Exercise 11-16
a.
Contribution margin
Operating leverage
=
—–––———————
Net income
$6,000
Operating leverage
=
———————
=
1.5
$4,000
b. (10% Change in rev. x 1.5 Oper. leverage) = 15% change in net inc.
Annual Income Statements
Sales volume in units (a)
250
% Change
275
Sales revenue (a x $60)
$15,000
+10%
$16,500
Variable costs (a x $36)
(9,000)
(9,900)
Contribution margin
6,000
6,600
Fixed costs
(2,000)
(2,000)
Net income
$ 4,000
+15%
$ 4,600
Exercise 11-17
N = Number of units to break-even
N = Fixed cost ÷ Contribution margin per unit
c.
Contribution margin = Sales price – Variable cost/Unit
= $64 – $40 = $24
Contribution margin ratio = Contribution margin per unit ÷ Sales price
Contribution margin ratio = $24 ÷ $64 = 37.50%
Exercise 11-19
a.
Sales price per unit
$200
Variable cost per unit
(80)
Contribution margin per unit
$120
b. Break-even in units = Fixed cost ÷ Contribution margin per unit
Break-even in units = $600,000 ÷ $120
Break-even in units = 5,000
c. Required sales in units
= (Fixed cost + Profit) ÷ Contribution margin/Unit
d. Margin of safety in units = 7,000 – 5,000 = 2,000 units
Margin of safety in sales $ = ($200 x 7,000) – ($200 x 5,000)
=
$1,400,000
Margin of safety computations:
Margin of safety in units = 30,000 – 25,000 = 5,000 units
Margin of Safety in $ = $150,000 – $125,000 = $25,000
Budgeted sales – Break-even sales
Margin of safety in %
=
–––––––––––––––––––––––––––––––––––
Budgeted sales
$150,000 – $125,000
Margin of safety in %
=
–––––––––––––––––––––––––––
$150,000
Margin of safety in %
=
16.7%
Problem 11-21
Requirement
Fixed
Variable
a.
x
b.
x
c.
x
d.
x
e.
x
f.
x
g.
x
h.
x
i.
x
j.
x
k.
x
l.
x
m.
x
n.
x
o.
x
p.
x
q.
x
r.
x
s.
x
t.
x
Problem 11-22
a.
No. of Houses Cleaned (a)
10
20
30
Total expected rental cost (b)
$900
$900
$900
Average per unit rental cost (b ÷ a)
$90
$45
$30
Type of Cost: Since the total rental cost remains constant at $900 regardless of the number
of houses cleaned, it is a fixed cost.
Problem 11-22 (continued)
b.
No. of Houses Cleaned (a)
10
20
30
Average per unit labor cost (b)
$60
$60
$60
Total labor cost (a x b)
$600
$1,200
$1,800
Type of Cost: Since the total labor cost increases proportionately with the number of houses
cleaned, it is a variable cost.
c.
No. of Houses Cleaned (a)
10
20
30
Average per unit supplies cost (b)
$5
$5
$5
Total cost of supplies (a x b)
$50
$100
$150
Type of Cost: Since the total cost of supplies increases proportionately with the number of houses
cleaned, supplies cost is a variable cost.
d.
No. of Houses Cleaned
10
20
30
Total expected rental cost
$ 900
$ 900
$ 900
Total labor cost
600
1,200
1,800
Total cost of supplies
50
100
150
Total cost
$1,550
$2,200
$2,850
e. The amount of total cost shown below was determined in part d.
No. of Houses Cleaned (a)
10
20
30
Total cost (b)
$1,550
$2,200
$2,850
Cost per unit (b ÷ a)
$ 155
$110
$95
The decline in the cost per unit is caused by the fixed cost behavior that is applicable to the
equipment rental.
f. Ms. Buchanan means average cost per unit. It would be virtually impossible to determine
actual cost per unit. Consider these questions. Exactly how much window cleaner was
Problem 11-23
a. If a branch fails to process at least 60,000 transactions, the branch is closed. Branches
that process more than 90,000 transactions are transferred out of the start-up division.
Accordingly, the relevant range is 60,000 to 90,000 transactions.
b.
No. of Transactions (a)
60,000
70,000
80,000
90,000
Total teller cost (b)
$96,000
$96,000
$96,000
$96,000
Average per unit teller cost (b ÷ a)
$1.60
$1.37
$1.20
$1.07
Type of Cost: Since the total teller cost remains constant at $96,000 regardless of the number
of transactions processed, it is a fixed cost.
c.
No. of Branches (a)
10
15
20
25
Teller costs per branch (b)
$96,000
$96,000
$96,000
$96,000
Total teller cost (a x b)
$960,000
$1,440,000
$1,920,000
$2,400,000
Type of Cost: Since the total teller cost increases proportionately with the number of
branches in operation, the cost is a variable cost.
Problem 11-24
a.
Sales Volume in Units (a)
200
250
300
350
400
Total cost of software (a x $150)
$30,000
$37,500
$45,000
$52,500
$60,000
Total cost of booth rental
8,000
8,000
8,000
8,000
8,000
Total cost of sales (b)
$38,000
$45,500
$53,000
$60,500
$68,000
Average cost per unit (b ÷ a)
$190
$182
$176.67
$172.86
$170
The cost of booth space is fixed.
b.
