Annual Worth and Capital Recovery Calculations 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 $1.2 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 10 to recover its investment plus a return of 15% per year?

$5,601,632

Explanation:

we must first calculate the present value of the required investments and the annual costs:

initial investment = $13,000,000 + $10,000,000/1.1 = $22,090,909

annual costs = $1,200,000 x 5.0188 (PV annuity factor, 15%, 10 periods) = $6,022,560

present value of initial investment + annual costs = $28,113,469

we must calculate an annuity that has a present value = $28,113,469 with a 15% discount rate and 10 years:

annuity = $28,113,469 / 5.0188 = $5,601,631.67 ≈ $5,601,632

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