Week 4 Individual Problems

 REVIEW QUESTION

TABLE 12.1 Relevant Cash Flows and NPVs for Bennett Company’s Projects

BREAKEVEN ANALYSIS

In the context of capital budgeting, the term risk refers to the uncertainty surrounding the cash flows that a project will generate. More formally, risk in capital budgeting is the degree of variability of cash flows. Projects with a broad range of possible cash flows are more risky than projects that have a narrow range of possible cash flows.

In many projects, risk stems almost entirely from the cash flows that a project will generate several years in the future because the initial investment is generally known with relative certainty. The subsequent cash flows, of course, derive from a number of variables related to revenues, expenditures, and taxes. Examples include the level of sales, the cost of raw materials, labor rates, utility costs, and tax rates. We will concentrate on the risk in the cash flows, but remember that this risk actually results from the interaction of these underlying variables. Therefore, to assess the risk of a proposed capital expenditure, the analyst needs to evaluate the probability that the cash inflows will be large enough to produce a positive NPV.
1. This equation makes use of the algebraic shortcut for the present value of an annuity, introduced in Personal FinanceExample 5.7 on page 175.

Example 12.1

Treadwell Tire Company, a tire retailer with a 10% cost of capital, is considering investing in either of two mutually exclusive projects, A and B. Each requires a $10,000 initial investment, and both are expected to provide constant annual cash inflows over their 15-year lives. For either project to be acceptable, its NPV must be greater than zero. In other words, the present value of the annuity (that is, the project’s cash inflows) must be greater than the initial cash outflow. If we let CF equal the annual cash inflow and CF0 equal the initial investment, the following condition must be met for projects with annuity cash inflows, such as A and B, to be acceptable:1

(12.1)

By substituting r = 10%, n = 15 years, and CF0 = $10,000, we can find the breakeven cash inflow, the minimum level of cash inflow necessary for Treadwell’s projects to be acceptable.

breakeven cash inflow
The minimum level of cash inflow necessary for a project to be acceptable, that is, NPV > $0.

My Finance Lab Financial Calculator

Calculator use Recognizing that the initial investment (CF0) is the present value (PV), we can use the calculator inputs shown at the left to find the breakeven cash inflow (CF), which is an ordinary annuity (PMT).
Spreadsheet use The breakeven cash inflow also can be calculated as shown on the following Excel spreadsheet.

The calculator and spreadsheet values indicate that, for the projects to be acceptable, they must have annual cash inflows of at least $1,315. Given this breakeven level of cash inflows, the risk of each project can be assessed by determining the probability that the project’s cash inflows will equal or exceed this breakeven level. The various statistical techniques that would determine that probability are covered in more advanced courses.2 For now, we can simply assume that such a statistical analysis results in the following:

• Probability of CFA > $1,315 → 100%
• Probability of CFB > $1,315 → 65%

Because project A is certain (100% probability) to have a positive net present value, whereas there is only a 65% chance that project B will have a positive NPV, project A seems less risky than project B. Of course, the expected level of annual cash inflow and NPV associated with each project must be evaluated in view of the firm’s risk preference before the preferred project is selected.

The example clearly identifies risk as it is related to the chance that a project is acceptable, but it does not address the issue of cash flow variability. Even though project B has a greater chance of loss than project A, it might result in higher potential NPVs. Recall that it is the combination of risk and return that determines value. Similarly, the benefit of a capital expenditure and its impact on the firm’s value must be viewed in light of both risk and return. The analyst must therefore consider the variability of cash inflows and NPVs to assess project risk and return fully.
2. Normal distributions are commonly used to develop the concept of the probability of success, that is, of a project having a positive NPV. The reader interested in learning more about this technique should see any second- or MBA-level managerial finance text.

SCENARIO ANALYSIS

Scenario analysis can be used to deal with project risk to capture the variability of cash inflows and NPVs. Scenario analysis is a behavioral approach that uses several possible alternative outcomes (scenarios) to obtain a sense of the variability of returns, measured here by NPV. This technique is often useful in getting a feel for the variability of return in response to changes in a key outcome. In capital budgeting, one of the most common scenario approaches is to estimate the NPVs associated with pessimistic (worst), most likely (expected), and optimistic (best) estimates of cash inflow. The range can be determined by subtracting the pessimistic-outcome NPV from the optimistic-outcome NPV.

