Question

U.S. Steel is considering a plant expansion to produce austenitic, precipitation hardened, duplex, and martensitic stainless steel round bars that is expected to cost $13 million now and another $10 million 1 year from now. If total operating costs will be $1.7 million per year starting 1 year from now, and the estimated salvage value of the plant is virtually zero, how much must the company make annually in years 1 through 11 to recover its investment plus a return of 17% per year? The company must make $ million annually in years 1 through 11 to recover its investment plus a return of 17% per year.

Answer 1

The present value of the costs (in millions) is:

Present Worth (PW) = 13 + 10 * P/F(17%, 1) + 1.7 * P/A(17%, 11)

(Note:

P/A = (1+i) ^n – 1 / i(1+i)^n = 1.17^11 – 1 / 0.17 * 1.17^11 = 4.62398922/0.956078167 = 4.8364

P/F = 1/(1+i)^n = 1 / (1+0.17)^1 = 1/1.17 = 0.8547)

= 13 + 10* 0.8547 + 1.7 * 4.8364

= 13 + 8.547+ 8.22188 = 29.76888

Annual revenue ($ million) = PW of costs / P/A(17%, 11) = 29.76888/4.8364 = 6.15517

The company must make $6.15517 million annually in years 1 through 11 to recover its investment plus a return of 17% per year.