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## 13.4 Internal Rate of Return

PLEASE NOTE: This book is currently in draft form; material is not final.

### Learning Objectives

1. Define and calculate the internal rate of return (IRR).
2. Apply the accept/reject decision rule for IRR.
3. Explain the limitations of IRR.

Internal rate of return (IRR)The discount rate where the NPV of an investment equals zero. is another widely used capital budgeting technique; essentially, it is the return we will receive over the life of our investment. It is calculated as the discount rate at which NPV equals zero. In other words, we set NPV equal to \$0 and solve for r. This is the rate that makes the present value of the cash flows equal to the initial investment. Unfortunately, for some projects there is no easy way to arrive at this rate without using a “guess and check” method; thankfully, computers can do this quite quickly.

How do we know if the project is acceptable or not? Each project that uses internal funds has a cost of capital. If the rate we earn is more than the rate it costs us, then we should undertake the project as it adds to corporate value. If what we earn is less than what it cost us, then the project subtracts from corporate value, and we should not undertake it. To do this we compare IRR to the cost of capital. If the IRR is greater than the cost of capital we should undertake the project.

This decision criterion will only work if the cash flows are ordinary, meaning net outflows early in the project followed by inflows afterward. When cash flows are not ordinary, IRR can produce unusual, sometimes multiple, results.

Here are our decision rules:

IRR decision criteria (ordinary cash flows ONLY):

• If the IRR is greater than cost of capital (IRR > WACC) than accept the project
• If the IRR is less than cost of capital (IRR < WACC) than reject the project.

Let’s find the IRR for Gator Lover’s Ice Cream potential projects by taking a look at Table 13.2 "Gator Lover’s Ice Cream: Internal Rate of Return".

Table 13.2 Gator Lover’s Ice Cream: Internal Rate of Return

 Firm’s Cost of Capital = 10% Project A Project B Initial Investment (\$48,000.00) (\$52,000.00) Year Operating Cash Inflows(after-tax) 1 \$15,000.00 \$18,000.00 2 \$15,000.00 \$20,000.00 3 \$15,000.00 \$15,000.00 4 \$15,000.00 \$12,000.00 5 \$15,000.00 \$10,000.00 IRR 16.99% 15.43%

If our WACC is 10%, then both projects should be accepted. IRR is, however, not acceptable for mutually exclusive projects! To see why, consider the following example—Which investment would you rather have:

1. Invest \$10,000 now and receive a guaranteed \$20,000 in one year.
2. Invest \$1 now and receive a guaranteed \$10 in one year.

Investment A is double your money (IRR = 100%) while investment B is ten times your money (IRR = 900%). But investment A is on a larger starting sum! We’d love to do investment B over and over again, since it has the higher return, but if we can only pick one of the two, then A is superior. Thus, the higher IRR doesn’t necessarily indicate the better investment.

IRR can be calculated by hand, by a financial calculator, or in a spreadsheet. The keystrokes for a financial calculator are similar as those for NPV, but at the conclusion we ask for IRR instead of entering an interest rate. For example, IRR for Project A is as follows:

<CF> <2ND> <CLR WORK> −48000 <ENTER> <DOWN ARROW> 15000 <ENTER> <DOWN ARROW> 5 <ENTER> <IRR> <CPT>

The answer of 16.99% is returned.

To solve in a spreadsheet, the corresponding spreadsheet formula is:

=IRR(cash flows from period 0 to n)

Using the numbers for Project A, the spreadsheet function looks like this:

=IRR(−48000, 15000, 15000, 15000, 15000, 15000) = 16.99%

## Shortfalls of IRR

IRR is more difficult than NPV to calculate by hand because we are calculating a rate of return. Our calculators or spredsheets ‘search’ for the interest rate. For us to calculate, it would take iterations where we try one interest rate, see if it’s too high or too low and then try again.

Cash flows that aren’t ordinary can produce unusual, sometimes multiple, results. Sadly, most calculators won’t alert the user to this fact, so care must be taken. And in the case of mutually exclusive projects, IRR fails to rank them properly. For these reasons, NPV is typically the preferred criteria, or is at least used to “double check” that IRR isn’t failing because of one of these unusual reasons.

### Key Takeaways

IRR is another method of capital budgeting techniques. We prefer NPV to IRR because of IRR’s potential shortfalls.

• IRR is defined as the discount rate where NPV = 0.
• IRR should never be used if cash flows aren’t ordinary, or if the projects are mutually exclusive.

### Exercises

1. Calculate the IRR for the projects listed in NPV exercises.
2. Which has the highest IRR?
3. If our hurdle rate is 10%, which should we accept?