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Question: All these cost of capital formulas—which ones do financial managers actually use?

Answer: The after-tax weighted-average cost of capital, most of the time. WACC is estimated for the company, or sometimes for an industry. We recommend industry WACCs when data are available for several closely comparable firms. The firms should have similar assets, operations, business risks, and growth opportunities.

Of course, conglomerate companies, with divisions operating in two or more unrelated industries, should not use a single company or industry WACC. Such firms should try to estimate a different industry WACC for each operating division.

Question: But WACC is the correct discount rate only for "average" projects. What if the project's financing differs from the company's or industry's?

Answer: Remember, investment projects are usually not separately financed. Even when they are, you should focus on the project's contribution to the firm's overall debt capacity, not on its immediate financing. (Suppose it's convenient to raise all the money for a particular project with a bank loan. That doesn't mean the project itself supports 100 percent debt financing. The company is borrowing against its existing assets as well as the project.)

But if the project's debt capacity is materially different from the company's existing assets, or if the company's overall debt policy changes, WACC should be adjusted. The adjustment can be done by the three-step procedure explained in Section 19.3.

Question: Could we do one more numerical example?

Answer: Sure. Suppose that WACC has been estimated as follows at a 30 percent debt ratio:

What is the correct discount rate at a 50 percent debt ratio?

First, let's repeat the three-step procedure.

Step 1. Calculate the opportunity cost of capital.

r = rDD/V + rEE/V = .09(.3) + .15(.7) = .132 or 13.2%

Step 2. Calculate the new costs of debt and equity. The cost of debt will be higher at 50 percent debt than 30 percent. Say it is rD = .095. The new cost of equity is rE = r + (r - rD) D/E

CHAPTER 19 Financing and Valuation 549

Step 3. Recalculate WACC.

= .095(1 - .35)(.5) + .169(.5) = .1154, or about 11.5%

Question: How do I use the capital asset pricing model to calculate the after-tax weighted-average cost of capital?

Answer: First plug the equity beta into the capital asset pricing formula to calculate rE, the expected return to equity. Then use this figure, along with the aftertax cost of debt and the debt-to-value and equity-to-value ratios, in the WACC formula. We covered this in Chapter 9. The only change here is use of the after-tax cost of debt, rD(1 - Tc).

Of course the CAPM is not the only way to estimate the cost of equity. For example, you might be able to use arbitrage pricing theory (APT—see Section 8.4) or the dividend-discount model (see Section 4.3).

Question: But suppose I do use the CAPM? What if I have to recalculate the equity beta for a different debt ratio?

Answer: The formula for the equity beta is

where pE is the equity beta, pA is the asset beta, and pD is the beta of the company's debt.

Question: Can I use the capital asset pricing model to calculate the asset beta and the opportunity cost of capital?

Answer: Sure. We covered this in Chapter 9. The asset beta is a weighted average of the debt and equity betas:29

Suppose you needed the opportunity cost of capital r. You could calculate pA and then r from the capital asset pricing model.

Question: I think I understand how to adjust for differences in debt capacity or debt policy. How about differences in business risk?

Answer: If business risk is different, then r, the opportunity cost of capital, is different.

Figuring out the right r for an unusually safe or risky project is never easy. Sometimes the financial manager can use estimates of risk and expected return for companies similar to the project. Suppose, for example, that a traditional pharmaceutical company is considering a major commitment to biotech research. The financial manager could pick a sample of biotech companies, estimate their

29This formula assumes Financing Rule 2. If debt is fixed, taxes complicate the formulas. For example, if debt is fixed and permanent, and only corporate taxes are considered, the formula for ßE changes to

550 PART V Dividend Policy and Capital Structure average beta and cost of capital, and use these estimates as benchmarks for the biotech investment.

But in many cases it's difficult to find a good sample of matching companies for an unusually safe or risky project. Then the financial manager has to adjust the opportunity cost of capital by judgment.30 Section 9.5 may be helpful in such cases.

Question: Let's go back to the cost of capital formulas. The tax rates are confusing. When should I use Tc and when T*?

