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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
210,000
35
Contribution margin ....
130,000
$13
*
90,000
$15
Fixed expenses ...........
118,000
100,000
*
Net operating income (loss)..
$ 12,000
*
$ (10,000)
*
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
40%
420,000
*
70%
Contribution margin ....
150,000
60%
*
180,000
30%
Fixed expenses...........
130,000
*
185,000
Net operating income (loss).
$ 20,000
*
$ (5,000)
*
*Given
Exercise 5-12 (30 minutes)
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:
Fixed expenses
Dollar sales to =
break even Overall CM ratio
$183,750
= = $350,000
0.525
3. The additional contribution margin from the additional sales is computed
as follows:
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
$ 6.00
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)
1. Variable expenses: $40 × (100% – 30%) = $28
2.
a.
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
Exercise 5-14 (continued)
Profit
= CM ratio × Sales − Fixed expenses
$60,000
= 0.30 × Sales − $180,000
0.30 × Sales
= $240,000
Sales
= $240,000 ÷ 0.30
Sales
= $800,000
In unit sales: $800,000 ÷ $40 per unit = 20,000 units
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
Profit
= CM ratio × Sales − Fixed expenses
$0
= 0.40 × Sales − $180,000
0.40 × Sales
= $180,000
Sales
= $180,000 ÷ 0.40
Sales
= $450,000
Exercise 5-14 (continued)
3. a.
Fixed expenses
Unit sales to =
break even Unit contribution margin
$180,000
= = 15,000 units
$12 per unit
Exercise 5-14 (continued)
c.
Fixed expenses
Unit sales =
to break even Unit contribution margin
$180,000
= =11,250 units
$16 per unit
In dollar sales: 11,250 units × $40 per unit = $450,000
Alternative solution:
Fixed expenses
Break-even point=
in sales dollars CM ratio
$180,000
= =$450,000
0.40
In unit sales: $450,000 ÷ $40 per unit =11,250 units
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
$210,000
= = 7.5
$28,000
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%).
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
Exercise 5-16 (continued)
3. Cost-volume-profit graph:
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
$18,000
$20,000
0100 200 300 400 500 600 700
Number of Persons
Total Sales
Total
Expenses
Total
Fixed
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:
Fixed expenses
Unit sales to =
break even Unit contribution margin
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*
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
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
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 5-18 (continued)
4. Margin of safety in dollar terms:
Margin of safety = Total sales - Break-even sales
in dollars
= $450,000 - $360,000 = $90,000
$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:
$50,000 incremental sales × 60% CM ratio = $30,000
Given that the company’s fixed expenses will not change, monthly net
operating income will also increase by $30,000.
Problem 5-19A (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 5-19A (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
The maximum profit is $270,000. This level of profit can be earned by selling 45,000 units at a price
of $58 each.
Problem 5-20A (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
$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%
Problem 5-20A (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)
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
just break even if it sells the same number of balls (30,000) as it did last
year.
Problem 5-20A (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
Problem 5-20A (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
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
