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Homework answers / question archive / Cash flows related to three mutually exclusive capital equipment projects are given in table below
Cash flows related to three mutually exclusive capital equipment projects are given in table below. Alternative Initial Cost Uniform annual Salvage Value A $1000 $125 $750 B $800 $120 $500 ? $600 $100 $250 D $500 $125 $0 Each of the alternatives have a 10-year of useful life. Assuming MARR% is varying from 0% to 100%. Please note you need to show the steps for getting full credit. Just selecting the correct option without showing the steps will result in getting zero points. 5.1. For the following condition 0%
For a given MARR, the project with the highest Net Present Worth (NPW) should be selected.
5.1). Using r (MARR) = 4.13% and n (project life) = 10 years, NPW for each Alternative is:
(P/A, r, n) = 1/r*[1-(1+r)^-n]; (P/F, r, n) = 1/(1+r)^n
Alternative A NPW = -initial cost + Uniform annual*(P/A, r, n) + Salvage value*(P/F, r, n)
= -1,000 + 125*(P/A, 4.13%, 10) + 750*(P/F, 4.13%, 10)
= -1,000 + 125*[1-(1+4.13%)^-10]/4.13% + 750/(1+4.13%)^10
=-1,000 + 1,007.33 + 500.38 = 507.72
Alternative B NPW = -800 + 120*(P/A, 4.13%, 10) + 500*(P/F, 4.13%, 10)
= -800 + 120*[1-(1+4.13%)^-10]/4.13% + 500/(1+4.13%)^10
= -800 + 967.04 + 333.59 = 500.63
Alternative C NPW = -600 + 100*(P/A, 4.13%, 10) + 250*(P/F, 4.13%, 10)
= -600 + 100*[1-(1+4.13%)^-10]/4.13% + 250/(1+4.13%)^10
= -600 + 805.87 + 166.79 = 372.66
Alternative D NPW = -500 + 125*(P/A, 4.13%, 10) + 0*(P/F, 4.13%, 10)
= -500 + 125*[1-(1+4.13%)^-10]/4.13% + 0
= -500 + 1,007.33 = 507.33
At the MARR of 4.13%, Alternative A has the highest NPW so Alternative A shoule be chosen (Option A)
5.2). Again, we calculate NPW using a MARR of 21.4%:
Alternative A NPW = -1,000 + 125*(P/A, 21.4%, 10) + 750*(P/F, 21.4%, 10)
= -1,000 + 125*[1-(1+21.4%)^-10]/21.4% + 750/(1+21.4%)^10
= -1,000 + 500.11 + 107.86 = -392.03
Alternative B NPW = -800 + 120*(P/A, 21.4%, 10) + 500*(P/F, 21.4%, 10)
= -800 + 120*[1-(1+21.4%)^-10]/21.4% + 500/(1+21.4%)^10
= -800 + 480.10 + 71.91 = -247.99
Alternative C NPW = -600 + 100*(P/A, 21.4%, 10) + 250*(P/F, 21.4%, 10)
= -600 + 100*[1-(1+21.4%)^-10]/21.4% + 250/(1+21.4%)^10
= -600 + 400.09 + 35.95 = -163.96
Alternative D NPW = -500 + 125*(P/A, 21.4%, 10) + 0*(P/F, 21.4%, 10)
= -500 + 125*[1-(1+21.4%)^-10]/21.4% + 0
= -500 + 500.11 = 0.11
At the MARR of 21.4%, Alternative D should be chosen as it has the highest NPW. (Option D)
