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Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
8. Dmytro runs a small company that makes skates and sells them for $450 each pair. He needs to sell 190 pairs of
skates to break even and has fixed costs of $28,500 per annum.
a. What is the contribution margin per pair of skates?
b. What are the variable costs per pair of skates?
c. What is the net income per annum if he sells 100 units above the break-even point?
9. Belle Inc. makes bags and sells them for $36 each. The total revenue at the break-even point is $81,000 per month
and the contribution margin per bag is $27.
a. Calculate the break-even volume.
b. Calculate the fixed costs per month.
c. Calculate the total revenue if the company sells 2500 bags in a month.
10. Elise and her friend Eloi developed an online car repair training course and sell it for $62.50 per course. The
contribution margin per course is $20 and to break even they need to have a total revenue of $175,000 per annum.
a. Calculate the break-even volume.
b. Calculate the fixed costs per annum.
c. Calculate the total revenue if they sell 3000 courses this year.
11. Zenith Lighting Inc. makes chandeliers and sells them for $650 each. The costs for administrative salaries, rent,
and utilities are $28,000 per month. The company also recruits a full-time sales person for a base salary of $3000
per month to sell the chandeliers. The sales person's commission on the sale of each chandelier is 5% on the selling
price. The variable costs (excluding the sales commission) are $220 per chandelier and the company can only
produce a maximum of 100 chandeliers every month. Calculate the maximum profit that can be made in a month.
12. Rehan a first semester student at a college, decided to start a trading business buying formal dress shirts for $10
from an overseas country and selling them to his college peers for $35 each. As he is not good at selling, he hired
his friend Ruby to sell these shirts and paid her 10% of the selling price as commission on every shirt she sold. If
he spent a flat rate of $20 on storage charges every month and could only purchase a maximum of 500 shirts every
month from his overseas vendor, calculate the maximum monthly profit that he can make in his business.
7.4 |
Contribution Margin Ratio
In Sections 7.2 and 7.3 you learned Cost-Volume-Profit (CVP) analysis and the Contribution
Margin (CM) approach to CVP analysis.
CVP analysis provides a relationship among the Selling Price (S), Total Revenue (TR),
Variable Costs (VC), Total Variable Costs (TVC), Fixed Costs (FC), Quantity (x) produced,
and Net Income (NI).
The CM approach provides information on the dollar amount from each unit of sales that is
available to cover the fixed costs and contribute towards the operating profits (Net Income).
In this section, you will learn about the Contribution Margin Ratio (CM ratio), which provides
information on the percent of each sales dollar that is available to cover fixed costs and contribute
to the net income.
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
Contribution Margin Ratio (CM Ratio)
The Total Contribution Margin (TCM) as a percent of the Total Sales Revenue (TR) is called
the Contribution Margin Ratio.
Total Contribution Margin = Total Revenue - Total Variable Costs
Therefore, CM Ratio =
Formula 7.4(a)
Total Revenue - Total Variable Costs
# 100%
Total Revenue
=
TR - TVC
# 100%
TR
Contribution Margin Ratio
CM Ratio =
For example, if the Total Sales are $200,000 and the Total Variable Costs are $140,000 then,
Using Formula 7.4(a), CM Ratio =
=
200, 000 - 140, 000
# 100 %
200, 000
60, 000
# 100%
200, 000
= 30.00%
The CM ratio measures the effect of Net Income when the Sales Revenue increases or decreases;
i.e., for each dollar increase in sales, the total contribution will increase by the amount equal
to the CM ratio and the Net Income will also increase by the amount equal to the CM ratio,
provided that the fixed costs remain the same. In the above example, if $20,000 in sales are
added, then the net income will increase by 30% of $20,000, which is equal to $6000.
The Contribution Margin Ratio is most useful when the increase or decrease in sales volume
is measured in sales amount.
