Sales mix, three products

The Janowski Company has three product lines of mugs—A, B, and C— with contribution margins of $5, $4, and $3, respectively. The president foresees sales of 168,000 units in the coming period, consisting of 24,000 units of A, 96,000 units of B, and 48,000 units of C. The company's fixed costs for the period are $405,000.

Required:
1. What is the company's breakeven point in units, assuming that the given sales mix is maintained?
2. If the sales mix is maintained, what is the total contribution margin when 168,000 units are sold? What is the operating income?
3. What would operating income be if the company sold 24,000 units of A, 48,000 units of B, and 96,000 units of C? What is the new breakeven point in units if these relationships persist in the next period?
4. Comparing the breakeven points in requirements 1 and 3, is it always better for a company to choose the sales mix that yields the lower breakeven point? Explain.

1. Sales of A, B, and C are in ratio 24,000 : 96,000 : 48,000. So for every 1 unit of A, 4 (96,000 ÷ 24,000) units of B are sold, and 2 (48,000 ÷ 24,000) units of C are sold.

Contribution margin of the bundle = 1 ? $5+ 4 ? $4 + 2 ? $3 = $5 + $16 + $6 = $27
Breakeven point in bundles = = 15,000 bundles
Breakeven point in units is:
Product A: 15,000 bundles × 1 unit per bundle 15,000 units
Product B: 15,000 bundles × 4 units per bundle 60,000 units
Product C: 15,000 bundles × 2 units per bundle 30,000 units
Total number of units to breakeven 105,000 units

Alternatively,
Let Q = Number of units of A to break even
4Q = Number of units of B to break even
4Q = Number of units of C to break even

Contribution margin – Fixed costs = Zero operating income

$5Q + $4(4Q) + $3(2Q) – $405,000 = 0
$27Q = $405,000
Q = 15,000 ($405,000 ÷ $27) units of A
4Q = 60,000 units of B
2Q = 30,000 units of C
Total = 105,000 units

2. Contribution margin:
A: 24,000 ? $5 $120,000
B: 96,000 ? $4 384,000
C: 48,000 ? $3 144,000
Contribution margin $648,000
Fixed costs 405,000
Operating income $243,000

3. Contribution margin
A: 24,000 ? $5 $120,000
B: 48,000 ? $4 192,000
C: 96,000 ? $3 288,000
Contribution margin $600,000
Fixed costs 405,000
Operating income $195,000

Sales of A, B, and C are in ratio 24,000 : 48,000 : 96,000. So for every 1 unit of A, 2 (48,000 ÷ 24,000) units of B and 4 (96,000 ÷ 24,000) units of C are sold.

Contribution margin of the bundle = 1 ? $5 + 2 ? $4 + 4 ? $3 = $5 + $8 + $12 = $25
Breakeven point in bundles = = 16,200 bundles
Breakeven point in units is:
Product A: 16,200 bundles × 1 unit per bundle 16,200 units
Product B: 16,200 bundles × 2 units per bundle 32,400 units
Product C: 16,200 bundles × 4 units per bundle 64,800 units
Total number of units to breakeven 113,400 units

Alternatively,
Let Q = Number of units of A to break even
2Q = Number of units of B to break even
4Q = Number of units of C to break even

Contribution margin – Fixed costs = Breakeven point

$5Q + $4(2Q) + $3(4Q) – $405,000 = 0
$25Q = $405,000
Q = 16,200 ($405,000 ÷ $25) units of A
4Q = 32,400 units of B
5Q = 64,800 units of C
Total = 113,400 units

Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C.

4. No, it is not always better to choose the sales mix with the lowest breakeven point because this calculation ignores the demand for the various products. The company should look to and sell as much of each of the three products as it can to maximize operating income even if this means that this sales mix results in a higher breakeven point.