13.1Corporate Taxes and the Evaluation of Equity-Financed

Capital Expenditures

The starting point for both the APVand the WACC approaches is the determination of

the unlevered cash flows of the firm or project that is being evaluated, defined first in

Chapter 9. Until we get to Chapter 15, we will assume that the unlevered cash flows,

that is, the after-tax cash flows generated directly by the real assets of the project or

firm, are unaffected by the amount of debt financing the firm uses. Because of this

assumption, we can compute the unlevered cash flow as the after-tax cash flows of the

project or firm under the assumption the project or firm is financed entirely with equity

(hence, the term “unlevered”). Having estimated the future unlevered cash flows of the

project or firm in this manner, we then need to estimate the appropriate cost of capi-

tal or discount rate for these cash flows.

The Cost of Capital

Distinguishing the Unlevered Cost of Capital from the WACC.For an all-equity-

financed, or “unlevered” firm, the appropriate risk-adjusted discount rate for a project’s

future cash flow when the cash flow has the same risk as the overall firm is the firm’s

cost of capital. This required rate of return on the firm’s assets is the same as the

2

The final cost was $100 million.

3

Personal taxes are discussed in Chapters 14 and 15.

⁴The analysis of debt capacity is discussed in Parts IVand V.

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Chapter 13

Corporate Taxes and the Impact of Financing on Real Asset Valuation

463

expected rate of return on the unlevered firm’s equity, as described in Chapter 11. In

the presence of corporate tax deductions for interest payments, we need to be concerned

with two costs of capital. The unlevered cost of capital,denoted r,is the expected

UA

return on the equity of the firm if the firm is financed entirely with equity. Because

there is no debt tax shield for a firm that is financed entirely with equity, and because

the two sides of the balance sheet “balance,” the unlevered cost of capital is also the

required rate of return on the firm’s unlevered assets. The weighted average cost of

capitalor WACCis a weighted average of the after-tax expected return paid by the firm

on its debt and equity. In the absence of a debt tax shield, debt subsidy, or other mar-

ket frictions that favor one form of financing over another, the WACCis the expected

return of the firm’s assets. In this case, the WACC and the unlevered cost of capital

are the same. However, we need to distinguish the two cost of capital concepts when-

ever there is a debt tax shield.

Note that the expected return paid by the firm to its equity holders is the same as

the expected return received by the equity holders. This point—that the expected rate

of return the firm pays for the use of the capital is the same as the expected rate of

return the investor receives for providing the capital—is not true, in general. When a

third party, such as the government taxing authority, favors one form of financing over

another, the cost of the favored form of financing will differ from the expected return

to investors. For example, the tax deductibility of interest implies that the cost of debt

financing to a corporation (as measured by the after-tax return paid by the corporation)

may be less than the rate of return on a firm’s debt received by the firm’s debt hold-

ers. Because of this, the WACC differs from unlevered cost of capital when there is a

debt tax shield.

Why It Is Important to Calculate the Unlevered Cost of Capital fora Levered

Firm.If, as is generally assumed, cash flow horizon does not affect the discount rate,

then valuing an equity-financed project that is a scale replication of a comparison all-

equity firm is straightforward. In this case, the project is a miniaturized version of the

comparison firm’s equity, implying that the project’s cost of capital is the expected rate

of return on the comparison firm’s equity. Chapter 11 described a variety of techniques

for estimating this expected rate of return. For example, measuring the comparison

firm’s market beta and using this beta in the CAPM risk-expected return formula is one

way to generate the project’s cost of capital.

However, the inclusion of debt financing complicates this analysis. To value an all-

equity-financed project when the comparison firm has debt financing, it is necessary to

calculate the required rate of return on the comparison firm’s equity in the hypotheti-

cal case of a comparison firm that is all equity financed. Moreover, when the project

adds to the ability of the firm adopting the project to take on tax-advantaged debt, it

is necessary to understand how shifting the comparison firm’s debt affects the risk of

the comparison firm’s equity. While Chapter 11 studied this issue in the absence of

taxes, a real-world application of the valuation techniques developed in this text

requires us to account for the effect of taxes.

