Sales mix, two products

The Stackpole Company retails two products: a standard and a deluxe version of a luggage carrier. The budgeted income statement for next period is as follows:

Standard Carrier Deluxe Carrier Total
Units sold 187,500 62,500 250,000
Revenues at $28 and $50 per unit $5,250,000 $3,125,000 $8,375,000
Variable costs at $18 and $30 per unit 3,375,000 1,875,000 5,250,000
Contribution margins at $10 and $20 per unit $1,875,000 $1,250,000 3,125,000
Fixed costs 2,250,000
Operating income $ 875,000

Required:
1. Compute the breakeven point in units, assuming that the company achieves its planned sales mix.
2. Compute the breakeven point in units (a) if only standard carriers are sold and (b) if only deluxe carriers are sold.
3. Suppose 250,000 units are sold but only 50,000 of them are deluxe. Compute the operating income. Compute the breakeven point in units. Compare your answer with the answer to requirement 1. What is the major lesson of this problem?

1. Sales of standard and deluxe carriers are in the ratio of 187,500 : 62,500. So for every 1 unit of deluxe, 3 (187,500 ÷ 62,500) units of standard are sold.

Contribution margin of the bundle = 3 ? $10 + 1 ? $20 = $30 + $20 = $50
Breakeven point in bundles = = 45,000 bundles
Breakeven point in units is:
Standard carrier: 45,000 bundles × 3 units per bundle 135,000 units
Deluxe carrier: 45,000 bundles × 1 unit per bundle 45,000 units
Total number of units to breakeven 180,000 units

Alternatively,
Let Q = Number of units of Deluxe carrier to break even
3Q = Number of units of Standard carrier to break even

Revenues – Variable costs – Fixed costs = Zero operating income

$28(3Q) + $50Q – $18(3Q) – $30Q – $2,250,000 = 0
$84Q + $50Q – $54Q – $30Q = $2,250,000
$50Q = $2,250,000
Q = 45,000 units of Deluxe
3Q = 135,000 units of Standard

The breakeven point is 135,000 Standard units plus 45,000 Deluxe units, a total of 180,000 units.

2a. Unit contribution margins are: Standard: $28 – $18 = $10; Deluxe: $50 – $30 = $20
If only Standard carriers were sold, the breakeven point would be:
$2,250,000 ? $10 = 225,000 units.
2b. If only Deluxe carriers were sold, the breakeven point would be:
$2,250,000 ? $20 = 112,500 units

= 200,000($10) + 50,000($20) – $2,250,000
= $2,000,000 + $1,000,000 – $2,250,000
= $750,000

Sales of standard and deluxe carriers are in the ratio of 200,000 : 50,000. So for every 1 unit of deluxe, 4 (200,000 ÷ 50,000) units of standard are sold.

Contribution margin of the bundle = 4 ? $10 + 1 ? $20 = $40 + $20 = $60
Breakeven point in bundles = = 37,500 bundles
Breakeven point in units is:
Standard carrier: 37,500 bundles × 4 units per bundle 150,000 units
Deluxe carrier: 37,500 bundles × 1 unit per bundle 37,500 units
Total number of units to breakeven 187,500 units

Alternatively,
Let Q = Number of units of Deluxe product to break even
4Q = Number of units of Standard product to break even

$28(4Q) + $50Q – $18(4Q) – $30Q – $2,250,000 = 0
$112Q + $50Q – $72Q – $30Q = $2,250,000
$60Q = $2,250,000
Q = 37,500 units of Deluxe
4Q = 150,000 units of Standard

The breakeven point is 150,000 Standard +37,500 Deluxe, a total of 187,500 units.

The major lesson of this problem is that changes in the sales mix change breakeven points and operating incomes. In this example, the budgeted and actual total sales in number of units were identical, but the propor¬tion of the product having the higher contribution margin declined. Operating income suffered, falling from $875,000 to $750,000. Moreover, the breakeven point rose from 180,000 to 187,500 units.