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 90,000 regular models and 18,000 deluxe models. A segmented income statement for the two products is as follows:

Regular Model Deluxe Model Total
Sales $13,500,000 $12,150,000 $25,650,000
Less: Variable costs 9,000,000 7,290,000 16,290,000
Contribution margin $4,500,000 $4,860,000 $9,360,000
Less: Direct fixed costs 1,200,000 960,000 2,160,000
Segment margin $3,300,000 $3,900,000 $7,200,000
Less: Common fixed costs 1,280,000
Operating income $5,920,000
Required:
1. Compute the number of regular models and deluxe models that must be sold to break even.
2. 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

To break even, Steinberg Company needs to sell approximately 38,889 regular models and 8,000 deluxe models. The company must generate sales revenue of approximately $7,698,935.19 to break even.

Step-by-step explanation:

1. Compute the number of regular models and deluxe models that must be sold to break even.

To calculate the break-even point, we need to determine the contribution margin per unit for each product by subtracting the variable costs per unit from the sales price per unit. For the regular model, the contribution margin per unit is $5,000,000 / 90,000 units = $55.56. For the deluxe model, the contribution margin per unit is $4,860,000 / 18,000 units = $270.
To break even, the total contribution margin must cover the fixed costs. Thus, the number of regular models to be sold can be calculated as:
Break-even point (in units) = Fixed costs / Contribution margin per unit
= $2,160,000 / $55.56 = 38,889 units
The number of deluxe models to be sold can be calculated as:
Break-even point (in units) = Fixed costs / Contribution margin per unit
= $2,160,000 / $270 = 8,000 units

2. 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.

To calculate the sales revenue needed to break even, we divide the fixed costs by the contribution margin ratio, which is the contribution margin divided by the total sales. From the income statement, the total contribution margin is $7,200,000 and the total sales revenue is $25,650,000. The contribution margin ratio is $7,200,000 / $25,650,000 = 0.281. Thus, the sales revenue needed to break even is:
Break-even sales revenue = Fixed costs / Contribution margin ratio
= $2,160,000 / 0.281 = $7,698,935.19