The Risk of the Components of the Firm’s Balance Sheet with Tax-Deductible Debt Interest

Afinancial manager who employs either the WACC or the APVmethod needs to under-

stand how debt financing and taxes affect the risks of various components of the firm’s

balance sheet. To develop this understanding we return to the simplified balance sheet of

Chapter 11. Exhibit 13.1, which mirrors Exhibit 11.3, Chapter 11’s balance sheet exhibit,

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464	Part IIIValuing Real Assets

EXHIBIT13.1

Balance Sheet fora Firm with Leverage When Debt Interest Is Corporate Tax Deductible

Assets

Liabilities and Equity

Debt Tax Shield (TX)	TD	Debt	D
	c
Unlevered Assets (UA)	D ETD	Equity	E
	c

presents the two sides of the balance sheet of a firm for which there is a corporate tax

deduction for debt interest payments, but no personal taxes. Exhibit 13.1 illustrates that

typically, the assets of the firm contain two components, one associated directly with the

firm’s operations and the other an indirect asset associated with a financing subsidy. The

former component, the unlevered assets (UA), is defined as the present value of the

unlevered cash flows; the other component, the debt tax shield (TX), is the present value

of the financing subsidy (that is, the present value of the debt-interest deduction for all

corporate profits taxes: federal, state, and city). The more debt the firm has, the big-

ger this tax shield. Note that the two sides of the balance sheet must add up to the same

number—that is, balance—implying that the value of the unlevered assets can be viewed

as the sum of the debt and equity, D E,less the value of the debt tax shield.⁵

Viewing the assets of the firm with value Aas a portfolio of unlevered assets with

value UAand debt tax shields with value TXimplies that the beta (or expected return)

of the assets is the portfolio-weighted average of the betas (or expected returns) of the

unlevered assets and debt tax shields; that is

UATX
	(13.1a)
AD EUAD ETX

and

UATX
r r r	(13.1b)
AD EUAD ETX

where

beta risk of the unlevered assets

UA

beta risk of the debt tax shield

TX

rexpected return of the unlevered assets

UA

rexpected return of the debt tax shield

TX

Static Perpetual Risk-Free Debt.Let Tdenote the effective corporate tax rate.

c

Exhibit 13.1 has the firm’s debt tax shield expressed as

TX TD	(13.2)
c

and thus

UAD ETD	(13.3)
c

The values for TXand UAboth in Exhibit 13.1 and in equations (13.2) and (13.3) are

developed in a model by Hamada (1972). If the firm issues default-free perpetual debt

(that is, debt that never matures) with aggregate face amount of Dand interest payments

⁵More generally, TXcan be viewed as the present value of anydebt financing subsidy.

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Chapter 13

Corporate Taxes and the Impact of Financing on Real Asset Valuation

465

equal to the risk-free rate, each interest payment of Drsaves TDrin taxes in the

fcf

year it is paid. The present value of the tax savings from the interest payments (see

Chapter 9 for the formula for the present value of a perpetuity) is

TDr

c f

TD

c r

f

The same present value is also achieved when the risk-free rate changes over time and

the firm rolls over one-period risk-free debt.

The Hamada model assumes that the tax shield is riskless and thus, each period’s

tax deduction arising from an interest payment should be discounted back to date 0 at

the risk-free rate. This implies that the beta of the debt tax shield in the Hamada model

is zero. Using this observation, and substituting equations (13.2) and (13.3) into equa-

tion (13.1a) yields

D ET D	(13.4)
c
AD EUA

In the typical case where the beta of the unlevered assets of the firm, ,is positive,

UA

equation (13.4) states that the beta of the combination of the unlevered assets and the

debt tax shield assets, ,must decline with an increase in leverage to reflect the

A

addition of the risk-free tax savings. To see this, note that the portfolio weight on ,

UA

D ETDT DD

c c

,which equals 1 ,declines as the leverage ratio

D ED ED E

increases, reflecting the fact that risk-free debt tax shields constitute a larger propor-

tion of the firm’s assets as leverage increases.

The key assumptions that lead to this result are: (1) The debt is perpetual; in other

words, it is either a perpetuity or consists of rolled over short-term debt positions.

(2)The debt is default-free and pays the risk-free rate. (3) The face value of the debt

and the tax rate do not change over time. The third assumption distinguishes the

Hamada model from other models that will be discussed later in this chapter.

Equity Betas and Asset Betas.Equity betas are also affected by taxes. Chapter 11

indicated that (assuming risk-free debt) the equity beta is

D
1	(13.5)
EEA

Substituting the right-hand side of equation (13.4) for in equation (13.5) gives

A

D^D ET^D

1 c

^EED E^UA

With a little simplification, this equation, which is based on the Hamada model,

becomes

D

1 (1T) (13.6)

E^cE^UA

Assuming that does not change with leverage,⁶equation (13.6) states that, for a given

UA

debt increase, the beta of the firm’s equity increases less the larger is the corporate tax

rate, and increases the most when there are no taxes. Reversing this equation also allows

us to identify from ,which is often a necessary step when using the discounted

UAE

cash flow method for valuation when debt tax shields exist.

⁶Chapters 16–19 discuss situations where this may not be the case.

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Markets and Corporate		the Impact of Financing on	Companies, 2002
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466Part IIIValuing Real Assets