The widespread availability of computers and spreadsheets has greatly enhanced the use of scenario analysis because technology allows analysts to create a wide range of different scenarios quickly.

SIMULATION

Simulation is a statistics-based behavioral approach that applies predetermined probability distributions and random numbers to estimate risky outcomes. By tying the various cash flow components together in a mathematical model and repeating the process numerous times, the financial manager can develop a probability distribution of project returns.

Figure 12.1 presents a flowchart of the simulation of the net present value of a project. The process of generating random numbers and using the probability distributions for cash inflows and cash outflows enables the financial manager to determine values for each of these variables. Substituting these values into the mathematical model results in an NPV. By repeating this process perhaps a thousand times, managers can create a probability distribution of net present values.
Although Figure 12.1 simulates only gross cash inflows and cash outflows, more sophisticated simulations using individual inflow and outflow components, such as sales volume, sale price, raw material cost, labor cost, and maintenance expense, are quite common. From the distribution of returns, the decision maker can determine not only the expected value of the return but also the probability of achieving or surpassing a given return. The use of computers has made the simulation approach feasible. Monte Carlo simulation programs, made popular by widespread use of personal computers, are described in the Focus on Practice box.
The output of simulation provides an excellent basis for decision making because it enables the decision maker to view a continuum of risk–return tradeoffs rather than a single-point estimate.

Matter of fact

Adjusting for Currency Risk
A survey of chief financial officers (CFOs) found that more than 40 percent of the CFOs believed that it was important to adjust an investment project’s cash flows or discount rates to account for foreign exchange risk.

 REVIEW QUESTION

DETERMINING RISK-ADJUSTED DISCOUNT RATES (RADRS)

A popular approach for risk adjustment involves the use of risk-adjusted discount rates (RADRs). This approach uses Equation 10.1 but employs a risk-adjusted discount rate, as noted in the expression3

(12.2)

The risk-adjusted discount rate (RADR) is the rate of return that must be earned on a given project to compensate the firm’s owners adequately (that is, to maintain or improve the firm’s share price). The higher the risk of a project, the higher the RADR and therefore the lower the net present value for a given stream of cash inflows.

3. The risk-adjusted discount rate approach can be applied in using the internal rate of return as well as the net present value. When the IRR is used, the risk-adjusted discount rate becomes the hurdle rate that must be exceeded by the IRR for the project to be accepted. When NPV is used, the projected cash inflows are merely discounted at the risk-adjusted discount rate.

Because the logic underlying the use of RADRs is closely linked to the capital asset pricing model (CAPM) developed in Chapter 8, here we review that model and discuss its use in finding RADRs.

APPLYING RADRS

Because the CAPM is based on an assumed efficient market, which does not always exist for real corporate (nonfinancial) assets such as plant and equipment, managers sometimes argue that the CAPM is not directly applicable in calculating RADRs. Instead, financial managers sometimes assess the total risk of a project and use it to determine the risk-adjusted discount rate (RADR), which can be used in Equation 12.2 to find the NPV.
To avoid damaging its market value, the firm must use the correct discount rate to evaluate a project. The Focus on Ethics box describes a real example of a company that failed to recognize (or that ignored) certain risks associated with their business operations. As a result, the firm experienced monetary sanctions. If a firm fails to incorporate all relevant risks in its decision-making process, it may discount a risky project’s cash inflows at too low a rate and accept the project. The firm’s market price may drop later as investors recognize that the firm itself has become more risky. Conversely, if the firm discounts a project’s cash inflows at too high a rate, it will reject acceptable projects. Eventually, the firm’s market price may drop because investors who believe that the firm is being overly conservative will sell their stock, putting downward pressure on the firm’s market value.
Unfortunately, there is no formal mechanism for linking total project risk to the level of required return. As a result, most firms subjectively determine the RADR by adjusting their existing required return. They adjust it up or down depending on whether the proposed project is more or less risky, respectively, than the average risk of the firm. This CAPM-type of approach provides a “rough estimate” of the project risk and required return because both the project risk measure and the linkage between risk and required return are estimates.

