# Strict adherence to the irr method would further

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Strict adherence to the IRR method would further dictate that mutually exclusive projects should be chosen on the basis of the greater IRR. In our example, each project has an IRR that exceeds the cost of capital (10%) so both projects should be accepted if they are independent. If, however, the projects are mutually exclusive, we would choose Project S because it has the higher IRR. Recall that this differs from our conclusion when using the NPV method. So, we have a conflict between the NPV and the IRR methods for ranking Projects S and L. A B C D E F G H 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113
Figure 10-4. Graph for Multiple IRRs: Project M (Millions of Dollars) Year = 0 1 2 Project M -1.60 10 -10 r = 10% NPV = -$0.774 Note: r NPV 0% -$1.600 10% -$0.774 25%$0.000 = IRR #1 = 25% 110% $0.894 400%$0.000 = IRR #2 = 400% 500% -$0.211 Because of the mathematics involved, it is possible for some (but not all) projects that have more than one change of signs in the cash flows to have more than one IRR. If you attempted to find the IRR with such a project using a financial calculator, you would get an error message. The procedure for correcting the problem is to store in a guess for the IRR, and then the calculator will report the IRR that is closest to your guess. You can then use a different "guess" value, and you should be able to find the other IRR. However, the nature of the mathematics creates a scenario in which one IRR is quite extraordinary (often, several hundred percent). The table shown below calculates Project M's NPV at the rates shown in the left column. These data are plotted to form the graph shown above. Notice that NPV = 0 at both 25% and 400%. Since the definition of the IRR is the rate at which the NPV = 0, there are two IRRs. 0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% -$0.30 -$0.10$0.10 $0.30$0.50 $0.70$0.90 Cost of Capital (%) NPV (Mil- lions) NPV = $1.6 +$10/(1+r) + ( $10)/(1+r) 2 IRR #1 = 25% IRR #2 = 400% A B C D E F G H 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 REINVESTMENT RATE ASSUMPTIONS MODIFIED INTERNAL RATE OF RETURN, MIRR Finding the MIRR for Projects S and L r = 10% Year = 1 2 3 4 Project S -10,000 5,000 4,000 3,000 1,000$3,300 $4,840$6,655 -10,000 Terminal Value (TV) = \$15,795 12.11% =RATE(F208,0,B209,F213) 12.11% =MIRR(B209:F209,B206,B206) 12.11% Year = 1 2 3 4 Project L -10,000 1,000 3,000 4,000 6,750 The IRR approach assumes that cash flows can be reinvested at the IRR, but it is more realistic to asssume that cash flows only can be reinvested at the cost of capital. For this reason, NPV is a better decision criterion than IRR. The modified internal rate of return is the discount rate that causes a project's cost (or cash outflows) to equal the present value of the project's terminal value. The terminal value is defined as the sum of the future values of the project's cash inflows, compounded at the project's cost of capital. To find MIRR, calculate the PV of the outflows and the FV of the inflows, and then find the rate that equates the two. Alternatively, you can solve using Excel's MIRR function. One advantage of using the MIRR, relative to the IRR, is that the MIRR assumes that cash flows received are
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