Week 4 Individual Problems
I HAVE HIGHLIGHTED IN YELLOW THE QUESTIONS TO ANSWER IN THE CHAPTER. I HAVE COPY AND PASTE CHAPTER 12.
Resource: Principles of Managerial Finance, Ch. 12
Complete the following problems in Ch. 12:
 P121
 P123
 P126
 P1217
 P1219
CHAPTER 12
12 Risk and Refinements in Capital Budgeting
Learning Goals
 LG 1 Understand the importance of recognizing risk in the analysis of capital budgeting projects.
 LG 2 Discuss risk and cash inflows, scenario analysis, and simulation as behavioral approaches for dealing with risk.
 LG 3 Review the unique risks that multinational companies face.
 LG 4 Describe the determination and use of riskadjusted discount rates (RADRs), portfolio effects, and the practical aspects of RADRs.
 LG 5 Select the best of a group of unequallived, mutually exclusive projects using annualized net present values (ANPVs).
 LG 6 Explain the role of real options and the objective and procedures for selecting projects under capital rationing.
Why This Chapter Matters to You
In your professional life
ACCOUNTING You need to understand the risk caused by the variability of cash flows, how to compare projects with unequal lives, and how to measure project returns when capital is being rationed.
INFORMATION SYSTEMS You need to understand how risk is incorporated into capital budgeting techniques and how those techniques may be refined in the face of special circumstances so as to design decision modules for use in analyzing proposed capital projects.
MANAGEMENT You need to understand behavioral approaches for dealing with risk, including international risk, in capital budgeting decisions; how to riskadjust discount rates; how to refine capital budgeting techniques when projects have unequal lives or when capital must be rationed; and how to recognize real options embedded in capital projects.
MARKETING You need to understand how the risk of proposed projects is measured in capital budgeting, how projects with unequal lives will be evaluated, how to recognize and treat real options embedded in proposed projects, and how projects will be evaluated when capital must be rationed.
OPERATIONS You need to understand how proposals for the acquisition of new equipment and plants will be evaluated by the firm’s decision makers, especially projects that are risky, have unequal lives, or may need to be abandoned or slowed, or when capital is limited.
In your personal life
Risk is present in all longterm decisions. When making personal financial decisions, you should consider risk in the decisionmaking process. Simply put, you should demand higher returns for greater risk. Failing to incorporate risk into your financial decisionmaking process will likely result in poor decisions and reduced wealth.
YPF Argentina Seizes Oil Company from Spanish Owners
YPF is the largest oil company in Argentina. After operating for more than 70 years as a stateowned enterprise, YPF was privatized in 1993 and later purchased by the Spanish firm, Repsol S.A. In the purchase agreement, the government of Argentina retained a “golden share,” essentially giving the government the right to outvote all other shareholders on certain matters.
After Repsol’s acquisition of YPF, the Argentinian company’s production faltered. In 2011, Argentina reported a deficit in international energy trade for the first time in almost 15 years (meaning that it imported more energy than it exported). Government officials began to point fingers at Repsol, accusing the company of mismanaging YPF and underinvesting in exploration and production in Argentina. Governors in several provinces revoked Repsol’s leases, an action that contributed to a 50% decline in YPF shares from February to early April. Finally, on April 16, 2012, Argentina’s president, Cristina Kirchner, announced that her country would sieze a majority state in YPF from Repsol, essentially expropriating the firm’s assets from Repsol. Repsol would receive some compensation in exchange for their YPF shares, but company officials insisted that the compensation they were offered was far below the value of the assets that had been seized.
A little more than a year later, Chevron Corp. announced that it would fund most of a $1.5 billion joint venture with YPF to develop the country’s shale oil and gas deposits. Commentators noted that in making such a large investment in Argentina, Chevron was demonstrating its willingness to take on not only the inherent risks associated with oil and gas exploration, but also the political risks of doing business in Argentina.
When firms undertake major investments, they cannot avoid taking risks. These risks may arise from the nature of the business that a company operates in, such as the risks of oil exploration, but political factors can also create risks that may diminish the value of a company’s investments. This chapter focuses on the tools available to managers that help them better understand the risks of major investments.
12.1 Introduction to Risk in Capital Budgeting
LG 1
In our discussion of capital budgeting thus far, we have assumed that a firm’s investment projects all have the same risk, which implies that the acceptance of any project would not change the firm’s overall risk. In actuality, these assumptions often do not hold: Projects are not equally risky, and the acceptance of a project can increase or decrease the firm’s overall risk. We begin this chapter by relaxing these assumptions and focusing on how managers evaluate the risks of different projects. Naturally, we will use many of the risk concepts developed in Chapter 8.
We continue the Bennett Company example from Chapter 10. The relevant cash flows and NPVs for Bennett Company’s two mutually exclusive projects—A and B—appear in Table 12.1.
In the following three sections, we use the basic risk concepts presented in Chapter 8 to demonstrate behavioral approaches for dealing with risk, international risk considerations, and the use of riskadjusted discount rates to explicitly recognize risk in the analysis of capital budgeting projects.
REVIEW QUESTION
TABLE 12.1 Relevant Cash Flows and NPVs for Bennett Company’s Projects
Project A  Project B  

