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. Present worth without inflation Year 0 1 2 3 4 5 Initial investment -159000 Annual operatint cost -66000 -66000 -66000 -66000 -66000 Salvage value 31800 Net cash flows -159000 -66000 -66000 -66000 -66000 -34200 Real rate of interest 18% 18% 18% 18% 18% 18% Discounting factor 1 0.847458 0.718184 0.608631 0.515789 0.437109 Present value -159000 -55932.2 -47400.2 -40169.6 -34042.1 -14949.1 Present worth -351493 Real rate = (1+nominal rate) / (1+inflaton rate ) -1 0.12 = (1+n) / (1+0.055) - 1 1.12 = (1+n) / (1.055) 1+n = 1.12*1.055 1.1816 n=1.1816-1 = 0.1816 b. Present worth with inflation. Year 0 1 2 3 4 5 Initial investment -159000 Annual operatint cost -66000 -66000 -66000 -66000 -66000 Salvage value 31800 Net cash flows -159000 -66000 -66000 -66000 -66000 -34200 Real rate of interest 12% 12% 12% 12% 12% 12% Discounting factor 1 0.892857 0.797194 0.71178 0.635518 0.567427 Present value -159000 -58928.6 -52614.8 -46977.5 -41944.2 -19406 Present worth -378871

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