Answer: Always use Tc, the marginal corporate tax rate, (1) when calculating WACC as a weighted average of the costs of debt and equity and (2) when discounting safe, nominal cash flows. In each case the discount rate is adjusted only for corporate taxes.31

APV in principle calls for T*, the net tax saving per dollar of interest paid by the firm. This depends on the effective personal tax rates on debt and equity income. T* is almost surely less than Tc, but it is very difficult to pin down the numerical difference. Therefore in practice Tc is almost always used as an approximation.

Question: When do I need adjusted present value (APV)?

Answer: The WACC formula picks up only one financing side effect: the value of interest tax shields on debt supported by a project. If there are other side effects—subsidized financing tied to a project, for example—you should use APV.

You can also use APV to show the value of interest tax shields:

where base-case NPV assumes all-equity financing. But it's usually easier to do this calculation in one step, by discounting project cash flows at an adjusted cost of capital (usually WACC). Remember, though, that discounting by WACC usually assumes Financing Rule 2, that is, debt rebalanced to a constant fraction of future project value. If this financing rule is not right, you may need APV to calculate PV(tax shield), as we did for the solar heater project in Table 19.1.32

Suppose, for example, that you are analyzing a company just after a leveraged recapitalization. The company has a very high initial debt level but plans to pay down the debt as rapidly as possible. APV could be used to obtain an accurate valuation.

30The judgment may be implicit. That is, the manager may not explicitly announce that the discount rate for a high-risk project is, say, 2.5 percentage points above the standard rate. But the project will not be approved unless it offers a higher-than-standard rate of return.

31Any effects of personal income taxes are reflected in rD and rE, the rates of return demanded by debt and equity investors.

32Having read Section 19.5, you may be wondering why we did not discount at the after-tax borrowing rate in Table 19.1. The answer is that we wanted to simplify and take one thing at a time. If debt is fixed and the odds of financial distress are low, interest tax shields are safe, nominal flows, and there is a case for using the after-tax rate. Doing so assumes that the firm will, or can, take out an additional loan with debt service exactly covered by the interest tax shields.

Investment decisions always have side effects on financing: Every dollar spent has to be raised somehow. Sometimes the side effects are irrelevant or at least unimportant. In an ideal world with no taxes, transaction costs, or other market imperfections, only investment decisions would affect firm value. In such a world firms could analyze all investment opportunities as if they were all-equity-financed. Firms would decide which assets to buy and then worry about getting the money to pay for them. No one making investment decisions would worry about where the money might come from because debt policy, dividend policy, and all other financing choices would have no impact on stockholders' wealth.

Side effects cannot be ignored in practice. There are two ways to take them into account. You can calculate NPV by discounting at an adjusted discount rate, or you can discount at the opportunity cost of capital and then add or subtract the present value of financing side effects. The second approach is called adjusted present value, or APV.

The most commonly used adjusted discount rate is the after-tax weighted-average cost of capital, or WACC:

Here rD and rE are the expected rates of return demanded by investors in the firm's debt and equity securities, respectively; D and E are the current market values of debt and equity; and V is the total market value of the firm (V = D + E).

Strictly speaking, this formula works only for projects that are carbon copies of the existing firm—projects with the same business risk that will be financed to maintain the firm's current, market debt ratio. But firms can use WACC as a benchmark rate to be adjusted for differences in business risk or financing. We suggested a three-step procedure for adjusting a company's WACC for differences between project and company debt ratios.

Discounting project cash flows at the WACC assumes that debt is rebalanced every period to keep a constant debt-to-market-value ratio. The amount of debt supported by a project is supposed to rise or fall with the project's after-the-fact success or failure. We called this Financing Rule 2. The WACC formula also assumes that financing matters only because of interest tax shields. When this or other assumptions are violated, only APV will give an absolutely correct answer.

