An automobile company is investigating the ad­visability of converting a plant that manufactures economy cars into one that will make retro-sports cars. The initial cost for equipment conversion will be $250 million with a 20% salvage value anytime within a 5-year period. The cost of pro­ducing a car will be $25,000, but it is expected to have a selling price of $43,000 (to dealers). The production capacity for the first year will be 4000 units. 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? Assume the production cost and selling price will remain con­stant for the 3-year period. Solve (a) by hand, and (b) using a spreadsheet.

Question

(a) By hand: Set PW of revenue equal to PW of expenses

4000(43,000 - 25,000)(P/A,12%,3) + G(43,000 - 25,000)(P/G,12%,3) = 250,000,000
- 0.20(250,000,000)(P/F,12%,3)

4000(18,000)(2.4018) + G(18,000)(2.2208) = 250,000,000 - 50,000,000(0.7118)
172,929,600 + 39,974.4G = 214,410,000
G = 1038 more cars per year

(b) By spreadsheet:

Answer 1

(a) By hand: Set PW of revenue equal to PW of expenses



4000(43,000 - 25,000)(P/A,12%,3) + G(43,000 - 25,000)(P/G,12%,3) = 250,000,000

- 0.20(250,000,000)(P/F,12%,3)



4000(18,000)(2.4018) + G(18,000)(2.2208) = 250,000,000 - 50,000,000(0.7118)

172,929,600 + 39,974.4G = 214,410,000

G = 1038 more cars per year



(b) By spreadsheet: