Ch9 Finance

Rule

Based on the IRR rule, an investment is acceptable if the IRR exceeds the required return. It should be rejected otherwise.

Payback Rule

Based on the payback rule, an investment is acceptable if its calculated payback period is less than some prespecified number of years.

How to find the crossover rate

In general, you can find the crossover rate by taking the difference in the cash flows and calculating the IRR using the difference. It doesn't make any difference which one you subtract from which. Basically find the differences in cashflow and cost and calculate IRR or NPV = 0 that IRR is the crossover rate because are indifferent between the two investments because the NPV of the difference in their cash flows is zero.

Weird things about payback

Project B's payback is also easy to calculate: It never pays back because the cash flows never total up to the original investment. Project C has a payback of exactly four years because it supplies the $130 that B is missing in Year 4. Project D is a little strange. Because of the negative cash flow in Year 3, you can easily verify that it has two different payback periods, two years and four years. Which of these is correct? Both of them; the way the payback period is calculated doesn't guarantee a single answer. Finally, Project E is obviously unrealistic, but it does pay back in six months, thereby illustrating the point that a rapid payback does not guarantee a good investment.

Example multiple periods

Suppose you were now looking at an investment with the cash flows shown in Figure 9.4. As illustrated, this investment costs $100 and has a cash flow of $60 per year for two years, so it's only slightly more complicated than our single- period example. If you were asked for the return on this investment, what would you say? There doesn't seem to be any obvious answer (at least not to us). Based on what we now know, we can set the NPV equal to zero and solve for the discount rate:

IRR

To illustrate the idea behind the IRR, consider a project that costs $100 today and pays $110 in one year. Suppose you were asked, "What is the return on this investment?" What would you say? It seems both natural and obvious to say that the return is 10 percent because, for every dollar we put in, we get $1.10 back. In fact, as we will see in a moment, 10 percent is the internal rate of return, or IRR, on this investment. Is this project with its 10 percent IRR a good investment?Once again, it would seem apparent that this is a good investment only if our required return is less than 10 percent. This intuition is also correct and illustrates the IRR rule:

Example

To see how we might calculate this number, suppose we are deciding whether to open a storein a new shopping mall. The required investment in improvements is $500,000. The storewould have a five-year life because everything reverts to the mall owners after that time. The required investment would be 100 percent depreciated (straight-line) over five years, so the depreciation would be $500,000/5 = $100,000 per year. The tax rate is 25 percent. Table 9.4 contains the projected revenues and expenses. Net income in each year, based on these figures, is also shown.

Conclusion

f the firm has a target AAR of less than 20 percent, then this investment is acceptable; otherwise, it is not. The average accounting return rule is: Based on the average accounting return rule, a project is acceptable if its average accounting return exceeds a target average accounting return.

Payback Period and Net Present Value [ LO1, 2] If a project with conventional cashflows has a payback period less than the project's life, can you definitively state thealgebraic sign of the NPV? Why or why not? If you know that the discounted payback period is less than the project's life, what can you say about the NPV? Explain.

A payback period less than the project's life means that the NPV is positive for a zero discount rate, but nothing more definitive can be said. For discount rates greater than zero, the payback period will still be less than the project's life, but the NPV may be positive, zero, or negative, depending on whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback includes the effect of the relevant discount rate. If a project's discounted payback period is less than the project's life, it must be the case that NPV is positive.

net present value rule

An investment should be accepted if the net present value is positive and rejected if it is negative. In the unlikely event that the net present value turned out to be exactly zero, we would be indifferent between taking the investment and not taking it. The task of coming up with the cash flows and the discount rate is much more challenging. The second thing to keep in mind about our example is that the −$2,422 NPV is an estimate. Like any estimate, it can be high or low. The only way to find out the true NPV would be to place the investment up for sale and see what we could get for it.

Nonconventional Cash Flows

Suppose we have a strip-mining project that requires a $60 investment. Our cash flow in the first year will be $155. In the second year, the mine will be depleted, but we will have to spend $100 to restore the terrain. As Figure 9.6 illustrates, both the first and third cash flows are negative.

