Cost Volume Profit Analysis

Cost-Volume-Profit Cost-Volume-Profit AnalysisAnalysis

Introduction:Introduction:

CVP analysis is a technique that may be used by a management accountant to evaluate how costs and profits are affected by changes in the volume of business activities. Managers are often faced with decision situations involving sales level, sales mix, selling prices and the right combination of these factors that will produce acceptable profits.

CVP analysis is a systematic method of examining the relationship between change in volume (or output) and changes in sales prices and expenses on the profit of the firm. It helps in identifying the effect on profit of a specified level of activity or turnover changes. It enables the management to change the key variables in CPV relationships and quickly see the effects on the profit figure.

Techniques of CVP AnalysisTechniques of CVP Analysis The key elements in the CVP analysis are selling prices, sales

volume, variable cost per unit, total fixed costs and the sales mix (if the firm is dealing with more than one product at a time).

Two basic techniques of CVP analysis:

1. The Contribution Margin Analysis

2. The Break-Even Analysis

1.Contribution margin 1.Contribution margin analysisanalysis CM= Sales-Variable Cost CM Ratio= selling price-variable cost 100

selling price As the selling price p.u and the variable cost p.u are assumed to

be constant, the CM p.u also remains constant. Ex: selling price is Rs.50 and variable cost is Rs.30. So, the CM is Rs.20 p.u. Each unit sold by the firm generates a contribution of Rs.20, which is available to recover fixed costs and after they are covered, to contribute to the profit of the firm.

CM Ratio= 50-30 100 =40%

50 CM Ratio is also known as Profit-Volume Ratio (PV ratio) or

Contribution to sales ratio. Suppose in the above case, the firm is selling 1000 units and the

fixed cost of operations is Rs.12,000. the contribution margin and the net profit will be:

CM=Sales*CM Ratio

= (1,000*50)*40%

=Rs.20,000

Net Profit= CM-Fixed Cost

= 20,000-12,000

= Rs.8,000

Now if sales increases by 100 units or Rs.5,000, then the CM as well as NP both will increase by 40% of Rs.5000 i.e. Rs.2,000.

Verification : CM= sales *CM ratio

=55,000*40%

=Rs.22,000

Net Profit= 22,000-12,000

=Rs.10,000 The CM is the difference btw sales and variable cost.

CM=Sales-VC

Or VC=sales-CM Now if sales is 100% and the CM ratio is 40%, the VC Ratio is

(100-40)=60%. So if that sales are increasing by Rs.5,000 then the VC will also increase by 60% of Rs.5,000 i.e. Rs.3,000. The existing VC Rs.30,000( 1,000*30) and the new VC will be Rs.33,000 (1,100*30). So, VC Ratio is defined as :

VC Ratio =100% - CM Ratio

In case, the sales volume is expressed in no. of units, the CM per unit (called Unit Contribution Margin) is relevant to find out the total CM.

Total CM = No. of units sold * CM per unit

If sales are given in total money value, the CM Ratio is relevant.

Total CM= Total sales *CM Ratio

2. Break even analysis2. Break even analysis Is the fundamental technique of CVP Analysis. The BE point is the

sales level at which the contribution margin is just equal to the fixed cost, and the firm has no profit no loss.

Any sales level below the BE Level will therefore result in loss and sales level above the BE Level will bring profit to the firm.

Break even Equation:

Net Profit (NP)= Sales(S)-Variable cost(VC)- fixed cost (F)

or S = VC+F+NP

No. of units sold (U) *S.P =(no. of units sold*VC p.u) +F+NP

U*S.P = U*VC+F+NP At BE Level, the profit is zero and the above equation can be

written as:

U*S.P= U*VC+F

U(S.P-VC)=F

U = F

S.P-VC

U= F

Contribution p.u

illustration 1:illustration 1: R Ltd. is selling at present, 8,000 units of a product at a selling

price of Rs. 20 p.u. The variable cost is Rs. 10 p.u and the fixed costs are Rs.60,000 p.a. The firm can use the BE equation to answer the foll:

i. What is the BE sales level for the firm?

ii. How many units the firm must sell to earn a profit of Rs.40,000

iii. What will be the profit if the fixed costs are reduced by Rs.10,000 and the variable costs are reduced by 10%.

iv. What selling price will give a profit of Rs. 40,000 at a sales of 8,000 units.

v. How much extra sales must be made to meet the extra fixed cost of Rs.5,000

Solution : i. 6,000 units or Rs.1,20,000; ii. U=10,000; iii. NP= Rs.38,000; iv. S.P = Rs. 22.50; v. U=6,500

Margin of safetyMargin of safety A firm may be interested in evaluating and measuring the risk

involved in operating at different volumes. An important measure of risk, known as Margin Of Safety, is an integral part of CVP Analysis. The Margin Of Safety is the difference between actual sales (or the budgeted sales) and the BE sales for a given period. So, the margin of safety indicates by how much the sales can decrease before the firm incurs the loss.

