Brealey−Meyers: Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
C H A P T E R N I N E T E E N
FINANCING AND V A L U A T I O N
522
Brealey−Meyers: Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
WE FIRST ADDRESSED problems of capital budgeting in Chapter 2. At that point we said hardly a word about financing decisions; we proceeded under the simplest possible assumption about fi-nancing, namely, all-equity financing. We were really assuming an idealized Modigliani–Miller (MM) world in which all financing decisions are irrelevant. In a strict MM world, firms can analyze real in-vestments as if they are to be all-equity-financed; the actual financing plan is a mere detail to be worked out later.
Under MM assumptions, decisions to spend money can be separated from decisions to raise money. In this chapter we reconsider the capital budgeting decision when investment and financing decisions interact and cannot be wholly separated.
In the early chapters you learned how to value a capital investment opportunity by a four-step procedure:
1. Forecast the project’s incremental after-tax cash flow, assuming the project is entirely equity-financed.
2. Assess the project’s risk.
3. Estimate the opportunity cost of capital, that is, the expected rate of return offered to investors by the equivalent-risk investments traded in capital markets.
4. Calculate NPV, using the discounted-cash-flow formula.
In effect, we were thinking of each project as a mini-firm, and asking, How much would that mini-firm be worth if we spun it off as a separate, all-equity-financed enterprise? How much would investors be willing to pay for shares in the project?
Of course, this procedure rests on the concept of value additivity. In well-functioning capital mar-kets the market value of the firm is the sum of the present value of all the assets held by the firm1— the whole equals the sum of the parts.
In this chapter we stick with the value-additivity principle but extend it to include value contributed by financing decisions. There are two ways of doing this:
1. Adjust the discount rate. The adjustment is typically downward, to account for the value of inter-est tax shields. This is the most common approach. It is usually implemented via the after-tax weighted-average cost of capital or “WACC.”
2. Adjust the present value. That is, start by estimating the project’s “base-case” value as an all-equity-financed mini-firm, and then adjust this base-case NPV to account for the project’s impact on the firm’s capital structure. Thus
Adjusted NPV 1APV for short2 base-case NPV
NPV of financing decisions caused by project acceptance
Once you identify and value the side effects of financing a project, calculating its APV (adjusted net present value) is no more than addition or subtraction.
This is a how-to-do-it chapter. In the next section, we explain and derive the after-tax weighted-average cost of capital, reviewing required assumptions and the too-common mistakes people make using this formula. Section 19.2 then covers the tricks of the trade: helpful tips on how to estimate continued
1All assets means intangible as well as tangible assets. For example, a going concern is usually worth more than a haphazard pile of tangible assets. Thus, the aggregate value of a firm’s tangible assets often falls short of its market value. The difference is ac-counted for by going-concern value or by other intangible assets such as accumulated technical expertise, an experienced sales force, or valuable growth opportunities.
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Brealey−Meyers: Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
524 PART V Dividend Policy and Capital Structure
inputs and how the formula is used in practice. Section 19.3 shows how to recalculate the weighted-average cost of capital when capital structure or asset mix changes.
Section 19.4 turns to the Adjusted Present Value or APV method. This is simple enough in con-cept: Just value the project by discounting at the opportunity cost of capital—not the WACC— and then add the present values gained or lost due to financing side effects. But identifying and valuing the side effects is sometimes tricky, so we’ll have to work through some numerical examples.
Section 19.5 reexamines a basic and apparently simple issue: What should the discount rate be for a risk-free project? Once we recognize the tax deductibility of debt interest, we will find that all risk-free, or debt-equivalent, cash flows can be evaluated by discounting at the after-tax inter-est rate. We show that this rule is consistent with both the weighted-average cost of capital and with APV.
We conclude the chapter with a question and answer section designed to clarify points that man-agers and students often find confusing. An Appendix providing more details and more formulas can be obtained from the Brealey–Myers website.2
19.1 THE AFTER-TAX WEIGHTED-AVERAGE COST OF CAPITAL
Think back to Chapter 17 and Modigliani and Miller’s (MM’s) proposition I. MM showed that, without taxes or financial market imperfections, the cost of capital does not depend on financing. In other words, the weighted average of the ex-pected returns to debt and equity investors equals the opportunity cost of capital, regardless of the debt ratio:
Weighted-average return to debt and equity rD D rE E
r,a constant,independent of D/V
Hereris the opportunity cost of capital, the expected rate of return investors would demand if the firm had no debt at all; r and r are the expected rates of return on debt and equity, the “cost of debt” and “cost of equity.” The weights D/V and E/V are the fractions of debt and equity, based on market values; V, the total market value of the firm, is the sum of D and E.
