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Problem 5-28B (continued)
5.
a.
Contribution margin $105,000
Degree of operating leverage= = = 7.00
Net operating income $15,000
Problem 5-29B (75 minutes)
1.
a.
Selling price .....................
$42.00
100%
Variable expenses ............
25.20
60%
Contribution margin ..........
$16.80
40%
Profit
= Unit CM × Q − Fixed expenses
$0
= $16.80 × Q − $470,400
$16.80Q
= $470,400
Q
= $470,400 ÷ $16.80 per skateboard
Q
= 28,000 skateboards
Alternative solution:
Unit sales to break even
=
Fixed expenses
CM per unit
=
$470,400
=
28,000
skateboards
$16.80
b. The degree of operating leverage would be:
Degree of operating leverage
=
Contribution margin
Net operating income
=
$739,200
=
2.75
$268,800
2. The new CM ratio will be:
Selling price ..........................
$42.00
100%
Variable expenses ..................
28.56
68%
Contribution margin ...............
$13.44
32%
Problem 5-29B (continued)
Problem 5-29B (continued)
Thus, sales will have to increase by 11,000 skateboards (55,000
skateboards, less 44,000 skateboards currently being sold) to earn the
Problem 5-29B (continued)
5. The new CM ratio would be:
Selling price ........................
$42.00
100%
Variable expenses ................
15.12
*
36%
Contribution margin .............
$26.88
64%
*$25.20 – ($25.20 × 40%) = $15.12
The new break-even point would be:
Profit
= Unit CM × Q − Fixed expenses
$0
= $26.88Q × Q − $936,096*
$26.88Q
= $936,096
Q
= $936,096 ÷ $26.88Q per skateboard
Q
= 34,825 skateboards
Problem 5-29B (continued)
6.
a.
Profit
= Unit CM × Q − Fixed expenses
$268,800
= $26.88 × Q − $936,096*
$26.88Q
= $268,800 + $936,096
Q
= $1,204,896 ÷ $26.88 per skateboard
Q
= 44,825 skateboards
*$470,400 × 1.99 = $936,096
Alternative solution:
Unit sales to achieve
same level of profit
=
Net operating income + Fixed expenses
CM per unit
=
$268,800 + $936,096
=
44,825 units
$26.88
Thus, the company will have to sell 825 more skateboards (44,825 –
44,000 = 825) than now being sold to earn a profit of $268,800 each
year. However, this is still less than the 55,000 skateboards that
would have to be sold to earn a $268,800 profit if the plant is not
automated and variable labor costs rise next year [see part (3)
above].
Problem 5-29B (continued)
b. The contribution income statement would be:
Sales
(44,000 skateboards × $42.00 per skateboard)..
$1,848,000
Variable expenses
(44,000 skateboards × $15.12 per skateboard)..
665,280
Contribution margin ............................................
1,182,720
Fixed expenses ...................................................
936,096
Net operating income ..........................................
$ 246,624
Degree of operating leverage
=
Contribution margin
Net operating income
=
$1,182,720
=
4.80
$246,624
c. This problem shows the difficulty faced by some companies. When
variable labor costs increase, it is often difficult to pass these cost
Problem 5-30B (30 minutes)
1. The contribution margin per stein would be:
Selling price ........................................................
$32
Variable expenses:
Purchase cost of the steins ................................
$16
Commissions to the student salespersons ...........
6
22
Contribution margin .............................................
$10
Since there are no fixed costs, the number of unit sales needed to yield
the desired $8,000 in profits can be obtained by dividing the target
profit by the unit contribution margin:
Unit sales to achieve
target profit
=
Target profit + Fixed expenses
CM per unit
=
$8,000 + $0
= 800 steins
$10 per stein
800 steins x $32 per stein = $25,600 in total sales
2. Since an order has been placed, there is now a “fixed” cost associated
with the purchase price of the steins (i.e., the steins can’t be returned).
For example, an order of 280 steins requires a “fixed” cost (investment)
of $4,480 (= 280 steins × $16 per stein). The variable costs drop to
© The McGraw-Hill Companies, Inc., 2013. All rights reserved.
40 Introduction to Managerial Accounting, 6th Edition
172 steins x $32 per stein = $5,504 total sales
Problem 5-30B (30 minutes)
Problem 5-31B (45 minutes)
1. The contribution margin per unit on the first 30,000 units is:
Per Unit
Selling price ..........................
$2.90
Variable expenses ..................
1.84
Contribution margin ...............
$1.06
The contribution margin per unit on anything over 30,000 units is:
Per Unit
Selling price ..........................
$2.90
Variable expenses ..................
2.03
Contribution margin ...............
$0.87
Fixed costs on the first 30,000 units ..........................
$47,200
Less contribution margin from the first 30,000 units ..
31,800
Remaining unrecovered fixed costs ...........................
15,400
Add monthly rental cost of the additional space
needed to produce more than 30,000 units.............
2,360
Total fixed costs to be covered by remaining sales .....
$17,760
Problem 5-31B (continued)
The additional sales of units required to cover these fixed costs would
be:
Total remaining fixed costs
=
$17,760
= 20,414 units
Unit CM on added units
$.87 per unit
Therefore, a total of 50,414 units (30,000 + 20,414) must be sold for
the company to break even. This number of units would equal total
sales of:
50,414 units × $2.90 per unit = $146,201 in total sales.
2.
Total remaining fixed costs
=
$10,527
= 12,100 units
Unit CM on added units
$.87 per unit
Thus, the company must sell 12,100 units above the break-even point to
earn a profit of $10,527 each month. These units, added to the 50,414
units required to break even, equal total sales of 62,514 units each
month to reach the target profit.
3. If a bonus of $0.15 per unit is paid for each unit sold in excess of the
break-even point, then the contribution margin on these units would
drop from $0.87 to only $0.72 per unit.
