of value should be used.

BEP (in Value) = Fixed Cost × Total Cost

Total Sales – Variable Costs

= Rs. 50,000 × Rs. 2,00,000

Rs. 2,00,000 – Rs. 1,20,000

= Rs. 50,000 × Rs. 2,00,000

Rs. 80,000 = Rs. 1,25,000

ii) Change in Sales Mix Ratio New Sales mix X : Y: Z = 30:50:20

Sales

X = Rs. 2,00,000 × 30100 = Rs. 60,000

Y = Rs. 2,00,000 × 50100 = Rs. 1,00,000

Z = Rs. 2,00,000 × 20100 = Rs. 40,000

Variable Cost Ratio (as variable cost per unit remains same)

X = Rs. 50,000Rs. 80,000 =

58

Y = Rs. 60,000

Rs. 1,00,000 = 610

Z = Rs. 10,000Rs. 20,000 =

12

X y Z TotalRs.

Sales (Rs.) 60,000 1,00,000 40,000 200,000Variable Costs (Rs.) 37,500 60,000 20,000 117500Contribution (Rs.) 22,500 40,000 20,000 82,500Fixed Costs — 50,000Profit — — — 32,500

Break even point after change in sales mix

= Fixed Cost × Sales

Sales – Variable Costs

= Rs. 50,000 × Rs. 2,00,000

Rs. 2,00,000 – Rs. 1,17,500 = Rs. 50,000 × Rs. 2,00,000

Rs. 82,500

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Cost Volume Profit Analysis = Rs. 1,21,212.12Illustration 12A firm produces and sells three products A, B and C. From the following data, calculated the break even point.

Product No. of Units Sold SP per unit VC per unitRs. Rs.

A 600 50 30B 1500 60 45C 1000 30 15

Fixed costs are Rs. 33,000 per year.SolutionFirstly we calculate the over all P/V ratio which is :

= SP – VC

SP or 1– VCSP

Product SP VC P/V Ratio TotalSales

%SaleProceeds

OverallP/V Ratio

(Rs.) (Rs.) (Rs.)A 50 30 0.40 30,000 0.20 0.08B 60 45 0.25 9000 0.60 0.15C 30 15 0.50 30,000 0.20 0.10

Rs. 1,50,000 1.00 0.33

The overall P/V ratio is 0.33 (P/V Ratio × % sales proceeds). P/V ratio can also be computed as per preceding illustration.

∴ Overall Break Even Point = Fixed CostsP/V Ratio

= Rs. 33,000

0.33

= Rs. 100,000

The break up of total sales at Break Even Point will be:

% Sales Proceeds Sales proceeds No. of UnitsA 0.20 Rs. 20,000 400B 0.60 Rs. 60,000 1000C 0.20 Rs. 20,000 667

Rs. 1,00,000

14.8 MARGIN OF SAFETyThe margin of safety is the difference between actual sales and sales at break even point. Margin of Safety = Actual Sales – Sales at BEPSuppose the actual sales of X Y Z Ltd. (example given in 16.3) is 1,20,000

304


units and sales at break even point is 90,000 units, thenM/S = 1,20,000 units – 90,000 units = 30,000 units Sale price was Rs. 3 per unit.M/S = Rs. 3,60,000 – Rs. 2,70,000 = Rs. 90,000It can be expressed in terms of Rupees or in units, and is a absolute measure. It can be expressed in relative terms and is

M/S = Actual Sales – Sales at Break Even Points

Actual Sales × 100

= Rs. 1,20,000 – Rs. 90,000

Rs. 1,20,000 × 100 = 30,000

1,20,000 × 100 = 25%

If we use the sales data in terms of rupees and compute the relative margin of safety, the answer will remain the same, for example

M/S = Rs. 3,60,000 – Rs. 2,70,000

Rs. 3,60,000 × 100

= Rs. 90,000

Rs. 3,60,000 × 100 = 25%

Margin of safety can also be computed from profit and P/V ratio, which is

M/S = Profit

P/V Ratio

Higher margin of safety provides greater protection to the company. The size of margin of safety is an indicator of soundness of business. It shows how much sales may decrease before the firm will suffer a loss. Sales beyond the break-even point represent margin of safety. Larger the margin of safety, greater the soundness of the business, smaller the margin of safety, weaker will be the soundness of the business. The following actions help in improving the margin of safety:1) Increase the level of production2) Reduce the fixed and / or variable costs3) Increase the selling price4) Substitute the existing product with more profitable products5) From the product mix, remove the product whose contribution ratio is

very lowIllustration 13Calculate the P/V ratio, fixed expenses and break even point from the following data: Sales Rs. 6,00,000Profit Rs. 40,000 Margin of safety Rs. 1,60,000Solution:We know

