Also, note that Excel's MIRR function allows for discounting and reinvestment to occur at different rates. MIRR is defined as reinvestment at the WACC, though Excel allows the calculation of MIRR where reinvlikely to occur at a different rate than WACC.As is stated in the text, NPV is superior to the IRR because (1) the NPV assumes that cash flows are reinvescost of capital whereas the IRR assumes reinvestment at the IRR, and (2) it is more likely, in a competitive that the actual reinvestment rate will be the cost of capital than the IRR, especially if the IRR is quite highMIRR setup can be used to prove that NPV indeed does assume reinvestment at the WACC and IRR at theIf negative cash flows occur in years beyond Year 1, those cash flows should be discounted at the cost of capadded to the Year 0 cost to find the total PV of costs. If both positive and negative flows occurred in a givenegative flows should be discounted, and the positive ones compounded, rather than just dealing with the nflow. This can make a difference.

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r = 10%Year =1234Project S-10,0005,0004,0003,0001,000$3,300$4,840$6,655-10,000Terminal Value (TV) =$15,79512.11%=RATE(F208,0,B209,F213)12.11%=MIRR(B209:F209,B206,B206)12.11%Year =1234Project L-10,0001,0003,0004,0006,750For Project L, using the MIRR function:=MIRR(B220:F220,B206,B206) =12.66%Notes:NPV PROFILES (Section 10.7)Figure 10-6. NPV Profile for Project S1. In Figure 10-5 we find the discount rate that forces the present value of the terminal value to equal the project's cost. That discount rate is defined as the MIRR. $10,000 =TV/(1+MIRR)N= $15,795/(1+MIRR)4. We can find the MIRR with a calculator or Excel.2. If S and L are independent, both should be accepted as both MIRRs exceed the cost of capital. they are mutually exclusive, then L should be chosen because it has the higher MIRR.An NPV profile shows how a project's NPV declines as the WACC used to calculate the NPV increases. Figfor the multiple IRR example, shows a NPV profile. Normally, though, the cash flows change sign only oncnegative for the Time = 0 cash flow and then positive cash flows thereafter, so normally NPV profiles look lin Figure 10-6.NPVS229230231232233234235236237238239240241242243244245246247248

Cost of capital = 10.00%Year =01234Project S-10,000.005,0004,0003,0001,000r0 (r = 10%)Calculator: N = 4, PV = -10000, PMT = 0, FV = 15795. Press I/YR to get:MIRRS=ExcelRate function--Easier:MIRRS=ExcelMIRR function--Easiest: MIRRS=0 (r = 10%)MIRRL=

If

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0%$3,000.005%1,804.2410%788.2014.489%0.00 NPV = $0, so IRR = 14.489%15%-83.3020%-837.19The Crossover RateYear =01234Project S-$10,000$5,000$4,000$3,000$1,000Project L-10,0001,0003,0004,0006,750$0$4,000$1,000-$1,000-$5,75011.975%The crossover rate is the rate at which the NPV of Project S is equal to the NPV of Project L. The easiest wthe crossover rate is to subtract one project's cash flows from the others and find the IRR of this differentiflow stream.D= CFS− CFLIRR D=0%2%4%6%8%10%12%14%16%18%20%-$1,000$2,000PROJECT S's NPV PROFILECost of Capital (%)Net Present Value for SNPVS= 0, so IRR = 14.489%ABCDEFG249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295

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Figure 10-7. NPV Profiles for Projects S and L: Shows Why Conflict OccursCost of Capital0%$3,000.00$4,750.005%1,804.242,682.0610%788.201,004.03Crossover =11.975%428.38428.3813.549%156.400.0014.489%0.00-243.6520%-$837.19-$1,513.31NPVSNPVLNPVS= NPVLIRRL=NPVL= 0IRRS=NPVS= 0PROFITABILITY INDEX (PI) (Section 10.8)0%10%20%30%-$2,000-$1,000$0$1,000$2,000$3,000$4,000$5,000