11 3 A project requiring a $170,000 initial investment is expected to provide operating cash inflows of $52,000, $78,000, and $100,000 at the end of each of the next

Example 10.11 3 A project requiring a $170,000 initial investment is expected to provide operating cash inflows of $52,000, $78,000, and $100,000 at the end of each of the next

3 years. The NPV of the project (at the firm’s 10% cost of capital) is $16,867 and its IRR is 15%. Clearly, the project is acceptable (NPV = $16,867 7 $0 and IRR = 15% 7 10% cost of capital). Table 10.5 demonstrates calculation of the project’s future value at the end of its 3-year life, assuming both a 10% (its cost of capital) and a 15% (its IRR) rate of return. A future value of $248,720 results from reinvestment at the 10% cost of capital, and a future value of $258,470 results from reinvestment at the 15% IRR.

4. To eliminate the reinvestment rate assumption of the IRR, some practitioners calculate the modified internal rate of return (MIRR). The MIRR is found by converting each operating cash inflow to its future value measured at the end of the project’s life and then summing the future values of all inflows to get the project’s terminal value. Each

future value is found by using the cost of capital, thereby eliminating the reinvestment rate criticism of the tradi- tional IRR. The MIRR represents the discount rate that causes the terminal value just to equal the initial investment. Because it uses the cost of capital as the reinvestment rate the MIRR is generally viewed as a better measure of a pro- ject’s true profitability than the IRR. Although this technique is frequently used in commercial real estate valuation and is a preprogrammed function on some financial calculators, its failure to resolve the issue of conflicting rankings and its theoretical inferiority to NPV have resulted in the MIRR receiving only limited attention and acceptance in

CHAPTER 10

Capital Budgeting Techniques

TA B L E 1 0 . 5 Reinvestment Rate Comparisons for a Project a

Reinvestment rate

Operating

Number of

years earnings

Year

inflows

interest (t)

Future value Future value

Future value end of year 3

NPV @ 10% = $16,867 IRR = 15%

a Initial investment in this project is $170,000.

If the future value in each case in Table 10.5 were viewed as the return received 3 years from today from the $170,000 initial investment, the cash flows would be those given in Table 10.6. The NPVs and IRRs in each case are shown below the cash flows in Table 10.6. You can see that at the 10% reinvestment rate, the NPV remains at $16,867; reinvestment at the 15% IRR produces an

In more depth

NPV of $24,418.

From this result, it should be clear that the NPV technique assumes reinvest- To read about Modified

ment at the cost of capital (10% in this example). (Note that with reinvestment at Internal Rate of Return, go to

10%, the IRR would be 13.5%.) On the other hand, the IRR technique assumes www.myfinancelab.com

an ability to reinvest intermediate cash inflows at the IRR. If reinvestment does not occur at this rate, the IRR will differ from 15%. Reinvestment at a rate lower than the IRR would result in an IRR lower than that calculated (at 13.5%, for example, if the reinvestment rate were only 10%). Reinvestment at a rate higher than the IRR would result in an IRR higher than that calculated.

TA B L E 1 0 . 6

Project Cash Flows after Reinvestment

Reinvestment rate

Initial investment

Year

Operating cash inflows

NPV @ 10%

IRR

PART 5

Long-Term Investment Decisions

Timing of the Cash Flow Another reason why the IRR and NPV methods may provide different rankings

for investment options has to do with differences in the timing of cash flows. Go back to the timelines for investments A and B in Figure 10.1 on page 392. The up-front investment required by each investment is similar, but after that the timing of each project’s cash flows is quite different. Project B has a large cash inflow almost immediately (in Year 1), whereas Project A provides cash flows that are distributed evenly across time. Because so much of Project B’s cash flows arrive early in its life (especially compared to the timing for Project A), the NPV of Project B will not be particularly sensitive to changes in the discount rate. Project A’s NPV, on the other hand, will fluctuate more as the discount rate changes. In essence, Project B is somewhat akin to a short-term bond, whose price doesn’t change much when interest rates move, and Project A is more like a long-term bond whose price fluctuates a great deal when rates change.

You can see this pattern if you review the NPV profiles for projects A and B in Figure 10.4 on page 405. The red line representing project A is considerably steeper than the blue line representing project B. At very low discount rates, project A has a higher NPV, but as the discount rate increases, the NPV of project A declines rapidly. When the discount rate is high enough, the NPV of project B overtakes that of project A.

We can summarize this discussion as follows. Because project A’s cash flows arrive later than project B’s cash flows do, when the firm’s cost of capital is rela- tively low (to be specific, below about 10.7 percent), the NPV method will rank project A ahead of project B. At a higher cost of capital, the early arrival of project B’s cash flows becomes more advantageous, and the NPV method will rank project B over project A. The differences in the timing of cash flows between the two projects does not affect the ranking provided by the IRR method, which always puts project B ahead of project A. Table 10.7 illustrates how the conflict in rankings between the NPV and IRR approaches depends on the firm’s cost of capital.

