Chapter 5
Cost-Volume-Profit Relationships
Solutions to Questions
5-1 The contribution margin (CM) ratio is
the ratio of the total contribution margin to total
5-2 Incremental analysis focuses on the
changes in revenues and costs that will result
from a particular action.
5-4 Operating leverage measures the impact
on net operating income of a given percentage
change in sales. The degree of operating
leverage at a given level of sales is computed by
dividing the contribution margin at that level of
sales by the net operating income at that level
of sales.
increased, then both the fixed cost line and the
total cost line would shift upward and the break–
5-7 The margin of safety is the excess of
budgeted (or actual) sales over the break-even
volume of sales. It is the amount by which sales
5-9 A higher break-even point and a lower
net operating income could result if the sales
mix shifted from high contribution margin
products to low contribution margin products.
Such a shift would cause the average
contribution margin ratio in the company to
decline, resulting in less total contribution
margin for a given amount of sales. Thus, net
Exercise 5-1 (20 minutes)
1. The new income statement would be:
Total
Per Unit
Sales (8,050 units) …..
$209,300
$26.00
Variable expenses ……
144,900
18.00
Contribution margin ….
64,400
$ 8.00
Fixed expenses ……….
56,000
Net operating income .
Original net operating income ..
400
New net operating income …….
2. The new income statement would be:
Total
Sales (7,950 units) …………
$206,700
Variable expenses ………….
143,100
Contribution margin ………..
63,600
Fixed expenses ……………..
Net operating income ……..
Original net operating income ………….
$8,000
New net operating income ………………
$7,600
Exercise 5-1 (continued)
3. The new income statement would be:
Total
Per Unit
Sales (7,000 units) …….
$182,000
$26.00
Variable expenses ……..
126,000
18.00
Contribution margin ……
$ 8.00
Fixed expenses …………
Net operating income …
Exercise 5-2 (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 1. Draw a line parallel to the volume axis to represent the total
fixed expense. For this company, the total fixed expense is $12,000.
Total expense ……………………………………………..
$60,000
Step 3. Choose some volume of sales and plot the point representing
total sales dollars at the activity level you have selected. We’ll use the
sales level of 2,000 units again.
Total sales revenue (2,000 units × $36 per unit) …
$72,000
2. The break-even point is the point where the total sales revenue and the
= $12,000 − $12,000
= $0
Exercise 5-2 (continued)
$80,000
CVP Graph
Exercise 5-3 (15 minutes)
1. The profit graph is based on the following simple equation:
Profit
= Unit CM × Q − Fixed expenses
Profit
= ($19 − $15) × Q − $12,000
Profit
= $4 × Q − $12,000
$0
$5,000
Profit Graph
Exercise 5-3 (continued)
2. Looking at the graph, the break-even point appears to be 3,000 units.
This can be verified as follows:
Exercise 5-4 (10 minutes)
1. The company’s contribution margin (CM) ratio is:
Total sales ……………………….
$300,000
Total variable expenses ………
240,000
= Total contribution margin …
$ 60,000
÷ Total sales …………………….
= CM ratio ……………………….
2. The change in net operating income from an increase in total sales of
$1,500 can be estimated by using the CM ratio as follows:
Change in total sales ………………….
$1,500
× CM ratio ……………………………….
20%
= Estimated change in net
operating income …………………….
$ 300
Total sales ……………….
$300,000
÷ Total units sold ………
40,000
units
= Selling price per unit .
per unit
Increase in total sales …
÷ Selling price per unit .
per unit
= Increase in unit sales
units
Original total unit sales .
units
New total unit sales ……
units
Original
New
Total unit sales………….
40,000
40,200
Sales ………………………
$300,000
$301,500
Variable expenses ……..
Contribution margin ……
Fixed expenses …………
Net operating income …
Exercise 5-5 (20 minutes)
1. The following table shows the effect of the proposed change in monthly
advertising budget:
Sales With
Additional
Current
Advertising
Sales
Budget
Difference
Sales ………………………
$225,000
$240,000
$15,000
Variable expenses ……..
135,000
144,000
9,000
Contribution margin ……
90,000
96,000
6,000
Fixed expenses …………
75,000
83,000
8,000
Net operating income …
$ 15,000
$ 13,000
$(2,000)
Alternative Solution 1
Expected total contribution margin:
$240,000 × 40% CM ratio ………………
$96,000
Incremental contribution margin ………..
Change in net operating income …………
Alternative Solution 2
Less incremental advertising expense ….