APV is, in concept at least, simple. First calculate the present value of the project as if there are no important side effects. Then adjust present value to calculate the project's total impact on firm value. The rule is to accept the project if APV is positive:

Accept project if APV = base-case NPV

present value of financing > 0 side effects

 NUMMARY

The base-case NPV is the project's NPV computed assuming all-equity financing and perfect capital markets. Think of it as the project's value if it were set up as a separate mini-firm. You would compute the mini-firm's value by forecasting its

PART V Dividend Policy and Capital Structure cash flows and discounting at the opportunity cost of capital for the project. The cash flows should be net of the taxes that an all-equity-financed mini-firm would pay.

Financing side effects are evaluated one by one and their present values are added to or subtracted from base-case NPV. We looked at several cases:

1. Issue costs. If accepting the project forces the firm to issue securities, then the present value of issue costs should be subtracted from base-case NPV.

2. Interest tax shields. Debt interest is a tax-deductible expense. Most people believe that interest tax shields contribute to firm value. Thus a project that prompts the firm to borrow more generates additional value. The project's APV is increased by the present value of interest tax shields on debt the project supports.

3. Special financing. Sometimes special financing opportunities are tied to project acceptance. For example, the government might offer subsidized financing for socially desirable projects. You simply compute the present value of the financing opportunity and add it to base-case NPV.

Remember not to confuse contribution to corporate debt capacity with the immediate source of funds for investment. For example, a firm might, as a matter of convenience, borrow \$1 million for a \$1 million research program. But the research would be unlikely to contribute \$1 million in debt capacity; a large part of the \$1 million new debt would be supported by the firm's other assets.

Also remember that debt capacity is not meant to imply an absolute limit on how much the firm can borrow. The phrase refers to how much it chooses to borrow. Normally the firm's optimal debt level increases as its assets expand; that is why we say that a new project contributes to corporate debt capacity.

Calculating APV may require several steps: one step for base-case NPV and one for each financing side effect. Many firms try to calculate APV in a single calculation. They do so by the following procedure: After-tax cash flows are forecasted in the usual way—that is, as if the project is all-equity-financed. But the discount rate is adjusted to reflect the financing side effects. If the discount rate is adjusted correctly, the result is APV:

NPV at adjusted discount rate

NPV at opportunity cost of capital present value of financing side effects

WACC is the leading example of an adjusted discount rate.

This chapter is almost 100 percent theory. The theory is difficult. If you think you understand all the formulas, assumptions, and relationships on the first reading, we suggest psychiatric assistance. We can, however, offer one simple, bullet-proof, easy-to-remember rule: Discount safe, nominal cash flows at the after-tax borrowing rate.

The adjusted-present-value rule was developed in:

S. C. Myers: "Interactions of Corporate Financing and Investment Decisions—Implications for Capital Budgeting," Journal of Finance, 29:1-25 (March 1974).

The Harvard Business Review has published a popular account of APV:

T. A. Luehrman, "Using APV: A Better Tool for Valuing Operations," Harvard Business Review 75:145-154 (May-June 1997).

There have been dozens of articles on the weighted-average cost of capital and other issues discussed in this chapter. Here are two:

J. Miles and R. Ezzell: "The Weighted Average Cost of Capital, Perfect Capital Markets, and Project Life: A Clarification," Journal of Financial and Quantitative Analysis, 15:719-730 (September 1980).

R. A. Taggart, Jr.: "Consistent Valuation and Cost of Capital Expressions with Corporate and Personal Taxes," Financial Management, 20:8-20 (Autumn 1991).

The valuation rule for safe, nominal cash flows is developed in:

R. S. Ruback: "Calculating the Market Value of Risk-Free Cash Flows," Journal of Financial Economics, 15:323-339 (March 1986).

1. Calculate the weighted-average cost of capital (WACC) for Federated Junkyards of America, using the following information:

• Debt: \$75,000,000 book value outstanding. The debt is trading at 90 percent of par. The yield to maturity is 9 percent.

• Equity: 2,500,000 shares selling at \$42 per share. Assume the expected rate of return on Federated's stock is 18 percent.

• Taxes: Federated's marginal tax rate is Tc = .35.