305

Cost Volume Profit Analysis M/S = Profit

P/V Ratio

= Rs. 40,000

Rs. 1,60,000 = 0.25

Contribution = P/V ratio × sales = 0.25 × Rs. 6,00,000 = Rs. 1,50,000 Contribution = Fixed Costs + Profit Fixed Cost = Contribution – Profit = Rs. 1,50,000 – Rs. 40,000 = Rs. 1,10,000

BEP (in value) = FC

P/V Ratio = 1,10,000

0.25 = Rs. 4,40,000

14.9 ANGlE OF INCIDENCEThe angle formed at the intersection of the total sales revenue line and the total cost line is called the angle of incidence. It depicts the difference between the slope of the total sales revenue line and total cost line. Graphically it is as follows :

Angle of incidence

Total costC

Sales

Y

B

X

Cos

t/Rev

enue

BEPO

Fixed cost

Output (in units)

Angle ABC is the angle of incidence. It reflects the responsiveness or sensitivity of profit to variation in the volume sold. The higher the angle of incidence, the greater the responsiveness of profits to variation in the sales volume and vice versa. In subsection 16.4 of this unit, we observed that small change in sales brings wide fluctuations in profits.Activity 2During boom period high angle of incidence is better and in recession period low angle of incidence is better? Comment....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

A

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.......................................................................................................................

14.10 BREAk EVEN ChARTSThe effect of change in sales volume, price and costs on profit can be depicted graphically as follows :14.10.1 Effect of Price Change on ProfitWhen price is increased, the slope of sales revenue line become more steep and break even point lowers from BEP0 to BEP1, the margin of safety increases from BEP0X to BEP1X angle of incidence also increases. The reverse happens in case of decrease in price.

New Sales Line

(Rs)

Variable costFixed cost

NEW M/S

Old M/S

Total cost

Actual Sales

Output (units)

BEP1

BEP1

BEP1BEP1O X

YC

ost/S

ales

Profit after change in price

Profit after change in priceOld

Sales L

ine

14.10.2 Effect of Change in Fixed Cost on ProfitIncrease in fixed cost leads to increase in break even point, lowers the margin of safety and no impact on angle of incidence (Parallel lines)

Sales Line

BEP1

BEP1

Variable cost

Total cost

Actual Sales

Output (units)Effect of Change in Variable Cost

XO

Y

New Total Cost

BEP0

Cos

t/Sal

es (R

s.)

Old M/S

New M/S

Old fixed cost

New fixed cost

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Cost Volume Profit Analysis14.10.3 Effect of Change in Variable CostIncrease in variable costs leads to higher break even point, lowers the margin of safety and reduces the angle of incidence.

New M/S

Old M/S

X

Y

O Actual Sales

Fixed cost

Output (units)

New profit Old profit New variable costOld variable cost

BEP1BEP0

BEP0

Cos

t/Rev

enue

Sales Line

BEP1

Activity 3Try to find out the relationships between change in price, fixed cost, variable costs and volume on profit, margin of safety and profit volume ratio through the following equations: Break Even Points (in units) =

Fixed CostSales Price – Variable Cost Per Unit

Break Even Points (in value) = Fixed CostP/V Ratio

Margin of Safety = Actual Sales – Sales at BEP

P/V Ratio = Sales – Variable Costs

Sales = Contribution

Sales

14.11 PROFIT VOlUME GRAPhProfit-Volume Graph is the graphical representation of the relationship between profit and volume. It shows profit or loss at different levels of output. It is also called the P/V graph. This type of graph may be preferred to know the profit or loss directly at different levels of activity. Following steps are involved in the construction of profit- volume graph:1) Fixed Costs and profits are depicted on the y-axis or vertical axis.2) Sales are shown on the x-axis or horizontal axis.3) Area above the sales line (x-axis) is a “profit area” and below it is the

“loss area”. At zero output, the loss equals to fixed cost. Profit at a particular sales level is depicted on y-axis above the sales line.

