Cost and Management Accounting

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LESSON# 30
COST ­ VOLUME ­ PROFIT ANALYSIS
(Break-even Approach)
Break-even
Cost-volume-profit analysis can be used to calculate break-even.
Break-even is the point where sales revenue equals total cost, i.e. (here is neither a profit nor a loss.
Profit (or loss) is the difference between contribution margin and fixed costs.
Thus the break-even point occurs where contribution margin equals fixed costs
Target Contribution Margin
Target contribution margin is the amount which if equal to fixed cost will give nil net profit,
whereas, if we need to earn a target profit, such profit will be added up into the fixed cost to have
target contribution margin.
Contribution margin per unit can be assumed to be constant for all levels of output in the relevant
range. Similarly, fixed costs can be assumed to be a constant amount in total.
The relationships may be depicted thus:
Contribution Margin per unit
Selling price per unit less variable costs per unit
Total contribution
Volume x (Selling price per unit less variable costs per unit)
Target Contribution Margin
Fixed costs + Profit target
Target Sales in number of units
Target Contribution Margin
Unit contribution
Contribution may be calculated in total, or on a per-unit basis using selling prices and variable costs
per unit.
The difference between contribution and fixed costs is profit (or loss); thus when contribution
equals fixed costs, break-even occurs. In this way a target profit may be converted into a target
contribution margin which may be used to calculate the number of units required to achieve the
desired target profit.
Contribution margin to sales ratio
Contribution to sales ratio (C/S ratio) =
Contribution Margin in Rs
Sales in Rs
Note: you may encounter the term profit to volume (or P/V) ratio, which is synonymous with the
contribution to sales ratio. Profit to volume is an inaccurate description, however, and should not
be used. The C/S ratio is conveniently written as a percentage.
Break even point refers to the volume (sales) at which the entity earns no profit and suffers no
loss.
It is the point where
Contribution margin = Fixed cost
And
Target profit = 0
Contribution margin ­ Fixed cost = 0 Profit
Contribution margin = Fixed cost + 0 Profit
At break even point the target contribution is equal to the fixed cost
Contribution Margin ­ Fixed cost = Profit
185 Cost & Management Accounting (MGT-402)
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Contribution margin = Fixed cost + Profit
Practice Question
Q. 1
Income Statement
Rs.
Sales
700 units x Rs 8
5,600
Variable cost 700 units x Rs 6
4,200
Contribution margin
1,400
Fixed cost
1,000
Profit
400
Variable cost over sales
4,200 x 100 = 75%
5,600
Contribution margin over sales
1,400 x 100 = 25%
5,600
Per Unit Calculation
Sales price
Rs 8
Less Variable cost
(6)
Contribution Margin
2
6 / 8 x 100 = 75%
2 / 8 x 100 = 25%
Total
per unit
%
Sales
700 units x Rs 8
5,600
8
100%
Variable cost 700 units x Rs 6
4,200
6
75%
Contribution margin
1,400
2
25%
Fixed cost
1,000
Profit
400
Break even sales in Rupees
Remember the formula to calculate required amount in absence of certain information:
Given Amount x
% of required amount =
Required Amount
% of given amount
Here, to calculate break even sale, we need contribution margin to be equal to the fixed cost so
that the profit is zero.
Now if the target contribution margin is equal to Rs. 1,000 then what would be the sales at this
point?
Now the above formula will be applied to calculate breakeven sales:
Target CM is the given amount and its % is 25, so the sale which is 100% will be:
Rs 1,000 x
100 = Rs 4,000
25
OR
186 Cost & Management Accounting (MGT-402)
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Rs 1,000 x 1 =
Rs. 4,000
25
OR
Rs 1,000 =
Rs. 4,000
25
So,
Break even Sales in Rs. =
Fixed cost
C/S ratio
Check
Income Statement
Rs.
Sales
500 units x Rs 8
4,000
Variable cost 500 units x Rs 6
3,000
Contribution margin
1,000
Fixed cost
1,000
Profit
0
Break even sales in units
Simple formula:
Break even sales in Rupees = number of units
Sales price per unit
4,000 = 500 units
8
Direct formula
Target CM
CM per unit
Here the target contribution margin is equal to the fixed
Fixed Cost
CM per unit
Rs. 1,000
= 500 units
2
Break even sales in Rupees =
Target CM
Contribution to sales ratio
Break even sales in units=
Target CM
Contribution margin per unit
Q. 2
Calculate Sales to target profit of Rs. 500, using the information given in practice question no. 1.
Sales
***
Variable cost
(***)
Contribution margin
***
Fixed cost
1,000
Profit
500.
187 Cost & Management Accounting (MGT-402)
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Target contribution margin = Fixed cost + Target profit
=
1,000 +
500
=
1,500
Sales to earn target profit of Rs. 500
= Rs 1,500 x 100 = Rs. 6,000
25
=
Rs 1,500 = Rs. 6,000
0.25
Check
Income Statement
Rs.
Sales
6,000
Less Variable cost
4,500
Contribution Margin
1,500
Less Fixed cost
1,000
Profit
500
Fixed cost + Target profit
Contribution to sales ratio
Problem Question
A company sold fans at Rs 2,000 each. Variable cost Rs. 1,200 each and fixed cost Rs. 610,000.
Calculate:
a. Calculate break even sales in Rupees.
b. Break even sales in units.
c. Sales in units to earn a profit of Rs. 20,000.
Multiple Choice Questions
The following details relate to a shop which currently sells 25,000 pairs of shoes annually.
Selling price per pair of shoes
Rs.40
Purchase cost per pair of shoes
Rs.25
Total annual fixed costs
Rs.
Salaries
100,000
40,000
Other fixed expenses
100,000
Q. 1
What is the contribution per pair of shoes?
A Rs.15
B Rs.30
C Rs.7.50
D Rs.18
Q. 2
What is the break-even number of pairs of shoes?
A 14,000
B 16,000
C 28,000
D 32,000
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