Example 12.5

Bennett Company wishes to use the risk-adjusted discount rate approach to determine, according to NPV, whether to implement project A or project B. In addition to the data presented in part A ofTable 12.1, Bennett’s management after much analysis subjectively assigned “risk indexes” of 1.6 to project A and 1.0 to project B. The risk index is merely a numerical scale used to classify project risk: Higher index values are assigned to higher-risk projects and vice versa. The CAPM-type relationship used by the firm to link risk (measured by the risk index) and the required return (RADR) is shown in the following table. Management developed this relationship after analyzing CAPM and the risk–return relationships of the projects that they considered and implemented during the past few years.

	Risk index	Required return (RADR)
	0.0	6% (risk-free rate, RF)
	0.2	7
	0.4	8
	0.6	9
	0.8	10
Project B →	1.0	11
	1.2	12
	1.4	13
Project A →	1.6	14
	1.8	16
	2.0	18

Because project A is riskier than project B, its RADR of 14% is greater than project B’s 11%. The net present value of each project, calculated using its RADR, is found as shown on the time lines inFigure 12.3. The results clearly show that project B is preferable because its risk-adjusted NPV of $9,798 is greater than the $6,063 risk-adjusted NPV for project A. As reflected by the NPVs in part B of Table 12.1, if the discount rates were not adjusted for risk, project A would be preferred to project B.
My Finance Lab Financial Calculator

Calculator use We can again use the preprogrammed NPV function in a financial calculator to simplify the NPV calculation. The keystrokes for project A—the annuity—typically are as shown at the left. The keystrokes for project B—the mixed stream—are also shown at the left. The calculated NPVs for projects A and B of $6,063 and $9,798, respectively, agree with those shown in Figure 12.3.
Spreadsheet use Analysis of projects using risk-adjusted discount rates (RADRs) also can be performed as shown on the following Excel spreadsheet.

The usefulness of risk-adjusted discount rates should now be clear. The real difficulty lies in estimating project risk and linking it to the required return (RADR).

PORTFOLIO EFFECTS

As noted in Chapter 8, because investors are not rewarded for taking diversifiable risk, they should hold a diversified portfolio of securities to eliminate that risk. Because a business firm can be viewed as a portfolio of assets, is it similarly important that the firm maintain a diversified portfolio of assets?
It seems logical that the firm could reduce the variability of its cash flows by holding a diversified portfolio. By combining two projects with negatively correlated cash inflows, the firm could reduce the combined cash inflow variability and therefore the risk.
Are firms rewarded for diversifying risk in this fashion? If they are, the value of the firm could be enhanced through diversification into other lines of business. Surprisingly, the value of the stock of firms whose shares are traded publicly in an efficient marketplace is generally not affected by diversification. In other words, diversification is not normally rewarded and therefore is generally not necessary.
Why are firms not rewarded for diversification? It is because investors themselves can diversify by holding securities in a variety of firms; they do not need the firm to do it for them. And investors can diversify more readily. They can make transactions more easily and at a lower cost because of the greater availability of information and trading mechanisms.
Of course, if a firm acquires a new line of business and its cash flows tend to respond more to changing economic conditions (that is, greater nondiversifiable risk), greater returns would be expected. If, for the additional risk, the firm earned a return in excess of that required (IRR > r), the value of the firm could be enhanced. Also, other benefits, such as increased cash, greater borrowing capacity, and guaranteed availability of raw materials, could result from and therefore justify diversification, despite any immediate impact on cash flow.
Although a strict theoretical view supports the use of a technique that relies on the CAPM framework, the presence of market imperfections causes the market for real corporate assets to be inefficient at least some of the time. The relative inefficiency of this market, coupled with difficulties associated with measurement of nondiversifiable project risk and its relationship to return, tends to favor the use of total risk to evaluate capital budgeting projects. Therefore, the use of total risk as an approximation for the relevant risk does have widespread practical appeal.

