Question

A process for producing the mosquito repellant Deet has an initial investment of $185,000 with annual costs of $49,000. Income is expected to be $90,000 per year.

What is the annual breakeven production quantity for both payback periods if net profit, that is, income minus cost, is $10 per gallon?

When i = 0%, the annual breakeven production quantity is determined to be gallons per year.

When i = 12%, the annual breakeven production quantity is determined to be gallons per year.

Answer 1

1) At i = 0%, the annual BE production quantity is 4111 gallons per year.
i = 0%: np = 185,000/(90,000 - 49,000) = 4.5 years
i = 0%; np = 4.5 years:
10 * BE = 185,000 / 4.5
Breakeven production quantity = 4111 gallons per year

2) At i = 12%, the annual BE production quantity is 4100 gallons per year.
Working:
i = 12%: -185,000 + (90,000 -49,000)(P/A,12%,np) = 0
Spreadsheet function: = NPER(12%,41000,-185,000) displays 6.88 years
i = 12%; np = 6.88 years:
10 * BE = 185,000 (A/P,12%,6.88)
BE = 18,500 (A/P,12%,6.88)
Breakeven production quantity = 4100 gallons per year