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

$5.5228 million

Or

$5,522,800

Explanation:

First, calculate the present value of all cash outflows

Present value of cash outflow = Initial Cost + ( Year 1 cost x Discount factor 15%, 1 year ) + ( Annual Cost x Annuity factor 15%, 10 years )

Where

Initial cost = $13 million

Year 1 cost = $10 million

Discount factor 15%, 1 year = 1 / ( 1 + 15% )^1 = 0.8696

Annual Cost = $1.2 million

Annuity factor 15%, 10 years = 1 - ( 1 + 15% )^-10 / 15% = 5.019

Placing value sin the formula

Present value of cash outflow = $13 million + ( $10 million x 0.8696 ) + ( $1.2 million x 5.019 )

Present value of cash outflow = $13 million + $8.696 million + $6.0228 million

Present value of cash outflow = $27.7188 million

Now use the following formula to calculate the annual revenue required to recover its investment plus a return of 15% per year

Present value of Annual revenue = Annual Revenue x Annuity factor 15%, 10 years

Annual Revenue = Present value of Annual revenue / Annuity factor 15%, 10 years

Where

Present value of Annual revenue = $27.7188 million

Annuity factor 15%, 10 years = 1 - ( 1 + 15% )^-10 / 15% = 5.019

Placing value sin the formula

Annual Revenue = $27.7188 million / 5.019

Annual Revenue = $5.5228 million

Annual Revenue = $5,522,800