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 $1.5 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 12 to recover its investment plus a return of 22% per year?

Answer 1

ANSWER:

Initial cost = $13 million

cost in 1st year = $10 million

operating cost = $1.5 million

annual revenue = ?

i = 22%

n = 12 years.

we need to find the annual revenue and for that the present worth of this investment will be zero at i = 22%

pw = initial cost + cost in 1st year(p/f,i,n) + operating cost(p/a,i,n) + annual revenue(p/a,i,n)

0 = -13,000,000 - 10,000,000(p/f,22%,12) - 1,500,000(p/a,22%,12) + annual revenue(p/a,22%,12)

0 = -13,000,000 - 10,000,000 * 0.8197 - 1,500,000 * 4.1274 + annual revenue * 4.1274

0 = -13,000,000 - 8,196,721.31 - 6,191,061.88 + annual revenue * 4.1274

0 = -27,387,783.19 + annual revenue * 4.1274

27,387,783.19 = annual revenue * 4.1274

annual revenue = 27,387,783.19 / 4.1274

annual revenue = $6,635,642.74

so the annual revenue that us steel must earn is $6,635,642.74 per annum.