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Problem 3-29 (75 minutes)
1.
a.
Selling price .....................
$37.50
100%
Variable expenses ............
22.50
60%
Contribution margin ..........
$15.00
40%
Profit
= Unit CM × Q − Fixed expenses
$0
= $15 × Q − $480,000
$15Q
= $480,000
Q
= $480,000 ÷ $15 per skateboard
Q
= 32,000 skateboards
Alternative solution:
Fixed expenses
Unit sales =
to break even Unit CM
$480,000
= $15 per skateboard
= 32,000 skateboards
b. The degree of operating leverage would be:
Contribution margin
Degree of operating leverage = Net operating income
$600,000
= = 5.0
$120,000
2. The new CM ratio will be:
Selling price ..........................
$37.50
100%
Variable expenses ..................
25.50
68%
Contribution margin ...............
$12.00
32%
Problem 3-29 (continued)
Thus, sales will have to increase by 10,000 skateboards (50,000
skateboards, less 40,000 skateboards currently being sold) to earn the
same amount of net operating income as earned last year. The
Problem 3-29 (continued)
6.
a.
Profit
= Unit CM × Q − Fixed expenses
$120,000
= $24 × Q − $912,000*
$24Q
= $120,000 + $912,000
Q
= $1,032,000 ÷ $24.00 per skateboard
Q
= 43,000 skateboards
*480,000 × 1.9 = $912,000
Alternative solution:
Target profit + Fixed expenses
Unit sales to attain =
target profit Unit CM
$120,000 + $912,000
=
$24 per skateboard
= 43,000 skateboards
Thus, the company will have to sell 3,000 more skateboards (43,000
– 40,000 = 3,000) than now being sold to earn a profit of $120,000
each year. However, this is still less than the 50,000 skateboards that
would have to be sold to earn a $120,000 profit if the plant is not
automated and variable labor costs rise next year [see part (3)
above].
Problem 3-30 (30 minutes)
1. The contribution margin per stein would be:
Selling price ........................................................
$30
Variable expenses:
Purchase cost of the steins ................................
$15
Commissions to the student salespersons ...........
6
21
Contribution margin .............................................
$ 9
Target profit $7,200
= = 800 steins
Unit CM $9 per stein
800 steins × $30 per stein = $24,000 in total sales
2. Since an order has been placed, there is now a “fixed” cost associated
Selling price ................................................
$30
Variable expenses (commissions only) ..........
6
Contribution margin .....................................
$24
Since the “fixed” cost of $3,000 must be recovered before Marbury
shows any profit, the break-even computation would be:
Fixed expenses $3,000
Unit sales = = =125 steins
to break even Unit CM $24 per stein
125 steins × $30 per stein =$3,750 in total sales
If a quantity other than 200 steins were ordered, the answer would
change accordingly.
Problem 3-31 (45 minutes)
1. The contribution margin per unit on the first 30,000 units is:
Per Unit
Selling price ..........................
$2.50
Variable expenses ..................
1.60
Contribution margin ...............
$0.90
The contribution margin per unit on anything over 30,000 units is:
Per Unit
Selling price ..........................
$2.50
Variable expenses ..................
1.75
Contribution margin ...............
$0.75
Thus, for the first 30,000 units sold, the total amount of contribution
margin generated would be:
30,000 units × $0.90 per unit = $27,000.
Since the fixed costs on the first 30,000 units total $40,000, the $27,000
contribution margin above is not enough to permit the company to
break even. Therefore, in order to break even, more than 30,000 units
will have to be sold. The fixed costs that will have to be covered by the
additional sales are:
Fixed costs on the first 30,000 units ..........................
$40,000
Less contribution margin from the first 30,000 units ...
27,000
Remaining unrecovered fixed costs ............................
13,000
Add monthly rental cost of the additional space
needed to produce more than 30,000 units .............
2,000
Total fixed costs to be covered by remaining sales ......
$15,000
Problem 3-31 (continued)
The additional sales of units required to cover these fixed costs would
be:
Total remaining fixed costs $15,000
=
Unit contribution margin on added units $0.75 per unit
=20,000 units
25% × ($40,000 + $2,000) = $10,500
Thus,
Target profit $10,500
= =17,500 units
Unit contribution margin $0.60 per unit
