Week 8 IRR Method
The Internal Rate of Return (IRR) Method
The Internal Rate of Return (IRR) of a project is formally defined as that rate of return which, in the NPV equation, produces an NPV of zero.
For your purposes, however, you can think of the IRR as simply the rate of return that must be operating to produce the set of cash flows in the problem.
| A simple example: | You invest $100 and get back $110 a year later. per the rate of return formula you learned two weeks ago, the IRR would be: | |
| IRR | = (FV/PV)(1/n) - 1 | |
| = (110/100)(1/1) - 1 | ||
| = .10, or 10% |
Notice that 10% in this situation satisfies the formal requirement that the IRR be the rate that produces an NPV of zero:
NPV @10% = 110/(1+.1)1 - 100 = 0
When analyzing projects with IRR, those projects with IRRs greater than the firm’s required rate of return are accepted, and those with IRRs less than the required rate of return are rejected.
Calculating the IRR of Amalgamated Hat Rack’s plastic extruder project.
Unless the set of cash flows under consideration is very simple, such as the example just presented, calculating an IRR can be exceedingly cumbersome. To illustrate, consider the NPV analysis of Amalgamated Hat Rack’s plastic extruder project that discused previously (see Week 8: Net Present Value Method).
| Year | Future Cash Flow |
PV of future cash flow |
|||
| ________________________________________ | |||||
| 1 | $18 | $18 / (1 + .10)1 | = | $16.364 | |
| 2 | $18 | $18 / (1 + .10)2 | = | $14.876 | |
| 3 | $18 | $18 / (1 + .10)3 | = | $13.524 | |
| 4 | $18 | $18 / (1 + .10)4 | = | $12.294 | |
| 5 | $18 | $18 / (1 + .10)5 | = | $11.177 | |
| 6 | $18 | $18 / (1 + .10)6 | = | $10.161 | |
| 7 | $18 | $18 / (1 + .10)7 | = | $ 9.237 | |
| Total PV of future cash flows | = | $87.632 | |||
| Minus initial investment | -$100,000 | ||||
| NPV | -$12.638 | ||||
As you can see, the NPV at a 10%required rate of return is -$12,638. The question now, however, is what required rate of return would produce an NPV of zero?
To answer this question you would have to replace the 10% in the NPV analysis with other selected rates and note the results. You would do this over and over again until, finally, you achieved an NPV of zero and then you would know that the rate you used to produce the NPV of zero must be the IRR.
Fortunately, Microsoft’s Excel program can come to your rescue. One of Excel’s built in functions is the RATE function. The RATE function allows you to merely plug in all the input variables and the computer will automatically calculate the IRR.
In this example Excel’s RATE function tells us the IRR for Amalgamated Hat Rack’s plastic extruder project is 6.136% (to three decimal places).
The accept/reject decision: Recall that projects with IRRs above the firm’s required rate of return are accepted and those with IRRs below the firm’s required rate of return are rejected. In the case of the plastic extruder project Amalgamated’s required rate of return is 10% and the IRR of the project is 6.136%. Therefore the project is rejected.
Problems with the IRR Method
The IRR doesn’t relate directly to firm value
- Remember, your ultimate objective as a financial manager is to determine the alternative that most increases the value of the firm.
- If you evaluate with IRR you would choose a 100% return on a $5 investment over a 50% return on a $500 investment.
- In so doing you would pass up the (possibly) vastly greater impact on the value of your firm that the $500 investment would have.
Remember, when in doubt, always use the NPV method.