Question

Steinberg Company produces commercial printers. One is the regular model, a basic model that is designed to copy and print in black and white. Another model, the deluxe model, is a color printer-scanner-copier. For the coming year, Steinberg expects to sell 100,000 regular models and 20,000 deluxe models. A segmented income statement for the two products is as follows:

Regular Model Deluxe Model Total

Sales $12,000,000 $10,720,000 $22,720,000
Less: Variable costs 7,200,000 6,432,000 13,632,000
Contribution margin $4,800,000 $4,288,000 $9,088,000
Less: Direct fixed costs 1,200,000 960,000 2,160,000
Segment margin $3,600,000 $3,328,000 $6,928,000
Less: Common fixed costs 1,702,400
Operating income $5,225,600

Required:
a. Compute the number of regular models and deluxe models that must be sold to break even.
b. Using information only from the total column of the income statement, compute the sales revenue that must be generated for the company to break even.

Answer 1

Results are below.

Step-by-step explanation:

First, we need to calculate the sales proportion of each product:

Regular= 12,000,000/22,720,000= 0.53

Deluxe= 10,720,000/22,720,000= 0.47

Now, we will determine the break-even point for the company as a whole:

Break-even point (units)= Total fixed costs / Weighted average contribution margin

Total fixed costs= 2,160,000 + 1,702,400= $3,862,400

Unitary contribution margin:

Regular= 4,800,000/100,000= $48

Delux= 4,288,000/20,000= $214.4

Weighted average contribution margin= (0.53*48) + (0.47*214.4)

Weighted average contribution margin= $128.35

Break-even point (units)= 3,862,400/128.35

Break-even point (units)= 30,093

For each product:

Regular= 0.53*30,093= 15,949

Deluxe= 0.47*30,093= 14,144

Finally, we need to calculate the break-even point in dollars for the whole company:

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 3,862,400/ (9,088,000/22,720,000)

Break-even point (dollars)= 3,862,400/0.4

Break-even point (dollars)= $9,206,000