The Net income (NI) can also be calculated using the CM ratio, as follows:
Formula 7.4(b)
Net Income
NI = (CM Ratio × TR) - FC
The relationship among Total Revenue (Sales Amount), Total Variable Costs, Contribution
Margin, Contribution Margin Ratio, Fixed Costs, and Net Income is shown in the following
diagram in a table form (vertical analysis):
-
-
Total Amount
Unit Price
Sales
TR
S
Variable Costs
TVC
VC
Contribution
Margin
TCM
CM
Fixed Costs
FC
Net Income
NI
Percent of Sales
237
238
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
Example 7.4(a)
Calculating the Contribution Ratio and Net Income
A company reported the following statement:
Number of units produced: 2000
Selling price per unit: $30
Variable cost per unit: $12
Fixed costs:
$15,000
Calculate the contribution margin ratio and net income.
Solution
Total Amount
Unit Price
Percent of Sales
$60,000.00
$30.00
100%
- TVC
$24,000.00
$12.00
40%
TCM
$36,000.00
$18.00
60%
TR
- FC
$15,000.00
NI
$21,000.00
From Formula 7.4(a),
CM Ratio =
Substituting the values, TR - TVC
# 100%
TR
=
60, 000.00 - 24, 000.00
# 100 %
60, 000.00
=
36, 000.00
# 100 %
60, 000.00
= 60.00%
From Formula 7.4(a),
NI = (CM Ratio × TR) - FC
Substituting the values,
= (0.60 × 60,000.00) - 15,000.00
= 36,000.00 - 15,000.00
= $21,000.00
Therefore, the contribution margin ratio of the company was 60.00% and the net income
was $21,000.00.
Example 7.4(b)
Calculating the Total Revenue Required to Break-Even, Given TVC as a Percent of TR
The variable costs of a product that a firm manufactures are 40% of selling price. The fixed costs
per year are $150,000. Calculate the break-even point in sales dollars.
Solution
At the break-even point in sales,
Net Income = 0
Therefore, TCM = FC = $150,000.00
TVC = 0.40TR
TCM = 0.60TR
0.60TR = 150,000.00
TR
Total Amount
% of Sales
$250,000.00
100%
- TVC
TCM
- FC
40%
$150,000.00
$150,000.00
TR = $250,000.00
NI
Therefore, the break-even point in sales dollars is $250,000.00
0
60%
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
Example 7.4(c)
239
Calculating the Sales Amount and the Contribution Margin Ratio, Given NI, TVC, and FC
The net income of a manufacturing company was $250,000. The variable costs are $192,500
and fixed costs are $107,500.
(i) Calculate the amount of sales.
(ii) Calculate the contribution margin ratio.
(iii) Calculate the amount of sales at break-even point.
Solution
Total Amount
% of Sales
$550,000.00
TR
- TVC
$192,500.00
TCM
$357,500.00
- FC
$107,500.00
NI
$250,000.00
(i) Using, 65%
TCM - FC = NI
TCM = FC + NI
Substituting the values,
= 107,500.00 + 250,000.00
= $357,500.00
Using,
TR - TVC = TCM
TR = TVC + TCM
Substituting the values, = 192,500.00 + 357,500.00
= $550,000.00
Therefore, the amount of sales was $550,000.00.
(ii) Using CM Ratio =
Substituting the values,
TCM
# 100 %
TR
=
357, 500.00
# 100 %
550, 000.00
= 65.00%
Therefore, the contribution margin ratio is 65.00%.
(iii) At break-even, Net Income = 0
Therefore, Total Contribution Margin = Total Fixed Costs = $107,500.00
Using, TCM
CM Ratio = TR # 100 %
107, 500.00
Substituting the values, 65% =
# 100 %
TR
TR =
107, 500.00
# 100
0.65
= $165,384.62
Total Amount
TR
% of Sales
$165,384.62
- TVC
TCM
$107,500.00
- FC
$107,500.00
NI
Therefore, the amount of sales at break-even point is $165,384.62.
0
65%
240
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
Example 7.4(d)
Calculating the Additional Sales Required to Break-Even When Variable Costs Increase
Alfred Yeung Toys and Gifts has a fixed cost of $360,000 per annum and the variable costs are
70% of sales. If the variable costs increased to 75% of sales, what additional sales must be made
to break-even?
