Question

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1) Find the present worth of earthmoving equipment that has a first cost today of $149,000, an annual operating cost of $65,000, and a salvage value of 20% of the first cost after 5 years, these estimates being in future dollars. Assume that the real interest rate is 8% per year and that inflation has averaged 3.5% per year.

Solve with inflation (a) not accounted for and (b) accounted for.

2)Find the present worth of earthmoving equipment that has a first cost today of $149,000, an annual operating cost of $65,000, and a salvage value of 20% of the first cost after 5 years, these estimates being in future dollars. Assume that the real interest rate is 8% per year and that inflation has averaged 3.5% per year. Solve with inflation (a) not accounted for and (b) accounted for.

Answer 1

Present Worth of Equipment= Present Worth of Benefits-Present Worth of Costs

Present Worth of Cost=First Cost+Present Worth of Annual Operating cost

=149000+65000(P/A,r,5)

(P/A,r,t) this compounding factor is used when we need to find present worth of annual cash flows at given rate r and for number of years we have cash flow

In this case we have annual operating cost worth $65000 for 5 years and r can take 2 values 1) without inflation r=8% 2) with inflation=8%+3.5%

(P/F,r,t) this compounding factor used when we have single cash flow in future such as Salvage value of equipment realized after 5 years in this case

Present Worth of Benefits=Salvage Value*(P/F,r,t)

We should solve this question in 2 cases

Case 1) when inflation rate is not considered
r=8%

Net Presetn Worth when inflation is not considered=20%*149000(P/F,r,5)-149000+-65000(P/A,r,5)

=29800(P/F,8%,5)-149000-65000(P/A,8%,5)

(P/F,8%,5)=0.6806

(P/A,8%,5)=3.993

=29800*0.6806-149000-65000*(3.993)

Present Worth when inflation rate is not considered=-$388263.12

Case 2) when inflation rate is considered
r=8%

Net Present Worth when inflation is considered=20%*149000(P/F,r,5)-149000+-65000(P/A,r,5)

=29800(P/F,11.5%,5)-149000-65000(P/A,11.5%,5)

(P/F,11.5%,5)=0.5803

(P/A,11.5%,5)=3.6499

=29800*0.5803-149000-65000*(3.6499)

Present Worth when inflation rate is considered=-$368950.56