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Exercise 3-17 (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:
Fixed expenses
Unit sales to =
break even Unit contribution margin
$108,000
= = 6,000 stoves
$18.00 per stove
2. An increase in variable expenses as a percentage of the selling price
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 ............................
$400,000
$50
$450,000
$45
**
Variable expenses .........
256,000
32
320,000
32
Contribution margin ......
144,000
$18
130,000
$13
Fixed expenses .............
108,000
108,000
Net operating income....
$ 36,000
$ 22,000
decreases.
Exercise 3-17 (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
Q
= $143,000 ÷ $13
Q
= 11,000 stoves
Alternative solution:
Target profit + Fixed expenses
Unit sales to attain =
target profit Unit contribution margin
$35,000 + $108,000
=
$13
= 11,000 stoves
Exercise 3-18 (30 minutes)
1.
Profit
= Unit CM × Q − Fixed expenses
$0
= ($30 − $12) × Q − $216,000
$0
= ($18) × Q − $216,000
$18Q
= $216,000
Q
= $216,000 ÷ $18
Q
= 12,000 units, or at $30 per unit, $360,000
Alternative solution:
Fixed expenses
Unit sales
=
to break even Unit contribution margin
$216,000
= = 12,000 units
$18
or at $30 per unit, $360,000
3.
Target profit + Fixed expenses
Units sold to attain
=
target profit Unit contribution margin
$90,000 + $216,000
=$18
= 17,000 units
Total
Unit
Sales (17,000 units × $30 per unit) .......
$510,000
$30
Variable expenses
(17,000 units × $12 per unit) .............
204,000
12
Contribution margin ..............................
306,000
$18
Fixed expenses ....................................
216,000
Net operating income ...........................
$ 90,000
Exercise 3-18 (continued)
4. Margin of safety in dollar terms:
Margin of safety = Total sales - Break-even sales
in dollars
= $450,000 - $360,000 = $90,000
Margin of safety in percentage terms:
Margin of safety in dollars
Margin of safety =
percentage Total sales
$90,000
= = 20%
$450,000
5. The CM ratio is 60%.
Expected total contribution margin: ($500,000 × 60%) ..
$300,000
Present total contribution margin: ($450,000 × 60%) .....
270,000
Increased contribution margin .......................................
$ 30,000
Alternative solution:
Problem 3-19 (45 minutes)
1.
Sales (15,000 units × $70 per unit) ......................
$1,050,000
Variable expenses (15,000 units × $40 per unit) ...
600,000
Contribution margin .............................................
450,000
Fixed expenses ...................................................
540,000
Net operating loss ...............................................
$ (90,000)
2.
Fixed expenses
Unit sales to=
break even Unit contribution margin
$540,000
=$30 per unit
=18,000 units
3. See the next page.
36 Managerial Accounting for managers, 4th Edition
Problem 3-19 (continued)
3.
Unit
Selling
Price
Unit
Variable
Expense
Unit
Contribution
Margin
Volume
(Units)
Total
Contribution
Margin
Fixed
Expenses
Net operating
income (loss)
$70
$40
$30
15,000
$450,000
$540,000
$ (90,000)
$68
$40
$28
20,000
$560,000
$540,000
$ 20,000
$66
$40
$26
25,000
$650,000
$540,000
$110,000
$64
$40
$24
30,000
$720,000
$540,000
$180,000
$62
$40
$22
35,000
$770,000
$540,000
$230,000
$60
$40
$20
40,000
$800,000
$540,000
$260,000
$58
$40
$18
45,000
$810,000
$540,000
$270,000
$56
$40
$16
50,000
$800,000
$540,000
$260,000
Problem 3-20 (75 minutes)
1.
a.
Selling price .....................
$25
100%
Variable expenses ............
15
60%
Contribution margin..........
$10
40%
Profit
= Unit CM × Q − Fixed expenses
$0
= $10 × Q − $210,000
$10Q
= $210,000
Q
= $210,000 ÷ $10
Q
= 21,000 balls
Alternative solution:
Fixed expenses
Unit sales to =
break even Unit contribution margin
$210,000
= $10
= 21,000 balls
b. The degree of operating leverage is:
Contribution margin
Degree of =
operating leverage Net operating income
$300,000
= = 3.33 (rounded)
$90,000
2. The new CM ratio will be:
Selling price ....................
$25
100%
Variable expenses ............
18
72%
Contribution margin .........
$ 7
28%
The new break-even point will be:
Profit
= Unit CM × Q − Fixed expenses
$0
= $7 × Q − $210,000
$7Q
= $210,000
Q
= $210,000 ÷ $7
Problem 3-20 (continued)
Alternative solution:
Fixed expenses
Unit sales to =
break even Unit contribution margin
$210,000
=
$7
= 30,000 balls
3.
Profit
= Unit CM × Q − Fixed expenses
$90,000
= $7 × Q − $210,000
$7Q
= $90,000 + $210,000
Q
= $300,000 ÷ $7
Q
= 42,857 balls (rounded)
Alternative solution:
Target profit + Fixed expenses
Unit sales to attain =
target profit Unit contribution margin
$90,000 + $210,000
= = 42,857 balls
$7
below:
Present
Expected
Break-even point (in balls) .................................
21,000
30,000
Sales (in balls) needed to earn a $90,000 profit ..
30,000
42,857
Note that if variable costs do increase next year, then the company will
year.
Problem 3-20 (continued)
4. The contribution margin ratio last year was 40%. If we let P equal the
new selling price, then:
P =
$18 + 0.40P
0.60P =
$18
P =
$18 ÷ 0.60
P =
$30
To verify:
Selling price ....................
$30
100%
Variable expenses ...........
18
60%
Contribution margin ........
$12
40%
5. The new CM ratio would be:
Selling price ........................
$25
100%
Variable expenses ................
9*
36%
Contribution margin .............
$16
64%
*$15 – ($15 × 40%) = $9
The new break-even point would be:
Profit
= Unit CM × Q − Fixed expenses
$0
= $16 × Q − $420,000
$16Q
= $420,000
Q
= $420,000 ÷ $16
Q
= 26,250 balls
Alternative solution:
Fixed expenses
Unit sales to =
break even Unit contribution margin
$420,000
= = 26,250 balls
$16
Problem 3-20 (continued)
6.
a.
Profit
= Unit CM × Q − Fixed expenses
$90,000
= $16 × Q − $420,000
$16Q
= $90,000 + $420,000
Q
= $510,000 ÷ $16
Q
= 31,875 balls
Alternative solution:
Unit sales to attain Target profit + Fixed expenses
=
target profit Unit contribution margin
$90,000 + $420,000
=
$16
= 31,875 balls
b. The contribution income statement would be:
Sales (30,000 balls × $25 per ball) ....................
$750,000
Variable expenses (30,000 balls × $9 per ball) ...
270,000
Contribution margin ..........................................
480,000
Fixed expenses .................................................
420,000
Net operating income ........................................
$ 60,000
Contribution margin
Degree of =
operating leverage Net operating income
$480,000
= = 8
$60,000
