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Exercise 3-6 (10 minutes)
1. The equation method yields the required unit sales, Q, as follows:
Profit
= Unit CM × Q − Fixed expenses
$6,000
= ($140 − $60) × Q − $40,000
$6,000
= ($80) × Q − $40,000
$80 × Q
= $6,000 + $40,000
Q
= $46,000 ÷ $80
Q
= 575 units
Exercise 3-7 (continued)
4. The formula method also gives an answer that is identical to the
Exercise 3-9 (20 minutes)
1. The company’s degree of operating leverage would be computed as
follows:
Contribution margin ...............
$36,000
÷ Net operating income .........
$12,000
Degree of operating leverage .
3.0
2. A 10% increase in sales should result in a 30% increase in net operating
income, computed as follows:
Degree of operating leverage ...................................
3.0
× Percent increase in sales ......................................
10%
Estimated percent increase in net operating income ..
30%
3. The new income statement reflecting the change in sales is:
Amount
Percent
of Sales
Sales ...........................
$132,000
100%
Variable expenses ........
92,400
70%
Contribution margin ......
39,600
30%
Fixed expenses ............
24,000
Net operating income ...
$ 15,600
Net operating income reflecting change in sales ......
$15,600
Original net operating income (a) ...........................
12,000
Change in net operating income (b) .......................
$ 3,600
Percent change in net operating income (b ÷ a) .....
30%
Exercise 3-11 (30 minutes)
1.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($40 − $28) × Q − $150,000
$0
=
($12) × Q − $150,000
$12Q
=
$150,000
Q
=
$150,000 ÷ $12 per unit
Q
=
12,500 units, or at $40 per unit, $500,000
Fixed expenses
Unit sales =
to break even Unit contribution margin
$150,000
= =12,500 units
$12 per unit
or, at $40 per unit, $500,000.
2. The contribution margin at the break-even point is $150,000 because at
Exercise 3-11 (continued)
4. Margin of safety in dollar terms:
Margin of safety = Total sales - Break-even sales
in dollars
= $600,000 - $500,000 = $100,000
Exercise 3-12 (30 minutes)
1.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($90 − $63) × Q − $135,000
$0
=
($27) × Q − $135,000
$27Q
=
$135,000
Q
=
$135,000 ÷ $27 per lantern
Q
=
5,000 lanterns, or at $90 per lantern, $450,000 in sales
Fixed expenses
Unit sales =
to break even Unit contribution margin
$135,000
= = 5,000 lanterns,
$27 per lantern
or at $90 per lantern, $450,000 in sales
2. An increase in variable expenses as a percentage of the selling price
3.
Present:
8,000 Lanterns
Proposed:
10,000 Lanterns*
Total
Per Unit
Total
Per Unit
Sales ..............................
$720,000
$90
$810,000
$81
**
Variable expenses ...........
504,000
63
630,000
63
Contribution margin .........
216,000
$27
180,000
$18
Fixed expenses ...............
135,000
135,000
Net operating income ......
$ 81,000
$ 45,000
*
8,000 lanterns × 1.25 = 10,000 lanterns
**
$90 per lantern × 0.9 = $81 per lantern
