You are reviewing the cashflows from four different four year projects for your

Question

You are reviewing the cashflows from four different four year projects for your company. Using both the NPV and IRR methods, provide values for each, rate them from best to worst, and select one to undertake. Your cost of capital is 12% in each instance. If there is an NPV/IRR conflicts, show how to solve it using either the Fisher Intersection or the Profitability Index.

Project X Project W Project T Project Q
Yr0 ($5,000) ($10,000) ($13,000) ($7,500)
Yr1 $ 700 $ 0 $ 0 $ 0
Yr2 $2,000 $ 5,000 $ 0 $3,650
Yr3 $3,000 $ 5,000 $ 0 $3,650
Yr4 $1,200 $ 5,000 $21,750 $3,650

Explanation / Answer

Let CashX = Cash flow from year X Let r = cost of capital NPV = Cash1 + Cash2/(1+r) + Cash3/(1+r)^2 + Cash4/(1+r)^3 IRR is the same equation, but instead of plugging in r, you assume the NPV is 0 and determine what r is needed to make this occur. So... Project X NPV = -5000 + 700/1.12 + 2000/1.12^2 + 3000/1.12^3 + 1200/1.12^4 NPV = 117.35 0 = -5000 + 700/(1+r) + 2000/(1+r)^2 + 3000/(1+r)^3 + 1200/(1+r)^4 r = 13.01% (can determine this though intense algebra, a computer program, or guess and check) Project W NPV = -10000 + 0/1.12 + 5000/1.12^2 + 5000/1.12^3 + 5000/1.12^4 NPV = 722.46 0 = -10000 + 0/(1+r) + 5000/(1+r)^2 + 5000/(1+r)^3 + 5000/(1+r)^4 r = 14.71% Project T NPV = -13000 + 0/1.12 + 0/1.12^2 + 0/1.12^3 + 21750/1.12^4 NPV = 822.52 0 = -13000 + 0/(1+r) + 0/(1+r)^2 + 0/(1+r)^3 + 21750/(1+r)^4 r = 13.73% Project Q NPV = -7500 + 0/1.12 + 3650/1.12^2 + 3650/1.12^3 + 3650/1.12^4 NPV = 327.40 0 = -7500 + 0/(1+r) + 3650/(1+r)^2 + 3650/(1+r)^3 + 3650/(1+r)^4 r = 13.65% So ranking them by NPV, we have T, W, Q and X

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