This approach is appropriate for a firm whose stock is widely traded and for which there is very little chance of bankruptcy. (The probability of bankruptcy is a function of total risk, not just systematic risk.)
Just as the beta (systematic risk) of a portfolio of securities can be computed as the weighted average of the individual security betas, a firm may be considered as a portfolio of assets, each having its own beta. From this perspective, the systematic risk of the firm is simply the weighted average of the systematic risk of the individual assets.
The All-Equity Case
For example, consider the security market line shown in Figure. The firm has a beta of 1.2 and is financed exclusively with internally generated equity capital. The market risk premium is 7 percent.When considering projects of average risk —that is, projects that are highly correlated with the firm’s returns on its existing assets and that have a beta similar to the firm’s beta (1.2) —the firm should use the computed 13.4 percent cost of equity, or 5% + 1.2 (7%), from Figure. When considering projects having estimated betas different from 1.2, it should use an equity discount rate equal to the required return calculated from the security market line.
For example, if a project’s estimated beta is 1.7 and the risk-free rate is 5 percent, the project’s required equity return would be 16.9 percent, or 5% + 1.7 (7%), and this would be used as the risk-adjusted discount rate for that project, assuming the project is financed with 100 percent equity.
The Equity and Debt Case
Next, we develop a procedure for computing the risk -adjusted discount rate for projects financed with both debt and equity. To better understand the material in this section, we briefly introduce the concept of a weighted cost of capital, which is developed more extensively in Chapter. At this point, it is only necessary to recognize that the required return on the project discussed in this section reflects the project’s equity return requirement and the debt return requirement for the funds expected to be used to finance the project. Consider the example of Vulcan Industries,with a current capital structure consisting of 50 percent debt and 50 percent equity.
Vulcan is considering expanding into a new line of business and wants to compute the rate of return that will be required on projects in this area. Vulcan has determined that the debt capacity associated with projects in its new business line is such that a capital structure consisting of 40 percent debt and 60 percent common equity is appropriate to finance these new projects.Vulcan’s company beta has been estimated to be 1.3, but the Vulcan management does not believe that this beta risk is appropriate for the new business line. Vulcan’s managers must estimate the beta risk appropriate for projects in this new line of business and then determine the risk -adjusted return requirement on these projects.
Because the beta risk of projects in this new business line is not directly observable, Vulcan’s managers have decided to rely on surrogate market information. They have identified a firm, Olympic Materials, that competes exclusively in the line of business into which Vulcan proposes expanding. The beta of Olympic has been estimated to be 1.50.
Risk-Adjusted Discount Rates and the SML
Recall from previous Chapter that a firm’s beta is computed as the slope of its characteristic line and that actual security returns are used in the computations. Accordingly, a firm’s computed beta is a measure of both its business risk and its financial risk.When a beta is computed for a firm such as Olympic, it reflects both the business and financial risk of that firm.
To determine the beta associated with Vulcan’s proposed new line of business using the observed beta from another firm (Olympic) that competes exclusively in that business line, it is necessary to convert the observed beta, often called a leveraged beta, bl, into an unleveraged, or pure project beta, bu. This unleveraged beta can then be releveraged to reflect the amount of debt capacity appropriate for this type of project and that will be used by Vulcan to finance it. The following equation can be used to convert a leveraged beta into an unleveraged, or pure project, beta:βu = βl/1 + (1 – T) (B/E)
where βu is the unleveraged beta for a project or firm, bl is the leveraged beta for a project or firm, B is the market value of the firm’s debt, E is the market value of the firm’s equity, and T is the firm’s marginal tax rate.
The use of this equation can be illustrated for the Vulcan Materials example. The beta, bl, for Olympic has been computed to be 1.50. Olympic has a capital structure consisting of 20 percent debt and 80 percent common equity and a tax rate of 35 percent. Substituting these values into Equation yieldsβu = 1.50/1 + (1 – 0.35) (0.25) = 1.29
The unleveraged, or pure project beta for the proposed new line of business of Vulcan is estimated to be 1.29. Vulcan intends to finance this new line of business with a capital structure consisting of 40 percent debt and 60 percent common equity. In addition, Vulcan’s tax rate is 40 percent. Equation can be rearranged to compute the leveraged beta associated with this new line of business, given Vulcan’s proposed target capital structure for the project:βl = βu [1 + (1 – T)(B/E)] = 1.29[1 + (1 – 0.4)(0.667)] = 1.81
With a risk-free rate of 5 percent and a market risk premium of 7 percent, the required return on the equity portion of the proposed new line of business is computed from the security market line aske = 5% + 1.81(7%) = 17.7%
If the after-tax cost of debt, ki , used to finance the new line of business is 8 percent, the riskadjusted required return, ka*, on the new line of business, given the proposed capital structure of 40 percent debt and 60 percent equity, is a weighted average of the marginal, after-tax debt and equity costs, orka* = 0.4(8%) + 0.6(17.7%) = 13.8%
Therefore, the risk-adjusted required rate of return on the proposed new line of business for Vulcan is 13.8 percent. This number reflects both the pure project risk and the financial risk associated with the project as Vulcan anticipates financing it. Equations provide only an approximation of the effect of leverage on beta.
Capital market imperfections, such as the existence of risky debt and uncertainty regarding future levels of debt, introduce error into the beta adjustments just presented. Hence, this procedure should be used with caution. This general procedure is used by many different firms, including Boeing Corporation.