A. Relevant cash flows  
Initial investment  −$42,000  −$45,000 
Year  Operating cash inflows  
1  $14,000  $28,000 
2  14,000  12,000 
3  14,000  10,000 
4  14,000  10,000 
5  14,000  10,000 
B. Decision technique  
NPV @ 10% cost of capitala  $11,071  $10,924 
aFrom Figure 10.2 on page 402; calculated using a financial calculator.
12.2 Behavioral Approaches for Dealing with Risk
LG 2
Behavioral approaches can be used to get a “feel” for the level of project risk, whereas other approaches try to quantify and measure project risk. Here we present a few behavioral approaches for dealing with risk in capital budgeting: breakeven analysis, scenario analysis, and simulation.
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.
risk (in capital budgeting)
The uncertainty surrounding the cash flows that a project will generate or, more formally, the degree of variability of 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 15year 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 MBAlevel 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 pessimisticoutcome NPV from the optimisticoutcome NPV.
TABLE 12.2 Scenario Analysis of Treadwell’s Projects A and B
Example 12.2
Continuing with Treadwell Tire Company, assume that the financial manager created three scenarios for each project: pessimistic, most likely, and optimistic. The cash inflows and resulting NPVs in each case are summarized in Table 12.2. Comparing the ranges of cash inflows ($1,000 for project A and $4,000 for B) and, more important, the ranges of NPVs ($7,606 for project A and $30,424 for B) makes it clear that project A is less risky than project B. Given that both projects have the same most likely NPV of $5,212, the assumed riskaverse decision maker will take project A because it has less risk (smaller NPV range) and no possibility of loss (all NPVs > $0).
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 statisticsbased 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.
simulation
A statisticsbased behavioral approach that applies predetermined probability distributions and random numbers to estimate risky outcomes.
FIGURE 12.1 NPV Simulation
Flowchart of a net present value simulation
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 singlepoint estimate.
in practice focus on PRACTICE: The Monte Carlo Method: The Forecast Is for Less Uncertainty
Most capital budgeting decisions involve some degree of uncertainty. For example, a company faces some degree of uncertainty associated with the demand for a new product. One method of accounting for this uncertainty is to average the highest and the lowest prediction of sales. However, such a method is flawed. Producing the average of the expected possible demand can lead to gross overproduction or gross underproduction, neither of which is as profitable as having the right volume of production.
To combat uncertainty in the decisionmaking process, some companies use a Monte Carlo simulation program to model possible outcomes. Developed by mathematicians in World War II while working on the atomic bomb, the Monte Carlo method was not widely used until the advent of the personal computer. A Monte Carlo simulation program randomly generates values for uncertain variables over and over to simulate a model. The simulation then requires project practitioners to develop low, high, and most likely cost estimates along with correlation coefficients. Once these inputs are derived, the Monte Carlo program can be run through just a few simulations, or thousands, in just a few seconds.
A Monte Carlo program usually builds a histogram of the results, referred to as a frequency chart,for each forecast or output cell that the user wants to analyze. The program then delivers a percentage likelihood that a particular forecast will fall within a specified range, much like a weather forecast. The program also has an optimization feature that allows a project manager with budget constraints to figure out which combination of possible projects will result in the highest profit.
One of the problems with using a Monte Carlo program is the difficulty of establishing the correct input ranges for the variables and determining the correlation coefficients for those variables. However, the work put into developing the input for the program can often clarify some uncertainty in a proposed project. Although Monte Carlo simulation is not the perfect answer to capital budgeting problems, it is another tool that corporations, including ALCOA, Motorola, Intel, Procter & Gamble, and Walt Disney, use to manage risk and make more informed business and strategic decisions.
A Monte Carlo simulation program requires the user to first build an Excel spreadsheet model that captures the input variables for the proposed project. What issues and what benefits can the user derive from this process?
REVIEW QUESTIONS
EXCEL REVIEW QUESTION
My Finance Lab
12.3 International Risk Considerations
LG 3
Although the basic techniques of capital budgeting are the same for multinational companies (MNCs) as for purely domestic firms, firms that operate in several countries face risks that are unique to the international arena. Two types of risk—exchange rate risk and political risk—are particularly important.
Exchange rate risk reflects the danger that an unexpected change in the exchange rate between the dollar and the currency in which a project’s cash flows are denominated will reduce the market value of that project’s cash flow. The dollar value of future cash inflows can be dramatically altered if the local currency depreciates against the dollar. In the short term, specific cash flows can be hedged by using financial instruments such as currency futures and options. Longterm exchange rate risk can best be minimized by financing the project, in whole or in part, in local currency.
exchange rate risk
The danger that an unexpected change in the exchange rate between the dollar and the currency in which a project’s cash flows are denominated will reduce the market value of that project’s cash flow.
Political risk is much harder to protect against. Firms that make investments abroad may find that the hostcountry government can limit the firm’s ability to return profits back home. Governments can seize the firm’s assets or otherwise interfere with a project’s operation. The difficulties of managing political risk after the fact make it even more important that managers account for political risks before making an investment. They can do so either by adjusting a project’s expected cash inflows to account for the probability of political interference or by using riskadjusted discount rates (discussed later in this chapter) in capital budgeting formulas. In general, it is much better to adjust individual project cash flows for political risk subjectively than to use a blanket adjustment for all projects.
In addition to unique risks that MNCs must face, several other special issues are relevant only for international capital budgeting. One of these special issues is taxes. Because only aftertax cash flows are relevant for capital budgeting, financial managers must carefully account for taxes paid to foreign governments on profits earned within their borders. They must also assess the impact of these tax payments on the parent company’s U.S. tax liability.
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.
Another special issue in international capital budgeting is transfer pricing. Much of the international trade involving MNCs is, in reality, simply the shipment of goods and services from one of a parent company’s subsidiaries to another subsidiary located abroad. The parent company therefore has discretion in setting transfer prices, the prices that subsidiaries charge each other for the goods and services traded between them. The widespread use of transfer pricing in international trade makes capital budgeting in MNCs very difficult unless the transfer prices that are used accurately reflect actual costs and incremental cash flows.
transfer prices
Prices that subsidiaries charge each other for the goods and services traded between them.
Finally, MNCs often must approach international capital projects from a strategic point of view,rather than from a strictly financial perspective. For example, an MNC may feel compelled to invest in a country to ensure continued access, even if the project itself may not have a positive net present value. This motivation was important for Japanese automakers that set up assembly plants in the United States in the early 1980s. For much the same reason, U.S. investment in Europe surged during the years before the market integration of the European Community in 1992. MNCs often invest in production facilities in the home country of major rivals to deny these competitors an uncontested home market. MNCs also may feel compelled to invest in certain industries or countries to achieve a broad corporate objective such as completing a product line or diversifying raw material sources, even when the project’s cash flows may not be sufficiently profitable.
REVIEW QUESTION
12.4 RiskAdjusted Discount Rates
LG 4
The approaches for dealing with risk that have been presented so far enable the financial manager to get a “feel” for project risk. Unfortunately, they do not explicitly recognize project risk. We will now illustrate the most popular riskadjustment technique that employs the net present value (NPV) decision method. The NPV decision rule of accepting only those projects with NPVs > $0 will continue to hold. Close examination of the basic equation for NPV, Equation 10.1, should make it clear that because the initial investment (CF0) is known with certainty, a project’s risk is embodied in the present value of its cash inflows:
Two opportunities to adjust the present value of cash inflows for risk exist: (1) The cash inflows (CFt) can be adjusted, or (2) the discount rate (r) can be adjusted. Adjusting the cash inflows is highly subjective, so here we describe the more popular process of adjusting the discount rate. In addition, we consider the portfolio effects of project analysis as well as the practical aspects of the riskadjusted discount rate.
DETERMINING RISKADJUSTED DISCOUNT RATES (RADRS)
A popular approach for risk adjustment involves the use of riskadjusted discount rates (RADRs). This approach uses Equation 10.1 but employs a riskadjusted discount rate, as noted in the expression3
(12.2) 
The riskadjusted 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.
riskadjusted discount rate (RADR)
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.
3. The riskadjusted 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 riskadjusted 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 riskadjusted discount rate.
Personal Finance Example 12.3
Talor Namtig is considering investing $1,000 in either of two stocks, A or B. She plans to hold the stock for exactly 5 years and expects both stocks to pay $80 in annual endofyear cash dividends. At the end of year 5, she estimates that stock A can be sold to net $1,200 and stock B can be sold to net $1,500. Talor has carefully researched the two stocks and believes that although stock A has average risk, stock B is considerably riskier. Her research indicates that she should earn an annual return on an averagerisk stock of 11%. Because stock B is considerably riskier, she will require a 14% return from it. Talor makes the following calculations to find the riskadjusted net present values (NPVs) for the two stocks:
Although Talor’s calculations indicate that both stock investments are acceptable (NPVs > $0) on a riskadjusted basis, she should invest in Stock B because it has a higher NPV.
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.
Review of CAPM
In Chapter 8, we used the capital asset pricing model (CAPM) to link the relevant risk and return for all assets traded in efficient markets. In the development of the CAPM, the total risk of an asset was defined as
Total risk = Nondiversifiable risk + Diversifiable risk  (12.3) 
For assets traded in an efficient market, the diversifiable risk, which results from uncontrollable or random events, can be eliminated through diversification. The relevant risk is therefore thenondiversifiable risk, the risk for which owners of these assets are rewarded. Nondiversifiable risk for securities is commonly measured by using beta, which is an index of the degree of movement of an asset’s return in response to a change in the market return.
Using beta, βj, to measure the relevant risk of any asset j, the CAPM is
rj = RF + [βj × (rm − RF)]  (12.4) 
where
In Chapter 8, we demonstrated that the required return on any asset could be determined by substituting values of RF, βj, and rm into the CAPM (Equation 12.4). Any security that is expected to earn in excess of its required return would be acceptable, and those that are expected to earn an inferior return would be rejected.
FIGURE 12.2 CAPM and SML
CAPM and SML in capital budgeting decision making
Using CAPM to Find RADRs
If we assume for a moment that real corporate assets such as computers, machine tools, and specialpurpose machinery are traded in efficient markets, the CAPM can be redefined as
rproject j = RF + [βproject j × (rm − RF)]  (12.5) 
The security market line (SML)—the graphical depiction of the CAPM—is shown for Equation 12.5in Figure 12.2. Any project having an IRR above the SML would be acceptable because its IRR would exceed the required return, rproject; any project with an IRR below rproject would be rejected. In terms of NPV, any project falling above the SML would have a positive NPV, and any project falling below the SML would have a negative NPV.4
Example 12.4
Figure 12.2 shows two projects, L and R. Project L has a beta, βL, and generates an internal rate of return, IRRL. The required return for a project with risk βL is rL. Because project L generates a return greater than that required (IRRL > rL), this project is acceptable. Project L will have a positive NPV when its cash inflows are discounted at its required return, rL. Project R, on the other hand, generates an IRR below that required for its risk, βR (IRRR < rR). This project will have a negative NPV when its cash inflows are discounted at its required return, rR. Project R should be rejected.
4. Whenever the IRR is above the cost of capital or required return (IRR > r), the NPV is positive, and whenever the IRR is below the cost of capital or required return (IRR < r), the NPV is negative. Because by definition the IRR is the discount rate that causes NPV to equal zero and the IRR and NPV always agree on accept–reject decisions, the relationship noted in Figure 12.2 logically follows.
in practice focus on ETHICS: Ethics and the Cost of Capital
At the dawn of the new millennium, the company formerly known as British Petroleum was trying to reinvent itself. BP introduced a new corporate logo, a green, yellow, and white sunburst that “symbolized energy in all its dynamic forms.” In its 2009 sustainability review, BP defined sustainability as “the capacity to endure as a group: by renewing assets; creating and delivering better products and services that meet the evolving needs of society; attracting successive generations of employees; contributing to a sustainable environment; and retaining the trust and support of our customers, shareholders and the communities in which we operate.”a
However, BP’s environmental track record didn’t always support the image that the company was trying to portray. In 2005, a fire at BP’s Texas City Refinery killed 15 workers and injured many more. The following year, BP shut down its Prudhoe Bay oil field due to corrosion in an oil transit line that resulted in an oil spill. BP was widely criticized for these events, but that did not stop it from causing the largest oil spill in U.S. history when the Deepwater Horizon offshore oil platform exploded and sank in April 2010.
The Deepwater Horizon accident and subsequent oil spill had a significant impact on BP’s cost of capital. By June 2010, BP’s stock price was 50 percent below precrisis levels, and the company’s bonds traded at levels comparable to junkrated companies. Over the course of a single week, when BP’s “top kill” attempt to stop the leak proved unsuccessful, the yield on the company’s main 5year dollar bond jumped by 2 percent. The bond rating agencies downgraded BP, although the firm continued to possess one of the highest investment grade credit ratings. However, the rating agencies warned that further downgrades could follow if the crisis, and the expected costs, continued to escalate.
 Is the ultimate goal of the firm—to maximize the wealth of the owners for whom the firm is being operated—ethical?
 Why might ethical companies benefit from a lower cost of capital than less ethical companies?
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 riskadjusted 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 decisionmaking 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 CAPMtype 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 riskadjusted 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 higherrisk projects and vice versa. The CAPMtype 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% (riskfree 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 riskadjusted NPV of $9,798 is greater than the $6,063 riskadjusted 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 riskadjusted discount rates (RADRs) also can be performed as shown on the following Excel spreadsheet.
FIGURE 12.3 Calculation of NPVS for Bennett Company’s Capital Expenditure Alternatives Using RADRs
Time lines depicting the cash flows and NPV calculations using RADRs for projects A and B
Note: When we use the risk indexes of 1.6 and 1.0 for projects A and B, respectively, along with the table above, a riskadjusted discount rate (RADR) of 14% results for project A and an RADR of 11% results for project B.
The usefulness of riskadjusted 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 welldeveloped 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 CAPMtype 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 divisionbydivision 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.
TABLE 12.3 Bennett Company’s Risk Classes and RADRs
Risk class  Description  Riskadjusted discount rate, RADR 

