FREE online courses on Capital Budgeting Analysis - Three Economic Criteria
for Evaluating Capital Projects - Modified Internal Rate of Return
Besides determining the Net Present Value of a project, we
can calculate the rate of return earned by the project. This is called the
Internal Rate of Return. Internal Rate of Return (IRR) is one of the most
popular economic criteria for evaluating capital projects since managers can
identify with rates of return. Internal Rate of Return is calculating by finding
the discount rate whereby the Net Investment amount equals the total present
value of all cash inflows; i.e. Net Present Value = 0. If we have equal cash
inflows each year, we can solve for IRR easily.
Example 11 - Calculate Internal Rate of Return
Referring back to example 6, we would solve for IRR as
follows:
$ 5,788 x discount factor = $ 24,100 or $ 24,100 / $ 5,788 =
4.164.
If we look in the Present Value Tables for n = 5 years, we
want to find a present value factor nearest to 4.164. By referring to published
present value tables, we find the following:
At 6%, n = 5
4.2124
4.2124
As Calculated
4.1640
At 7%, n = 5
4.1002
Difference .0484 .1122
.06 + (.0484 / .1122) x (.07 - .06) = .0643
Internal Rate of Return = 6.43%
If the Internal Rate of Return were higher than our cost of
capital, then we would accept this project. In our example, the IRR (6.43%) is
less than our cost of capital (12%). Therefore, we would not invest in this
project.
One of the problems with IRR is the so-called reinvestment
rate assumption. IRR makes the assumption that every year you will be able to
earn the IRR each time you reinvest your cash inflows. This assumption can
result in some major distortions between Net Present Value and Internal Rate of
Return. We will correct this distortion by modifying our IRR calculation.
Example - IRR
Distortions from Reinvestment Rate Assumption
A summary of four simple projects with IRR and NPV:
Cash Inflows
|
Project
|
Investment
|
Year-1
|
Year-2
|
IRR
|
NPV
|
|
A
|
$ 2,000
|
$ - 0
|
$ 4,500
|
50%
|
$ 3,130
|
|
B
|
2,000
|
1,500
|
2,250
|
50%
|
2,810
|
|
C
|
2,000
|
2,450
|
1,000
|
55%
|
2,640
|
|
D
|
2,000
|
-0-
|
4,210
|
45%
|
2,940
|
If we use IRR, we would select Project C, but if we go by
NPV, we would select Project A.
In order to eliminate the reinvestment rate assumption, we
will modify the Internal Rate of Return so that the reinvestment rate is our
cost of capital. This will give us a more accurate IRR for our project.
Fortunately, we can use spreadsheets like Microsoft Excel to calculate Modified
Internal Rate of Return.
Example 13 -
Calculate Modified IRR Using Microsoft Excel
Referring back to Example 6, we have the following:
$ 5,788 annual project cash inflows
$ 24,100 net investment amount
12% cost of capital
The formula for calculating Modified IRR in a Microsoft Excel
Spreadsheet is: @MIRR(A1:An, k%, r%)
A1:An is the cell range for entering our data. We always
enter the net investment in the first cell and the cash inflows in each cell
thereafter. k% refers to our cost of capital and r% is the rate we believe we
can earn when we reinvest cash inflows.
If we assume that we can earn our cost of capital on
reinvested cash flows, then we would enter the following from our example:
Cell
Input
Output
A1
-24,100
A2 5,788
A3 5,788
A4 5,788
A5 5,788
A6 5,788
B1
@MIRR(A1:A6, 12%, 12%)
9%
The Modified IRR on our project is 9%.
