# Cost and Management Accounting

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LESSON# 29
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 unaffected
by 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.
181 Cost & Management Accounting (MGT-402)
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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)
9,000 (10 x 100)
1,000
10,000
Variable cost (90 x 75)
(6,750) (10 x 75)
(750)
(7,500)
Contribution margin
2,250
250
2,500
Fixed cost
(2,250)
0
2,250
Profit / Loss
0
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
182 Cost & Management Accounting (MGT-402)
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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
200 x Rs 90
18,000
Variable cost 200 x Rs 75
(15,000)
Contribution margin
3,000
Fixed cost
(2,500)
Profit
500
Analysis
183 Cost & Management Accounting (MGT-402)
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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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