Problem 5-19B (60 minutes)
1.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
(($58 − $37.60) × Q) − $401,880
$0
=
($20.40 × Q) − $401,880
$20.40Q
=
$401,880
Q
=
$401,880 ÷ $20.40 per shirt
Q
=
19,700 shirts
Break-even sales ……………..
Actual sales …………………….
Sales short of break-even ….
Sales (18,200 shirts × $58.00 per shirt) …………………
Variable expenses (18,200 shirts × $37.60 per shirt) ..
Contribution margin …………………………………………..
Fixed expenses …………………………………………………
Net operating loss …………………………………………….
$(30,600)
Problem 5-19B (continued)
2. Cost-volume-profit graph:
$0
$100
$200
$300
$400
$500
$600
$700
$800
$900
$1,000
$1,100
$1,200
$1,300
0 10,000 20,000 30,000
Dollars (000)
Number of Shirts
Break-even point: 19,700 shirts,
or $1,142,600 in sales
Fixed Expenses
Total Expenses
Total Sales
Actual sales …………………………….
Excess over break-even sales ……..
Problem 5-19B (continued)
4. The variable expenses will now be $38.30 ($37.60 + $0.70) per shirt,
and the contribution margin will be $19.70 ($58.00 – $38.30) per shirt.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
(($58.00 − $38.30) × Q) − $401,880
$0
=
($19.70 × Q) − $401,880
$19.70Q
=
$401,880
Q
=
$401,880 ÷ $19.70 per shirt
Q
=
20,400 shirts
Problem 5-19B (continued)
Alternative solution:
Sales (23,140 shirts × $58 per shirt) ………………..
$1,342,120
Variable expenses [(19,700 shirts × $37.60 per
shirt) + (3,440 shirts × $38.30 per shirt)] ……….
872,472
Contribution margin ………………………………………
469,648
Fixed expenses …………………………………………….
401,880
Net operating income ……………………………………
$ 67,768
6. a. The new variable expense will be $27 per shirt (the invoice price).
Profit
=
Unit CM × Q − Fixed expenses
$0
=
(($58.00 − $27.00) × Q) − $564,200
$0
=
($31.00 × Q) − $564,200
$31Q
=
$564,200
Q
=
$564,200 ÷ $31.00 per shirt
Q
=
18,200 shirts
18,200 shirts × $58.00 shirt = $1,055,600 in sales
b. Although the change will lower the break-even point from 19,700
shirts to 18,200 shirts, the company must consider whether this
reduction in the break-even point is more than offset by the possible
loss in sales arising from having the sales staff on a salaried basis.
Under a salary arrangement, the sales staff may have far less
incentive to sell than under the present commission arrangement,
resulting in a loss of sales and a reduction in profits. Although it
generally is desirable to lower the break-even point, management
must consider the other effects of a change in the cost structure. The
break-even point could be reduced dramatically by doubling the
selling price per shirt, but it does not necessarily follow that this
would increase the company’s profit.
$120,000
$120,000 ÷ $8 per unit
15,000 units
Unit contribution margin
Incremental contribution margin:
Less increased fixed costs:
Increase in monthly net operating income …………
Problem 5-20B (60 minutes)
1. The CM ratio is 30%.
Total
Per Unit
Percentage
Sales (13,500 units) ………
$270,000
$20
100%
Variable expenses …………
162,000
12
60%
Contribution margin ………
$108,000
$ 8
40%
Problem 5-20B (continued)
Since the company presently has a loss of $12,000 per month, if the
changes are adopted, the loss will turn into a profit of $16,000 per
month.
3.
Sales (27,000 units × $18 per unit*) …………..
$486,000
Variable expenses
(27,000 units × $12 per unit) ………………….
324,000
Contribution margin …………………………………
162,000
Fixed expenses ($120,000 + $30,000) …………
150,000
Net operating income (loss) ………………………
$ 12,000)
*$20 – ($20 × 0.10) = $18
4.
Profit
=
Unit CM × Q − Fixed expenses
$4,400
=
(($20.00 − $12.40*) × Q) − $120,000
$4,400
=
($7.60 × Q) − $120,000
$7.60Q
=
$124,400
Q
=
$124,400 ÷ $7.60 per unit
Q
=
16,368 units
$7.60** per unit
Sales (20,300 units) ….
Variable expenses …….
Contribution margin ….
Fixed expenses ………..
Problem 5-20B (continued)
5. a. The new CM ratio would be:
Per Unit
Percentage
Sales ……………………………………
$20
100%
Variable expenses……………………
6
30%
Contribution margin …………………
$14
70%
Problem 5-20B (continued)
c. Whether or not one would recommend that the company automate
its operations depends on how much risk he or she is willing to take,
and depends heavily on prospects for future sales. The proposed
Problem 5-21B (60 minutes)
1. The CM ratio is 50%:
Selling price ………………….
$80
100%
Variable expenses …………..
40
50%
Contribution margin ………..
$40
50%
2.
Dollar sales to
break even
=
=
=
$360,000 in sales
3. $53,000 increased sales × 50% CM ratio = $26,500 increase in
4. a.
Degree of operating leverage
=
Contribution margin
Net operating income
=
$1,080,000
=
1.20
$900,000
b. 1.20 × 14% = 16.80% increase in net operating income. In dollars,
Problem 5-21B (continued)
5.
Last Year:
37,500 units
Proposed:
56,250 units*
Total
Per Unit
Total
Per Unit
Sales ………………………
$3,000,000
$80.00
$4,005,000
$71.20
**
Variable expenses ……..
