Internal rate of return
(IRR).
Definition of IRR
The internal rate of return of a set of cash flows is the cost of capital which, when applied to discount all of the cash flows (including any initial investment flow at Time 0) results in a Net Present Value (NPV) of NIL.
For an investor, the IRR of an investment proposal therefore represents their expected rate of return on their investment in the project.
Example 1
A project requires an investment today of $100m, with $110m being receivable one year from now.
The IRR of this project is 10%, because that is the cost of capital which results in an NPV of $0, as follows:
PV of Time 0 outflow $100m
= $(100m)
PV of Time 1 inflow $110m
= $110m x 1.1-1
= $100m
NPV = - $100m + $100m
= $0.
Determining IRR
Unless the pattern of cash flows is very simple, it is normally only possible to determine IRR by trial and error (iterative) methods.
Example 2
Using straight line interpolation and the following data:
First estimated rate of return 5%, positive NPV = $+4m.
Second estimated rate of return 6%, negative NPV = $-4m.
The straight-line-interpolated estimated IRR is the mid-point between 5% and 6%.
This is 5.5%.
Using iteration, the straight-line estimation process could then be repeated, using the value of 5.5% to recalculate the NPV, and so on.
The IRR function in Excel uses a similar trial and error method.
IRR project analysis decision rule
In simple IRR project analysis the decision rule would be that:
(1) All opportunities with above the required IRR should be accepted.
(2) All other opportunities should be rejected.
However this assumes the unlimited availability of further capital with no increase in the cost of capital.
A more refined decision rule is that:
(1) All opportunities with IRRs BELOW the required IRR should still be REJECTED; while
(2) All other opportunities remain eligible for further consideration (rather than automatically being accepted).
