Identifying the Unlevered Cost of Capital

Chapter 11 examined how one could value a project using a risk-adjusted discount rate

estimated from the stock returns of comparison firms.⁷

These risk-adjusted discount

rates required an adjustment for the effect of leverage. However, the unlevering pro-

cedure described in Chapter 11 assumed no taxes. With corporate tax deductions for

interest, the procedure for identifying a project’s unlevered cost of capital is very sim-

ilar to the procedure used in Chapter 11. However, the formula for unlevering the betas

must be modified whenever the betas of the debt tax shields differ from the betas of

unlevered assets.

The formula for unlevering the equity betas of comparison firms in the presence

of corporate taxes is embedded in equation (13.6) which, when reversed, reads

E	(13.7)
UAD
1 (1T)
cE

Since is the same as the beta of the firm (as well as the beta of its equity) assum-

UA

ing that the firm is all-equity financed, substituting into a risk-expected return for-

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mula gives the desired unlevered cost of capital.

The Marriott Example Revisited.Valuations with the risk-adjusted discount rate

method typically use comparisons with traded securities. When debt tax shields exist,

it is the betas and required rates of return of the unlevered assetsof comparison firms,

and not their assets, that are perceived as being similar to those of the project being

valued. For this reason, equation (13.7) and related equations that generate or

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rfrom observable statistics like are central to the risk-adjusted discount rate

UAE

method. To illustrate this point, Example 13.1 reworks Example 11.2 to account for

corporate taxes.

Example 13.1:Using the Comparison Method to Obtain Beta and rwith Taxes

Recall from Example 11.2 that Marriott identified three comparison firms for its restaurant

division.For these comparison firms, equity beta estimates ( ), book values of debt (D),

E

and market values of equity (E) have been identified as follows:

Comparison Firm		D (in $ billions)	E (in $ billions)
	E

Church’s Chicken	.75	.004	.096
McDonald’s	1.00	2.300	7.700
Wendy’s	1.08	.210	.790

Estimate the unlevered cost of capital for Marriott’s restaurant division.Assume that the risk-

free rate is 4 percent per year, the risk premium on the market portfolio is 8.4 percent per year,

the corporate tax rate is 34 percent, the CAPM holds, the debt of the comparison firms is risk

free, and all three firms are equally good as comparisons for Marriott’s restaurant division.

Answer:Using equation (13.7), first find the unlevered asset betas of the three firms,

then average.

⁷This comparison firm can be the firm adopting the project if the project’s cash flow and the firm

have similar unlevered asset betas.

Grinblatt947Titman: Financial	III. Valuing Real Assets	13. Corporate Taxes and	© The McGraw947Hill
Markets and Corporate		the Impact of Financing on	Companies, 2002
Strategy, Second Edition		Real Asset Valuation

Chapter 13

Corporate Taxes and the Impact of Financing on Real Asset Valuation

467

Comparison Firm
	UA

	.75
Church’s Chicken	.73
	.004
	1 .66
	.096

	1.00
McDonald’s	.84
	2.3
	1 .66
	7.7

	1.08
Wendy’s	.92
	.21
	1 .66
	.79

	.73 .84 .92
Marriott (average of above)	.83
	3

Applying the CAPM risk-expected return equation using this estimate of Marriott’s restaurant

unlevered asset beta gives the restaurant unlevered cost of capital, 10.97 percent per year,

since

.1097.04 .83(.084)

Example 13.1, using the same comparison firms as Example 11.2, concludes that

.83 and that the unlevered cost of capital is 10.97 percent. This is larger than

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the respective unlevered beta and cost of capital in Example 11.2, namely, .78 and 10.55

percent. The reason is that the risk-free tax savings from debt mitigates the increase in

equity betas that is generated by the leverage of the three comparison firms. Thus, the

reduction in beta arising from the unleveraging equation is not as great here as it was

in the absence of taxes.

The Hamada Formula Is Not Always Correct.If the firm uses debt in a flexible

manner, the Hamada formulas for leveraging and unleveraging equity betas, represented

in equations (13.6) and (13.7), are not correct. For example, if the firm issues debt as

the value of the unlevered assets rises and retires debt as the value of the unlevered

assets falls, then equity betas will move more in response to leverage changes than

equation (13.6) suggests they should. As this chapter later shows, in the extreme case

where the issuance and retirement of debt is perfectly positively correlated with the

value of the unlevered assets, the correct formula for leveraging and unleveraging

equity betas is the same as in the no-tax case. However, if firms tend to retire debt

when they are doing well, then the Hamada formula overstates the impact of leverage

on equity betas. The tendency of firms to retire debt when they do well, which is espe-

cially common following leveraged recapitalizations, is consistent with Kaplan and

Stein’s (1990) observation that equity betas are less sensitive to changes in leverage

than predicted by equation (13.6).