Break-even analysis. Binders-For-School Ltd 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 company will charge $60 for each textbook and has determined that the high-capacity machine will be more economically beneficial if sales are greater than 800 books. What is the variable cost per unit under the low-capacity machine scenario?
A) $20
B) $40
C) $60
D) $80

Question

Quizplus · Accepted Answer

To determine the variable cost per unit under the low-capacity machine scenario, we need to use the break-even analysis formula:

Break-even point (in units) = Fixed costs / (Price per unit - Variable cost per unit)

For the high-capacity machine scenario, the break-even point is 800 units. Therefore, we can plug in the numbers to solve for the variable cost per unit:

800 = $10,000 / ($60 - $30)
800 = $10,000 / $30
$24.00 = Variable cost per unit

Now, we can use the same formula to solve for the variable cost per unit under the low-capacity machine scenario:

800 = $2,000 / ($60 - Variable cost per unit)
800($60 - Variable cost per unit) = $2,000
$48,000 - 800Variable cost per unit = $2,000
-800Variable cost per unit = -$46,000
Variable cost per unit = $57.50

Therefore, the variable cost per unit under the low-capacity machine scenario is $57.50, which means the best choice is to stick with the low-capacity machine if the company anticipates selling fewer than 800 textbooks.

Break-Even Analysis