Change in net operating income …………
$(2,000)
Exercise 5-5 (continued)
2. The $3 increase in variable expenses will cause the unit contribution
margin to decrease from $30 to $27 with the following impact on net
operating income:
Expected total contribution margin with the
Exercise 5-6 (10 minutes)
1. The equation method yields the required unit sales, Q, as follows:
Profit
= Unit CM × Q − Fixed expenses
$6,000
= ($140 − $60) × Q − $40,000
= $46,000 ÷ $80
= 575 units
2. The formula approach yields the required unit sales as follows:
Exercise 5-7 (20 minutes)
1. The equation method yields the break-even point in unit sales, Q, as
follows:
2. The equation method can be used to compute the break-even point in
sales dollars as follows:
Unit contribution margin
CM ratio = Unit selling price
3. The formula method gives an answer that is identical to the equation
method for the break-even point in unit sales:
Exercise 5-7 (continued)
4. The formula method also gives an answer that is identical to the
equation method for the break-even point in dollar sales:
Exercise 5-8 (10 minutes)
1. To compute the margin of safety, we must first compute the break-even
unit sales.
Profit
= Unit CM × Q − Fixed expenses
$0
= ($25 − $15) × Q − $8,500
$0
= ($10) × Q − $8,500
= $8,500
= $8,500 ÷ $10
Sales (at the budgeted volume of 1,000 units) ..
Break-even sales (at 850 units) ……………………
Margin of safety (in dollars) ………………………..
2. The margin of safety as a percentage of sales is as follows:
Margin of safety (in dollars) ………………….
÷ Sales …………………………………………….
Margin of safety percentage ………………….
Exercise 5-9 (20 minutes)
1. The company’s degree of operating leverage would be computed as
follows:
Degree of operating leverage .
2. A 10% increase in sales should result in a 30% increase in net operating
income, computed as follows:
× Percent increase in sales …………………………..……
Estimated percent increase in net operating income ..
3. The new income statement reflecting the change in sales is:
Amount
Percent
of Sales
Sales ………………………
$132,000
100%
Variable expenses ……..
92,400
70%
Contribution margin ……
30%
Original net operating income (a) ………………………
Change in net operating income (b) …………………..
Percent change in net operating income (b ÷ a) …..
Exercise 5-10 (20 minutes)
1. The overall contribution margin ratio can be computed as follows:
Total contribution margin
2. The overall break-even point in sales dollars can be computed as
follows:
3. To construct the required income statement, we must first determine
the relative sales mix for the two products:
Predator
Runway
Total
Original dollar sales ……
$100,000
$50,000
$150,000
Percent of total …………
67%
33%
100%
Sales at break-even ……
$75,000
$37,500
$112,500
Predator
Runway
Total
Sales ………………………
$75,000
$37,500
$112,500
Variable expenses* …….
Contribution margin ……
$56,250
$33,750
Fixed expenses …………
Net operating income …
Exercise 5-11 (30 minutes)
1.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($40 − $28) × Q − $150,000
$0
=
($12) × Q − $150,000
$12Q
=
$150,000
Q
=
$150,000 ÷ $12 per unit
Q
=
12,500 units, or at $40 per unit, $500,000
2. The contribution margin at the break-even point is $150,000 because at
that point it must equal the fixed expenses.
3.
Sales (14,000 units × $40 per unit) …………..
Fixed expenses …………………………………….
Net operating income …………………………….
Target profit + Fixed expenses
Units sold to attain
=
target profit Unit contribution margin
Exercise 5-11 (continued)
4. Margin of safety in dollar terms:
Margin of safety = Total sales – Break-even sales
in dollars
= $600,000 – $500,000 = $100,000
5. The CM ratio is 30%.
Expected total contribution margin: $680,000 × 30% ….
$204,000
Present total contribution margin: $600,000 × 30% ……
180,000
Increased contribution margin ………………………………..
$ 24,000
Exercise 5-12 (30 minutes)
1.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($90 − $63) × Q − $135,000
$0
=
($27) × Q − $135,000
$27Q
=
$135,000
$135,000 ÷ $27 per lantern
5,000 lanterns, or at $90 per lantern, $450,000 in sales
2. An increase in variable expenses as a percentage of the selling price
would result in a higher break-even point. If variable expenses increase
as a percentage of sales, then the contribution margin will decrease as a
percentage of sales. With a lower CM ratio, more lanterns would have to
be sold to generate enough contribution margin to cover the fixed costs.
3.
Present:
8,000 Lanterns
Proposed:
10,000 Lanterns*
Total
Per Unit
Total
Per Unit
Sales …………………………
$720,000
$90
$810,000
$81
**
Variable expenses ………..
Contribution margin ………
Net operating income ……
*
8,000 lanterns × 1.25 = 10,000 lanterns
**
$90 per lantern × 0.9 = $81 per lantern
Exercise 5-12 (continued)
4.
Profit
=
Unit CM × Q − Fixed expenses
$72,000
=
($81 − $63) × Q − $135,000
$72,000
=
($18) × Q − $135,000
$18Q
=
$207,000