Magnitude of the Initial Investment Suppose someone offered you the following two investment options. You could

invest $2 today and receive $3 tomorrow, or you could invest $1,000 today and receive $1,100 tomorrow. The first investment provides a return (an IRR) of

50 percent in just one day, a return that surely would surpass any reasonable hurdle rate. But after making this investment, you’re only better off by $1. On the

Ranking Projects A and B Using IRR and NPV Methods

TA B L E 1 0 . 7

Method

Project A

Project B

IRR

NPV

if r 6 10.7%

if r 7 10.7%

CHAPTER 10

Capital Budgeting Techniques

other hand, the second choice offers a return of 10 percent in a single day. That’s far less than the first opportunity, but earning 10 percent in a single day is still a very high return. In addition, if you accept this investment, you will be $100 better off tomorrow than you were today.

Most people would choose the second option presented above, even though the rate of return on that option (10 percent) is far less than the rate offered by the first option (50 percent). They reason (correctly) that it is sometimes better to accept a lower return on a larger investment than to accept a very high return on

a small investment. Said differently, most people know that they are better off taking the investment that pays them a $100 profit in just one day rather than the investment that generates just a $1 profit. 5

The preceding example illustrates what is known as the scale (or magnitude) problem. The scale problem occurs when two projects are very different in terms of how much money is required to invest in each project. In these cases, the IRR and NPV methods may rank projects differently. The IRR approach (and the PI method) may favor small projects with high returns (like the $2 loan that turns into $3), whereas the NPV approach favors the investment that makes the investor the most money (like the $1,000 investment that yields $1,100 in one day). In the case of the Bennett Company’s projects, the scale problem is not likely to be the cause of the conflict in project rankings because the initial invest- ment required to fund each project is quite similar.

To summarize, it is important for financial managers to keep an eye out for conflicts in project rankings provided by the NPV and IRR methods, but differ- ences in the magnitude and timing of cash inflows do not guarantee conflicts in ranking. In general, the greater the difference between the magnitude and timing of cash inflows, the greater the likelihood of conflicting rankings. Conflicts based on NPV and IRR can be reconciled computationally; to do so, one creates and analyzes an incremental project reflecting the difference in cash flows between the two mutually exclusive projects.

WHICH APPROACH IS BETTER? Many companies use both the NPV and IRR techniques because current tech-

nology makes them easy to calculate. But it is difficult to choose one approach over the other because the theoretical and practical strengths of the approaches differ. Clearly, it is wise to evaluate NPV and IRR techniques from both theoret- ical and practical points of view.

Theoretical View On a purely theoretical basis, NPV is the better approach to capital budgeting as

a result of several factors. Most important, the NPV measures how much wealth

a project creates (or destroys if the NPV is negative) for shareholders. Given that the financial manager’s objective is to maximize shareholder wealth, the NPV approach has the clearest link to this objective and, therefore, is the “gold stan- dard” for evaluating investment opportunities.

5. Note that the profitability index also provides an incorrect ranking in this example. The first option has a PI of 1.5 ($3 , $2), and the second option’s PI equals 1.1 ($1,100 , $1,000). Just like the IRR, the PI suggests that the

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PART 5

Long-Term Investment Decisions

In addition, certain mathematical properties may cause a project with a multiple IRRs

nonconventional cash flow pattern to have multiple IRRs—more than one IRR. 6

More than one IRR resulting

Mathematically, the maximum number of real roots to an equation is equal to its

from a capital budgeting

number of sign changes. Take an equation like x 2 - 5 x+6=0 , which has two project with a nonconventional sign changes in its coefficients—from positive (+ x 2 ) to negative (-5 x) and then

cash flow pattern; the maximum number of IRRs for a from negative (-5 x) to positive (+6) . If we factor the equation (remember fac- project is equal to the number

toring from high school math?), we get ( x - 2) * (x - 3) , which means that x

of sign changes in its cash

can equal either 2 or 3—there are two correct values for x. Substitute them back

flows.

into the equation, and you’ll see that both values work.

This same outcome can occur when finding the IRR for projects with non- conventional cash flows, because they have more than one sign change. Clearly, when multiple IRRs occur for nonconventional cash flows, the analyst faces the time-consuming need to interpret their meanings so as to evaluate the project. The fact that such a challenge does not exist when using NPV enhances its theo- retical superiority.

Practical View Evidence suggests that in spite of the theoretical superiority of NPV, financial

managers use the IRR approach just as often as the NPV method. The appeal of the IRR technique is due to the general disposition of business people to think in terms of rates of return rather than actual dollar returns. Because interest rates,

profitability, and so on are most often expressed as annual rates of return, the use of IRR makes sense to financial decision makers. They tend to find NPV less intuitive because it does not measure benefits relative to the amount invested. Because a variety of techniques are available for avoiding the pitfalls of the IRR, its widespread use does not imply a lack of sophistication on the part of finan- cial decision makers. Clearly, corporate financial analysts are responsible for identifying and resolving problems with the IRR before the decision makers use it as a decision technique.