Question

A road can be paved with either asphalt or concrete. Concrete costs $1,500,000 per mile and...

A road can be paved with either asphalt or concrete. Concrete costs $1,500,000 per mile and lasts 20 years. Assume the annual maintenance costs are $50,000 for concrete and $80,000 for asphalt per mile per year. Use an interest rate of 8% per year. Assume the asphalt road costs $600,000 per mile. How long it must last to be the preferred alternative?

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Answer #1

Let the road be x miles long

First we estimate the annual cost of concrete road

AW(C)=1500000*(A/P,0.08,20)+50000*x

Let us calculate the interest factor

So,

AW(C)=1500000*0.10185221+50000x=152778.315+50000x

Similarly, we estimate the annual cost of asphalt road

AW(A)=600000*0.10185221+80000x=61111.326+80000x

Set AW(A)<AW(C)

61111.326+80000x<152778.315+50000x

30000x<152778.315-61111.326

x<3.05 miles

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