What are the key assumptions underlying your calculation? For what type of project would Federated's weighted-average cost of capital be the right discount rate?

2. Suppose Federated Junkyards decides to move to a more conservative debt policy. A year later its debt ratio is down to 15 percent (D/V = .15). The interest rate has dropped to 8.6 percent. Recalculate Federated's WACC under these new assumptions. The company's business risk, opportunity cost of capital, and tax rate have not changed. Use the three-step procedure explained in Section 19.3.

3. True or false? Use of the WACC formula assumes a. A project supports a fixed amount of debt over the project's economic life.

b. The ratio of the debt supported by a project to project value is constant over the project's economic life.

c. The firm rebalances debt, each period, keeping the debt-to-value ratio constant.

4. What is meant by the flow-to-equity valuation method? What discount rate is used in this method? What assumptions are necessary for this method to give an accurate valuation?

5. True or false? The APV method a. Starts with a base-case value for the project.

b. Calculates the base-case value by discounting project cash flows, forecasted assuming all-equity financing, at the WACC for the project.

c. Is especially useful when debt is to be paid down on a fixed schedule.

d. Can be used to calculate an adjusted discount rate for a company or a project.

6. Explain the difference between Financing Rules 1 (debt fixed) and 2 (debt rebalanced).

7. What is meant by financing "side effects" in an APV valuation? Give at least three examples of side effects encountered in practice.

8. A project costs \$1 million and has a base-case NPV of exactly zero (NPV = 0). What is the project's APV in the following cases?

a. If the firm invests, it has to raise \$500,000 by stock issue. Issue costs are 15 percent of net proceeds.

b. The firm has ample cash on hand. But if it invests, it will have access to \$500,000 of debt financing at a subsidized interest rate. The present value of the subsidy is \$175,000.

QUIZ

Brealey-Meyers: Principles of Corporate Finance, Seventh Edition

V. Dividend Policy and Capital Structure

19. Financing and Valuation

© The McGraw-H Companies, 2003

PART V Dividend Policy and Capital Structure c. If the firm invests, its debt capacity increases by \$500,000. The present value of interest tax shields on this debt is \$76,000.

9. Whispering Pines, Inc., is all-equity-financed. The expected rate of return on the company's shares is 12 percent.

a. What is the opportunity cost of capital for an average-risk Whispering Pines investment?

b. Suppose the company issues debt, repurchases shares, and moves to a 30 percent debt-to-value ratio (D/V = .30). What will the company's weighted-average cost of capital be at the new capital structure? The borrowing rate is 7.5 percent and the tax rate is 35 percent.

Consider the APV of the solar heater project, as calculated in Table 19.1. How would the APV change if the net tax shield per dollar of interest were not Tc = .35, but T = .10? Consider a project lasting one year only. The initial outlay is \$1,000 and the expected inflow is \$1,200. The opportunity cost of capital is r = .20. The borrowing rate is rD = .10, and the net tax shield per dollar of interest is T = Tc = .35.

a. What is the project's base-case NPV?

b. What is its APV if the firm borrows 30 percent of the project's required investment?

12. The WACC formula seems to imply that debt is "cheaper" than equity—that is, that a firm with more debt could use a lower discount rate. Does this make sense? Explain briefly.

13. What discount rate should be used to value safe, nominal cash flows? Explain briefly.

14. The U.S. government has settled a dispute with your company for \$16 million. It is committed to pay this amount in exactly 12 months. However, your company will have to pay tax on the award at a marginal tax rate of 35 percent. What is the award worth? The one-year Treasury rate is 5.5 percent.

PRACTICE

### QUESTIONS

Table 19.2 shows a book balance sheet for the Wishing Well Motel chain. The company's long-term debt is secured by its real estate assets, but it also uses short-term bank financing. It pays 10 percent interest on the bank debt and 9 percent interest on the secured debt. Wishing Well has 10 million shares of stock outstanding, trading at \$90 per share. The expected return on Wishing Well's common stock is 18 percent.

