Break-even analysis. A cement contractor has determined that he will maximize pretax operating cash flow buying a large cement truck if he is able to sell more than 500 yards of cement per month. The price of a yard of cement is $60, and the variable costs for a large truck are $20 per yard. The variable costs for a small truck are $40 per yard, and the fixed costs for the small truck are $10,000. What are the fixed costs associated with the large truck?

Question

Quizplus · Accepted Answer

To determine the fixed costs associated with the large truck, we need to perform a break-even analysis.

Let X be the number of yards of cement sold in a month.

For the small truck, the total cost (TC) is: 
TC = 10,000 + 40X

For the large truck, the total cost (TC) is: 
TC = FC + 20X

where FC is the fixed cost associated with the large truck.

To determine the break-even point, we need to set the total cost equations equal to each other:

10,000 + 40X = FC + 20X

Simplifying the equation:

10,000 = FC + 20X - 40X 
10,000 = FC - 20X 
20X = FC - 10,000 
X = (FC - 10,000)/20

We know that the break-even sales volume is 500 yards of cement per month. So:

(FC - 10,000)/20 = 500

Solving for FC:

FC - 10,000 = 20,000 
FC = 30,000

Therefore, the fixed costs associated with the large truck are $30,000.

The best choice is C.

Break-Even Analysis