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4) After plotting profits and fixed costs, these two points are joined by a diagonal line which is called profit line or contribution line or fixed cost recovery line or profit-volume line. The break even point occurs at a point where contribution line intersects the horizontal line.

Let us see the following illustration how a P/V graph is prepared.Illustration 13Prepare a P/V graph with the help of the following data : Output = 2,00,000 units Sales = Rs.6,00,000 FC = Rs. 1,00,000 VC = Rs.4,00,000 Profit = Rs.1,00,000 Solution

Profit Volume Graph

Proft

Sales volume

Cos

t/Rev

enue

Fixed cost

BEP

Contribution line

Loss area

+ 1,00,000

2,00,000

– 1,00,000

Y

0

Better P/V ratio is an index of sound financial health. P/V ratio can be improved by taking following steps:

● Increase in Sale Price ● Decrease in variable costs ● Change in sales mix, i.e. producing more of an item where P/V ratio

is high along with demand or droping or decrease the production of a products whose P/V ratio is very low as per situation.

Illustration 14ABC Ltd., a multi product company, furnishes the following data:

Particulars Period I Period IISales (Rs) 45,000 50,000

Total Cost (Rs) 40,000 43,000Assuming that there is no change in price and variable costs. Fixed expenses are incurred equally in the two periods. Calculate the following :i) Profit volume ratioii) Fixed expensesiii) Break even pointiv) Percentage M/S to sales in Period II

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Cost Volume Profit Analysisv) Sales required to earn profit of Rs. 10,000 vi) Profit when sales is Rs. 80,000 .Solution

Sales (Rs.) Total Cost (Rs.) Profit (Rs.)Period II 50,000 43,000 7,000Period I 45,000 40,000 5000

Change 5000 3000 2000

i) P/V ratio = Change in ProfitChange in Sales =

Rs. 2000Rs. 5000 = 0.40

ii) Fixed expenses Contribution = Sales × P/V ratio Period I Contribution = Rs.50,000 × 0.40 = Rs. 20,000

Contribution = Fixed Cost + Profit Rs. 20,000 = F C + Rs. 7000 F C = Rs. 13,000 Period II Contribution = Rs.45,000 × 0.40 = Rs.18,000 F C = Contribution – Profit = Rs.18,000 – Rs. 5000 = Rs. 13000iii) Break even point BEP (in Value) =

Fixed CostsP/V Ratio

= Rs. 13,000

0.40 = Rs. 32,500

iv) Margin of Safety (M/S) = Actual Sales – BEP (in value) = Rs. 50,000 – Rs. 32,500 = Rs. 17,500

% of M/S to Sales = Rs. 17,500Rs. 50,000 × 100

= 35%v) Sales required to earn a desired profit of Rs. 10,000

= FC + DPP/V Ratio

= Rs. 13,000 + Rs. 10,000

0.40 = Rs. 57,500vi) Profit when sales is Rs. 80,000 Contribution = Sales × P/V ratio = Rs.80,000 × 0.40 = Rs. 32,000

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∴ Profit = Contribution – FC = Rs. 32,000 – Rs. 13,000 = Rs. 19,000Activity 4 : Think on the following relationships:1) An increase in selling price increases the amount of contribution

resulting in higher P/V ratio or contribution ratio and vice versa.2) An increase in fixed cost increases the break-even point but does not

affect the P/V ratio.3) An increase in variable cost per unit reduces the contribution per

unit, increases the break-even point and lowers the P/V ratio and vice versa.

4) Increase in P/V ratio lowers the break even point and vice versa.

