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:
Fixed expenses
Unit sales to =
break even Unit contribution margin
$108,000
= = 6,000 stoves
$18.00 per stove
or at $50 per stove, $300,000 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
3.
Present:
8,000 Stoves
Proposed:
10,000 Stoves*
Per Unit
Total
Per Unit
Sales ……………………….
$50
$450,000
$45
**
Variable expenses ………
32
320,000
32
Contribution margin ……
$18
130,000
$13
Fixed expenses ………….
108,000
Net operating income….
$ 22,000
*8,000 stoves × 1.25 = 10,000 stoves
**$50 × 0.9 = $45
As shown above, a 25% increase in volume is not enough to offset a
10% reduction in the selling price; thus, net operating income
decreases.
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
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 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
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
2. The contribution margin is $216,000 because the contribution margin is
equal to the fixed expenses at the break-even point.
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
Problem 5-19 (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
18,000 units × $70 per unit = $1,260,000 to break even
3. See the next page.
4. At a selling price of $58 per unit, the contribution margin is $18 per unit.
Therefore:
Fixed expenses
Unit sales to =
break even Unit contribution margin
$540,000
=
$18
= 30,000 units
30,000 units × $58 per unit = $1,740,000 to break even
This break-even point is different from the break-even point in part (2)
because of the change in selling price. With the change in selling price,
the unit contribution margin drops from $30 to $18, resulting in an
increase in the break-even point.
Problem 5-20 (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
2. The new CM ratio will be:
Selling price ………………..
$25
100%
Variable expenses …………
18
72%
Contribution margin ………
$ 7
28%
= Unit CM × Q − Fixed expenses
$0
= $7 × Q − $210,000
= $210,000
Q
= $210,000 ÷ $7
Problem 5-20 (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%
Therefore, to maintain a 40% CM ratio, a $3 increase in variable costs
would require a $5 increase in the selling price.
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:
= Unit CM × Q − Fixed expenses
= $16 × Q − $420,000
= $420,000 ÷ $16
= 26,250 balls
Problem 5-20 (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
Thus, the company will have to sell 1,875 more balls (31,875 –
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