Solutions Manual, Chapter 3 1
Chapter 3
Cost-Volume-Profit Relationships
Solutions to Questions
3-1 The contribution margin (CM) ratio is
the ratio of the total contribution margin to total
sales revenue. It can also be expressed as the
3-2 Incremental analysis focuses on the
profits when sales increase.
3-6 (a) If the selling price decreased, then
the total revenue line would rise less steeply,
and the break-even point would occur at a
higher unit volume. (b) If the fixed cost
increased, then both the fixed cost line and the
total cost line would shift upward and the break-
3-7 The margin of safety is the excess of
budgeted (or actual) sales over the break-even
3-9 A higher break-even point and a lower
net operating income could result if the sales
contribution margin ratio, the break-even point
2 Managerial Accounting for Managers, 4th Edition
The Foundational 15
1. The contribution margin per unit is calculated as follows:
Total contribution margin (a) …………..
$8,000
Total units sold (b) ……. …….. …………
1,000
units
Contribution margin per unit (a) ÷ (b) .
$8.00
per unit
2. The contribution margin ratio is calculated as follows:
Total contribution margin (a) …………..
$8,000
Total sales (b) ………….. …….. …………
$20,000
Contribution margin ratio (a) ÷ (b) ……
40%
3. The variable expense ratio is calculated as follows:
Total variable expenses (a) ……………..
$12,000
Total sales (b) ………….. …….. …………
$20,000
Variable expense ratio (a) ÷ (b) ……….
60%
4. The increase in net operating is calculated as follows:
Contribution margin per unit (a) …………………
$8.00
per unit
Increase in unit sales (b) ………………………….
1
unit
Increase in net operating income (a) × (b) …..
$8.00
5. If sales decline to 900 units, the net operating would be computed as
follows:
Per Unit
Sales (900 units) ……….
$20.00
Variable expenses ………
12.00
Contribution margin ……
$ 8.00
Fixed expenses ………….
Net operating income ….
Solutions Manual, Chapter 3 3
The Foundational 15 (continued)
6. The new net operating income would be computed as follows:
Per Unit
Sales (900 units) ……….
$22.00
Variable expenses ………
12.00
Contribution margin ……
$10.00
Fixed expenses ………….
Net operating income ….
7. The new net operating income would be computed as follows:
Per Unit
Sales (1,250 units) ……..
$20.00
Variable expenses ………
13.00
Contribution margin ……
$ 7.00
Fixed expenses ………….
7,500
Net operating income ….
8. The equation method yields the break-even point in unit sales, Q, as
follows:
Profit
= Unit CM × Q − Fixed expenses
$0
= ($20 − $12) × Q − $6,000
$0
= ($8) × Q − $6,000
$8Q
= $6,000
Q
= $6,000 ÷ $8
Q
= 750 units
9. The equation method yields the dollar sales to break-even as follows:
Profit
= CM ratio × Sales − Fixed expenses
$0
= 0.40 × Sales − $6,000
0.40 × Sales
= $6,000
Sales
= $6,000 ÷ 0.40
Sales
= $15,000
The dollar sales to break-even ($15,000) can also be computed by
4 Managerial Accounting for Managers, 4th Edition
The Foundational 15 (continued)
10. The equation method yields the target profit as follows:
Profit
= Unit CM × Q − Fixed expenses
$5,000
= ($20 − $12) × Q − $6,000
$5,000
= ($8) × Q − $6,000
$8Q
= $11,000
Q
= $11,000 ÷ $8
Q
= 1,375 units
11. The margin of safety in dollars is calculated as follows:
Sales ……………………………………………………..
$20,000
Break-even sales (at 750 units) ……………………
15,000
Margin of safety (in dollars) ………………………..
$ 5,000
Margin of safety (in dollars) (a) ……………..
$5,000
Sales (b) …………………………………………..
$20,000
Margin of safety percentage (a) ÷ (b) …….
25%
12. The degree of operating leverage is calculated as follows:
Contribution margin (a) …………………..
$8,000
Net operating income (b) ………………….
$2,000
Degree of operating leverage (a) ÷ (b) ..
4.0
operating income, computed as follows:
Degree of operating leverage (a) ………………………..
4.0
Percent increase in sales (b) ………………………………
5%
Percent increase in net operating income (a) × (b) …
20%
14. The degree of operating leverage is calculated as follows:
Contribution margin (a) . ………………….
$14,000
Net operating income (b) …………………
$2,000
Degree of operating leverage (a) ÷ (b) .
7.0
Solutions Manual, Chapter 3 5
The Foundational 15 (continued)
15. A 5% increase in sales should result in 35% increase in net operating
income, computed as follows:
Degree of operating leverage (a) ………………………..
7.0
Percent increase in sales (b) ………………………………
5%
Percent increase in net operating income (a) × (b) …
35%
6 Managerial Accounting for Managers, 4th Edition
Exercise 3-1 (20 minutes)
1. The new income statement would be:
Total
Per Unit
Sales (10,100 units) ……..
$353,500
$35.00
Variable expenses ………..
202,000
20.00
Contribution margin ………
151,500
$15.00
Fixed expenses ……………
135,000
Net operating income ……
$ 16,500
approach:
Original net operating income ….
$15,000
Change in contribution margin
(100 units × $15.00 per unit) ..
1,500
New net operating income ………
$16,500
2. The new income statement would be:
Total
Per Unit
Sales (9,900 units) …………
$346,500
$35.00
Variable expenses ………….
198,000
20.00
Contribution margin ………..
148,500
$15.00
Fixed expenses ……………..
135,000
Net operating income ……..
$ 13,500
approach:
Original net operating income ………….
$15,000
Change in contribution margin
(-100 units × $15.00 per unit) ……….
(1,500)
New net operating income ………………
$13,500
Solutions Manual, Chapter 3 7
Exercise 3-1 (continued)
3. The new income statement would be:
Per Unit
Sales (9,000 units) …….
$35.00
Variable expenses ……..
20.00
Contribution margin ……
$15.00
Fixed expenses …………
Net operating income …
8 Managerial Accounting for Managers, 4th Edition
Exercise 3-2 (30 minutes)
1. The CVP graph can be plotted using the three steps outlined in the text.
The graph appears on the next page.
Step 2. Choose some volume of sales and plot the point representing
total expenses (fixed and variable) at the activity level you have
Fixed expenses ……………………………………………
$ 24,000
Variable expenses (8,000 units × $18 per unit) …..
144,000
Total expense ……………………………………………..
$168,000
sales level of 8,000 units again.
Total sales revenue (8,000 units × $24 per unit) …
$192,000
2. The break-even point is the point where the total sales revenue and the
can be verified as follows:
Profit
= Unit CM × Q − Fixed expenses
= ($24 − $18) × 4,000 − $24,000
= $6 × 4,000 − $24,000
= $24,000− $24,000
= $0
Exercise 3-2 (continued)
$150,000
$200,000
CVP Graph
Exercise 3-3 (15 minutes)
1. The profit graph is based on the following simple equation:
Profit
= Unit CM × Q − Fixed expenses
Profit
= ($16 − $11) × Q − $16,000
Profit
= $5 × Q − $16,000
To plot the graph, select two different levels of sales such as Q=0 and
$0
$5,000
Profit Graph