14.12 ASSUMPTION IN BREAk EVEN ANAlySISBreak even analysis is based on certain assumption, which are:1) All costs can be segregated in two parts i.e., fixed and variable.2) Fixed costs remains constant at various levels of activity.3) Variable costs changes directly with production. It means variable

cost per unit remains constant.4) Selling price per unit remains constant at all various levels of activity.5) Technological methods and efficiency of men and machines will not

be changed.6) Production and sales are perfectly synchronized i.e., no inventory

exists in the beginning or at the end of the period.7) Either there is only one product or if several products are being

produced and sold then sales mix remains constant.8) Break even analysis assumes linear relationship in total costs and total

revenues.9) Break even analysis ignores the capital employed in the business.The above assumptions are also the limitations of this analysis e.g. selling price per unit and variable cost per unit remains constant at any level of activity. The production and sales can be increased upto the maximum plant capacity so long as contribution is positive. This assumption is valid if it is not necessary to reduce the selling price per unit to increase the sales.The variable cost per unit do not have a linear relationship with level of production because of laws of return. In economic theory, initially total cost will increase at a decreasing rate, then at a constant rate and finally at increasing rate.Further production and sales are not perfectly synchronized as there will be some opening and closing inventory. Technological methods and efficiency of men and machines keeps changing. To increase the sales, price concessions are offered to the customers. The break even chart, therefore becomes curve-linear having the following shape.

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Cost Volume Profit Analysis

Cos

t/Sal

es R

even

ue(R

s.)

Sales Volume

Sale Revenue

X

Y

Total Cost

BEP2

BEP1

In curve-linear model, the optimum production level is where the total revenue exceeds the total cost by the largest amount. There are two break-even points, one at the lower capacity level and other at the higher capacity level. No firm would like to operate at a lower level then BEP1 as it is loss zone and beyond BEP2 point which is again a loss zone. The economist’s model is valid over a range of activity and it allows production, inputs costs, selling price to vary. The accountant model is valid only for a short relevant range of activity where only quantity varies, price and cost structure is constant.Check your ProgressA. 1) In cost-volume-profit analysis, profit is determined by a) Sales Revenue x P/V ratio - Fixed Cost b) Sales units x contribution per unit - fixed costs c) Total contribution - Fixed cost d) All the above 2) Variable costs per unit a) Goes on increasing with production b) Goes on decreasing with production c) Remains constant with change in production d) None of these 3) Variable cost are those which a) Are directly apportioned to cost unit or cost centre b) Varies directly with production c) Depends upon the demand d) Depends upon the sale 4) In accounting, marginal cost per unit goes on, with increase

in production a) Increases b) Decreases c) Remain constant d) None of these 5) Which is not a fixed cost a) Property tax b) Power c) Insurance premium d) Rent

O

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6) Fixed cost per unit with increase in production a) Increases b) Decreases c) Remains constant d) Can’t say 7) Semi variable cost are segregated into fixed and variable costs

with the help of a) Scatter diagram b) Method of least square c) High and low points method d) All the above 8) Telephone charges is a a) Fixed cost b) Variable cost c) Semi-variable cost d) Marginal cost 9) The break even points in units is equal to a) Fixed cost/PV ratio b) Fixed cost x sales/total contribution c) Fixed cost/contribution per unit d) Fixed cost/total contribution 10) At the break-even point, which equation will be true. a) Variable cost - fixed cost = contribution b) Sales = variable cost + fixed cost c) Sales – fixed cost = contribution d) Sales – contribution = variable cost 11) When fixed costs increases, the break even point a) Increases b) Decreases c) No effect d) Can’t say 12) When variable costs decreases, then break even point a) Increases b) Decreases c) No effect d) Can’t say 13) When selling price decreases, then break even point a) Increases b) Decreases c) No effect d) Can’t say 14) When sales increases then break even point a) Increases b) Decreases c) Remains constant d) None of these 15) Contribution is a) Fixed cost + profit b) Sales - variable cost c) Fixed cost – loss d) All the above

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Cost Volume Profit Analysis 16) P/V ratio is a) Profit/volume b) Contribution/sales c) Profit/contribution d) Profit/sales 17) Profit - volume ratio is improved by reducing a) Variable cost b) Fixed cost c) Both of them d) None of them 18) The price reduction policy, _____ the P/V ratio and _____ the

break even point a) Reduces, reduces b) Reduces, increases c) Increases, reduces d) Increases, increases 19) Shut down point occurs when a) Net profit is zero b) Sale revenue - variable cost + fixed costs c) Losses are greater than fixed cost d) None of the above 20) The break even point and shut down point are a) Synonymous b) Anonymous c) Different d) Can’t say 21) The sales of a firm is Rs. 3,00,000, fixed cost is Rs. 90,000, and

variable costs are Rs. 2,00,000, the break even point will occur at

a) 2,70,000 units b) Rs. 2,70,000 c) Rs. 3,25,000 d) 3,25,000 units 22) The financial accounts of a firm reveals the position at two time

periods is as follows:

Period Sales Rs. Profit Rs.

