Break-even analysis. Binders-For-School, Inc., is in the process of determining whether to purchase a high-capacity machine to make textbooks for the upcoming school year. The high-capacity machine will generate fixed costs of $10,000 per year versus the $2,000 fixed costs of using a low-capacity machine. The variable costs per unit when using the high-capacity machine will be $30. The firm will charge $60 for each textbook and has determined that the high-capacity machine will maximize pretax operating cash flow if sales are greater than 800 books. What is the variable cost per unit under the low-capacity machine scenario?

Question

Quizplus · Accepted Answer

To determine the break-even point, we need to consider when the total revenue equals the total cost. Let x be the number of textbooks sold.
For the high-capacity machine, the total cost is:
Total Cost = $10,000 + $30x 
The total revenue is:
Total Revenue = $60x 
To find the break-even point, we set Total Cost equal to Total Revenue:
$10,000 + $30x = $60x 
Solving for x, we get:
x = 400 
Therefore, if sales are less than 400, the low-capacity machine would be the better option since it has lower fixed costs. If sales are greater than 400, the high-capacity machine should be used.

Now, for the low-capacity machine scenario, let y be the variable cost per unit. The total cost is:
Total Cost = $2,000 + yx 
The total revenue is:
Total Revenue = $60x 
To find the break-even point, we set Total Cost equal to Total Revenue:
$2,000 + yx = $60x 
Substituting x = 400, we get:
$2,000 + 400y = $24,000 
Solving for y, we get:
y = $40 
Therefore, the variable cost per unit under the low-capacity machine scenario is $40.

The best choice(s) is to use the high-capacity machine if sales are greater than 400 textbooks, but use the low-capacity machine if sales are less than or equal to 400 textbooks.

Break-Even Analysis