Question

need to show work on how to get 13.7% whithout excel

2. A small start-up company invested in a new plant with an initial cost of $10 million. Operating costs for the plant were $3 million per year for 7 years. There was a special one-time charge of $1 million in year 2 to correct unexpected equipment problems. Revenues were $3 million in year 1, and increased by $1 million per thereafter through year 7. Determine the company's rate of return on this investment. (Answer: 13.7%)

Answer 1

Let the rate of return be i%, then as per given condition PW should be equal to 0 at i%, therefore

-10m - 3m*(P/A, i%,7) - 1m * (P/F, i%, 2) + 3m *(P/A, i%,7) + 1m * (P/G, i%,7) = 0

-10m- 1m * (P/F, i%, 2) + 1m * (P/G, i%,7) = 0

- (P/F, i%, 2) +  (P/G, i%,7) = 10

Using trail and error method

When i = 13%, value of - (P/F, i%, 2) +  (P/G, i%,7) = 11.132199 - 0.783147 = 10.349053

When i = 14%, value of - (P/F, i%, 2) +  (P/G, i%,7) = 10.648883 - 0.769468 = 9.879415

using interpolation

i = 13% + (10.349053 - 10) / (10.349053 - 9.879415) *(14% - 13%)

i = 13% + 0.7432%

i = 13.74% ~ 13.7% (rounding to one decimal place)

Pls comment if you require further explanation