Calculate Wishing Well's WACC. Assume that the book and market values of Wishing Well's debt are the same. The marginal tax rate is 35 percent. Suppose Wishing Well is evaluating a new motel and resort on a romantic site in Madison County, Wisconsin. Explain how you would forecast the after-tax cash flows for this project. (Hints: How would you treat taxes? Interest expense? Changes in working capital?)

To finance the Madison County project, Wishing Well will have to arrange an additional \$80 million of long-term debt and make a \$20 million equity issue. Underwriting fees,

 TABLE 19.2 Cash, marketable securities 100 Accounts payable 120 Balance sheet for Inventory 50 Bank loan 280 Wishing Well, Inc. Accounts receivable 200 Current liabilities 400 (figures in \$ millions). Current assets 350 Real estate 2,100 Long-term debt 1,800 Other assets 150 Equity 400 Total 2,600 Total 2,600

Brealey-Meyers: Principles of Corporate Finance, Seventh Edition

V. Dividend Policy and Capital Structure

19. Financing and Valuation

© The McGraw-H Companies, 2003

CHAPTER 19 Financing and Valuation

Cash and marketable

securities

1,500

Short-term debt

75,600

Accounts receivable

120,000

Accounts payable

62,000

Inventories

125,000

Current liabilities

137,600

Current assets

246,500

Property, plant,

Long-term debt

208,600

and equipment

302,000

Deferred taxes

45,000

Other assets

89,000

Shareholders' equity

246,300

Total

637,500

Total

Simplified book balance sheet for Rensselaer Felt (figures in \$ thousands).

TABLE 19.3

Simplified book balance sheet for Rensselaer Felt (figures in \$ thousands).

spreads, and other costs of this financing will total \$4 million. How would you take this into account in valuing the proposed investment?

4. Table 19.3 shows a simplified balance sheet for Rensselaer Felt. Calculate this company's weighted-average cost of capital. The debt has just been refinanced at an interest rate of 6 percent (short term) and 8 percent (long term). The expected rate of return on the company's shares is 15 percent. There are 7.46 million shares outstanding, and the shares are trading at \$46. The tax rate is 35 percent.

5. How will Rensselaer Felt's WACC and cost of equity change if it issues \$50 million in new equity and uses the proceeds to retire long-term debt? Assume the company's borrowing rates are unchanged. Use the three-step procedure from Section 19.3.

6. Look one more time at practice question 4. Renssalaer Felt's pretax operating income is \$100.5 million. Assume for simplicity that this figure is expected to remain constant forever. Value the company by the flow-to-equity method.

7. Rapidly growing companies may have to issue shares to finance capital expenditures. In doing so, they incur underwriting and other issue costs. Some analysts have tried to adjust WACC to account for these costs. For example, if issue costs are 8 percent of equity issue proceeds, and equity issues account for all of equity financing, the cost of equity might be divided by 1 - .08 = .92. This would increase a 15 percent cost of equity to 15/.92 = 16.3 percent.

Explain why this sort of adjustment is not a smart idea. What is the correct way to take issue costs into account in project valuation?

8. Digital Organics (DO) has the opportunity to invest \$1 million now (t = 0) and expects after-tax returns of \$600,000 in t = 1 and \$700,000 in t = 2. The project will last for two years only. The appropriate cost of capital is 12 percent with all-equity financing, the borrowing rate is 8 percent, and DO will borrow \$300,000 against the project. This debt must be repaid in two equal installments. Assume debt tax shields have a net value of \$.30 per dollar of interest paid. Calculate the project's APV using the procedure followed in Table 19.1.

9. You are considering a five-year lease of office space for R&D personnel. Once signed, the lease cannot be canceled. It would commit your firm to six annual \$100,000 payments, with the first payment due immediately. What is the present value of the lease if your company's borrowing rate is 9 percent and its tax rate is 35 percent? Note: The lease payments would be tax-deductible.