I 2,30,000 50,000

II 3,00,000 80,000

The profit volume ratio for the firm will be a) 3/7 b) 5/8 c) 3/8 d) 13/53 23) The fixed cost of a firm is Rs. 90,000, variable cost per unit is

Rs. 2 and sale price is Rs. 3 per unit. The break even point will occur at

a) 30,000 units b) 50,000 units c) 90,000 units d) Rs. 90,000 24) The sales volume in value required to earn the target profit, the

formula is a) Target profit/contribution per unit b) (Fixed cost + Target profit) P/V ratio

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c) Fixed cost + Target profit/contribution on per unit d) (Fixed cost + Target profit) / PV ratio 25) The contribution per unit is Rs. 2 and fixed costs are Rs. 15,000

for earning a profit of Rs. 50,000, the company must have sales of a) Rs. 1,30,000 b) Rs. 1,00,000 c) 32,500 units d) Rs. 32,500 26) Margin of safety is expressed as a) Profit / P/V ratio b) (Actual sales – sales at BEP ) / Actual sales c) Actual sales – Sales at BEP d) All of the above 27) The margin of safety point lies a) To the left of break even point b) To the right of break even point c) On break even point d) Can’t say 28) The sale at a BEP for a firm is Rs. 4,80,000 and the actual sales

made by the firm Rs. 8,00,000, the margin of safety will be a) Rs. 12,80,000 b) Rs. 3,20,000 c) Rs. 4,80,000/8,00,000 d) Rs. 800,000 29) The profit of a company is Rs. 30,000 by selling 10,000 units

at a price of Rs. 10 per unit. The variable cost to sale ratio is 60 per cent. Find margin of safety level.

a) Rs. 75,000 b) Rs. 30,000 c) Rs. 1,00,000 d) Rs. 12,000 30) In the above question, determine the break even point a) Rs. 20,000 b) Rs. 25,000 c) Rs. 30,000 d) Rs. 40,000 B) State whether the following statement are True or False. i) Contribution is the difference between the total sales and fixed

cost. ii) At break even point contribution equals to fixed cost. iii) Profit volume graph shows profit or loss at different levels of

sales. iv) Profit volume graph can also be called P/V graph. v) P/V ratio can be improved by decreasing the selling price. vi) P/v ratio can be improved by reducing the fixed costs. vii) Margin of safety may be improved by increasing selling price

and reducing fixed cost. viii) At break-even point sales equal to total cost.

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Cost Volume Profit Analysis14.13 lET US SUM UPBreak even analysis helps is ascertaining the level of production where total costs equals to total revenue. Below this level of production, there are losses and above this point depicts the profit zone. Like marginal costing this analysis is also based on cost classification into fixed and variable costs. Break even analysis helps in measuring the effect of charges in volume, costs, selling price and product mix on profit. In fact, break even analysis is cost-volume profit analysis.Break even point can be determined both mathematically (equation technique and contribution margin technique) and graphically. It is expressed in terms of units or invalue terms. This technique is very useful in profit planning and decision making. It can be applied to estimate profits at a given sales volume, sales volume required to earn a desired profit, calculating sale volume required to offset price reduction, ascertaining the margin of safety, measuring the effect of changes in profit factors etc. The other tools in this analysis are profit-volume ratio, margin of safety and angle of incidence.There are inherent limitations in the break even analysis –classification of costs into fixed and variable costs, fixed costs remains fixed, variable cost per unit is constant, selling price per unit is constant etc. In spite of its limitation the break even point is a useful technique in decision making if it used by those who understand its limitations.

14.14 kEy WORDSBreak Even Point is the level of sales (volume or value) where total costs equals to total revenue or no profit no loss point.Cost-volume-Profit analysis is technique to study the effects of costs and volume variations on profit.Margin of Safety is the difference between actual sales and sales at break even point. It shows the amount by which sales may decrease before losses occur.Profit Volume Ratio is a relationship between contribution to sales.Mixed Costs are those costs which has both fixed and variable elements. These are also known as semi-variable costs.