1,500,000
40.00
2,250,000
40.00
Contribution margin ……
1,500,000
$40.00
1,755,000
$31.20
Fixed expenses …………
180,000
243,000
Net operating income …
$1,320,000
$1,512,000
*
37,500 units × 1.5 = 56,250 units
**
$80 per unit × .89 = $71.20 per unit
No, the changes should not be made.
6.
Expected total contribution margin:
37,500 units × 200% × $37.50 per unit* ………..
$2,812,000
Present total contribution margin:
37,500 units × $40.00 per unit ……………………..
1,500,000
Incremental contribution margin, and the amount
by which advertising can be increased with net
operating income remaining unchanged ………….
$1,312,000
*$80.00 – ($40.00 + $2.50) = $37.50
Problem 5-22B (30 minutes)
1.
Product
Sinks
Mirrors
Vanities
Total
Percentage of total
sales …………………….
32%
40%
28%
100%
Sales ………………………
$204,800
100
%
$256,000
100
%
$179,200
100
%
$640,000
100
%
Variable expenses ……..
61,440
30
%
204,800
80
%
98,560
55
%
364,800
57
%
Contribution margin ……
$143,360
70
%
$ 51,200
20
%
$ 80,640
45
%
275,200
43
%*
Fixed expenses …………
224,120
Net operating income ..
$51,080)
*$275,200 ÷ $640,000 = 43%.
Problem 5-22B (continued)
2.
Break-even sales
=
=
=
$521,209 in sales
3. Memo to the president:
Although the company met its sales budget of $640,000 for the month,
the mix of products sold changed substantially from that budgeted. This
is the reason the budgeted net operating income was not met, and the
Problem 5-23B (45 minutes)
1. a.
Alvaro
Bazan
Total
%
%
%
Sales …………………….
€1,350
100
€810
100
€2,160
100
Variable expenses
810
60
162
20
972
45
Contribution margin ….
€ 540
40
€648
80
1,188
55
Fixed expenses ………..
560
Net operating income .
€ 628
b.
Break-even sales
=
=
=
€1,018.18 in sales
Margin of safety
=
Actual sales – Break-even sales
€2,160.00 – €1,018.18 = €1,141.82
Margin of safety percentage
=
Margin of safety
Actual sales
=
€1,141.82
=
52.86%
€2,160.00
Problem 5-23B (continued)
2. a.
Alvaro
Bazan
Cano
Total
%
%
%
%
Sales ………………………..
€1,350
100
€810
100
€540
100
€2,700
100
Variable expenses ………..
810
60
162
20
405
75
1,377
51
Contribution margin ……..
€ 540
40
€648
80
€135
25
1,323
49
Fixed expenses ……………
560
Net operating income …..
€ 763
b.
Break-even sales
=
=
=
€1,142.86 in sales
Margin of safety
=
Actual sales – Break-even sales
€2,700.00 – €1,142.86 = €1,557.14
Margin of safety percentage
=
Margin of safety
Actual sales
=
€1,557.14
=
57.67%
€2,700.00
Solutions Manual Alternate Problems, Chapter 5 5-16
Problem 5-23B (continued)
3. The reason for the increase in the break-even point can be traced to the
decrease in the company’s average contribution margin ratio when the
third product is added. Note from the income statements above that this
ratio drops from 55% to 49% with the addition of the third product.
57.67%. Thus, the addition of the new product shifts the company
Problem 5-24B (60 minutes)
1. a. April’s Income Statement:
Standard
Deluxe
Pro
Total
Amount
%
Amount
%
Amount
%
Amount
%
Sales ………………………
$141,000
100
$130,000
100
$516,000
100
$787,000
100
Variable expenses:
Production ……………..
56,400
40
45,500
35
154,800
30
256,700
32.6
Selling …………………..
7,050
5
6,500
5
25,800
5
39,350
5.0
Total variable expenses .
63,450
45
52,000
40
180,600
35
296,050
37.6
Contribution margin ……
$77,550
55
$78,000
60
$335,400
65
490,950
62.4
Fixed expenses:
Production ………………
107,000
Advertising ……………..
106,000
Administrative ………….
57,000
Total fixed expenses ……
270,000
Net operating income …..
$220,950
Problem 5-24B (continued)
1. b. May’s Income Statement:
Standard
Deluxe
Pro
Total
Amount
%
Amount
%
Amount
%
Amount
%
Sales ……………………….
$376,000
100
$130,000
100
$258,000
100
$764,000
100.0
Variable expenses:
Production ……………..
150,400
40
45,500
35
77,400
30
273,300
35.8
Selling …………………..
18,800
5
6,500
5
12,900
5
38,200
5.0
Total variable expenses .
169,200
45
52,000
40
90,300
35
311,500
40.8
Contribution margin ……
$206,800
55
$78,000
60
$167,700
65
452,500
59.2
Fixed expenses:
Production ……………..
107,000
Advertising …………….
106,000
Administrative …………
57,000
Total fixed expenses …..
270,000
Net operating income ….
$182,500
Problem 5-24B (continued)
2. The sales mix has shifted over the last month from a greater
concentration of Pro rackets to a greater concentration of Standard
3. The break-even in dollar sales can be computed as follows:
Unit sales to break even
=
Fixed expenses
CM ratio
=
$270,000
=
$432,692 (rounded)
.624
4. May’s break–even point has gone up. The reason is that the division’s
5.
Standard
Pro
Increase in sales …………………………….
$27,000
$27,000
Multiply by the CM ratio ……………………
× 55%
× 65%
Increase in net operating income* ………
$14,850
$17,550
*Assuming that fixed costs do not change.