10. Consider another perpetual project like the crusher described in Section 19.1. Its initial investment is \$1,000,000, and the expected cash inflow is \$85,000 a year in perpetuity. The opportunity cost of capital with all-equity financing is 10 percent, and the project allows the firm to borrow at 7 percent. Assume the net tax advantage to borrowing is \$.35 per dollar of interest paid (T* = Tc = .35).

Use APV to calculate this project's value.

PART V Dividend Policy and Capital Structure

a. Assume first that the project will be partly financed with \$400,000 of debt and that the debt amount is to be fixed and perpetual.

b. Then assume that the initial borrowing will be increased or reduced in proportion to changes in the future market value of this project.

Explain the difference between your answers to (a) and (b).

Suppose the project described in practice question 10 is to be undertaken by a university. Funds for the project will be withdrawn from the university's endowment, which is invested in a widely diversified portfolio of stocks and bonds. However, the university can also borrow at 7 percent. The university is tax exempt.

The university treasurer proposes to finance the project by issuing \$400,000 of perpetual bonds at 7 percent and by selling \$600,000 worth of common stocks from the endowment. The expected return on the common stocks is 10 percent. He therefore proposes to evaluate the project by discounting at a weighted-average cost of capital, calculated as

400,000

600,000 1,000,000

What's right or wrong with the treasurer's approach? Should the university invest? Should it borrow? Would the project's value to the university change if the treasurer financed the project entirely by selling common stocks from the endowment? What is meant by an adjusted discount rate (r* in our notation)? In what circumstances would an adjusted discount rate not equal WACC?

The Bunsen Chemical Company is currently at its target debt ratio of 40 percent. It is contemplating a \$1 million expansion of its existing business. This expansion is expected to produce a cash inflow of \$130,000 a year in perpetuity.

The company is uncertain whether to undertake this expansion and how to finance it. The two options are a \$1 million issue of common stock or a \$1 million issue of 20-year debt. The flotation costs of a stock issue would be around 5 percent of the amount raised, and the flotation costs of a debt issue would be around VA percent.

Bunsen's financial manager, Miss Polly Ethylene, estimates that the required return on the company's equity is 14 percent, but she argues that the flotation costs increase the cost of new equity to 19 percent. On this basis, the project does not appear viable.

On the other hand, she points out that the company can raise new debt on a 7 percent yield which would make the cost of new debt percent. She therefore recommends that Bunsen should go ahead with the project and finance it with an issue of long-term debt.

Is Miss Ethylene right? How would you evaluate the project?

Curtis Bog, chief financial officer of Sphagnum Paper Corporation, is reviewing a consultant's analysis of Sphagnum's weighted-average cost of capital. The consultant proposes

= (1 - .35) (.1032 (.552 + .183(.452 = .1192, or about 12%

Mr. Bog wants to check that this calculation is consistent with the capital asset pricing model. He has observed or estimated the following numbers:

Brealey-Meyers: Principles of Corporate Finance, Seventh Edition

V. Dividend Policy and Capital Structure

19. Financing and Valuation

© The McGraw-Hill Companies, 2003

CHAPTER 19 Financing and Valuation

Betas

Expected market risk premium (rm - rf) Risk-free rate of interest (rf)

.085

### 9 percent

Note: We suggest you simplify by ignoring personal income taxes and assuming that the promised and expected rates of returns on Sphagnum debt are equal.

15. Nevada Hydro is 40 percent debt-financed and has a weighted-average cost of capital of 9.7 percent:

Banker's Tryst Company is advising Nevada Hydro to issue \$75 million of preferred stock at a dividend yield of 9 percent. The proceeds would be used to repurchase and retire common stock. The preferred issue would account for 10 percent of the preis-sue market value of the firm.

Banker's Tryst argues that these transactions would reduce Nevada Hydro's WACC to 9.4 percent:

WACC = (1 - .35)(.085)(.40) + .09(.10) + .125(.50) = .094, or 9.4%

Do you agree with this calculation? Explain.

16. Sometimes APV is particularly useful in international capital investment decisions. What kinds of tax or financing side effects are encountered in international projects?