Special Elements of Capital Budgeting Risk
The techniques of risk analysis presented in this chapter will serve a firm well whether it operates only in the United States or multinationally. However, managers of multinational firms need to be aware of special elements of risk when investing abroad. When evaluating a capital expenditure to be made in another country, the parent firm must be concerned with the cash flows that can be expected to be received by the parent —not the cash flows that will accrue to the overseas subsidiary making the investment. There are several reasons for focusing on cash flows to the parent.
First, the host country might block the subsidiary from remitting funds back to the parent. Hence, these “captive” funds are not available to the parent for reinvestment in projects offering the highest rate of return. Second, the parent needs to be concerned with the prospect that its assets in foreign subsidiaries could be taken by the host government with inadequate or no compensation.Third, the parent must consider exchange rate risk between the host country’s currency and the dollar.
Related to exchange rate risk is the higher risk of inflation in many countries, particularly developing countries. The risk of highly volatile inflation and the ability of a firm to protect itself from this risk adds additional uncertainty to investments made abroad. Finally, more uncertainty may be associated with tax rates in the host country than is typical in the United States. Each of these factors affects the risk of the cash flows that can be expected from investments in other countries. Although multinational firms predominantly use standard capital budgeting procedures, such as NPV and IRR, to evaluate their investments abroad, there is evidence that many multinational firms also use the risk analysis techniques discussed in this chapter.
A recent study of the capital budgeting practices of affiliates of U.S.–based multinational firms found that sensitivity analysis and simulation are widely used for assessing project risk.a In addition, some financial managers reported that they relied more heavily on their own personal feelings about political and economic events in the host country than on quantitative methods to evaluate project risk.
Johnson & Johnson and Proprietary Competitive Informationa
During the 1970s, Johnson & Johnson’s (J&J) plaster bandage roll dominated the market for casting materials. In 1980, 3M Company introduced a stronger and lighter fiberglass cast.The early version of this product had some initial problems that 3M resolved by 1985.At that time, 3M was set to mount a major challenge to J&J’s leadership in the casting market.
In 1985 a disgruntled contract employee at 3M, Philip Stegora, sent samples of the new casting tape to four rival firms, including J&J. He offered to explain the new technology to anyone who contacted him through a Minneapolis post office box and agreed to pay him $20,000. None of the competitors accepted the offer (nor did they report it to 3M). However, Skip Klintworth, Jr., then the CEO of a small castmaker in Tulsa, heard about the offer from colleagues at one of the four firms that were contacted. He tipped off the FBI. By 1987 Stegora was tracked down and convicted of mail fraud and transporting stolen property across state lines.
The story does not end with Stegora’s conviction. Although none of the competitors accepted Stegora’s offer, J&J did perform chemical tests on the samples it received and used this information in developing its own competitive products. Although the evidence indicates that J&J’s use of this information was largely unintentional, in 1991 J&J was ordered to pay 3M $116.3 million for infringing on its patents and misappropriating trade secrets.This case raises questions about the appropriate response of a firm when it is offered stolen trade secrets. What actions do you think J&J and the other three firms should have taken when they received the stolen property from Stegora?
Computing the Risk-Adjusted Net Present Value
Suppose a company is considering a project whose net investment is $50,000 with expected cash inflows of $10,000 per year for 10 years. Using Equation , as shown in Table , the project’s NPV is $– 1,670 when evaluated at a risk -adjusted discount rate (ka*)and $6,500 when evaluated at the weighted average cost of capital (ka). Assuming that the 16 percent RADR figure has been determined correctly by using the security market line with an accurate beta value, the project should not be accepted even though its NPV, calculated using the company’s weighted cost of capital, is positive. This new product project is similar to Project .
The new product project discussed in the previous paragraph has an internal rate of return of about 15 percent, compared to its 16 percent required return. Therefore, the project should be rejected, according to the IRR decision rule.When the IRR technique is used, the RADR given by the SML frequently is called the hurdle rate. Some finance practitioners use the term hurdle rate to describe any risk-adjusted discount rate. Figure illustrates the difference between the use of a single discount rate, the weighted cost of capital,9 for all projects regardless of risk level and a discount rate based on the security market line for each project.
In the example shown in Figure, Projects 1, 2, 3, and 4 are being evaluated by the firm. Using the weighted cost of capital approach,
Calculation of NPV at Weighted Average Cost of Capital and Risk-
The firm would adopt Projects 3 and 4. However, if the firm considered the differential levels of systematic risk for the four alternatives, it would accept Projects 1 and 3 and reject Projects 2 and 4. In general, the risk-adjusted discount rate approach is considered preferable to the weighted cost of capital approach when the projects under consideration differ significantly in their risk characteristics.
Risk-Adjusted Discount Rate Versus Weighted Cost of Capital
The one problem remaining with this suggested procedure involves the determination of beta values for individual projects. Thus far, the most workable approach available is the use of surrogate market information, as illustrated in the Vulcan Industries example. For example, if an aluminum firm is considering investing in the leisure -time product industry, the beta for this new project could be computed using the average beta for a sample of firms engaged principally in the leisure product industry.
Although the beta for the aluminum firm might be 1.3—resulting in a required equity return on projects of average risk of 14.1 percent, or 5% + (1.3 *7%) —this would not be the appropriate rate for leisure product projects. Assuming a beta of 0.9 for leisure product firms, the leisure product projects would be required to earn an equity return of only percent, or 5% + (0.9*7%), because of the lower average level of systematic risk associated with leisure product projects.
This assumes that the leisure product projects are financed in the same manner as the firms used to generate the surrogate betas. Otherwise, the beta adjustment procedure in Equations must be used.
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Financial Management Tutorial
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