Resource: Principles of Managerial Finance, Ch. 12

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Complete the following problems in Ch. 12:P-12-1P12-3P12-6P12-17P12-19


12 Risk and Refinements in Capital BudgetingLearning GoalsLG 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 risk-adjusted discount rates (RADRs), portfolio effects, and the practical aspects of RADRs.LG 5 Select the best of a group of unequal-lived, 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 risk-adjust 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 long-term decisions. When making personal financial decisions, you should consider risk in the decision-making process. Simply put, you should demand higher returns for greater risk. Failing to incorporate risk into your financial decision-making 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 state-owned 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 risk-adjusted discount rates to explicitly recognize risk in the analysis of capital budgeting projects. REVIEW QUESTION12–1

Are most mutually exclusive capital budgeting projects equally risky? If you think about a firm as a portfolio of many different kinds of investments, how can the acceptance of a project change a firm’s overall risk?TABLE 12.1 Relevant Cash Flows and NPVs for Bennett Company’s Projects


Project A

Project B

A. Relevant cash flows



Initial investment




Operating cash inflows
















B. Decision technique



NPV @ 10% cost of capitala



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 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


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.TABLE 12.2 Scenario Analysis of Treadwell’s Projects A and BExample 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 risk-averse 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 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.


A statistics-based 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 single-point 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 decision-making 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 QUESTIONS12–2

Define risk in terms of the cash flows from a capital budgeting project. How can determination of the breakeven cash inflow be used to gauge project risk?12–3

Describe how each of the following behavioral approaches can be used to deal with project risk: (a) scenario analysis and (b) simulation. EXCEL REVIEW QUESTION

My Finance Lab12–4

To judge the sensitivity of a project’s NPV, financial managers will often compare a project’s forecasted cash inflows to the breakeven cash flows. Based on the information provided at MFL, develop a spreadsheet to compare forecasted and breakeven cash inflows.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. Long-term 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 host-country 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 risk-adjusted 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 after-tax 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 QUESTION12–5

Briefly explain how the following items affect the capital budgeting decisions of multinational companies: (a) exchange rate risk; (b) political risk; (c) tax law differences; (d)transfer pricing; and (e) a strategic, rather than a strict, financial viewpoint.12.4 Risk-Adjusted 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 risk-adjustment 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 risk-adjusted discount rate.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


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.

risk-adjusted 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 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.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 end-of-year 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 average-risk 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 risk-adjusted net present values (NPVs) for the two stocks:

Although Talor’s calculations indicate that both stock investments are acceptable (NPVs > $0) on a risk-adjusted 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


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)]



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 makingUsing CAPM to Find RADRs

If we assume for a moment that real corporate assets such as computers, machine tools, and special-purpose machinery are traded in efficient markets, the CAPM can be redefined as

rproject j = RF + [βproject j × (rm − RF)]


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.4Example 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 junk-rated 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 5-year dol