Exercise 5-4 (10 minutes)
1. The company’s contribution margin (CM) ratio is:
Total sales ……………………….
$200,000
Total variable expenses ………
120,000
Total contribution margin (a) .
$ 80,000
Total contribution margin (a) .
$80,000
Total sales (b) …………………..
$200,000
CM ratio (a) ÷ (b) ……………..
40%
2. The change in net operating income from an increase in total sales of
$1,000 can be estimated by using the CM ratio as follows:
Change in total sales (a) ……………………………………
$1,000
CM ratio (b) ……………………………………………………
40%
Estimated change in net operating income (a) × (b) .
$400
This computation can be verified as follows:
Total sales (a) ……………………..
$200,000
Total units sold (b) ……………….
units
Selling price per unit (a) ÷ (b) ..
per unit
Increase in total sales (a) ………
Selling price per unit (b) ………..
per unit
Increase in unit sales (a) ÷ (b) .
units
Increase in unit sales ……………
units
Original total unit sales ………….
units
New total unit sales ………………
units
Original
New
Total unit sales ……………
50,000
50,250
Sales …………………………
$200,000
$201,000
Variable expenses ………..
120,000
120,600
Contribution margin ……..
80,000
80,400
Fixed expenses ……………
65,000
65,000
Net operating income ……
$ 15,000
$ 15,400
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 …………………………
$180,000
$189,000
$ 9,000
Variable expenses ………..
126,000
132,300
6,300
Contribution margin ……..
54,000
56,700
2,700
Fixed expenses ……………
30,000
35,000
5,000
Net operating income ……
$ 24,000
$ 21,700
$ (2,300)
Assuming no other important factors need to be considered, the
increase in the advertising budget should not be approved because it
would lead to a decrease in net operating income of $2,300.
Alternative Solution 1
Present total contribution margin:
Incremental contribution margin ………..
Change in net operating income …………
Alternative Solution 2
Incremental contribution margin:
$9,000 × 30% CM ratio …………………
$2,700
Less incremental advertising expense ….
5,000
Change in net operating income …………
$ (2,300)
Exercise 5-5 (continued)
2. The $2 increase in variable expense will cause the unit contribution
margin to decrease from $27 to $25 with the following impact on net
operating income:
Expected total contribution margin with the
higher-quality components:
2,000 units × 1.1 × $25 per unit …………
$55,000
Exercise 5-6 (20 minutes)
1. The break-even point in unit sales, Q, is computed as follows:
Profit
= Unit CM × Q − Fixed expenses
$0
= ($15 − $12) × Q − $4,200
$0
= ($3) × Q − $4,200
$3Q
= $4,200
Q
= $4,200 ÷ $3
Q
= 1,400 baskets
2. The break-even point in dollar sales is computed as follows:
Unit sales to break even (a) ……………………….
1,400
Selling price per unit (b) …………………………...
$15
Dollar sales to break even (a) × (b) …………….
$21,000
3. The new break-even point in unit sales, Q, is computed as follows:
Profit
= Unit CM × Q − Fixed expenses
$0
= ($15 − $12) × Q − $4,800
$0
= ($3) × Q − $4,800
$3Q
= $4,800
Q
= $4,800 ÷ $3
Q
= 1,600 baskets
The break-even point in dollar sales is computed as follows:
Unit sales to break even (a) ……………………….
Selling price per unit (b) …………………………...
$15
Dollar sales to break even (a) × (b) …………….
Exercise 5-7 (10 minutes)
1. The required unit sales, Q, to attain the target profit is computed as
follows:
Profit
= Unit CM × Q − Fixed expenses
$10,000
= ($120 − $80) × Q − $50,000
$10,000
= ($40) × Q − $50,000
$40 × Q
= $10,000 + $50,000
= $60,000 ÷ $40
= 1,500 units
2. One approach to solving this requirement is to compute the unit sales
required to attain the target profit and then multiply this quantity by the
selling price per unit:
Profit
= Unit CM × Q − Fixed expenses
$15,000
= ($120 − $80) × Q − $50,000
$15,000
= ($40) × Q − $50,000
$40 × Q
= $15,000 + $50,000
Q
= $65,000 ÷ $40
Q
= 1,625 units
Unit sales to attain the target profit (a) …………
Selling price per unit (b) …………………………...
Dollar sales to attain target profit (a) × (b) ……
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
= ($30 − $20) × Q − $7,500
$0
= ($10) × Q − $7,500
$10Q
= $7,500
= $7,500 ÷ $10
Sales (at the budgeted volume of 1,000 units) ..
Less break-even sales (at 750 units) …………….
Margin of safety (in dollars) ………………………..
2. The margin of safety as a percentage of sales is as follows:
Margin of safety (in dollars) (a) …………….
$7,500
Sales (b) ………………………………………….
$30,000
Margin of safety percentage (a) ÷ (b) ……
25%
Exercise 5-9 (20 minutes)
1. The company’s degree of operating leverage would be computed as
follows:
Contribution margin (a) ……………………..