RADRS IN PRACTICE

Despite the appeal of total risk, RADRs are often used in practice. Their popularity stems from two facts: (1) They are consistent with the general disposition of financial decision makers toward rates of return, and (2) they are easily estimated and applied. The first reason is clearly a matter of personal preference, but the second is based on the computational convenience and well-developed procedures involved in the use of RADRs.
In practice, firms often establish a number of risk classes, with a RADR assigned to each. Like the CAPM-type risk–return relationship described earlier, management develops the risk classes and RADRs based on both CAPM and the risk–return behaviors of past projects. Each new project is then subjectively placed in the appropriate risk class, and the corresponding RADR is used to evaluate it. This evalution is sometimes done on a division-by-division basis, in which case each division has its own set of risk classes and associated RADRs, similar to those for Bennett Company in Table 12.3. The use of divisional costs of capital and associated risk classes enables a large multidivisional firm to incorporate differing levels of divisional risk into the capital budgeting process and still recognize differences in the levels of individual project risk.

5. Note that the 10 percent RADR for project B using the risk classes in Table 10.3 differs from the 11 percent RADR used in the preceding example for project B. This difference is attributable to the less precise nature of the use of risk classes.

COMPARING PROJECTS WITH UNEQUAL LIVES

The financial manager must often select the best of a group of unequal-lived projects. If the projects are independent, the length of the project lives is not critical. But when unequal-lived projects are mutually exclusive, the impact of differing lives must be considered because the projects do not provide service over comparable time periods. This step is especially important when continuing service is needed from the project under consideration. The discussions that follow assume that the unequal-lived, mutually exclusive projects being compared are ongoing. If they were not, the project with the highest NPV would be selected.

The Problem

A simple example will demonstrate the general problem of noncomparability caused by the need to select the best of a group of mutually exclusive projects with differing usable lives.

Example 12.7

The AT Company, a regional cable television company, is evaluating two projects, X and Y. The relevant cash flows for each project are given in the following table. The applicable cost of capital for use in evaluating these equally risky projects is 10%.

	Project X	Project Y
Initial investment	−$70,000	−$85,000
Year	Annual cash inflows
1	$28,000	$35,000
2	33,000	30,000
3	38,000	25,000
4	–	20,000
5	–	15,000
6	–	10,000

My Finance Lab Financial Calculator

Calculator use Employing the preprogrammed NPV function in a financial calculator, we use the keystrokes shown at the left for project X and for project Y to find their respective NPVs of $11,277.24 and $19,013.27.
Spreadsheet use The net present values of two projects with unequal lives also can be compared as shown on the following Excel spreadsheet.

Ignoring the differences in project lives, we can see that both projects are acceptable (both NPVs are greater than zero) and that project Y is preferred over project X. If the projects were independent and only one could be accepted, project Y—with the larger NPV—would be preferred. If the projects were mutually exclusive, their differing lives would have to be considered. Project Y provides 3 more years of service than project X.

The analysis in the preceding example is incomplete if the projects are mutually exclusive (which will be our assumption throughout the remaining discussions). To compare these unequal-lived, mutually exclusive projects correctly, we must consider the differing lives in the analysis; an incorrect decision could result from simply using NPV to select the better project. Although a number of approaches are available for dealing with unequal lives, here we present the most efficient technique: the annualized net present value (ANPV) approach.

RECOGNIZING REAL OPTIONS

The procedures described in Chapters 10 and 11 and thus far in this chapter suggest that to make capital budgeting decisions, we must (1) estimate relevant cash flows, (2) apply an appropriate decision technique such as NPV or IRR to those cash flows, and (3) recognize and adjust the decision technique for project risk. Although this traditional procedure is believed to yield good decisions, a more strategic approach to these decisions has emerged in recent years. This more modern view considers any real options, opportunities that are embedded in capital projects (“real,” rather than financial, asset investments) that enable managers to alter their cash flows and risk in a way that affects project acceptability (NPV). Because these opportunities are more likely to exist in, and be more important to, large “strategic” capital budgeting projects, they are sometimes called strategic options.

