Principles of Managerial Finance

Resource: Principles of Managerial Finance, Ch. 12

Complete the following problems in Ch. 12:

  • P-12-1
  • P12-3
  • P12-6
  • P12-17
  • P12-19



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 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.


12–1Are 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 −$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.


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

NPV equals open parenthesis CF over r close parenthesis × open square bracket 1 − 1 over open parenthesis 1 plus r close parenthesis to the n power close square bracket − CF sub 0 is greater than $0 (12.1)

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

breakeven cash inflow

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

My Finance Lab Financial Calculator

Calculator use Recognizing that the initial investment (CF0) is the present value (PV), we can use the calculator inputs shown at the left to find the breakeven cash inflow (CF), which is an ordinary annuity (PMT).

Spreadsheet use The breakeven cash inflow also can be calculated as shown on the following Excel spreadsheet.

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

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

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

The example clearly identifies risk as it is related to the chance that a project is acceptable, but it does not address the issue of cash flow variability. Even though project B has a greater chance of loss than project A, it might result in higher potential NPVs. Recall that it is the combination of risk and return that determines value. Similarly, the benefit of a capital expenditure and its impact on the firm’s value must be viewed in light of both risk and return. The analyst must therefore consider the variability of cash inflows and NPVs to assess project risk and return fully.

2. Normal distributions are commonly used to develop the concept of the probability of success, that is, of a project having a positive NPV. The reader interested in learning more about this technique should see any second- or MBA-level managerial finance text.


Save time and excel in your essays and homework. Hire an essay writer for the best price for the top-notch grade you deserve.
275 words per page

You essay will be 275 words per page. Tell your writer how many words you need, or the pages.

12 pt Times New Roman

Unless otherwise stated, we use 12pt Arial/Times New Roman as the font for your paper.

Double line spacing

Your essay will have double spaced text. View our sample essays.

Any citation style

APA, MLA, Chicago/Turabian, Harvard, our writers are experts at formatting.

We Accept
Image 3