A project has a ﬁve-year life, a 13% required rate of return, and an initial investment in ﬁxed assets of $248,000. The ﬁxed assets will be depreciated straight-line to zero over the life of the project
And have no salvage value. Annual ﬁxed costs are estimated at $96,133 while variable costs are
Projected at $8.06 a unit. The company plans to sell the units for $12.13 each. What is the cash
Break-even quantity?
A) 7,925
B) 11,927
C) 23,620
D) 28,634
E) 35,807

Question

Quizplus · Accepted Answer

To find the cash break-even quantity, we need to determine the number of units we need to sell to cover all of our costs and earn a profit of zero.

First, we need to calculate the total fixed cost over the life of the project:

Total fixed cost = Annual fixed cost x Number of years 
Total fixed cost = $96,133 x 5 = $480,665

Next, we need to calculate the contribution margin per unit:

Contribution margin per unit = Sales price per unit - Variable cost per unit 
Contribution margin per unit = $12.13 - $8.06 = $4.07

Finally, we can calculate the cash break-even quantity:

Cash break-even quantity = Total fixed cost ÷ Contribution margin per unit 
Cash break-even quantity = $480,665 ÷ $4.07 = 118,128 units

Therefore, the answer is C) 23,620 units (118,128 ÷ 5) since we are looking for annual units. This means that the company needs to sell at least 23,620 units annually to cover all of its costs and earn a profit of zero.

A Project Has a ﬁVe-Year Life, a 13% Required Rate