The Internal Rate Return(IRR)
August 27th, 2008The definition of “The Internal Rate of Return” is the discount rate that equates the present value, PV of a project’s expected cash inflows to a present value of the project’s costs. In other words, at IRR,
I = PV
NPV = 0
Decision rule: accept the project if the IRR exceeds the cost of capital. Otherwise, reject it.
Example 1:
Assume the same data given in example 1 (NPV) and set of the following equality (I = PV):
$12,950 = $3,000 X PVIFA
PVIFA = $12,950 = 4.317
$3,000
Which stands somewhere between 18 percent and 20 percent in the 10-year line of Appendix D. The interpolation follows:
PV Factor
18% 4.494 4.494
IRR 4.317
20% _____ 4.192
Difference 0.177 0.302
Therefore,
IRR = 18% + 0.17 (20% - 18%)
0.302
= 18% + 0.586(2%) = 18% + 1.17% = 19.17%
Since the IRR of the investment is grater than the cost of capital (12 percent), accept the project.
The advantage of using the IRR method is that it does consider the time value of money and, therefore, is more exact and realistic than the ARR method.
The shortcoming of this method :
(1) It is time-consuming to compute, especially when the cash inflows are not even, although most business calculators have a program to calculate IRR,
(2) It fails to recognize the varying sizes of investment in competing projects and their respective dollar profitability.
When cash inflows are not even, IRR is computed by the trial-and-error method, as follows:
1. Compute NPV at cost of capital, denoted here as r1.
2. See if NPV is positive or negative.
3. If NPV is positive, then pick another rate (r2) much smaller than r1. The true IRR, at which NPV = 0, must lie somewhere in between these two rates.
4. Compute NPV using r2.
5. Interpolate to get the exact rate.