Drawbacks to index

The PI is obviously similar to the NPV. However, consider an investment that costs $5 and has a $10 present value and an investment that costs $100 with a $150 present value. The first of these investments has an NPV of $5 and a PI of 2. The second has an NPV of $50 and a PI of 1.5. If these are mutually exclusive investments, then the second one is preferred even though it has a lower PI. This ranking problem is similar to the IRR ranking problem we saw in the previous section. In all, there seems to be little reason to rely on the PI instead of the NPV. Our discussion of the PI is summarized as follows:

The Profitability Index

Another tool used to evaluate projects is called the profitability index (PI) or benefit-cost ratio. This index is defined as the present value of the future cash flows divided by the initial investment. So, if a project costs $200 and the present value of its future cash flows is $220, the profitability index value would be $220/$200 = 1.1. Notice that the NPV for this investment is $20, so it is a desirable investment. More generally, if a project has a positive NPV, then the present value of the future cash flows must be bigger than the initial investment. The profitability index will be bigger than 1 for a positive NPV investment and less than 1 for a negative NPV investment. How do we interpret the profitability index? In our example, the PI was 1.1. This tells us that,per dollar invested, $1.10 in value or $.10 in NPV results. The profitability index measures "bang for the buck"—that is, the value created per dollar invested. For this reason, it is often proposed as a measure of performance for government or other not-for-profit investments. Also, when capital is scarce, it may make sense to allocate it to projects with the highest PIs. We will return to this issue in a later chapter.

Disadvantages

As we will now see, the use of this rule has a number of problems. You should recognize the chief drawback to the AAR immediately. Above all else, the AAR is not a rate of return in any meaningful economic sense. Instead, it is the ratio of two accounting numbers and it is not comparable to the returns offered, for example, in financial markets One of the reasons the AAR is not a true rate of return is that it ignores time value. When we average figures that occur at different times, we are treating the near future and the more distant future in the same way. There was no discounting involved when we computed the average net income, for example. The second problem with the AAR is similar to the problem we had with the payback period rule concerning the lack of an objective cutoff period. Because a calculated AAR is really not comparable to a market return, the target AAR must somehow be specified. There is no generally agreed-upon way to do this. One way of doing it is to calculate the AAR for the firm as a whole and use this as a benchmark, but there are lots of other ways as well. The third, and perhaps worst, flaw in the AAR is that it doesn't even look at the right things. Instead of cash flow and market value, it uses net income and book value. These are both poor substitutes. As a result, an AAR doesn't tell us what we really want to know; namely, what effect will taking this investment have on share price? Does the AAR have any redeeming features? About the only one is that it almost always can be computed. The reason is that accounting information will almost always be available, both for the project under consideration and for the firm as a whole. We hasten to add that once the accounting information is available, we can always convert it to cash flows, so even this is not a particularly important fact. The AAR is summarized in the following table:

IRR vs NPV

At this point, you may be wondering if the IRR and NPV rules always lead to identical decisions. The answer is yes, as long as two very important conditions are met. First, the project's cash flows must be conventional, meaning that the first cash flow (the initial investment) is negative and all the rest are positive. Second, the project must be independent, meaning that the decision to accept or reject this project does not affect the decision to accept or reject any other. The first of these conditions is typically met, but the second often is not. In any case, when one or both of these conditions are not met, problems can arise. We discuss some of these next.

Drawbacks

Despite its flaws, the IRR is very popular in practice—more so than even the NPV. It probably survives because it fills a need that the NPV does not. In analyzing investments, people in general, and financial analysts in particular, seem to prefer talking about rates of return rather than dollar values. In a similar vein, the IRR also appears to provide a simple way of communicating information about a proposal. One manager might say to another, "Remodeling the clerical wing has a 20 percent return." This may somehow seem simpler than saying, "At a 10 percent discount rate, the net present value is $4,000." Finally, under certain circumstances, the IRR may have a practical advantage over the NPV. We can't estimate the NPV unless we know the appropriate discount rate, but we can still estimate the IRR. Suppose we didn't know the required return on an investment, but we found, for example, that it had a 40 percent return. We would probably be inclined to take it because it would be unlikely that the required return would be that high. The advantages and disadvantages of the IRR are summarized as follows:

Long vs Short Examples

ow we have a problem. The NPV of the shorter-term investment is actually negative, meaning that taking it diminishes the value of the shareholders' equity. The opposite is true for the longer-term investment—it increases share value. Our example illustrates two primary shortcomings of the payback period rule. First, by ignoring time value, we may be led to take investments (like Short) that actually are worth less than they cost. Second, by ignoring cash flows beyond the cutoff, we may be led to reject profitable longer-term investments (like Long). More generally, using a payback period rule will tend to bias us toward shorter-term investments.

NPV Is our Workhorse because:

1) NPV rule account for the time value of money. 2) NPV rule account for the risk of the cash flows. 3) NPV rule provide an indication about the increase in value.

