Question

The road to Yosemite was repaved after the recent flooding. The repaving cost $1.5 million dollars.    Major maintenance will happen after the repaving every 5 years and will cost $500,000 dollars each time. Minor maintenance happens every year after the repaving and cost 25,000 per year.   What is the capitalized cost of the road repaving and both major and minor maintenance at an interest rate of 9 percent per year compounded monthly?

Answer 1

As per the information given in the question the cost associated with the repaving of the road are as follows

The repaving cost (P1) = $1,500,000

Major maintenance cost after every 5 year= $500,000

Minor maintenance cost every year = $25,000

Rate of interest (r)=9%=0.09 per year compounded monthly

Through the interest is compounded monthly the compounding period (M)=12

Effective interest rate (i) = (1+r/M)^M-1 = (1+0.09/12)¹²-1= 0.093807=9.3807%

Effective life (N)= ∞ (Infinite)

As Major maintenance cost after every 5 year= $500,000

Annual worth of major maintenance cost (A) = $500,000(A/F,9.3807%,5)

A =$500,000[i/{(1+i)^N-1}]

A =$500,000[0.093807/{(1+0.093807)⁵-1}]

A =$500,000[0.093807/{(1.093807)⁵-1}]

A =$500,000(0.165829989)=82914.9945

The perpetual value of major maintenance cost (P2) =82914.9945(P/A, 9.3807%,∞)

P2 =82914.9945(1/0.093807)= $883,889.2034

As Minor maintenance cost every year = $25,000

The perpetual value of minor maintenance cost (P3) =$25,000 (P/A, 9.3807%,∞)

P3 =$25,000(1/0.093807)= $266,504.6319

Capitalised cost = P1+P2+P3 = $1,500,000 + $883,889.2034 + $266,504.6319

Capitalised cost =$2,650,393.8353   or Approx $2,650,394

The required capitalised cost =$2,650,394