U.S. Steel is considering a plant expansion to produce austenitic, precipitation

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 $17 million now and another $10 million 1 year from now. If total operating costs will be $1.3 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 19% per year? The company must make $ million annually in years 1 through 12 to recover its investment plus a return of 19% per year.

Explanation / Answer

Annual cash inflows required to recover the investment plus 19% return = Present value of cash outflows / Annuity factor @ 19% for 12 years Calculation of present value of cash outflows Year Cash outflow (in millions) Discount factor @ 19% Present Value 0 $17.00 1 $17.00 1 $11.30 0.840336 $9.50 2 $1.30 0.706165 $0.92 3 $1.30 0.593416 $0.77 4 $1.30 0.498669 $0.65 5 $1.30 0.419049 $0.54 6 $1.30 0.352142 $0.46 7 $1.30 0.295918 $0.38 8 $1.30 0.248671 $0.32 9 $1.30 0.208967 $0.27 10 $1.30 0.175602 $0.23 11 $1.30 0.147565 $0.19 12 $1.30 0.124004 $0.16 Present value of cash outflows $31.40 Annuity factor = [1 - (1+r)^-n]/r r = rate of return = 19% n = no.of years = 12 Annuity factor = [1 - (1+0.19)^-12]/0.19 Annuity factor @ 19% for 12 years = 4.610504 Annual cash inflows required to recover the investment plus 19% return = $31.40 million / 4.610504 Annual cash inflows required to recover the investment plus 19% return = $6.81 million The company must make $6.81 million annually in years 1 through 12 to recover its investment plus a return of 19% per year.

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