$48,000
Net operating income (b) ……………………
$10,000
Degree of operating leverage (a) ÷ (b) …
4.8
2. A 5% increase in unit sales should result in a 24% increase in net
operating income, computed as follows:
Degree of operating leverage (a) …………………………..……….
Percent increase in unit sales (b) ……………………………………
Estimated percent increase in net operating income (a) × (b) .
3. The new income statement reflecting the change in unit sales is:
Amount
Percent
of Sales
Sales ……………………….
$84,000
100%
Variable expenses ………
33,600
40%
Contribution margin ……
50,400
60%
Fixed expenses ………….
38,000
Net operating income ….
$12,400
Net operating income reflecting change in sales ……
Original net operating income (a) ………………………
10,000
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
Overall CM ratio = Total sales
2. The overall break-even point in dollar sales can be computed as follows:
Overall break-even
Total fixed expenses
=Overall CM ratio
$24,000
=30%
= $80,000
3. To construct the required income statement, we must first determine
the relative sales mix for the two products:
Claimjumper
Makeover
Total
Original dollar sales …….
$30,000
$70,000
$100,000
Percent of total ………….
30%
70%
100%
Sales at break-even …….
$24,000
$56,000
$80,000
Claimjumper
Makeover
Total
Sales ……………………….
$24,000
$56,000
Variable expenses* …….
Contribution margin ……
$16,000
Fixed expenses ………….
Net operating income ….
$ 0
Exercise 5-11 (20 minutes)
a.
Case #1
Case #2
Number of units sold ..
15,000
*
4,000
Sales …………………….
$180,000
*
$12
$100,000
*
$25
Variable expenses…….
120,000
*
8
60,000
15
Contribution margin ….
60,000
$ 4
40,000
$10
*
Fixed expenses ………..
50,000
*
32,000
*
Net operating income .
$ 10,000
$ 8,000
*
Case #3
Case #4
Number of units sold ..
10,000
*
6,000
*
Sales …………………….
$200,000
$20
$300,000
*
$50
Variable expenses…….
70,000
*
7
35
Contribution margin ….
$13
*
$15
Fixed expenses ………..
118,000
*
Net operating income (loss)..
*
*
b.
Case #1
Case #2
Sales ……………………..
$500,000
*
100%
$400,000
*
100%
Variable expenses …….
400,000
80%
260,000
*
65%
Contribution margin ….
100,000
20%
*
140,000
35%
Fixed expenses ………..
93,000
100,000
*
Net operating income ..
$ 7,000
*
$ 40,000
Case #3
Case #4
Sales …………………….
$250,000
100%
$600,000
*
100%
Variable expenses ……
100,000
420,000
Contribution margin …
Fixed expenses ……….
130,000
*
185,000
Net operating income (loss).
$ 20,000
*
1.
Flight Dynamic
Sure Shot
Total Company
Amount
%
Amount
%
Amount
%
Sales ……………
$150,000
100
$250,000
100
$400,000
100.0
Variable
expenses ……
30,000
20
160,000
64
190,000
47.5
Contribution
margin ……….
$120,000
80
$ 90,000
36
210,000
52.5*
Fixed expenses
183,750
Net operating
income ………
$ 26,250
*$210,000 ÷ $400,000 = 52.5%
2. The break-even point for the company as a whole is:
0.525
3. The additional contribution margin from the additional sales is computed
as follows:
$100,000 × 52.5% CM ratio = $52,500
Exercise 5-13 (20 minutes)
Total
Per Unit
1.
Sales (20,000 units × 1.15 = 23,000 units)…..
$345,000
$ 15.00
Variable expenses …………………………………..
207,000
9.00
Contribution margin ………………………………..
138,000
Fixed expenses ………………………………………
70,000
Net operating income ………………………………
$ 68,000
2.
Sales (20,000 units × 1.25 = 25,000 units)…..
$337,500
$13.50
Variable expenses …………………………………..
225,000
9.00
Contribution margin ………………………………..
112,500
$ 4.50
Fixed expenses ………………………………………
70,000
Net operating income ………………………………
$ 42,500
3.
Sales (20,000 units × 0.95 = 19,000 units)…..
$313,500
$16.50
Variable expenses …………………………………..
171,000
9.00
Contribution margin ………………………………..
142,500
$ 7.50
Fixed expenses ………………………………………
90,000
Net operating income ………………………………
$ 52,500
4.
Sales (20,000 units × 0.90 = 18,000 units)…..
$302,400
$16.80
Variable expenses …………………………………..
172,800
9.60
Contribution margin ………………………………..
129,600
$ 7.20
Fixed expenses ………………………………………
70,000
Net operating income ………………………………
$ 59,600
Exercise 5-14 (30 minutes)
2. The break-even points in unit sales (Q) and dollar sales are computed as
follows:
Selling price ……………………..
