Gregory Enterprises sells two products, larges and smalls. Larges sell for $120 per unit with variable costs of $80 per unit. Smalls sell for $30 per unit with variable costs of $10 per unit. Total fixed costs for the company are $40,000. Gregory Enterprises typically sells three larges for every two smalls. What is the break-even point in total units?

Question

Quizplus · Accepted Answer

First, we need to calculate the contribution margin per unit for each product.

For larges: 
Contribution margin = selling price - variable cost 
Contribution margin = $120 - $80 
Contribution margin = $40

For smalls: 
Contribution margin = selling price - variable cost 
Contribution margin = $30 - $10 
Contribution margin = $20

Next, we need to calculate the sales mix. We know that for every 3 larges sold, 2 smalls are sold. This is a ratio of 3:2 or 3/5 for larges and 2/5 for smalls.

To determine the weighted average contribution margin per unit, we multiply the contribution margin per unit by the sales mix percentage and then add them together:

Weighted average contribution margin = (3/5 x $40) + (2/5 x $20) 
Weighted average contribution margin = $24 + $8 
Weighted average contribution margin = $32

Using the contribution margin ratio (weighted average contribution margin / selling price per unit), we can calculate the break-even point in total units.

Break-even point = fixed costs / contribution margin ratio 
Break-even point = $40,000 / ($32 / (($120 x 3) + ($30 x 2))) 
Break-even point = $40,000 / ($32 / ($360 + $60)) 
Break-even point = $40,000 / ($32 / $420) 
Break-even point = $40,000 / 13.125 
Break-even point = 3,048 units

Therefore, the break-even point in total units is 3,048 or approximately 1,250 units rounded up to the nearest whole unit. The best choice is B.

Gregory Enterprises Sells Two Products, Larges and Smalls