Table 12.4 briefly describes some of the more common types of real options—abandonment, flexibility, growth, and timing. It should be clear from their descriptions that each of these types of options could be embedded in a capital budgeting decision and that explicit recognition of them would probably alter the cash flow and risk of a project and change its NPV.
By explicitly recognizing these options when making capital budgeting decisions, managers can make improved, more strategic decisions that consider in advance the economic impact of certain contingent actions on project cash flow and risk. The explicit recognition of real options embedded in capital budgeting projects will cause the project’s strategic NPV to differ from its traditional NPV,as indicated by Equation 12.6.

(12.6)

Application of this relationship is illustrated in the following example.

It is important to realize that the recognition of attractive real options when determining NPV could cause an otherwise unacceptable project (NPVtraditional < $0) to become acceptable (NPVstrategic > $0). The failure to recognize the value of real options could therefore cause management to reject projects that are acceptable. Although doing so requires more strategic thinking and analysis, it is important for the financial manager to identify and incorporate real options in the NPV process. The procedures for doing so efficiently are emerging, and the use of the strategic NPV that incorporates real options is expected to become more commonplace in the future.

CAPITAL RATIONING

Firms commonly operate under capital rationing in that they have more acceptable independent projects than they can fund. In theory, capital rationing should not exist. Firms should accept all projects that have positive NPVs (or IRRs > the cost of capital). However, in practice, most firms operate under capital rationing. Generally, firms attempt to isolate and select the best acceptable projects subject to a capital expenditure budget set by management. Research has found that management internally imposes capital expenditure constraints to avoid what it deems to be “excessive” levels of new financing, particularly debt. Although failing to fund all acceptable independent projects is theoretically inconsistent with the goal of maximizing owner wealth, here we will discuss capital rationing procedures because they are widely used in practice.
The objective of capital rationing is to select the group of projects that provides the highest overall net present value and does not require more dollars than are budgeted. As a prerequisite to capital rationing, the best of any mutually exclusive projects must be chosen and placed in the group of independent projects. Two basic approaches to project selection under capital rationing are discussed here.

FOCUS ON VALUE

Not all capital budgeting projects have the same risk as the firm’s existing portfolio of projects. The financial manager must adjust projects for differences in risk when evaluating their acceptability. Without such an adjustment, management could mistakenly accept projects that destroy shareholder value or could reject projects that create shareholder value. To ensure that neither of these outcomes occurs, the financial manager must make sure that only those projects that create shareholder value are recommended.
Risk-adjusted discount rates (RADRs) provide a mechanism for adjusting the discount rate so that it is consistent with the risk–return preferences of market participants. Procedures for comparing projects with unequal lives, for explicitly recognizing real options embedded in capital projects, and for selecting projects under capital rationing enable the financial manager to refine the capital budgeting process further. These procedures, along with risk-adjustment techniques, should enable the financial manager to make capital budgeting decisions that are consistent with the firm’s goal of maximizing stock price.