Solution
Sales at break-even when TVC = 0.70TR
Total Amount
% of Sales
100%
TR
- TVC
TCM
- FC
70%
$360,000.00
30%
$360,000.00
0
NI
TVC = 0.70TR
At BE, NI = 0
Therefore, TCM = FC = 360,000.00
Also, TCM = TR - 0.70TR
= 0.30TR
360, 000.00
0.30
TR =
TR = $1,200,000.00
Sales at break-even when TVC = 0.75TR
Total Amount
100%
TR
- TVC
TCM
- FC
% of Sales
75%
$360,000.00
25%
$360,000.00
NI
0
TVC = 0.75TR
At BE, NI = 0
Therefore, TCM = FC = 360,000.00
Also, TCM = TR - 0.75TR
= 0.25TR
360, 000.00
0.25
TR = $1,440,000.00
TR =
Therefore, the additional sales required to break-even is: 1,440,000.00 - 1,200,000.00 = $240,000.00
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
Example 7.4(e)
241
Calculating the Change in Net Income when the Selling Price is Reduced and the Sales
Volume is Increased
A manufacturer of air-conditioning units has fixed costs of $120,000 per annum. The variable
costs are 40% of sales and profit was $66,000. When the selling price was reduced by 2%, the
sales volume increased by 24%.
(i) What was the original sales revenue?
(ii) What were the original variable costs?
(iii) What is the new sales revenue?
(iv) What are the new variable costs?
(v) What is the amount of change in net income?
Solution
Using, Contribution margin - Fixed costs = Net income
Rearranging,
TCM = FC + NI
Substituting the values, = 120,000.00 + 66,000.00
= $186,000.00
TCM = TR - TVC
Substituting the values, = TR - 0.40TR
= 0.60TR
Therefore, 0.60TR = 186,000.00
186, 000.00
(i) TR
=
S=
0.60
= $310,000.00
Total Amount
% of Sales
TR
$310,000.00
100%
- TVC
$124,000.00
40%
TCM
$186,000.00
60%
- FC
$120,000.00
NI
$66,000.00
Therefore, the original sales revenue is $310,000.00.
(ii) TVC = 0.40TR
= 0.40 × 310,000.00
= $124,000.00
Therefore, the original variable costs are $124,000.00.
(iii) When the sale price was reduced by 2%, the sales volume increased by 24%.
Therefore, the new sales amount is equal to:
Total Amount
= 310,000.00(1 - 0.02)(1 + 0.24)
TR
$376,712.00
= 310,000.00 × 0.98 × 1.24
= $376,712.00
% of Sales
- TVC
100%
40%
TCM
$226,027.20
- FC
(iv)New TVC = 0.40TR
= 0.40 × 376,712.00
NI
= $150,684.80
Therefore, the new variable cost is $150,684.80.
$120,000.00
$106,027.20
(v)TCM = 0.60TR
= 0.60 × 376,712.00 = $226,027.20
NI = TCM - FC
= 226,027.20 - 120,000.00 = $106,027.20
Therefore, the change in net income = $106,027.20 - $66,000.00 = $40,027.20
60%
242
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
Example 7.4(f)
Calculating the Change in Net Income when the Contribution Margin Rate Changes
A manufacturer of computer keyboards has fixed costs of $100,000. The variable costs are 80% of
the sales.
(i) What is the sales revenue at break-even?
(ii) What are the variable costs at break-even?
(iii) If the contribution margin rate is increased by 20% of sales and the fixed costs are
increased by $25,000, calculate the new sales revenue at break-even.
(iv) After the changes in the contribution margin rate and the fixed costs, calculate the net
income when the sales are $400,000.