17. Consider a different financing scenario for the solar water heater project discussed in Section 19.4. The project requires \$10 million and has a base-case NPV of \$170,000. Suppose the firm happens to have \$5 million banked that could be used for the project.

The government, eager to encourage solar energy, offers to help finance the project by lending \$5 million at a subsidized rate of 5 percent. The loan calls for the firm to pay the government \$647,500 annually for 10 years (this amount includes both principal and interest).

a. What is the value of being able to borrow from the government at 5 percent? Assume the company's normal borrowing rate is 8 percent and the corporate tax rate is 35 percent.

b. Suppose the company's normal debt policy is to borrow 50 percent of the book value of its assets. It calculates the present value of interest tax shields by the procedure shown in Table 19.1 and includes this present value in APV. Should it do so here, given the government's offer of cheap financing?

18. Table 19.4 is a simplified book balance sheet for Phillips Petroleum in June 2001. Other information:

Number of outstanding shares (N) 256.2 million

Price per share (P) \$59 Beta based on 60 monthly returns, against the S&P Composite: p = .66 Interest rates

Treasury bills 3.5%

20-year Treasury bonds 5.8 New issue rate for Phillips assuming straight long-term debt 7.4

Marginal tax rate 35%

 TABLE 19.4 Current assets 2,202 Current liabilities 2,780 Simplified book balance sheet for Net property, plant, and equipment 15,124 Long-term debt 6,268 Phillips Petroleum, Investments and other assets 3,428 Deferred taxes 2,144 June 2001 (figures in Other liabilities 2,510 \$ millions). Shareholders' equity 7,052 Total 20,754 Total 20,754

a. Calculate Phillips's WACC. Use the capital asset pricing model and the data given above. Make additional assumptions and approximations as necessary.

b. What would Phillips's WACC be if it moved to and maintained a debt—market value ratio (D/V) of 25 percent?

19. In question 18 you calculated a WACC for Phillips Petroleum. Phillips could also use an industry WACC. Under what conditions would the industry WACC be the better choice? Explain.

CHALLENGE QUESTIONy

1. In footnote 21 we referred to the Miles-Ezzell formula:

Derive this formula as the adjusted discount rate (r*) for a one-period project. Then show that the formula correctly values projects of any life if the company follows Financing Rule 2.

In Section 19.3 we proposed a three-step procedure for calculating WACC at different debt ratios. The Miles-Ezzell formula can be used for the same purpose. Set up a numerical example and use these two approaches to calculate how WACC changes with financial leverage. Assume T* = Tc. You will get slightly different numerical answers. Why?

Consider a project generating a level, perpetual stream of cash flows. The project is financed at an initial debt-to-value ratio L. The debt is likewise perpetual. But the company follows Financing Rule 1: The dollar amount of debt is kept constant. Derive a formula for the adjusted discount rate r* to fit these assumptions.33 What does this formula imply for (a) the difference between WACC and the opportunity cost of capital r and (b) the formulas for levering and relevering the cost of equity? Financing Rule 2 ties the level of future interest tax shields to the future value of the project or company. That means the interest tax shields are risky and worth less than if the company followed Financing Rule 1. Does that mean that Financing Rule 1 is better for stockholders?

33Here you are following in MM's footsteps. See F. Modigliani and M. H. Miller, "Corporate Income Taxes and the Cost of Capital: A Correction," American Economic Review 53 (June 1963), pp. 433-443, and "Some Estimates of the Cost of Capital to the Electric Utility Industry," American Economic Review 56 (June 1966), pp. 333-391.

Some materials on cash and stock dividends is ValuePro provides software and data for estimat-provided by: ing WACCs:

www.e-analytics.com

www.dripcentral.com (information on dividend reinvestment plans)

John Graham's website contains material on capital structure:

www.valuepro.net

PART FIVE

RELATED

WEBSITES

www.duke.edu/~jgraham

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### Responses

• Prudenzio
HOw will Rensselaer Felt's WACC and cost of equity?
7 years ago
• Fortunata
How will Rensselaer Felt's WACC and cost of equity change if it issues \$50 million in new equity?
7 years ago