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 10 to recover its investment plus a return of 21% per year?

The company must make $____ million annually in years 1 through 10 to recover its investment plus a return of 21% per year.

Answer 1

Solution :-

Present Value of Costs = $13,000,000 + [ $10,000,000 / ( 1 + 0.21 ) ]

= $13,000,000 + ( $10,000,000 * 0.8264 )

= $13,000,000 + $8,264,462.81

= $21,264,462.81

Now let Annual Revenue be X

Annual Expense = $1,500,000

Net Annual Revenue = ( X - $1,500,000 )

Now as per question :-

= $21,264,462.81 = ( X - $1,500,000 ) * ( P/A , 21% , 10 )

= $21,264,462.81 = ( X - $1,500,000 ) * 4.0541

( X - $1,500,000 ) = $5,245,203.23

X = $6,745,203.23

Therefore the Company must make annual revenue of $6,745,203.23 in year 1 through 10 to recover its investment plus a return of 21% per year.

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