I  Belowaverage risk: Projects with low risk. Typically involve routine replacement without renewal of existing activities.  8% 
II  Average risk: Projects similar to those currently implemented. Typically involve replacement or renewal of existing activities.  10%a 
III  Aboveaverage risk: Projects with higher than normal, but not excessive, risk. Typically involve expansion of existing or similar activities.  14% 
IV  Highest risk: Projects with very high risk. Typically involve expansion into new or unfamiliar activities.  20% 
aThis RADR is actually the firm’s cost of capital, which is discussed in detail in Chapter 9. It represents the firm’s required return on its existing portfolio of projects, which is assumed to be unchanged with acceptance of the “averagerisk” project.
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.
Example 12.6
Assume that the management of Bennett Company decided to use risk classes to analyze projects and so placed each project in one of four risk classes according to its perceived risk. The classes ranged from I for the lowestrisk projects to IV for the highestrisk projects. Associated with each class was an RADR appropriate to the level of risk of projects in the class as given in Table 12.3. Bennett classified as lowerrisk those projects that tend to involve routine replacement or renewal activities; higherrisk projects involve expansion, often into new or unfamiliar activities.
The financial manager of Bennett has assigned project A to class III and project B to class II. The cash flows for project A would be evaluated using a 14% RADR, and project B’s would be evaluated using a 10% RADR.5 The NPV of project A at 14% was calculated in Figure 12.3 to be $6,063, and the NPV for project B at a 10% RADR was shown in Table 12.1 to be $10,924. Clearly, with RADRs based on the use of risk classes, project B is preferred over project A. As noted earlier, this result is contrary to the preferences shown in Table 12.1, where differing risks of projects A and B were not taken into account.
REVIEW QUESTIONS
12.5 Capital Budgeting Refinements
LG 5
LG 6
Refinements must often be made in the analysis of capital budgeting projects to accommodate special circumstances. These adjustments permit the relaxation of certain simplifying assumptions presented earlier. Three areas in which special forms of analysis are frequently needed are (1) comparison of mutually exclusive projects having unequal lives, (2) recognition of real options, and (3) capital rationing caused by a binding budget constraint.
COMPARING PROJECTS WITH UNEQUAL LIVES
The financial manager must often select the best of a group of unequallived projects. If the projects are independent, the length of the project lives is not critical. But when unequallived 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 unequallived, 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 unequallived, 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.
Annualized Net Present Value (ANPV) Approach
The annualized net present value (ANPV) approach6 converts the net present value of unequallived, mutually exclusive projects into an equivalent annual amount (in NPV terms) that can be used to select the best project.7 This net present value based approach can be applied to unequallived, mutually exclusive projects by using the following steps:
annualized net present value (ANPV) approach
An approach to evaluating unequallived projects that converts the net present value of unequallived, mutually exclusive projects into an equivalent annual amount (in NPV terms).
 Step 1 Calculate the net present value of each project j, NPVj, over its life, nj, using the appropriate cost of capital, r.
 Step 2 Convert the NPVj into an annuity having life nj. That is, find an annuity that has the same life and the same NPV as the project.
 Step 3 Select the project that has the highest ANPV.
6. This approach is also called the “equivalent annual annuity (EAA)” or the “equivalent annual cost.” The termannualized net present value (ANPV) is used here due to its descriptive clarity.
7. The theory underlying this as well as other approaches for comparing projects with unequal lives assumes that each project can be replaced in the future for the same initial investment and that each will provide the same expected future cash inflows. Although changing technology and inflation will affect the initial investment and expected cash inflows, the lack of specific attention to them does not detract from the usefulness of this technique.
Example 12.8
By using the AT Company data presented earlier for projects X and Y, we can apply the threestep ANPV approach as follows:
My Finance Lab Solution Video
 Step 1 The net present values of projects X and Y discounted at 10%—as calculated in the preceding example for a single purchase of each asset—are
 Step 2 In this step, we want to convert the NPVs from Step 1 into annuities. For project X, we are trying to find the answer to the question, what 3year annuity (equal to the life of project X) has a present value of $11,277.24 (the NPV of project X)? Likewise, for project Y we want to know what 6year annuity has a present value of $19,013.27. Once we have these values, we can determine which project, X or Y, delivers a higher annual cash flow on a present value basis. My Finance Lab Financial Calculator
Calculator use The keystrokes required to find the ANPV on a financial calculator are identical to those demonstrated in Chapter 5 for finding the annual payments on an installment loan. These keystrokes are shown at the left for project X and for project Y. The resulting ANPVs for projects X and Y are $4,534.74 and $4,365.59, respectively. (Note that the calculator solutions are shown as negative values because the PV inputs were entered as positive values.) Spreadsheet use The annualized net present values of two projects with unequal lives also can be compared as shown on the following Excel spreadsheet.
 Step 3 Reviewing the ANPVs calculated in Step 2, we can see that project X would be preferred over project Y. Given that projects X and Y are mutually exclusive, project X would be the recommended project because it provides the higher annualized net present value.
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.
real options
Opportunities that are embedded in capital projects that enable managers to alter their cash flows and risk in a way that affects project acceptability (NPV). Also 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.
TABLE 12.4 Major Types of Real Options
Option type  Description 