Benefits

Despite its shortcomings, the payback period rule is often used by large and sophisticated companies when they are making relatively minor decisions. There are several reasons for this. The primary reason is that many decisions do not warrant detailed analysis because the cost of the analysis would exceed the possible loss from a mistake. As a practical matter, it can be said that an investment that pays back rapidly and has benefits extending beyond the cutoff period probably has a positive NPV. Small investment decisions are made by the hundreds every day in large organizations. Moreover, they are made at all levels. As a result, it would not be uncommon for a corporation to require, for example, a two-year payback on all investments of less than $10,000. Investments larger than this would be subjected to greater scrutiny. The requirement of a two-year payback is not perfect for reasons we have seen, but it does exercise some control over expenditures and limits possible losses. In addition to its simplicity, the payback rule has two other positive features. First, because it is biased toward short-term projects, it is biased toward liquidity. In other words, a payback rule tends to favor investments that free up cash for other uses quickly. This could be important for a small business; it would be less so for a large corporation. Second, the cash flows that are expected to occur later in a project's life are probably more uncertain. Arguably, a payback period rule adjusts for the extra riskiness of later cash flows, but it does so in a rather draconian fashion—by ignoring them altogether.

Mutually Exclusive Investments

Even if there is a single IRR, another problem can arise concerning mutually exclusive investment decisions. If two investments, X and Y, are mutually exclusive, then taking one of them means that we cannot take the other. Two projects that are not mutually exclusive are said to be independent. For example, if we own one corner lot, then we can build a gas station or an apartment building, but not both. These are mutually exclusive alternatives Thus far, we have asked whether a given investment is worth undertaking. A related question comes up often: Given two or more mutually exclusive investments, which one is the best? The answer is simple enough: The best one is the one with the largest NPV. Can we also say that the best one has the highest return? As we show, the answer is no. Investment A has higher IRR but look at NPV to see what's worth more

Net Present value

For reasons that will be obvious in a moment, the difference between an investment's market value and its cost is called the net present value of the investment, abbreviated NPV. In other words, net present value is a measure of how much value is created or added today by undertaking an investment. Given our goal of creating value for the stockholders, the capital budgeting process can be viewed as a search for investments with positive net present values Capital budgeting becomes much more difficult when we cannot observe the market price for at least roughly comparable investments . We will first try to estimate the future cash flows we expect the new business to produce. We will then apply our basic discounted cash flow procedure to estimate the present value of those cash flows. Once we have this estimate, we will then estimate NPV as the difference between the present value of the future cash flows and the cost of the investment. As we mentioned in Chapter 5, this procedure is often called discounted cash flow (DCF) valuation.

Net Present Value [ LO1] Concerning NPV: Describe how NPV is calculated, and describe the information this measure provides about a sequence of cash flows. What is the NPV criterion decision rule? Why is NPV considered a superior method of evaluating the cash flows from a project? Suppose the NPV for a project's cash flows is computed to be $2,500. What does this number represent with respect to the firm's shareholders?

NPV is the present value of a project's cash flows. NPV specifically measures, after considering the time value of money, the net increase or decrease in firm wealth due to the project. The decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. b. NPV is superior to the other methods of analysis presented in the text because it has no serious flaws. The method unambiguously ranks mutually exclusive projects, and can differentiate between projects of different scale and time horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and not certain, but this is a problem shared by the other performance criteria, as well. A project with NPV = $2,500 implies that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted.

Continued

Page 294 will accept an investment using the IRR rule if the required return is less than 13.1 percent. As In our example, the NPV rule and the IRR rule lead to identical accept-reject decisions. We Figure 9.5 illustrates, the NPV is positive at any discount rate less than 13.1 percent, so we would accept the investment using the NPV rule as well. The two rules give equivalent results in this case

Payback Period [ LO2] Concerning payback: Describe how the payback period is calculated, and describe the information this measure provides about a sequence of cash flows. What is the payback criterion decision rule? What are the problems associated with using the payback period to evaluate cash flows? What are the advantages of using the payback period to evaluate cash flows? Are there any circumstances under which using payback might be appropriate? Explain.

Payback period is the accounting break-even point of a series of cash flows. To actually compute the payback period, it is assumed that any cash flow occurring during a given period is realized continuously throughout the period, and not at a single point in time. The payback is then the point in time for the series of cash flows when the initial cash outlays are fully recovered. Given some predetermined cutoff for the payback period, the decision rule is to accept projects that pay back before this cutoff, and reject projects that take longer to pay back. b. The worst problem associated with payback period is that it ignores the time value of money. In addition, the selection of a hurdle point for payback period is an arbitrary exercise that lacks any steadfast rule or method. The payback period is biased towards short-term projects; it fully ignores any cash flows that occur after the cutoff point. c. Despite its shortcomings, payback is often used because (1) the analysis is straightforward and simple and (2) accounting numbers and estimates are readily available. Materiality considerations often warrant a payback analysis as sufficient; maintenance projects are another example where the detailed analysis of other methods is often not needed. Since payback is biased towards liquidity, it may be a useful and appropriate analysis method for short-term projects where cash management is most important.

