Introduction to Finance

Modifi ed internal rate of return (MIRR)
solves some of the problems presented by IRR. 
MIRR rankings of mutually exclusive projects with comparably sized initial investments will 
agree with the NPV rankings of those projects. Additionally, the MIRR calculation always 
gives a single answer. It will not give us multiple answers as the IRR approach sometimes does.
MIRR is calculated in a three-step process:
1.
Using the required rate of return as the discount rate, fi nd the present value (PV) of all cash 
outfl ows. (For a conventional project, this will be just the initial cost of the project.) This step 
converts all the cash outfl ows into a lump-sum PV at time 0.
2.
Using the required return as the re-investment or compounding rate, compute the 
future
value (FV) of each cash infl ow as of the end of the project’s life, time 
N
, and add them 
together. This sum is sometimes called the 
terminal value
. This step converts all infl ows 
into a lump-sum future value at time 
N
.
3.
Find the discount rate that equates the PV of the outfl ows and the terminal value; this 
discount rate is the modifi ed internal rate of return.
Figure 17. 2
illustrates this process using the cash fl ow data from project A and a required return 
of 10 percent. 
In the fi rst step, the PV of the project’s outfl ows is its initial investment, $20,000.
Second, we fi nd the FV of each of the project’s infl ows as of the end of the fi fth and 
fi nal year of the project. The year one cash infl ow of $5,800 is compounded over four years 
to the end of year fi ve; its FV at the end of year fi ve is $8,491.78. The year-two cash fl ow is 
compounded for three years to the end of year fi ve; its FV at the end of year fi ve is $7,719.80. 
Similarly, we compute the FVs for the year three, four, and fi ve cash infl ows. The year fi ve 
cash infl ow needs no compounding as it occurs at the end of year fi ve. Adding the FVs yields 
the sum $35,409.58; this is the project’s terminal value.