Abandonment option  The option to abandon or terminate a project prior to the end of its planned life. This option allows management to avoid or minimize losses on projects that turn bad. Explicitly recognizing the abandonment option when evaluating a project often increases its NPV. 
Flexibility option  The option to incorporate flexibility into the firm’s operations, particularly production. It generally includes the opportunity to design the production process to accept multiple inputs, to use flexible production technology to create a variety of outputs by reconfiguring the same plant and equipment, and to purchase and retain excess capacity in capitalintensive industries subject to wide swings in output demand and long lead time in building new capacity from scratch. Recognition of this option embedded in a capital expenditure should increase the NPV of the project. 
Growth option  The option to develop followon projects, expand markets, expand or retool plants, and so on that would not be possible without implementation of the project that is being evaluated. If a project being considered has the measurable potential to open new doors if successful, recognition of the cash flows from such opportunities should be included in the initial decision process. Growth opportunities embedded in a project often increase the NPV of the project in which they are embedded. 
Timing option  The option to determine when various actions with respect to a given project are taken. This option recognizes the firm’s opportunity to delay acceptance of a project for one or more periods, to accelerate or slow the process of implementing a project in response to new information, or to shut down a project temporarily in response to changing product market conditions or competition. As in the case of the other types of options, the explicit recognition of timing opportunities can improve the NPV of a project that fails to recognize this option in an investment decision. 
(12.6) 
Application of this relationship is illustrated in the following example.
Example 12.9
Assume that a strategic analysis of Bennett Company’s projects A and B (see cash flows and NPVs inTable 12.1) finds no real options embedded in project A and two real options embedded in project B. The two real options in project B are as follows: (1) The project would have, during the first 2 years, some downtime that would result in unused production capacity that could be used to perform contract manufacturing for another firm; and (2) the project’s computerized control system could, with some modification, control two other machines, thereby reducing labor cost, without affecting operation of the new project.
Bennett’s management estimated the NPV of the contract manufacturing over the 2 years following implementation of project B to be $1,500 and the NPV of the computer control sharing to be $2,000. Management believed that there was a 60% chance that the contract manufacturing option would be exercised and only a 30% chance that the computer control sharing option would be exercised. The combined value of these two real options would be the sum of their expected values:
Substituting the $1,500 real options value along with the traditional NPV of $10,924 for project B (from Table 12.1) into Equation 12.7, we get the strategic NPV for project B:
NPVstrategic = $10,924 + $1,500 = $12,424
Bennett Company’s project B therefore has a strategic NPV of $12,424, which is above its traditional NPV and now exceeds project A’s NPV of $11,071. Clearly, recognition of project B’s real options improved its NPV (from $10,924 to $12,424) and causes it to be preferred over project A (NPV of $12,424 for B > NPV of $11,071 for A), which has no real options embedded in it.
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.
Internal Rate of Return Approach
The internal rate of return approach involves graphing project IRRs in descending order against the total dollar investment. This graph is called the investment opportunities schedule (IOS). By drawing the costofcapital line and then imposing a budget constraint, the financial manager can determine the group of acceptable projects. The problem with this technique is that it does not guarantee the maximum dollar return to the firm. It merely provides an intuitively appealing solution to capitalrationing problems.
internal rate of return approach
An approach to capital rationing that involves graphing project IRRs in descending order against the total dollar investment to determine the group of acceptable projects.
investment opportunities schedule (IOS)
The graph that plots project IRRs in descending order against the total dollar investment.
FIGURE 12.4 Investment Opportunities Schedule
Investment opportunities schedule (IOS) for Tate Company projects
Example 12.10
Tate Company, a fastgrowing plastics company, is confronted with six projects competing for its fixed budget of $250,000. The initial investment and IRR for each project are as follows:
My Finance Lab Solution Video
Project  Initial investment  IRR 