Solution
(i), (ii) When TVC = 80%TR
(i) At Break-even,NI = 0
Therefore, TCM = FC = $100,000.00
% of Sales
TCM = TR - TVC
Substituting the values, 100,000 = TR - 0.80TR
100,000 = 0.20TR
TR
$500,000.00
100%
- TVC
$400,000.00
80%
TCM
$100,000.00
20%
Therefore,
- FC
Total Amount
0.20TR = 100,000.00
100, 000.00
TRS = 0.20
$100,000.00
0
NI
= $500,000.00
Therefore, the sales revenue at break-even is $500,000.00.
(ii) TVC = 0.80TR
= 0.80 × 500,000.00
= $400,000.00
Therefore, the total variable costs at break-even are $400,000.00.
(iii) When TCM = 40%TR
(iii) New TCM = 20%TR + 20%TR
Total Amount
% of Sales
= 40%TR
New FC = 100,000.00 + 25,000.00
TR
$312,500.00
= $125,000.00
- TVC
At BE, NI = 0
TCM
$125,000.00
40%
TCM = FC = 125,000
- FC
$125,000.00
0.40TR = 125,000.00
NI
0
TR = $312,500.00
Therefore, the new sales revenue at break-even is $312,500.00.
(iv) TCM = 0.40TR
= 0.40 × 400,000.00
= $160,000.00
NI = TCM - FC
= 160,000.00 - 125,000.00
= $35,000.00
Therefore, the net income when sales are
$400,000.00 is $35,000.00.
(iv) When sales amount = 400,000.00
Total Amount
TR
% of Sales
$400,000.00
- TVC
TCM
$160,000.00
- FC
$125,000.00
NI
$35,000.00
40%
Chapter 7 | Break-Even and Cost-Volume-Profit Analysis
7.4 |
Exercises Answers to the odd-numbered problems are available at the end of the textbook
1. A company that makes chairs reported the following:
Number of units produced: 84
Selling price per unit: $90
Variable costs per unit: $65
Fixed costs:
$2100
Calculate the contribution margin ratio and net income.
2. A shoe store reported the following:
Number of units sold: 750
Selling price per unit: $45
Variable costs per unit: $30
Fixed costs:
$1440
Calculate the contribution margin ratio and net income.
3. The manufacturer of a product had fixed costs of $120,800 per year. The variable costs are 60% of selling price.
Calculate the break-even point in sales dollars.
4. The manufacturer of a product had fixed costs of $44,460. The variable costs are 35% of selling price. Calculate
the break-even point in sales dollars.
5. The net income of a postcard company was $15,920. The variable costs are $47,600 and the fixed costs are
$7880. Calculate the sales amount at the break-even point.
6. The net income of a construction company was $107,200. The variable costs are $342,000 and the fixed costs
are $120,800. Calculate the sales amount at the break-even point.
7. A bike manufacturing company has fixed costs of $120,000 per annum and the variable costs are 40% of sales.
If the variable costs increased to 60% of sales, what additional sales must be made to break-even?
8. A computer manufacturing company has fixed costs of $66,000 per annum and the variable costs are 85% of
sales. If the variable costs increased to 90% of sales, what additional sales must be made to break-even?
9. A company that produces cameras has fixed costs of $150,000 per annum. The variable costs are 45% of sales
and profit was $61,500. When the selling price was reduced by 10%, the sales volume increased by 20%.
a. What was the original sales revenue?
b. What were the original variable costs?
c. What is the new sales revenue?
d. What is the new variable costs?
e. What is the amount of change in net income?
10. A company that manufactures monitors has fixed costs of $78,500.00 per annum. The variable costs are 30% of
sales and the profit was $61,500. When the selling price was reduced by 15%, the sales volume increased by 25%.
a. What was the original sales revenue?
b. What were the original variable costs?
c. What is the new sales revenue?
d. What is the new variable costs?
e. What is the amount of change in net income?
11. Structures Inc. had a net income of $120,000, total revenue of $550,180, and total variable costs of $330,035.
What was its total revenue at break even?
12. Wongstah Software Corp. had a net income of $65,250, total revenue of $460,400, and total variable costs of
$350,455. What was its total revenue at break-even?
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