Consider a project with the following data: accounting break-even quantity = 16,700 units; cash break-even quantity = 15,000 units; life = four years; fixed costs = $150,000; variable costs = $32 per unit; required return = 15 percent. Ignoring the effect of taxes, find the financial break-even quantity. (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Answer: financial break-even quantity = 17381.8 units
Working notes for the above answer is as under
In order to calculate the financial breakeven, we need the OCF of the project. We can use the cashand accounting breakeven points to find this. First, we will use the cash breakeven to find the price ofthe product as follows:
15000 = $150,000/(P – $32);
Solving above equation we will get,
P =$42
Now that we know the product price, we can use the accounting breakeven equation to find thedepreciation. Doing so, we find the annual depreciation must be
16700 = ($150,000 + D)/($42 -$32)
Solving above equation we will get,
D = $17000
We now know the annual depreciation amount. Assuming straight-line depreciation is used, the initialinvestment in equipment must be five times the annual depreciation, or
Initial investment = 4 × $17000
=$ 68,000
The PV of the OCF must be equal to this value at the financial breakeven since the NPV is zero, so
$68000 = OCF(PVIFA15%,4)
OCF = $23818.04
We can now use this OCF in the financial breakeven equation to find the financial breakeven salesquantity.
QF= ($150,000 + $23818.04)/($42-32)
= 17381.8 units
