COST – VOLUME – PROFIT ANALYSIS (Contribution Margin Approach)

This topic is based on your knowledge of cost behavior and shows how this is applied in a decision-making situation. Cost-volume-profit (CVP) analysis is a technique which uses cost behavior theory to analyze the activity level as to the contribution margin and fixed cost relationship and the level at which there is neither a profit nor a loss (the break-even activity level). This is important management information because managers need to know the minimum activity level that must be achieved in order that the business does not incur losses. CVP analysis may also be used to predict profit levels at different volumes of activity based upon the assumption that costs and revenues exhibit a linear relationship with the level of activity.

Cost-volume-profit analysis determines how costs and profit react to a change in the volume or level of activity, so that management can decide the ‘best’ activity level.

Following are the assumptions which are used in CVP analysis.

1.  Variable costs and selling price (and hence contribution) per unit are assumed to be unaffectedby a change in activity level.

2.  Fixed costs, whilst not affected in total by a change in the activity level, will change per unit as the activity level changes and there are more (or less) units over which to “share out” the fixed costs If fixed costs per unit change with the activity level, then profit per unit must also change.

Thus, cost-volume-profit analysis is always based on contribution per unit (assumed to be constant unless a question clearly says otherwise) and never on profit per unit because profit per unit changes every time a few more or less units are made.

CVP is a relationship of four variables

Sales

Volume Variable cost

Cost Fixed cost

Cost Net income

Profit

This may be understood through the following equation

Volume @ sales price = Revenue Cost matching with the sales = (Cost) Result = Profit

CVP analysis is a tool for decision making. There are two approaches of CVP analysis:

1.  Contribution margin approach

2.  Break even analysis approach

Contribution Margin Approach & CVP Analysis

Contribution margin contributes to meet the fixed cost. Once the fixed cost has been met the incremental contribution margin is the profit. Income Statement as per the marginal costing system is used as a Standard format of Income Statement to analyze the Cost-Volume-Profit relationship.

Rs. Sales xxx Variable Cost xxx Contribution Margin xxx Fixed Cost xxx Profit xxx

PRACTICE QUESTION Basic question

90 units of product “PR” is sold for Rs. 100 per unit. Variable cost relating to production and selling is Rs. 75 per unit and fixed cost is Rs. 2,250.

Q. 1. Management decides to increase its sales by 10 units. Required: Prepare income statement and analyze.

Solution
Rs. Rs. Rs.
Sales (90 x 100) Variable cost (90 x 75) Contribution margin Fixed cost Profit / Loss 9,000 (6,750)2,250 (2,250) 0 (10 x 100) (10 x 75) 1,000 (750) 250 0 250 10,000 (7,500) 2,500 2,250 250
Analysis

This shows physical increase in volume causes an increase in contribution margin and if there is not increase in the fixed cost because of such change, the incremental contribution margin is added in the final profits.

Q. 2. Management decides to increase its sales price by 10%. Continue with the Q. 1. Required: Prepare income statement and analyze.

Solution

Sales 100 x Rs 110 11,000 Variable cost 100 x Rs. 75 (7,500) Contribution margin 3,500 Fixed cost (2,250) Profit 1,250

Analysis

This shows increase in sales price per unit causes an increase in the contribution margin, as there is not change in the volume the fixed will remain unchanged. So the incremental change is contribution margin is included into the profit.

Q. 3. Management decides to decrease its sales price by 10%. Continue with the Q. 1. Required: Prepare income statement and analyze.

Sales 100 x Rs 90 9,000 Variable cost 100 x Rs 75 (7,500) Contribution margin 1,500 Fixed cost (2,250) Loss (750)

Analysis

This shows decrease in sales price per unit causes a decrease in the contribution margin, as there is not change in the volume the fixed will remain unchanged. So the change in contribution margin is subtracted from the profits, which result into a loss of Rs. 750 in this case. Normally a decrease in sales price should case an increase in the sales volume.

Q.4. Management decides to decrease its sales price by 10% and expects an increase in sales volume by 50%. Continue with the Q. 1. Required: Prepare income statement and analyse.

Solution

Sales 150 x Rs 90 13,500 Variable cost 150 x Rs 75 (11,250) Contribution margin 2,250 Fixed cost (2,250) Loss 0

Analysis

This shows decrease in sales price per unit causes a decrease of Rs. 1,000 in the contribution margin, as well as an increase in volume is causing an increase in the profit, this results in an increase in profit. Here in this scenario the increase in the volume must be more than 50% to earn profits.

Q.5. Management decides to decrease its sales price by 10% and expects an increase in sales volume by 200%. Continue with the Q. 1. Required: Prepare income statement and analyse.

Solution

Sales 200 x Rs 90 18,000 Variable cost 200 x Rs 75 (15,000) Contribution margin 3,000 Fixed cost (2,250) Profit 750 Analysis

This shows decrease in sales price per unit causes a decrease of Rs. 1,000 in the contribution margin, as well as an increase in volume is causing an increase in the profit, this results in an increase in profit. Here in this scenario the increase in the volume must be more than 50% to earn profits.

Q.6. Management decides to increase its sales volume by 100% and it is also assumed that the fixed cost also increase upto Rs. 2,500. Continue with the Q. 5.

Required: Prepare income statement and analyse.
Solution
Sales Variable cost Contribution margin Fixed cost Profit 200 x Rs 90 200 x Rs 75 18,000 (15,000) 3,000 (2,500) 500
Analysis

This shows a decrease in fixed cost causes a decrease in the profits.

Q.7. Management decides to increase its sales volume by 100% and it is also assumed that the fixed cost also increase upto Rs. 2,500, and also there is an increase of 20% in the variable cost. Continue with the Q. 6. Required: Prepare income statement and analyse.

Solution

Sales 200 x Rs 90 18,000 Variable cost 200 x Rs 90 (18,000) Contribution margin 0 Fixed cost (2,500) Loss (2,500)

Sales *** Variable cost (***) Contribution margin *** Fixed cost (***) Profit / Loss ***

This lesson ends up at following lessons:

1.  At zero contribution margin the loss will be equal to the fixed cost

2.  Increase in variable cost reduces the contribution margin

3.  Sales – Variable cost = Contribution margin

4.  Contribution margin + Variable cost = Sales

5.  Contribution margin – Fixed cost = Profit

6.  Profit + Fixed cost = Contribution margin

7.  Sales – Variable cost = Fixed cost + Profit

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