A  −$ 80,000  12% 
B  −70,000  20 
C  −100,000  16 
D  −40,000  8 
E  −60,000  15 
F  −110,000  11 
The firm has a cost of capital of 10%. Figure 12.4 presents the IOS that results from ranking the six projects in descending order on the basis of their IRRs. According to the schedule, only projects B, C, and E should be accepted. Together they will absorb $230,000 of the $250,000 budget. Projects A and F are acceptable but cannot be chosen because of the budget constraint. Project D is not worthy of consideration; its IRR is less than the firm’s 10% cost of capital.
The drawback of this approach is that there is no guarantee that the acceptance of projects B, C, and E will maximize total dollar returns and therefore owners’ wealth.
Net Present Value Approach
The net present value approach is based on the use of present values to determine the group of projects that will maximize owners’ wealth. It is implemented by ranking projects on the basis of IRRs and then evaluating the present value of the benefits from each potential project to determinethe combination of projects with the highest overall present value. This method is the same as maximizing net present value because the entire budget is viewed as the total initial investment. Any portion of the firm’s budget that is not used does not increase the firm’s value. At best, the unused money can be invested in marketable securities or returned to the owners in the form of cash dividends. In either case, the wealth of the owners is not likely to be enhanced.
net present value approach
An approach to capital rationing that is based on the use of present values to determine the group of projects that will maximize owners’ wealth.
TABLE 12.5 Rankings for Tate Company Projects
Project  Initial investment  IRR  Present value of inflows at 10%  

B  −$ 70,000  20%  $112,000  
C  −100,000  16  145,000  
E  −60,000  15  79,000  
A  −80,000  12  100,000  
F  −110,000  11  126,500  Cutoff point 


D  −40,000  8  36,000  (IRR < 10%) 
Example 12.11
The projects described in the preceding example are ranked in Table 12.5 on the basis of IRRs. The present value of the cash inflows associated with the projects is also included in the table. Projects B, C, and E, which together require $230,000, yield a present value of $336,000. However, if projects B, C, and A were implemented, the total budget of $250,000 would be used, and the present value of the cash inflows would be $357,000, which is greater than the return expected from selecting the projects on the basis of the highest IRRs. Implementing B, C, and A is preferable because they maximize the present value for the given budget. The firm’s objective is to use its budget to generate the highest present value of inflows. Assuming that any unused portion of the budget does not gain or lose money, the total NPV for projects B, C, and E would be $106,000 ($336,000 − $230,000), whereas the total NPV for projects B, C, and A would be $107,000 ($357,000 − $250,000). Selection of projects B, C, and A will therefore maximize NPV.
REVIEW QUESTIONS
EXCEL REVIEW QUESTION
My Finance Lab
Summary
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.
Riskadjusted 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 riskadjustment 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 riskadjusted 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 marketbased 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 CAPMtype 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 unequallived, 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 unequallived 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.
OpenerinReview
The chapter opener describes the expropriation of a Spanish company’s investment in an Argentina oil and gas company as well as the decision by Chevron to undertake a major new investment in that country. If you were a financial analyst at Chevron, how might you use scenario analysis to evaluate the risk of entering into a joint venture in Argentina with YPF?
SelfTest Problem
(Solutions in Appendix)
LG 4
Risk index  Required return (RADR)  

