investment outlays when discounted at the cost of capital, and the numerator of the
right term is the compounded future value of the inflows, assuming that the cash in-
flows are reinvested at the cost of capital. The compounded future value of the cash
inflows is also called the terminal value,or TV.The discount rate that forces the PV of
the TV to equal the PV of the costs is defined as the MIRR.^11
We can illustrate the calculation with Project S:0123 4
Cash Flows 1,000 500 400 300 100.00
↓ r 10%
PV of costs^12 1,000 330.00
r 10%
484.00
r 10%
665.50
Terminal Value (TV) 1,579.50PV of TV 1,000
MIRR 12.1%NPV 0Using the cash flows as set out on the time line, first find the terminal value by com-
pounding each cash inflow at the 10 percent cost of capital. Then enter N 4, PV
1000, PMT 0, FV 1579.5, and then press the I button to find MIRRS12.1%.
Similarly, we find MIRRL11.3%.^13
The modified IRR has a significant advantage over the regular IRR. MIRR as-
sumes that cash flows from all projects are reinvested at the cost of capital, while the
regular IRR assumes that the cash flows from each project are reinvested at the proj-
ect’s own IRR. Since reinvestment at the cost of capital is generally more correct, the
modified IRR is a better indicator of a project’s true profitability. The MIRR also
eliminates the multiple IRR problem. To illustrate, with r 10%, Project M (the strip
mine project) has MIRR 5.6% versus its 10 percent cost of capital, so it should be
rejected. This is consistent with the decision based on the NPV method, because at
r 10%, NPV $0.77 million.Modified Internal Rate of Return (MIRR) 275↑↑↑↑(^11) There are several alternative definitions for the MIRR. The differences primarily relate to whether nega-
tive cash flows that occur after positive cash flows 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. Mc-
Carty, and Kenneth A. Jessell, “Discounted Cash Flow with Explicit Reinvestment Rates: Tutorial and Ex-
tension,”The Financial Review,August 1988, 369–385; and David M. Shull, “Interpreting Rates o fReturn:
A Modified Rate o fReturn Approach,”Financial Practice and Education,Fall 1993, 67–71
(^12) In this example, the only negative cash flow occurs at t 0, so the PV of costs is equal to CF 0.
(^13) With some calculators, including the HP-17B, you could enter the cash inflows in the cash flow register
(being sure to enter CF 0 0), enter I 10, and then press the NFV key to find TVS1,579.50. The HP-10B
does not have an NFV key, but you can still use the cash flow register to find TV. Enter the cash inflows in the
cash flow register (with CF 0 0), then enter I 10, then press NPV to find the PV of the inflows,
which is 1,078.82. Now, with the regular time value keys, enter N 4, I 10, PV 1078.82, PMT 0,
and press FV to find TVS1,579.50. Similar procedures can be used with other financial calculators.
Most spreadsheets have a function for finding the MIRR. Refer back to our spreadsheet for Project S,
with cash flows of 1,000, 500, 400, 300, and 100 in Cells B4:F4. You could use the Excelfunction wizard
to set up the following formula: MIRR(B4:F4,10%,10%).Here the first 10 percent is the cost of capital
used for discounting, and the second one is the rate used for compounding, or the reinvestment rate. In our
definition of the MIRR, we assume that reinvestment is at the cost of capital, so we enter 10 percent twice.
The result is an MIRR of 12.1 percent.