The NPV is the sum of the present value of the cash flows from the project, so the NPV of eachproject will be:Deepwater Fishing:NPV =–$850,000 + $320,000 / 1.14 + $470,000 / 1.142+ $410,000 /1.143NPV = $69,089.81Submarine Ride:NPV =–$1,650,000 + $810,000 / 1.14 + $750,000 / 1.142+ $690,000 / 1.143NPV = $103,357.31Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishingproject, choose the submarine ride project. The incremental IRR rule is always consistent withthe NPV rule.

124–SOLUTIONS MANUALa.The profitability index is the PV of the future cash flows divided by the initial investment. The cashflows for both projects are an annuity, so:PII= $19,800(PVIFA10%,3) / $35,000 = 1.407PIII= $9,400(PVIFA10%,3) / $16,000 = 1.461The profitability index decision rule implies that we accept Project II, since PIIIis greater thanthe PII.The NPV of each project is:NPVI=–$35,000 + $19,800(PVIFA10%,3) = $14,239.67NPVII=–$16,000 + $9,400(PVIFA10%,3) = $7,376.41The NPV decision rule implies accepting Project I, since the NPVIis greater than the NPVII.Using the profitability index to compare mutually exclusive projects can be ambiguous when themagnitudes of the cash flows for the two projects are of different scales. In this problem,Project I is more than twice as large as Project II and produces a larger NPV, yet theprofitability index criterion implies that Project II is more acceptable.a.The equation for the NPV of the project is:NPV =–$78,000,000 + $110,000,000 / 1.1–$13,000,000 / 1.12NPV = $11,256,198.35The NPV is greater than 0, so we would accept the project.The equation for the IRR of the project is:0 =–$78,000,000 + $110,000,000 / (1 + IRR)–$13,000,000 / (1 + IRR)2From Descartes’ rule of signs, we know there are two IRRs since the cash flows changesignstwice. From trial and error, the two IRRs are:IRR = 28.01%,–86.98%When there are multiple IRRs, the IRR decision rule is ambiguous. Both IRRs are correct; thatis, both interest rates make the NPV of the project equal to zero. If we are evaluating whether ornot to accept this project, we would not want to use the IRR to make our decision.a.The payback period is the time that it takes for the cumulative undiscounted cash inflows to equaltheinitial investment.

CHAPTER 5 -125Board game:Cumulative cash flows Year 1 = $700= $700Cumulative cash flows Year 2 = $700 + 550= $1,250Payback period = 1 + ($950–700) / $550= 1.45 yearsDVD:Cumulative cash flows Year 1= $1,500= $1,500Cumulative cash flows Year 2= $1,500 + 1,050= $2,550Payback period = 1 + ($2,100–1,500) / $1,050Payback period = 1.57 yearsSince the board game has a shorter payback period than the DVD project, the company shouldchoose the board game.The NPV is the sum of the present value of the cash flows from the project, so the NPV of eachproject will be:Board game:NPV =–$950 + $700 / 1.10 + $550 / 1.102+ $130 /1.103NPV = $238.58DVD:NPV =–$2,100 + $1,500 / 1.10 + $1,050 / 1.102+ $450 /1.103NPV = $469.50Since the NPV of the DVD is greater than the NPV of the board game, choose the DVD.The IRR is the interest rate that makes the NPV of a project equal to zero. So, the IRR of eachproject is:Board game:0 =–$950 + $700 / (1 + IRR) + $550 / (1 + IRR)2+ $130 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, wefind that:IRR = 27.51%DVD:0 =–$2,100 + $1,500 / (1 + IRR) + $1,050 / (1 + IRR)2+ $450 / (1 + IRR)3

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