0.0  7.0% (riskfree rate, RF)  
0.2  8.0  
0.4  9.0  
0.6  10.0  
0.8  11.0  
1.0  12.0  
1.2  13.0  
1.4  14.0  
1.6  15.0  
1.8  16.0  
2.0  17.0 
Project data are as follows:
Project A  Project B  

Initial investment (CF0)  −$15,000  −$20,000 
Project life  3 years  3 years 
Annual cash inflow (CF)  $7,000  $10,000 
Risk index  0.4  1.8 
 a.Ignoring any differences in risk and assuming that the firm’s cost of capital is 10%, calculate the net present value (NPV) of each project.
 b.Use NPV to evaluate the projects, using riskadjusted discount rates (RADRs) to account for risk.
 c.Compare, contrast, and explain your findings in parts a and b.
WarmUp Exercises
All problems are available in MyFinanceLab.
LG 2
Expected cash inflows  



Year  Pessimistic  Most likely  Optimistic 
1  $5,500  $ 8,000  $10,500 
2  6,000  9,000  12,000 
3  7,500  10,500  14,500 
4  6,500  9,500  11,500 
5  4,500  6,500  7,500 
LG 2
LG 4
Risk index  Required return  

0  4.0%  (current riskfree rate) 
1  4.5  
2  5.0  
3  5.5  
4  6.0  
5  6.5  (current IRR) 
6  7.0  
7  7.5  
8  8.0  
9  8.5  
10  9.0 
The firm is analyzing two projects based on their RADRs. Project Sourdough requires an initial investment of $12,500 and is assigned a risk index of 6. Project Greek Salad requires an initial investment of $7,500 and is assigned a risk index of 8. The two projects have 7year lives. Sourdough is projected to generate cash inflows of $5,500 per year. Greek Salad is projected to generate cash inflows of $4,000 per year. Use each project’s RADR to select the better project.
LG 5
Project M  Project N  

Initial investment  −$35,000  −$55,000 
Year  Cash inflows  
1  $12,000  $18,000 
2  25,000  15,000 
3  30,000  25,000 
4  –  10,000 
5  –  8,000 
6  –  5,000 
7  –  5,000 
LG 6
Project  Initial investment  IRR 

1  −$75,000  8% 
2  −40,000  10 
3  −35,000  7 
4  −50,000  11 
5  −45,000  9 
6  −20,000  6 
Problems
All problems are available in MyFinanceLab.
LG 1
Project  Initial investment  Details 

A  −$ 35,000  Replace existing office furnishings. 
B  −500,000  Purchase digital video editing equipment for use with several existing accounts. 
C  −450,000  Develop proposal to bid for a $2,000,000 per year 10year contract with the U.S. Navy, not now an account. 
D  −685,000  Purchase the exclusive rights to market a quality educational television program in syndication to local markets in the European Union, a part of the firm’s existing business activities. 
The media services business is cyclical and highly competitive. The board of directors has asked you, as chief financial officer, to do the following:
 a.Evaluate the risk of each proposed project and rank it “low,” “medium,” or “high.”
 b.Comment on why you chose each ranking.
LG 2
 a.If One Ring requires a 9% return on its investment, what minimum yearly cash inflow will be necessary for the company to go forward with this project?
 b.How would the minimum yearly cash inflow change if the company required a 12% return on its investment?
LG 2
 a.Find the NPV for each project. Are the projects acceptable?
 b.Find the breakeven cash inflow for each project.
 c.The firm has estimated the probabilities of achieving various ranges of cash inflows for the two projects as shown in the following table. What is the probability that each project will achieve at least the breakeven cash inflow found in part b?
Probability of achieving cash inflow in given range
Range of cash inflow ($ millions) Standard Plant Custom Plant $0 to $5 0% 5% $5 to $8 10 10 $8 to $11 60 15 $11 to $14 25 25 $14 to $17 5 20 $17 to $20 0 15 Above $20 0 10  d.Which project is more risky? Which project has the potentially higher NPV? Discuss the risk–return tradeoffs of the two projects.
 e.If the firm wished to minimize losses (that is, NPV < $0), which project would you recommend? Which would you recommend if the goal were to achieve a higher NPV?
LG 2
Project A  Project B  

Initial investment (CF0)  −$8,000  −$8,000 
Outcome  Annual cash inflows (CF)  
Pessimistic  $ 200  $ 900 
Most likely  1,000  1,000 
Optimistic  1,800  1,100 
 a.Determine the range of annual cash inflows for each of the two projects.
 b.Assume that the firm’s cost of capital is 10% and that both projects have 20year lives. Construct a table similar to this one for the NPVs for each project. Include the range of NPVs for each project.
 c.Do parts a and b provide consistent views of the two projects? Explain.
 d.Which project do you recommend? Why?
LG 2
Soft drinks  Snack foods  