REVIEW OF LEARNING GOALS

LG 1 Understand the importance of recognizing risk in the analysis of capital budgeting projects.The cash flows associated with capital budgeting projects typically have different levels of risk, and the acceptance of a project generally affects the firm’s overall risk. Thus, it is important to incorporate risk considerations in capital budgeting. Various behavioral approaches can be used to get a “feel” for the level of project risk. Other approaches explicitly recognize project risk in the analysis of capital budgeting projects.
LG 2 Discuss breakeven analysis, scenario analysis, and simulation as behavioral approaches for dealing with risk. Risk in capital budgeting is the degree of variability of cash flows, which for conventional capital budgeting projects stems almost entirely from net cash flows. Finding the breakeven cash inflow and estimating the probability that it will be realized make up one behavioral approach for assessing capital budgeting risk. Scenario analysis is another behavioral approach for capturing the variability of cash inflows and NPVs. Simulation is a statistically based approach that results in a probability distribution of project returns.
LG 3 Review the unique risks that multinational companies face. Although the basic capital budgeting techniques are the same for multinational and purely domestic companies, firms that operate in several countries must also deal with exchange rate and political risks, tax law differences, transfer pricing, and strategic issues.
LG 4 Describe the determination and use of risk-adjusted discount rates (RADRs), portfolio effects, and the practical aspects of RADRs. The risk of a project whose initial investment is known with certainty is embodied in the present value of its cash inflows, using NPV. There are two opportunities to adjust the present value of cash inflows for risk: (1) adjust the cash inflows or (2) adjust the discount rate. Because adjusting the cash inflows is highly subjective, adjusting discount rates is more popular. RADRs use a market-based adjustment of the discount rate to calculate NPV. The RADR is closely linked to CAPM, but because real corporate assets are generally not traded in an efficient market, the CAPM cannot be applied directly to capital budgeting. Instead, firms develop some CAPM-type relationship to link a project’s risk to its required return, which is used as the discount rate. Often, for convenience, firms will rely on total risk as an approximation for relevant risk when estimating required project returns. RADRs are commonly used in practice because decision makers find rates of return easy to estimate and apply.
LG 5 Select the best of a group of unequal-lived, mutually exclusive projects using annualized net present values (ANPVs). The ANPV approach is the most efficient method of comparing ongoing, mutually exclusive projects that have unequal usable lives. It converts the NPV of each unequal-lived project into an equivalent annual amount, its ANPV. The ANPV can be calculated using equations, a financial calculator, or a spreadsheet. The project with the highest ANPV is best.
LG 6 Explain the role of real options and the objective and procedures for selecting projects under capital rationing. Real options are opportunities that are embedded in capital projects and that allow managers to alter their cash flow and risk in a way that affects project acceptability (NPV). By explicitly recognizing real options, the financial manager can find a project’s strategic NPV. Some of the more common types of real options are abandonment, flexibility, growth, and timing options. The strategic NPV improves the quality of the capital budgeting decision.
Capital rationing exists when firms have more acceptable independent projects than they can fund. Capital rationing commonly occurs in practice. Its objective is to select from all acceptable projects the group that provides the highest overall net present value and does not require more dollars than are budgeted. The two basic approaches for choosing projects under capital rationing are the internal rate of return approach and the net present value approach. The NPV approach better achieves the objective of using the budget to generate the highest present value of inflows.

Personal Finance Problem

Personal Finance Problem

Personal Finance Problem

TO DO

Create a spreadsheet to answer the following questions.

• a. Calculate the NPV for each project over its respective life. Rank the projects in descending order on the basis of NPV. Which one would you choose?
• b. Use the annualized net present value (ANPV) approach to evaluate and rank the projects in descending order on the basis of ANPV. Which one would you choose?
• c. Compare and contrast your findings in parts a and b. Which project would you recommend that the firm choose? Explain.

TO DO

• a. For each of the two proposed replacement presses, determine:
  • (1) Initial investment.
  • (2) Operating cash inflows. (Note: Be sure to consider the depreciation in year 6.)
  • (3) Terminal cash flow. (Note: This is at the end of year 5.)
• b. Using the data developed in part a, find and depict on a time line the relevant cash flow stream associated with each of the two proposed replacement presses, assuming that each is terminated at the end of 5 years.
• c. Using the data developed in part b, apply each of the following decision techniques:
  • (1) Payback period. (Note: For year 5, use only the operating cash inflows—that is, exclude terminal cash flow—when making this calculation.)
  • (2) Net present value (NPV).
  • (3) Internal rate of return (IRR).
• d. Draw net present value profiles for the two replacement presses on the same set of axes, and discuss conflicting rankings of the two presses, if any, resulting from use of NPV and IRR decision techniques.
• e. Recommend which, if either, of the presses the firm should acquire if the firm has (1) unlimited funds or (2) capital rationing.
• f. The operating cash inflows associated with press A are characterized as very risky in contrast to the low-risk operating cash inflows of press B. What impact does that have on your recommendation?