$40
100%
Variable expenses ……………..
28
70%
Contribution margin …………..
$12
30%
Profit
= Unit CM × Q − Fixed expenses
$0
= $12 × Q − $180,000
$12Q
= $180,000
Q
= $180,000 ÷ $12
Q
= 15,000 units
In dollar sales: 15,000 units × $40 per unit = $600,000
= CM ratio × Sales − Fixed expenses
= 0.30 × Sales − $180,000
= $180,000
= $180,000 ÷ 0.30
= $600,000
3. The unit sales and dollar sales needed to attain the target profit are
computed as follows:
Profit
= Unit CM × Q − Fixed expenses
$60,000
= $12 × Q − $180,000
$12Q
= $60,000 + $180,000
= $240,000
= $240,000 ÷ $12
= 20,000 units
Exercise 5-14 (continued)
Alternative solution:
Profit
= CM ratio × Sales − Fixed expenses
$60,000
= 0.30 × Sales − $180,000
= $240,000
= $240,000 ÷ 0.30
Sales
= $800,000
4. The new break-even points in unit sales and dollar sales are computed
as follows:
The company’s new cost/revenue relation will be:
Selling price …………………………
$40
100%
Variable expenses ($28 – $4) …..
24
60%
Contribution margin ……………….
$16
40%
Profit
= Unit CM × Q − Fixed expenses
$0
= ($40 − $24) × Q − $180,000
$16Q
= $180,000
Q
= $180,000 ÷ $16 per unit
Q
= 11,250 units
In dollar sales: 11,250 units × $40 per unit = $450,000
Alternative solution:
Profit
= CM ratio × Sales − Fixed expenses
= 0.40 × Sales − $180,000
= $180,000
= $180,000 ÷ 0.40
= $450,000
Exercise 5-14 (continued)
4. The dollar sales required to attain the target profit is computed as
follows:
Profit
= CM ratio × Sales − Fixed expenses
= 0.40 × Sales − $180,000
Exercise 5-15 (15 minutes)
1.
Total
Per
Unit
Sales (15,000 games) ………
$300,000
$20
Variable expenses …………..
90,000
6
Contribution margin …………
210,000
$14
Fixed expenses ……………….
182,000
Net operating income ………
$ 28,000
The degree of operating leverage is:
2. a. Sales of 18,000 games represent a 20% increase over last year’s
sales. Because the degree of operating leverage is 7.5, net operating
income should increase by 7.5 times as much, or by 150% (7.5 ×
20%).
b. The expected total dollar amount of net operating income for next
year would be:
Total expected net operating income …………….
Exercise 5-16 (30 minutes)
1. The contribution margin per person would be:
Price per ticket ……………………………….
$35
Variable expenses:
Dinner ………………………………………..
$18
Favors and program ………………………
2
20
Contribution margin per person ………….
$15
The fixed expenses of the dinner-dance total $6,000 (= $2,800 + $900
+ $1,000 + $1,300). The break-even point would be:
= ($15) × Q − $6,000
= $6,000
= $6,000 ÷ $15
Alternative solution:
Fixed expenses
Unit sales to=
break even Unit contribution margin
$6,000
= = 400 persons
$15
or, at $35 per person, $14,000.
Variable cost per person ($18 + $2) ……………..
Exercise 5-16 (continued)
3. Cost-volume-profit graph:
$12,000
$14,000
$16,000
$18,000
$20,000
Total
Expenses
Total Sales
Break-even point:
400 persons or
$14,000 total sales
Exercise 5-17 (30 minutes)
1.
Profit
= Unit CM × Q − Fixed expenses
$0
= ($50 − $32) × Q − $108,000
$0
= ($18) × Q − $108,000
$18Q
= $108,000
Q
= $108,000 ÷ $18
Q
= 6,000 stoves, or at $50 per stove, $300,000 in sales
Alternative solution:
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 stoves would have to
be sold to generate enough contribution margin to cover the fixed costs.
3.
Present:
8,000 Stoves
Proposed:
10,000 Stoves*
Total
Per Unit
Total
Per Unit
Sales ……………………….
$50
**
Variable expenses……….
Contribution margin …….
Fixed expenses …………..
Net operating income ….
Exercise 5-17 (continued)
4.
Profit
= Unit CM × Q − Fixed expenses
$35,000
= ($45 − $32) × Q − $108,000
$35,000
= ($13) × Q − $108,000
$13 × Q
= $143,000
Exercise 5-18 (30 minutes)
1.
Profit
= Unit CM × Q − Fixed expenses
$0
= ($30 − $12) × Q − $216,000
$0
= ($18) × Q − $216,000
$18Q
= $216,000
2. The contribution margin is $216,000 because the contribution margin is
equal to the fixed expenses at the break-even point.
3. The unit sales to attain the target profit is computed as follows:
Target profit + Fixed expenses
Units sold to attain
=
target profit Unit contribution margin
Contribution margin ………………………..