Fundamentals of Financial Management (Concise 6th Edition)

348 Part 4 Investing in Long-Term Assets: Capital Budgeting

that cash " ows are reinvested at the WACC. For Project S, the! rst cash " ow,

$500, is compounded at WACC! 10% for 3 years and it grows to $665.50. The

second in" ow, $400, grows to $484.00; the third, to $330.00. The last in" ow is

received at the end, so it is not compounded at all. The sum of the future

values, $1,579.50, is called the “terminal value,” or TV.

3. We now have the cost at t! 0, "$1,000, and the TV at Year 4, $1,579.50. There
   is some discount rate that will cause the PV of the terminal value to equal the
   cost. That interest rate is de! ned as the MIRR. In a calculator, enter N! 4, PV!
   "1000, PMT! 0, and FV! 1579.50. Then when you press the I/YR key, you get
   the MIRR, 12.11%.


4. The MIRR can be found in a number of ways. Figure 11-4 illustrates how the
   MIRR is calculated: We compound each cash in" ow, sum them to determine
   the TV, and then! nd the rate that causes the PV of the TV to equal the cost.
   That rate is 12.11%. However, some of the better calculators have a built-in
   MIRR function that streamlines the process, as does Excel. We explain how to
   use the calculator function in the calculator tutorials, and we explain how to
   ! nd MIRR with Excel in the chapter Excel model.^15
   The MIRR has two signi! cant advantages over the regular IRR. First, whereas the
   regular IRR assumes that the cash " ows from each project are reinvested at

71

72

73

74

75

76

77

78

79

A B C D E F G H

0

!$1,000.00 $500 $400 $300 $100.00

$330.00

$484.00

$665.50

r = 10%^124

WACC = 10%

3

!$1,000.00 $1,579.50

$1,000 = TV/(1"MIRR)N = $1,579.50/(1"MIRR)^4. Solve for MIRR with calculator or Excel.

Calculator: N = 4, PV = !1000, PMT = 0, FV = 1579.5. Press I/YR to get:

Excel: = RATE(F70,0,B71,F75)

Direct Excel calculation, MIRR function: =MIRR(B71:F71,F69,F69)

Rate = MIRR

12.11%

12.11%

12.11%

Project S

Terminal Value (TV) =

69

70

F I G U R E 1 1! 4 Finding the MIRR for Projects S and L, WACC! 10%

(^15) Equation 11-2a summarizes these steps.
∑
t! 0
N
COFt
__(1 " r) (^) t!
∑
t! 0
N
CIFt(1 " r)N#t
__(1 " MIRR) (^) N
11-2a PV costs! ___(1 " MIRR)TV (^) N
COFt is the cash out$ ow at time t, and CIFt is the cash in$ ow 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 in$ ows, assuming the in$ ows 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 de! nitions for the MIRR. One di" erence relates to whether negative cash
$ ows, after the positive cash $ ows 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 $ ows 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, August
1988, pp. 369–385 and David M. Shull, “Interpreting Rates of Return: A Modi! ed Rate of Return Approach,”
Financial Practice and Education, Fall 1993, pp. 67–71.