Initial investment (CF0)  −$3,000  −$3,000 
Outcome  Annual cash inflows (CF)  
Pessimistic  $ 500  $ 400 
Most likely  750  750 
Optimistic  1,000  1,200 
 a.Determine the range of annual cash inflows for each of the two vending machines.
 b.Construct a table similar to this one for the NPVs associated with each outcome for both machines.
 c.Find the range of NPVs, and subjectively compare the risks associated with these machines.
Personal Finance Problem
LG 2
Assume a direct positive impact of inflation on the prevailing rates (Fisher effect) and answer the following questions. (Assume that inflation has an impact on the opportunity cost, but that the cash flows are contractually fixed and are not affected by inflation).
 a.What is the net present value (NPV) of the investment under the current required rate of return?
 b.What is the net present value (NPV) of the investment under a period of rising inflation?
 c.What is the net present value (NPV) of the investment under a period of falling inflation?
 d.From your answers in a, b, and c, what relationship do you see emerge between changes in inflation and asset valuation?
LG 2
 (1)The projected cash inflows are normally distributed with a mean of $36,000 and a standard deviation of $9,000.
 (2)The projected cash outflows are normally distributed with a mean of $30,000 and a standard deviation of $6,000.
 (3)The firm has an 11% cost of capital.
 (4)The probability distributions of cash inflows and cash outflows are not expected to change over the project’s 10year life.
 a.Describe how the foregoing data can be used to develop a simulation model for finding the net present value of the project.
 b.Discuss the advantages of using a simulation to evaluate the proposed project.
LG 4
Project (j)  



E  F  G  


Initial investment (CF0)  −$15,000  −$11,000  −$19,000 
Year (t)  Cash inflows (CFt)  
1  $ 6,000  $ 6,000  $ 4,000 
2  6,000  4,000  6,000 
3  6,000  5,000  8,000 
4  6,000  2,000  12,000 
Risk index (RIj)  1.80  1.00  0.60 
 a.Find the net present value (NPV) of each project using the firm’s cost of capital. Which project is preferred in this situation?
 b.The firm uses the following equation to determine the riskadjusted discount rate, RADRj, for each project j: RADRj = RF + [RIj × (r − RF)] where Substitute each project’s risk index into this equation to determine its RADR.
 c.Use the RADR for each project to determine its riskadjusted NPV. Which project is preferable in this situation?
 d.Compare and discuss your findings in parts a and c. Which project do you recommend that the firm accept?
LG 4
Risk index  Required return (RADR)  

0.0  7.0%  (riskfree rate, RF) 
0.2  8.0  
0.4  9.0  
0.6  10.0  
0.8  11.0  
1.0  12.0  
1.2  13.0  
1.4  14.0  
1.6  15.0  
1.8  16.0  
2.0  17.0 
The firm is considering two mutually exclusive projects, A and B. Following are the data that the firm has been able to gather about the projects.
Project A  Project B  

Initial investment (CF0)  −$20,000  −$30,000 
Project life  5 years  5 years 
Annual cash inflow (CF)  $7,000  $10,000 
Risk index  0.2  1.4 
All the firm’s cash inflows have already been adjusted for taxes.
 a.Evaluate the projects using riskadjusted discount rates.
 b.Discuss your findings in part a, and recommend the preferred project.
Personal Finance Problem
LG 2
 a.What is the net present value of the first investment?
 b.What is the net present value of the second investment?
 c.Being mutually exclusive, which investment should Lara choose? Explain.
 d.Which investment was relatively more risky? Explain.
LG 4
Project X  Project Y  



Initial investment (CF0)  −$70,000  −$78,000 
Year (t)  Cash inflows (CFt)  
1  $30,000  $22,000 
2  30,000  32,000 
3  30,000  38,000 
4  30,000  46,000 
 a.Use a riskadjusted discount rate approach to calculate the net present value of each project, given that project X has an RADR factor of 1.20 and project Y has an RADR factor of 1.40. The RADR factors are similar to project betas. (Use Equation 12.5 to calculate the required project return for each.)
 b.Discuss your findings in part a, and recommend the preferred project.
LG 4
Project X  Project Y  Project Z  



Initial investment (CF0)  −$180,000  −$235,000  −$310,000 
Year (t)  Cash inflows (CFt)  
1  $80,000  $50,000  $90,000 
2  70,000  60,000  90,000 
3  60,000  70,000  90,000 
4  60,000  80,000  90,000 
5  60,000  90,000  90,000 
Risk Classes and RADRs  

Risk class  Description  Riskadjusted discount rate (RADR) 
I  Lowest risk  10% 
II  Belowaverage risk  13 
III  Average risk  15 
IV  Aboveaverage risk  19 
V  Highest risk  22 
 a.Find the riskadjusted NPV for each project.
 b.Which project, if any, would you recommend that the firm undertake?
LG 5
Machine A  Machine B  Machine C  



Initial investment (CF0)  −$92,000  −$65,000  −$100,500 
Year (t)  Cash inflows (CFt)  
1  $12,000  $10,000  $30,000 
2  12,000  20,000  30,000 
3  12,000  30,000  30,000 
4  12,000  40,000  30,000 
5  12,000  −  30,000 
6  12,000  −  − 
 a.Calculate the NPV for each machine over its life. Rank the machines in descending order on the basis of NPV.
 b.Use the annualized net present value (ANPV) approach to evaluate and rank the machines in descending order on the basis of ANPV.
 c.Compare and contrast your findings in parts a and b. Which machine would you recommend that the firm acquire? Why?
LG 5
Project X  Project Y  Project Z  