In case of R Ltd., the BE sales level was 6,000 units. If the firm is operating at 6,000 units only, the margin of safety is zero and decline of even a single unit in sales volume will inflict a loss on the firm. If the firm expects a sales level of 8,000 units, then it has a margin of safety of 2,000 (8,000-6,000). The margin of safety can be presented as a % of sales or as an amount as follows:

Margin of safety =S.P *( actual sales- BE sales)

= Rs.20* (8,000-6,000)

=Rs.40,000

Or margin of safety= expected sales- BE sales

expected sales

=(8,000*20)- (6,000*20) =25%

(8,000*20)

A firm having large margin of safety is naturally less vulnerable to risk as compared to a firm having low margin of safety. The general rule is : the greater the margin of safety, lower the risk and vice versa.

Illustration 2: Two firms A and B Ltd. the sales and cost information for these 2 firms are given as follows:

Analyze the cost information. [the difference in margin of safety can be traced to the fact that the

cost structures of 2 firms is entirely different. B Ltd has higher fixed cost as compared to A ltd. and the former would suffer losses more quickly than the latter in case of decrease in sales. This highlights that margin of safety is an indicator of degree of risk of the co.. If the firm has high risk as indicated by low margin of safety, foll steps must be taken to improve the position:

(1) Increasing the overall sales level; (2) reduction in fixed cost or conversion of FC into VC; (3) reducing the BE Level by increasing contribution].

A Ltd. B Ltd.

sales (units) 10,000 10,000

Selling price p.u Rs. 20 Rs.20

Variable cost p.u Rs.15 Rs.10

Fixed cost Rs.40,000 Rs.90,000

illustration 3:illustration 3: The BOD of F Ltd. , manufacturing three products A, B, and C

have asked for advice on the production mixture of the Co. relevant info is as follows:

A B C

Standard cost p.u:Direct material (Rs.)Variable o/hs (Rs.)

103

302

205

Direct labor:Dept:X Y Z

Rate per hrRe.0.50 1.00 0.50

Hours 28516

Hours1668

Hours 301030

Data from current budget:Production per year Selling price p. unit (Rs.)Fixed o/hs per year Rs.2,00,000Forecast of max. possible sale for the yr

A10,00050

12,000

B5,00068

7,000

C6,00090

9,000

However the type of labor required by Dept.Y is in short supply and it is not possible to increase the manpower of the dept. beyond its present level.

Prepare a statement of the most profitable mixture of the products to be made and sold. The statement should show:

1. The profit expected on the current budgeted production; and

2. The profits which could be expected if the most profitable mixture was produced.

illustration 4:illustration 4: A co. presents the foll cost estimates for 3 prospective plants

X, Y and Z.

1. Calculate the % BE sales to annual capacity.

2. If sales are steady at 1,00,000 units per year and the unit selling price is Rs.4 per unit, what will be the profits earned with each of the plants? Assume that Plant X can be worked double shift with an additional expense of 10% in fixed cost and 5% in variable costs of all units.

Plant X Plant Y Plant Z

Annual fixed cost (Rs.) 60,000 1,08,000 1,20,000

Variable cost p. u (Rs.) 2.50 2.20 2.10

Annual capacity (units) 75,000 1,20,000 1,50,000

illustration 5:illustration 5: ABC Ltd. manufactures and sells four products- I, II, III, IV. The

sales mix in value comprises 331/3 %, 412/3 %, 16 2/3% and 8 1/3% resp. out of the total sales of Rs.60,000

Operating costs are 60%, 68%, 80% and 40% resp. of the selling price.

Fixed costs are Rs.14,700 per month. The firm proposes to change the sales mix for the next month

to 25%, 40%, 30% and 5% resp. Calculate:

1. Break even point for the products on an overall basis for the current month.

2. Break even point for the products on an overall basis for the next month assuming that the sales mix is changed.

illustration 6:illustration 6: M Ltd. manufacturers three products P, Q,R. the unit selling

prices of these products are Rs.100, Rs.80 and Rs.50 resp. The corresponding unit variable costs are Rs.50, Rs.40 and Rs.20. The propositions (quantity wise) in which these products are manufactured and sold are 20%, 30% and 50% resp. the total fixed costs are Rs.14,80,000.

Given the above information, work out the overall break even quantity and product wise break up of such quantity.