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
APV
NPV at opportunity
present value of
discount rate
cost of capital
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.
FURTHER READING
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).
CHAPTER 19 Financing and Valuation
553
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 QUIZ 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.
554PART 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.
10.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?
11.Consider a project lasting one year only. The initial outlay is $1,000 and the expected in-
flow 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
EXCEL
1.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.
2.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?)
3.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,
T A B L E 1 9 . 2
Balance sheet for Wishing Well, Inc. (figures in $ millions).
Cash, marketable securities
100
Accounts payable
120
Inventory
50
Bank loan
280
Accounts receivable
200
Current liabilities
400
Current assets
350
Real estate
2,100
Long-term debt
1,800
Other assets
150
Equity
400
Total
2,600
Total
2,600
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Financing and Valuation
555
T A B L E
1 9 . 3
Cash and marketable
securities
1,500
Short-term debt
75,600
Simplified book
Accounts receivable
120,000
Accounts payable
62,000
balance sheet for
Inventories
125,000
Current liabilities
137,600
Rensselaer Felt
Current assets
246,500
Long-term debt
208,600
(figures in
Property, plant,
$ thousands).
and equipment
302,000
Deferred taxes
45,000
Other assets
89,000
Shareholders’ equity
246,300
Total
637,500
Total
637,500
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 com-
pany’s weighted-average cost of capital. The debt has just been refinanced at an inter- EXCEL est 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.
556PART 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).
11.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
r rD
D
rE
E
V
V
.07 a
400,000
b .10 a
600,000
b
1,000,000
1,000,000
.088, or 8.8%
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?
12.What is meant by an adjusted discount rate (r* in our notation)? In what circumstances would an adjusted discount rate not equal WACC?
13.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 11⁄2 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 81⁄2 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?
14.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
D E
WACC 11 Tc 2rD V rE V
11 .352 1.1032 1.552 .1831.452
.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:
CHAPTER 19 Financing and Valuation
557
Betas
debt .15, equity 1.09
Expected market risk premium (rm rf )
.085
Risk-free rate of interest (rf )
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:
D E
WACC 11 Tc 2rD V rE V
11 .352 1.0852 1.402 .1251.602 .097
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 preissue market value of the firm.
Banker’s Tryst argues that these transactions would reduce Nevada Hydro’s WACC to 9.4 percent:
WACC 11 .3521.08521.402 .091.102 .1251.502.094, 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. Sup-
EXCEL
pose 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,
.66
against the S&P Composite:
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%
558
PART V
Dividend Policy and Capital Structure
T A B L E
1 9 . 4
Current assets
2,202
Current liabilities
2,780
Simplified book
Net property, plant,
balance sheet for
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 QUESTIONS
1. In footnote 21 we referred to the Miles–Ezzell formula:
1 r
r* r LrDT* c1 rD d WACC
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.
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?
3.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 com-
pany 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?
4.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 provided by:
www.e-analytics.com
www.dripcentral.com (information on dividend reinvestment plans)
John Graham’s website contains material on capital structure:
www.duke.edu/~jgraham
ValuePro provides software and data for estimating WACCs:
www.valuepro.net
PART FIVE RELATED WEBSITES
C H A P T E R T W E N T Y
UNDERSTANDING
O P T I O N S
562
FIGURE 20.1(A) SHOWS your payoff if you buy AOL Time Warner (AOL) stock at $55. You gain dollar- for-dollar if the stock price goes up and you lose dollar-for-dollar if it falls. That’s trite; it doesn’t take a genius to draw a 45-degree line.
Look now at panel (b), which shows the payoffs from an investment strategy that retains the upside potential of AOL stock but gives complete downside protection. In this case your payoff stays at $55 even if the AOL stock price falls to $50, $40, or zero. Panel (b)’s payoffs are clearly better than panel (a)’s. If a financial alchemist could turn panel (a) into (b), you’d be willing to pay for the service.
Of course alchemy has its dark side. Panel (c) shows an investment strategy for masochists. You lose if the stock price falls, but you give up any chance of profiting from a rise in the stock price. If you like to lose, or if somebody pays you enough to take the strategy on, this is the strategy for you.
Now, as you have probably suspected, all this financial alchemy is for real. You really can do all the transmutations shown in Figure 20.1. You do them with options, and we will show you how.
But why should the financial manager of an industrial company be interested in options? There are several reasons. First, companies regularly use commodity, currency, and interest-rate options to reduce risk. For example, a meatpacking company that wishes to put a ceiling on the cost of beef might take out an option to buy live cattle. A company that wishes to limit its future borrowing costs might take out an option to sell long-term bonds. And so on. In Chapter 27 we will explain how firms employ options to limit their risk.
Second, many capital investments include an embedded option to expand in the future. For instance, the company may invest in a patent that allows it to exploit a new technology or it may purchase adjoining land that gives it the option in the future to increase capacity. In each case the company is paying money today for the opportunity to make a further investment. To put it another way, the company is acquiring growth opportunities.
Here is another disguised option to invest: You are considering the purchase of a tract of desert land that is known to contain gold deposits. Unfortunately, the cost of extraction is higher than the current price of gold. Does this mean the land is almost worthless? Not at all. You are not obliged to mine the gold, but ownership of the land gives you the option to do so. Of course, if you know that the gold price will remain below the extraction cost, then the option is worthless. But if there is uncertainty about future gold prices, you could be lucky and make a killing.1
If the option to expand has value, what about the option to bail out? Projects don’t usually go on until the equipment disintegrates. The decision to terminate a project is usually taken by management, not by nature. Once the project is no longer profitable, the company will cut its losses and exercise its option to abandon the project. Some projects have higher abandonment value than others. Those that use standardized equipment may offer a valuable abandonment option. Others may actually cost money to discontinue. For example, it is very costly to decommission an offshore oil rig.
We took a peek at these investment options in Chapter 10, and we showed there how to use decision trees to analyze Magna Charter’s options to expand its airline operation or abandon it. In Chapter 22 we will take a more thorough look at these real options.
The other important reason why financial managers need to understand options is that they are often tacked on to an issue of corporate securities and so provide the investor or the company with the flexibility to change the terms of the issue. For example, in Chapter 23 we will show how warrants and
continued
1In Chapter 11 we valued Kingsley Solomon’s gold mine by calculating the value of the gold in the ground and then subtracting the value of the extraction costs. That is correct only if we know that the gold will be mined. Otherwise, the value of the mine is increased by the value of the option to leave the gold in the ground if its price is less than the extraction cost.