14.15 ANSWERS TO ChECk yOUR PROGRESSA 1 d 7 d 13 a 19 c 25 c

2 c 8 c 14 c 20 c 26 d

3 b 9 c 15 d 21 b 27 c

4 c 10 b 16 b 22 a 28 b

5 b 11 a 17 a 23 c 29 a

6 b 12 b 18 b 24 d 30 b

B) i) False ii) True iii) True iv) True v) False vi) False vii) True viii) True

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Marginal Costing and Cost Volume Profit Analysis 14.16 TERMINAl qUESTIONS

1) ‘Cost-volume profit analysis and break even point analysis are same’ Comment?

2) What are different methods of computing break even point?3) “The break even chart is an excellent planning device” Comment.4) Explain the significance of Profit-Volume ratio, Margin of Safety and

Angle of Incidence?5) What is Contribution ? How does it helps the management in taking

managerial decisions?6) Describe three ways to lower down the break even point?7) What are various ways to improve the margin of safety and P/V ratio?8) ‘A 10 per cent increase in production and sales leads to more than 10

percent increase in profit’ Explain9) ABC Ltd. manufactures and sells four type of products under the brand

names of P, Q, R and S. The sale mix in value comprises of 34%, 40%, 16% and 10% of P,Q, R and S respectively. The total budgeted sales (100%) are Rs. 60,000 per month. Operating costs are:

Variables costs ratio is (variable costs on % of sales)

P 60%Q 65%R 70%S 40%

Fixed costs is Rs. 15,000 per month. Calculate the break even point for the products on an overall basis. (Ans BEP Rs. 39062.50)

10) Explain from the following data, how the reduction in selling price would affect the break even point and margin of safety.

Selling price per unit Rs. 20 Variable costs Material Rs. 6 Labour Rs. 4 Variable overheads Rs. 2 Fixed overheads is Rs. 8000. Full capacity of the plant is 5000 units.

Reduced selling price is Rs. 16 per unit. [Ans. BEP increase by 1000 units and M/S decrease by Rs. 32000]11) The sales manager of a company found that with fixed cost Rs.

50,000, sales are increased from Rs. 30,000 to Rs. 4,00,000 and profit increased by Rs. 40,000. Compute the profit when sales is Rs. 5,00,000.

[Ans. Rs. 1,50,000] 12) ABC Ltd., has a margin of safety 37.5% with an overall contribution

sale ratio of 40%. The fixed cost is Rs. 5 lakhs. Calculate the following:

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Cost Volume Profit Analysis i) Break even point ii) Total Sales iii) Total variables costs iv) Profit [Ans. (i) Rs. 12,50,000 (ii) Rs. 20,00,000 (iii) Rs. 12,00,000 (iv) Rs. 3,00,000]13) The P/V ratio of a concern is 50% and margin of safety is 40%.

Calculate the net profit of the sales is Rs. 1,00,000. [Ans. Profit Rs. 20,000]14) X Ltd. was earned a contribution of Rs. 2,00,000 and net profit of Rs. 15,000 on sales of Rs. 800,000. What is the break even point and margin of safety. [Ans. Rs.200000, M/s is Rs. 600,000]15) Form the following cost information : 2001 2002 Sales (Rs) 150000 200000 Profit (Rs.) 30000 50000 Calculate : (i) P/V ratio (ii) Break even point (iii) Sales required to earn a profit of Rs. 80,000 (iv) Profit when sales is Rs. 250,000 [Ans. (i) 0.40 (ii) Rs. 75,000 (iii) Rs. 275,000 (iv) Rs. 70,000

14.17 FURThER READINGSHorngren, C.T., Gary L. Sundem and Frank H. Selto, “Management Accounting”, Prentice Hall of India, New Delhi, 1994.Kaplan, R.S., s, Engle Wood Cliffs, NJ., Prentice Hall Inc.

Note : These questions will help you to understand the unit better. Try to write answers for them. But do not submit your answers to the University. These are for your practice only.

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UNIT 13: MARGINAl COSTING - eGyanKosh