Question

An automobile company is investigating building a plant that to make cars. The initial cost for equipment will be $200 million with a 20% salvage value anytime within a 5- year period. The cost of producing a car will be $21,000, but it is expected to have a selling price of $33,000. The production capacity for the first year will be 4000 cars. At an interest rate of 12% per year, by what uniform amount will production have to increase each year in order for the company to recover its investment in 3 years?

Answer 1

Let n be the uniform amount the production has to be increased, then as per given condition

(33000 - 21000) *(4000 + n) + 0.2 * 200000000 * (A/F, 12%,3) = 200000000 * (A/P, 12%,3)

12000 *(4000 + n) + 40000000 * 0.296349 = 200000000 * 0.416349

12000 *(4000 + n)  = 200000000 * 0.416349 - 40000000 * 0.296349 = 71415840.00

n = (71415840.00 - 12000 * 4000) / 12000 = 1951.32 ~ 1952