Find the present worth of earthmoving equipment that has a first cost today of $

Question

Find the present worth of earthmoving equipment that has a first cost today of $159,000, an annual operating cost of $66,000, 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 12% per year and that inflation has averaged 5.5% per year. Solve with inflation (a) not accounted for and (b) accounted for.

a) The present worth with inflation not accounted for is $ .

b) The present worth with inflation accounted for is $

Explanation / Answer

a) The present worth with inflation not accounted for is $

Real interest rate = 12%

Present worth = 159000 + 66000*Present value annuity factor(12%,5) + 159000*20%*Present value interest factor(12%,5)

= 159000 + 66000*3.6047 + 31800*0.5674 = 159000 + 237910.20 + 18043.32 = 414953.52

b) The present worth with inflation accounted for is $

Real interest rate = 12%

Inflation rate = 5.5%

Inflation adjusted rate (Nominal rate) = [(1.12*1.055)-1]*100 = 18.16%

Present worth = 159000 + 66000*Present value annuity factor(18.16%,5) + 159000*20%*Present value interest factor(18.16%,5)

= 159000 + 66000*3.1158 + 31800*0.4342 = 159000 + 205642.80 + 13807.56 = 378450.36

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