10.4 Internal Rate of Return (IRR)

LG 4 10.4 Internal Rate of Return (IRR)

The internal rate of return (IRR) is one of the most widely used capital budgeting internal rate of return (IRR)

techniques. The internal rate of return (IRR) is the discount rate that equates the

The discount rate that equates

NPV of an investment opportunity with $0 (because the present value of cash

the NPV of an investment

inflows equals the initial investment). It is the rate of return that the firm will earn if

opportunity with $0 (because

it invests in the project and receives the given cash inflows. Mathematically, the IRR

the present value of cash inflows equals the initial

is the value of r in Equation 10.1 that causes NPV to equal $0.

investment); it is the rate of return that the firm will earn if n

CF t

(1 + IRR) t=1 t

it invests in the project and - $0 = a CF 0 (10.3)

receives the given cash inflows.

CF t

a t = CF 0 (10.3a)

t=1 (1 + IRR)

DECISION CRITERIA When IRR is used to make accept–reject decisions, the decision criteria are as

follows:

• If the IRR is greater than the cost of capital, accept the project.

PART 5

Long-Term Investment Decisions

These criteria guarantee that the firm will earn at least its required return. Such an outcome should increase the market value of the firm and, therefore, the wealth of its owners.

CALCULATING THE IRR Most financial calculators have a preprogrammed IRR function that can be used

to simplify the IRR calculation. With these calculators, you merely punch in all cash flows just as if to calculate NPV and then depress IRR to find the internal rate of return. Computer software, including spreadsheets, is also available for simpli- fying these calculations. All NPV and IRR values presented in this and subsequent chapters are obtained by using these functions on a popular financial calculator.

Example 10.8 3 We can demonstrate the internal rate of return (IRR) approach by using the Bennett Company data presented in Table 10.1. Figure 10.3 uses time lines to depict the

framework for finding the IRRs for Bennett’s projects A and B. We can see in the figure that the IRR is the unknown discount rate that causes the NPV to equal $0.

Calculator Use To find the IRR using the preprogrammed function in a finan- cial calculator, the keystrokes for each project are the same as those shown on pages 398 and 399 for the NPV calculation, except that the last two NPV key- strokes (punching I and then NPV) are replaced by a single IRR keystroke.

FIGURE 10.3 Calculation of IRRs for Bennett Company’s Capital Expenditure Alternatives

Time lines depicting the cash flows and IRR calculations for projects A and B

Project A

End of Year

42,000 NPV A =$

IRR A = 19.9%

Project B

End of Year

IRR? IRR? IRR?

IRR?

IRR? NPV B =$

0 IRR

B = 21.7%

CHAPTER 10

Capital Budgeting Techniques

Comparing the IRRs of projects A and B given in Figure 10.3 to Bennett Company’s 10% cost of capital, we can see that both projects are acceptable because

IRR A = 19.9% 7 10.0% cost of capital IRR B = 21.7% 7 10.0% cost of capital

Comparing the two projects’ IRRs, we would prefer project B over project A because IRR B = 21.7% 7 IRR A = 19.9% . If these projects are mutually exclu- sive, meaning that we can choose one project or the other but not both, the IRR decision technique would recommend project B.

Spreadsheet Use The internal rate of return also can be calculated as shown on the following Excel spreadsheet.

DETERMINING THE INTERNAL RATE

1 OF RETURN 2 Year-End Cash Flow

3 Year

Project A

Project B

11 Choice of project

Project B

Entry in Cell B10 is =IRR(B4:B9). Copy the entry in Cell B10 to Cell C10. Entry in Cell C11 is =IF(B10>C10,B3,C3).

It is interesting to note in the preceding Example 10.8 that the IRR suggests that project B, which has an IRR of 21.7%, is preferable to project A, which has an IRR of 19.9%. This conflicts with the NPV rankings obtained in an ear- lier example. Such conflicts are not unusual. There is no guarantee that NPV and IRR will rank projects in the same order. However, both methods should reach the same conclusion about the acceptability or nonacceptability of projects.

Personal Finance Example 10.9 3 Tony DiLorenzo is evaluating an investment opportunity. He is comfortable with the investment’s level of risk. Based on com-

peting investment opportunities, he feels that this investment must earn a min- imum compound annual after-tax return of 9% to be acceptable. Tony’s initial investment would be $7,500, and he expects to receive annual after-tax cash flows of $500 per year in each of the first 4 years, followed by $700 per year at the end of years 5 through 8. He plans to sell the investment at the end of year 8

PART 5

Long-Term Investment Decisions

To calculate the investment’s IRR (compound annual return), Tony first sum- marizes the after-tax cash flows as shown in the following table:

Year

Cash flow ( ⴚ or ⴙ )

0 - $7,500 (Initial investment) 1 500 2 500 3 500 4 500 5 700 6 700 7 700

Substituting the after-tax cash flows for years 0 through 8 into a financial calculator or spreadsheet, he finds the investment’s IRR of 9.54%. Given that the expected IRR of 9.54% exceeds Tony’s required minimum IRR of 9%, the invest-

ment is acceptable.

6 REVIEW QUESTIONS

10–7 What is the internal rate of return (IRR) on an investment? How is it

determined? 10–8 What are the acceptance criteria for IRR? How are they related to the

firm’s market value? 10–9 Do the net present value (NPV) and internal rate of return (IRR) always agree with respect to accept–reject decisions? With respect to ranking decisions? Explain.