To see why Investment A is not necessarily the better of the two investments, we've calculated the NPV of these investments for different required returns:

The IRR for A (24 percent) is larger than the IRR for B (21 percent). However, if you compare the NPVs, you'll see that which investment has the higher NPV depends on our required return. B has greater total cash flow, but it pays back more slowly than A. As a result, it has a higher NPV at lower discount rates. In our example, the NPV and IRR rankings conflict for some discount rates. If our required return is 10 percent, for instance, then B has the higher NPV and is the better of the two even though A has the higher return. If our required return is 15 percent, then there is no ranking conflict: A is better.

Internal Rate of Return [ LO5] Concerning IRR: Page 309 Page 310 Describe how the IRR is calculated, and describe the information this measure provides about a sequence of cash flows. What is the IRR criterion decision rule? What is the relationship between IRR and NPV? Are there any situations in which you might prefer one method over the other? Explain. Despite its shortcomings in some situations, why do most financial managers use IRR along with NPV when evaluating projects? Can you think of a situation in which IRR might be a more appropriate measure to use than NPV? Explain.

The IRR is the discount rate that causes the NPV of a series of cash flows to be exactly zero. IRR can thus be interpreted as a financial break-even rate of return; at the IRR, the net present value of the project is zero. The IRR decision rule is to accept projects with IRRs greater than the discount rate, and to reject projects with IRRs less than the discount rate. b. IRR is the interest rate that causes NPV for a series of cash flows to be zero. NPV is preferred in all situations to IRR; IRR can lead to ambiguous results if there are nonconventional cash flows, and it also ambiguously ranks some mutually exclusive projects. However, for stand-alone projects with conventional cash flows, IRR and NPV are interchangeable techniques. c. IRR is frequently used because it is easier for many financial managers and analysts to rate performance in relative terms, such as "12%," than in absolute terms, such as "$46,000." IRR may be a preferred method to NPV in situations where an appropriate discount rate is unknown or uncertain; in this situation, IRR would provide more information about the project than would NPV.

Continued

The NPV appears to be behaving in a peculiar fashion here. First, as the discount rate increases from 0 percent to 30 percent, the NPV starts out negative and becomes positive. This seems backward because the NPV is rising as the discount rate rises. It then starts getting smaller and becomes negative again. What's the IRR? To find out, we draw the NPV profile as shown in In Figure 9.7, notice that the NPV is zero when the discount rate is 25 percent, so this is the IRR. Or is it? The NPV is also zero at 33.33 percent. Which of these is correct? The answer is both or neither; more precisely, there is no unambiguously correct answer. This is the multiple rates of return problem. NPV is positive only if our required return is between 25 percent and 33.33 percent.

Graphing crossover point: where NPV is the same for investment A and B

The conflict between the IRR and NPV for mutually exclusive investments can be illustrated by plotting the investments' NPV profiles as we have done in Figure 9.8. In Figure 9.8, notice that the NPV profiles cross at about 11.1 percent. Notice also that at any discount rate less than 11.1 percent, the NPV for B is higher. In this range, taking B benefits us more than taking A, even though A's IRR is higher. At any rate greater than 11.1 percent, Investment A has the greater NPV. This example illustrates that when we have mutually exclusive projects, we shouldn't rank them based on their returns. More generally, anytime we are comparing investments to determine which is best, looking at IRRs can be misleading. Instead, we need to look at the relative NPVs to avoid the possibility of choosing incorrectly. Remember, we're ultimately interested in creating value for the shareholders, so the option with the higher NPV is preferred, regardless of the relative returns If this seems counterintuitive, think of it this way. Suppose you have two investments. One has a 10 percent return and makes you $100 richer immediately. The other has a 20 percent return and makes you $50 richer immediately. Which one do you like better? We would rather have $100 than $50, regardless of the returns, so we like the first one better.

More drawbacks

When compared to the NPV rule, the payback period rule has some rather severe shortcomings. First, we calculate the payback period by adding up the future cash flows. There is no discounting involved, so the time value of money is completely ignored. The payback rule also fails to consider any risk differences. The payback would be calculated the same way for both very risky and very safe projects Perhaps the biggest problem with the payback period rule is coming up with the right cutoff period: We don't really have an objective basis for choosing a particular number. Put another way, there is no economic rationale for looking at payback in the first place, so we have no guide for how to pick the cutoff. As a result, we end up using a number that is arbitrarily chosen