3. The increased labor cost will be $0.60 per unit, 1/3 of $1.80 per unit.
The new variable expense will therefore total $3.60 per unit, and the
new contribution margin ratio will be:
Sales ... $7.50 100%
Less variable expenses... 3.60 48
Contribution margin... $3.90 52%
The target profit per unit will be:
20% × $7.50 = $1.50.
Therefore,
Sales = Variable expenses + Fixed expenses + Profits
$7.50Q = $3.60Q + $108,000 + $1.50Q
$2.40Q = $108,000
Q = $108,000 ÷ $2.40 per unit
Q = 45,000 units
Alternative solution:
X = 0.48X + $108,000 + 0.20X
0.32X = $108,000
X = $108,000 ÷ 0.32
X = $337,500; or, at $7.50 per unit, 45,000 units
Case 6-33 (75 minutes)
Before proceeding with the solution, it is helpful first to restructure the data into contribution format for
each of the three alternatives. (The data in the statements below are in thousands.)
15% Commission 20% Commission Own Sales Force
Sales ... $16,000 100% $16,000 100% $16,000.0 100.0%
Less variable expenses:
Manufacturing ... 7,200 7,200 7,200.0
Commissions (15%, 20% 7.5%) ... 2,400 3,200 1,200.0
Total variable expenses... 9,600 60 10,400 65 8,400.0 52.5
Contribution margin... 6,400 40% 5,600 35% 7,600.0 47.5%
Less fixed expenses:
Manufacturing overhead... 2,340 2,340 2,340.0
Marketing... 120 120 2,520.0 *
Administrative ... 1,800 1,800 1,725.0 **
Interest... 540 540 540.0
Total fixed expenses ... 4,800 4,800 7,125.0
Income before income taxes ... 1,600 800 475.0
Less income taxes (30%)... 480 240 142.5
Net income ... $ 1,120 $ 560 $ 332.5
*$120,000 + $2,400,000 = $2,520,000.
**$1,800,000 – $75,000 = $1,725,000.
Case 6-33 (continued)
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