But you can’t look up r, the opportunity cost of capital, in The Wall Street Journal or find it on the Internet. So financial managers turn the problem around: They start with the estimates of rD and rE and then infer r. Under MM’s assumptions,
r rD D rE E
This formula calculates r, the opportunity cost of capital, as the expected rate of re-turn on a portfolio of all the firm’s outstanding securities.
2www.mhhe.com/bm7e.
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 525
We have discussed this weighted-average cost of capital formula in Chapters 9 and 17. However, the formula misses a crucial difference between debt and equity: Interest payments are tax-deductible. Therefore we move on to the after-tax weighted-average cost of capital, nicknamed WACC:
WACC rD11 Tc2 D rE E
Here T is the marginal corporate tax rate.
Notice that the after-tax WACC is less than the opportunity cost of capital (r), be-cause the “cost of debt” is calculated after tax as r 11 T 2. Thus the tax advantages of debt financing are reflected in a lower discount rate. Notice too that all the variables in the weighted-average formula refer to the firm as a whole. As a result, the formula gives the right discount rate only for projects that are just like the firm undertaking them. The formula works for the “average” project. It is incorrect for projects that are safer or riskier than the average of the firm’s existing assets. It is incorrect for projects whose acceptance would lead to an increase or decrease in the firm’s debt ratio.
Example: Sangria Corporation
Let’s calculate WACC for the Sangria Corporation. Its book and market value bal-ance sheets are
Sangria Corporation (Book Values, millions)
Asset value $100
$100
$ 50 Debt 50 Equity
$100
Sangria Corporation (Market Values, millions)
Asset value $125
$125
$ 50 Debt (D) 75 Equity (E)
$125 Firm Value (V)
We calculated the market value of equity on Sangria’s balance sheet by multiply-ing its current stock price ($7.50) by 10 million, the number of its outstanding shares. The company has done well and future prospects are good, so the stock is trading above book value ($5.00 per share). However, the book and market values of Sangria’s debt are in this case equal.
Sangria’s cost of debt (the interest rate on its existing debt and on any new bor-rowing) is 8 percent. Its cost of equity (the expected rate of return demanded by in-vestors in Sangria’s stock) is 14.6 percent.
The market value balance sheet shows assets worth $125 million. Of course we can’t observe this value directly, because the assets themselves are not traded. But we know what they are worth to debt and equity investors (50 75 $125 mil-lion). This value is entered on the left of the market value balance sheet.
Why did we show the book balance sheet? Only so you could draw a big X through it. Do so now.
When estimating the weighted-average cost of capital, you are not interested in past investments but in current values and expectations for the future. San-gria’s true debt ratio is not 50 percent, the book ratio, but 40 percent, because its
Brealey−Meyers: Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
526 PART V Dividend Policy and Capital Structure
assets are worth $125 million. The cost of equity, r .146, is the expected rate of return from purchase of stock at $7.50 per share, the current market price. It is not the return on book value per share. You can’t buy shares in Sangria for $5 anymore.
Sangria is consistently profitable and pays tax at the marginal rate of 35 percent. That is the final input for Sangria’s WACC. The inputs are summarized here:
Cost of debt (rD) Cost of equity (rE) Marginal tax rate (Tc) Debt ratio (D/V)
Equity ratio (E/V)
.08 .146 .35
50/125 .4
75/125 .6
The company’s WACC is
WACC .0811 .352 1.42 .1461.62 .1084,or 10.84%
That’s how you calculate the weighted-average cost of capital.3
Now let’s see how Sangria would use this formula. Sangria’s enologists have proposed investing $12.5 million in construction of a perpetual crushing ma-chine, which, conveniently for us, never depreciates and generates a perpetual stream of earnings and cash flow of $2.085 million per year pretax. The after-tax cash flow is
Pretax cash flow Tax at 35%
After-tax cash flow
$2.085 .730
$1.355 million
Notice: This after-tax cash flow takes no account of interest tax shields on debt sup-ported by the perpetual crusher project. As we explained in Chapter 6, standard capital budgeting practice calculates after-tax cash flows as if the project were all-equity-financed. However, the interest tax shields will not be ignored: We are about to discount the project cash flows by Sangria’s WACC, in which the cost of debt is entered after tax. The value of interest tax shields is picked up not as higher after-tax cash flows, but in a lower discount rate.
The crusher generates a perpetual cash flow of C $1.355 million, so NPV is
NPV 12.5 1.355 0
NPV 0 means a barely acceptable investment. The annual cash flow of $1.355 mil-lion per year amounts to a 10.84% rate of return on investment (1.355/12.5 .1084), exactly equal to Sangria’s WACC.
If project NPV 0, the return to equity investors must exactly equal the cost of equity, 14.6%. Let’s confirm that Sangria shareholders could actually forecast a 14.6% return on their investment in the perpetual crusher project.
3In practice it’s pointless to calculate discount rates to four decimal places. We do so here to avoid confusion from rounding errors. Earnings and cash flows are carried to three decimal places for the same reason.
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