Question

Consider a project with the following data: accounting break-even quantity = 14,200 units; cash break-even quantity = 10,300 units; life = five years; fixed costs = $170,000; variable costs = $27 per unit; required return = 12%. Ignoring the effect of taxes, find the financial break-even quantity. (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Break-even quantity            

Answer 1

In order to calculate the financial breakeven, we need the OCF of the project. We can use the cash and accounting breakeven points to find this. First, we will use the cash breakeven to find the price of the product as follows:

QC= FC/(P –v)

10,300 = $170,000/(P –$27)

P = $43.5

Now that we know the product price, we can use the accounting breakeven equation to find the depreciation. Doing so, we find the annual depreciation must be:

QA= (FC + D)/(P –v)

14,200 = ($170,000 + D)/($43.5–27)

Depreciation = $64,300

We now know the annual depreciation amount. Assuming straight-line depreciation is used, the initial investment in equipment must be five times the annual depreciation, or:

Initial investment = 5($64,300) = $321,500

The PV of the OCF must be equal to this value at the financial breakeven since the NPV is zero, so

$321,500 = OCF(PVIFA12%,5)

OCF = $89,186.64

We can now use this OCF in the financial breakeven equation to find the financial breakeven sales quantity.

QF= ($170,000 + 89,186.64)/($43.5–27)

QF= 15,708.28