Sales Volume
200
250
300
350
400
Average cost per unit (a)
$190
$182
$176.67
$172.86
$170
Price per package (a + $45)
$235
$227
$221.67
$217.86
$215
Problem 11-24 (continued)
c.
Trade Shows Attended (a)
1
2
3
4
5
Cost of booth rental (a x $8,000)
$8,000
$16,000
$24,000
$32,000
$40,000
The cost of booth space is variable.
d. The additional cost is $30 ÷ 50 units = $0.60 per unit.
Problem 11-25
Part 1
a. Since the total cost remains constant at $4,000 regardless of how many students attend
the course, the cost of instruction is a fixed cost.
b. c. and d.
Number of Students
18
% Change
20
% Change
22
Revenue ($600 per student)
$10,800
(10%)
$12,000
+10%
$13,200
Cost of instruction (fixed)
4,000
4,000
4,000
Profit
$ 6,800
(15%)
$ 8,000
+15%
$ 9,200
Percentage change in revenue: $1,200 ÷ $12,000 = 10%
Percentage change in profit: $1,200 ÷ $8,000 = 15%
e. Operating leverage caused the percentage increase in profitability to be greater than the
Part 2
cost of instruction is a variable cost.
Problem 11-25 (continued)
g. h. and i.
Number of Students
18
% Change
20
% Change
22
Revenue ($600 per student)
$10,800
(10%)
$12,000
+10%
$13,200
Cost of instruction (Variable)
6,480
7,200
7,920
Profit
$ 4,320
(10%)
$ 4,800
+10%
$ 5,280
j. Since costs as well as revenue change with changes in the number of students attending
the course, the change in profit is proportional to the change in revenue.
Part 3
k.
Number of Students Attempting to Attend
18
20
22
Number of students accepted (a)
18
20
20
Total cost of workbooks (b=[20 x $30])
$600
$600
$600
Cost per student (b ÷ a)
$33.33
$30
$30
l. Since the workbooks must be produced in advance, the total cost is incurred before any
m. RTS faces the risk of producing too many or too few workbooks. When too many are
n. A just-in-time inventory system would produce goods as needed to meet sales demand.
Problem 11-26
a.
University
Orlando
Diego
Tuition revenue (20 x $400)
$8,000
$8,000
Total cost of instruction
(4,600)
(20 x $230)
(4,600)
Net income
$3,400
$3,400
c.
University
Diego
Tuition revenue
(40 x $220)
$ 8,800
Total cost of instruction (variable)
(40 x $230)
(9,200)
b.
University
Orlando
Tuition revenue (40 x $220)
$8,800
Total cost of instruction (fixed)
(4,600)
Net income
$4,200
Net income (loss)
$ (400)
d. The strategy in Requirement b produced a profit because Orlando’s cost of instruction
is fixed. Accordingly, the increase in the number of students did not increase the total
e.
University
Orlando
Diego
Tuition revenue (10 x $400)
$ 4,000
$4,000
Total cost of instruction
(4,600)
(10 x $230)
(2,300)
Net income (loss)
$ (600)
$1,700
Problem 11-26 (continued)
f. When volume is insufficient to produce revenue that is above the level of fixed cost, the
g. When the revenue per unit is below the variable cost per unit, the enterprise will incur
additional losses for each unit produced and sold. This condition is depicted in
Problem 11-27
a.
Company Name
Wood
Lake
Contribution margin
$72,000
$136,000
Divided by net income
48,000
48,000
Operating leverage
1.50
2.83
b.
Company Name
Wood
Lake
Variable cost per unit (a)
$16.00
$8.00
Sales revenue (8,000 units x 110% x$25)
$220,000
$220,000
Variable cost (8,000 units x 110% x a)
(140,800)
(70,400)
Contribution margin
79,200
149,600
Fixed cost
(24,000)
(88,000)
Net income
$55,200
$61,600
Percentage change *
18.06%
45.16%
Problem 11-27 (continued)
c.
Company Name
Wood
Lake
Variable cost per unit (a)
$16.00
$8.00
Sales revenue (8,000 units x 90% x$25)
$180,000
$180,000
Variable cost (8,000 units x 90% x a)
(115,200)
(57,600)
Contribution margin
64,800
122,400
Fixed cost
(24,000)
(88,000)
Net income
$40,800
$34,400
Percentage change **
(18.06%)
(45.16%)
** Wood: ($40,800 − $48,000) $48,000 = (15.00%)
Lake: ($34,400 − $48,000) $48,000 = (28.33%)
d. The following memo is just an example. Students can form different opinions from
Memorandum
TO: Mr. Palvo Sorokin
FROM: John Doe
SUBJECT: Analysis and Recommendation Regarding Investment Opportunities
DATE: September 29, 2014
I have evaluated the income statements of Wood and Lake. Even though both companies
If the economy prospers in the long run, Lake will be the better choice for investment.
Problem 11-28
a. N = Number of units to break-even
Sales − Variable cost − Fixed cost = Profit
(Sales price x N) − (Variable cost per unit x N) = Fixed cost + Profit
b. N = Number of units to break-even
N = Fixed cost ÷ Contribution margin per unit