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16 '"'The IRR overstates the expected return for accepted projects because cash fiows cannot generally be reinvested at the IRR. Therefore, the average IRR for accepted projects is greater than the true expected rate of return. This imparts an upward bias on corporate projections based on IRRs. 15Excel's MIRR function allows you to enter a different reinvestment rate from the WACC for the cash infiows. However, we assume reinvestment at the WACC, so the WACC is entered twice in the Excel MIRR function, shown in Figure 11.4. 16Equation 11-2a summarizes these steps. N N L::c1F,(1 + rt-' ""' COF, t=O fa ( 1 +r)' = -'---'-(-1 -+-M-IR-R-,)N..-PV costs= TV (1 + MIRR)N ~ 11-2a COF, is the cash outfiow at timet, and CIF, is the cash infiow at time t. The left term is the PV of the investment outlays when discounted at the cost of capital; the numerator of the second term is the compounded value of the infiows, assuming the infiows are reinvested at the cost of capital. The MIRR is the discount rate that forces the PV of the TV to equal the PV of the costs. Also note that there are alternative definitions for the MIRR. One difference relates to whether negative cash fiows, after the positive cash fiows begin, should be compounded and treated as part of the TV or discounted and treated as a cost. A related issue is whether negative and positive flows in a given year should be netted or treated separately. For a complete discussion, see William R. McDaniel, Daniel E. McCarty, and Kenneth A Jessell, "Discounted Cash Flow with Explicit Reinvestment Rates: Tutorial and Extension," The Financial Review, vol. 23, no. 3 (August 1988), pp. 369-385; and David M. Shull, "Interpreting Rates of Return: A Modified Rate of Return Approach," Financial Practice and Education, vol. 10 (Fall 1993), pp. 67-71. Modified IRR (MIRR) The discount rate at which the present value of a project's cost is equal to the present value of its terminal value, where the terminal value is found as the sum of the future val-ues of the cash inflows, compounded at the firm's cost of capital.
382 Part 4 Investing in Long-Term Assets: Capital Budgeting FIGURE 11.4 Finding the MIRR for Project 5, WACC = 10% r22-71 1--72 1--73 -~ 2.2._ .1.§_ .12. 2§._ .1.2... * A I B I c I D I E I F I G WACC= 10% r=lO% 0 1 2 3 4 Project 5 I $5100 sdoo $3100 $100.00 $1,000.00 I I I : $330.00 $484.00 $665.50 $1,000.00 Terminal Value (TV)= $1,579.50 Calculator: N = 4, PV = -1000, PMT = 0, FV = 1579.5. Press 1/YR to solve for MIRR 12.11% Excel, RATE function: = RATE (F72,0,B73,F77) Rate= MIRR 12.11 o/o Excel, MIRR function: = MIRR (B73:F73,B70,B70) 12.11% The MIRR has two significant advantages over the regular IRR. First, whereas the regular IRR assumes that the cash flows from each project are reinvested at the IRR, the MIRR assumes that cash flows are reinvested at the cost of capital (or some other explicit rate). Since reinvestment at the IRR is generally not correct, the MIRR is generally a better indicator of a project's true profitability. Second, the MIRR eliminates the multiple IRR problem-there can never be more than one MIRR, and it can be compared with the cost of capital when deciding to accept or reject projects.