Initial investment (CF0)  −$78,000  $52,000  −$66,000 
Year (t)  Cash inflows (CFt)  
1  $17,000  $28,000  $15,000 
2  25,000  38,000  15,000 
3  33,000  −  15,000 
4  41,000  −  15,000 
5  −  −  15,000 
6  −  −  15,000 
7  −  −  15,000 
8  −  −  15,000 
 a.Calculate the NPV for each project over its life. Rank the projects in descending order on the basis of NPV.
 b.Use the annualized net present value (ANPV) approach to evaluate and rank the projects in descending order on the basis of ANPV.
 c.Compare and contrast your findings in parts a and b. Which project would you recommend that the firm purchase? Why?
LG 5
Alternative  Sell  License  Manufacture 
Initial investment (CF0)  −$200,000  −$200,000  −$450,000 
Year (t)  Cash inflows (CFt)  
1  $200,000  $250,000  $200,000 
2  250,000  100,000  250,000 
3  −  80,000  200,000 
4  −  60,000  200,000 
5  −  40,000  200,000 
6  −  −  200,000 
 a.Calculate the net present value of each alternative and rank the alternatives on the basis of NPV.
 b.Calculate the annualized net present value (ANPV) of each alternative, and rank them accordingly.
 c.Why is ANPV preferred over NPV when ranking projects with unequal lives?
Personal Finance Problem
The Butlers wish to choose the better alternative from a purely financial perspective. To perform this analysis they wish to do the following:
 a.Determine the NPV of the Samsung HD plasma TV.
 b.Determine the ANPV of the Samsung HD plasma TV.
 c.Determine the NPV of the Sony HD plasma TV.
 d.Determine the ANPV of the Sony HD plasma TV.
 e.Which set should the Butlers purchase? Why?
LG 6
NPVtraditional = −$1,700 < $0
Before recommending rejection of the proposed project, she has decided to assess whether there might be real options embedded in the firm’s cash flows. Her evaluation uncovered three options:
 Option 1: Abandonment. The project could be abandoned at the end of 3 years, resulting in an addition to NPV of $1,200.
 Option 2: Growth. If the projected outcomes occurred, an opportunity to expand the firm’s product offerings further would become available at the end of 4 years. Exercise of this option is estimated to add $3,000 to the project’s NPV.
 Option 3: Timing. Certain phases of the proposed project could be delayed if market and competitive conditions caused the firm’s forecast revenues to develop more slowly than planned. Such a delay in implementation at that point has an NPV of $10,000.
Jenny estimated that there was a 25% chance that the abandonment option would need to be exercised, a 30% chance that the growth option would be exercised, and only a 10% chance that the implementation of certain phases of the project would affect timing.
 a.Use the information provided to calculate the strategic NPV, NPVstrategic, for Asor Products’ proposed equipment expenditure.
 b.Judging on the basis of your findings in part a, what action should Jenny recommend to management with regard to the proposed equipment expenditure?
 c.In general, how does this problem demonstrate the importance of considering real options when making capital budgeting decisions?
LG 6
Project  Initial investment  IRR  Present value of inflows at 15% 

A  −$5,000,000  17%  $5,400,000 
B  −800,000  18  1,100,000 
C  −2,000,000  19  2,300,000 
D  −1,500,000  16  1,600,000 
E  −800,000  22  900,000 
F  −2,500,000  23  3,000,000 
G  −1,200,000  20  1,300,000 
 a.Use the internal rate of return (IRR) approach to select the best group of projects.
 b.Use the net present value (NPV) approach to select the best group of projects.
 c.Compare, contrast, and discuss your findings in parts a and b.
 d.Which projects should the firm implement? Why?
LG 6
Project  Initial investment  NPV at 13% cost of capital 

A  −$300,000  $ 84,000 
B  −200,000  10,000 
C  −100,000  25,000 
D  −900,000  90,000 
E  −500,000  70,000 
F  −100,000  50,000 
G  −800,000  160,000 
 a.Calculate the present value of cash inflows associated with each project.
 b.Select the optimal group of projects, keeping in mind that unused funds are costly.
LG 4
Spreadsheet Exercise
Isis Corporation has two projects that it would like to undertake. However, due to capital restraints, the two projects—Alpha and Beta—must be treated as mutually exclusive. Both projects are equally risky, and the firm plans to use a 10% cost of capital to evaluate each. Project Alpha has an estimated life of 12 years, and project Beta has an estimated life of 9 years. The cash flow data have been prepared as shown in the following table.
Cash flows  



Project alpha  Project beta  
CF 0  −$5,500,000  −$6,500,000 
CF 1  300,000  400,000 
CF 2  500,000  600,000 
CF 3  500,000  800,000 
CF 4  550,000  1,100,000 
CF 5  700,000  1,400,000 
CF 6  800,000  2,000,000 
CF 7  950,000  2,500,000 
CF 8  1,000,000  2,000,000 
CF 9  1,250,000  1,000,000 
CF 10  1,500,000  
CF 11  2,000,000  
CF 12  2,500,000 
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.
My Finance Lab
Visit www.myfinancelab.com for Chapter Case: Evaluating Cherone Equipment’s Risky Plans for Increasing Its Production Capacity, Group Exercises, and numerous online resources.
Integrative Case 5 Lasting Impressions Company
Lasting Impressions (LI) Company is a mediumsized commercial printer of promotional advertising brochures, booklets, and other directmail pieces. The firm’s major clients are ad agencies based in New York and Chicago. The typical job is characterized by high quality and production runs of more than 50,000 units. LI has not been able to compete effectively with larger printers because of its existing older, inefficient presses. The firm is currently having problems meeting run length requirements as well as meeting quality standards in a costeffective manner.
The general manager has proposed the purchase of one of two large, sixcolor presses designed for long, highquality runs. The purchase of a new press would enable LI to reduce its cost of labor and therefore the price to the client, putting the firm in a more competitive position. The key financial characteristics of the old press and of the two proposed presses are summarized in what follows.
 Old press Originally purchased 3 years ago at an installed cost of $400,000, it is being depreciated under MACRS using a 5year recovery period. The old press has a remaining economic life of 5 years. It can be sold today to net $420,000 before taxes; if it is retained, it can be sold to net $150,000 before taxes at the end of 5 years.
 Press A This highly automated press can be purchased for $830,000 and will require $40,000 in installation costs. It will be depreciated under MACRS using a 5year recovery period. At the end of the 5 years, the machine could be sold to net $400,000 before taxes. If this machine is acquired, it is anticipated that the current account changes shown in the following table would result.
Cash + $ 25,400 Accounts receivable + 120,000 Inventories − 20,000 Accounts payable + 35,000  Press B This press is not as sophisticated as press A. It costs $640,000 and requires $20,000 in installation costs. It will be depreciated under MACRS using a 5year recovery period. At the end of 5 years, it can be sold to net $330,000 before taxes. Acquisition of this press will have no effect on the firm’s net working capital investment.
 The firm estimates that its earnings before depreciation, interest, and taxes with the old press and with press A or press B for each of the 5 years would be as shown in the table at the top of the next page. The firm is subject to a 40% tax rate. The firm’s cost of capital, r, applicable to the proposed replacement is 14%.
Earnings before Depreciation, Interest, and Taxes for Lasting Impressions Company’s Presses Year Old press Press A Press B 1 $120,000 $250,000 $210,000 2 120,000 270,000 210,000 3 120,000 300,000 210,000 4 120,000 330,000 210,000 5 120,000 370,000 210,000
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 lowrisk operating cash inflows of press B. What impact does that have on your recommendation?