A process for producing the mosquito repellant Deet has an initial investment of $200,000 with annual costs of $50,000. Income is expected to be $90,000 per year. (a) What is the payback period at i = 0% per year? A i = 12% per year? (Note: Round your answers to the nearest integer.) (b) What is the annual breakeven production quantity for both payback periods (determined above) if net profit, that is, income minus cost, is $10 per gallon?

Question

What will be an ideal response?

Answer 1

(a) i = 0%: np = 200,000/(90,000 – 50,000)
= 5 years

i = 12%: -200,000 + (90,000 -50,000)(P/A,12%,np) = 0
(P/A,12%,np) = 5.0000

From 12% interest tables, value is slightly over 8 years. Round to np = 8 years

Spreadsheet function: = NPER(12%,40000,-200000) displays 8.08 years

(b) Develop the relation Revenue = Cost and solve for XBE = gallons per year

i = 0%; np = 5 years: 10XBE = 200,000/5
XBE = 4000 gallons per year

i = 12%; np = 8 years: 10XBE = 200,000(A/P,12%,8)
XBE = 20,000(0.2013)
= 4026 gallons per year