Question

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?

Answer 1

The company must make $25,157,480.59 annually in years 1 through 10 to recover its investment plus a return of 15% per year.

Step-by-step explanation:

To calculate the annual revenue needed, we need to find the present value of the investment cost and the present value of the annual operating costs. We will use the Annual Worth and Capital Recovery formulas to do this.

First, let's calculate the present value of the investment cost. The initial cost of $13 million is invested now, so we will use the present worth factor for a single cash flow. With a return rate of 15% per year and a time of 1 year, the present value of the investment cost is $13 million*(1+0.15)^-1 = $11,304,347.83. The second cost of $10 million is invested the following year, so we will use the present worth factor for two cash flows. The present value of the second cost is $10 million*(1+0.15)^-2 = $7,836,956.52.

Next, let's calculate the present value of the annual operating costs. The operating costs of $1.2 million per year starts 1 year from now and continues for 10 years. We will use the annual worth factor for an annuity. With a return rate of 15% per year and a term of 10 years, the present value of the annual operating costs is $1.2 million*(1-((1+0.15)^-10))/0.15 = $6,016,176.24.

Lastly, we add the present values of the investment cost and the annual operating costs to find the total annual revenue needed. $11,304,347.83 + $7,836,956.52 + $6,016,176.24 = $25,157,480.59.