Valuing a Business with the wacc Method When a Debt Tax Shield Exists

Consider the case of ExMart, currently an all-equity firm. Martin Chang is interested

in purchasing ExMart, financing 50 percent of the purchase with debt and the remain-

ing 50 percent with equity. To value ExMart, it is necessary to estimate its expected

future unlevered cash flows and discount them at the appropriate weighted average cost

of capital. This discount rate reflects Chang’s various sources of capital. Mathemati-

cally this can be expressed as

WACCw r w(1T) r	(13.8)
EED cD

where

WACCweighted average cost of capital

E

w market value of equity over market value of all financing

^ED E

D

w market value of debt over market value of all financing

^DD E

Tmarginal corporate tax rate if interest is fully tax deductible

c

(or,more generally, the debt financing subsidy in percentage terms)

The costs of the financing components are

rthe expected return on equity to investors

E

rthe expected return on debt to investors

D

The two expected returns rand rrepresent the expected rates of return that investors

ED

require as compensation for the riskiness of the firm’s equity and debt securities. The

term r (1T),the expected after-tax cost of debtto the firm, differs from rbecause

DcD

every dollar of interest paid to the debt holders represents a deduction on the corpo-

rate income tax statement that would not be available with equity financing.

Example 13.7 provides an illustrative calculation of the WACC.

Example 13.7:Computing a Weighted Average Cost of Capital

Mr.Chang believes that the required rate of return on ExMart equity when it is 50 percent

levered will be 12 percent per year.Since ExMart is a very stable business, it will be able

to borrow at the risk-free rate of 8 percent per year.If the marginal corporate tax rate is 25

percent, what is the WACC for ExMart?

Answer:WACC 5 .5 3 .12 1 .5(1 2 .25) 3 .08 5 .09 or 9%.

WACC Components: The Cost of Equity Financing

One input for calculating the WACC is r,the required expected rate of return on the

E

equity (see Chapter 11), which also is known as the cost of equityfinancing. This rate

of return can be determined in many ways. Typically, one uses expected return formu-

las from the Capital Asset Pricing Model, the arbitrage pricing theory, or the dividend

discount model to compute r. With the CAPM and APT, equity betas estimated from

E

historical return data are generally used in the formulas. Note that the expected rate of

return of a firm’s equity obtained with these methods is the relevant cost of equity

financing, whether or not there are tax advantages to debt financing.

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Chapter 13

Corporate Taxes and the Impact of Financing on Real Asset Valuation

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WACC Components: The Cost of Debt Financing

The methods used to estimate r,the firm’s pretax cost of debt, which is the other

D

major input in the WACC formula, are generally not the same as those used to calcu-

late the cost of equity capital.

Default-Free Debt.Practitioners typically assume that the firm’s pretax cost of debt

is the yield to maturity of the firm’s debt. (The yield to maturity, being certain, lacks

the bar over rin contrast to the expected value of an uncertain return, r.) The yield

DD

to maturity provides a fairly accurate estimate of a firm’s pretax cost of debt when the

debt is highly rated and not callable or convertible. (Chapter 2 notes that default rates

on investment-grade debt are negligible.) Example 13.8 illustrates how to use the

CAPM to calculate the WACC of a firm with debt of this type.

Example 13.8:Computing the After-Tax Cost of Debt and WACC When

Default Is Unlikely

The financing of United Technologies (UT) consists of 20 percent debt and 80 percent equity.

With so little debt, the firm is able to borrow at the risk-free rate of 8 percent per year.The

interest expense is tax deductible and the corporate tax rate is 34 percent.Assuming that

the CAPM holds, the expected return of the market portfolio is 14 percent, and the beta of

the firm’s equity is 1.2, what is the WACC of United Technologies?

Answer:Using the CAPM, UT’s cost of equity is

r8% 1.2 (14%8%)15.2%

E

The firm’s cost of debt in this case is

r(1T)8% (1.34)

D c

Therefore,

w r wr(1T)

WACC

EEDD c

.815.2% .28%.66

13.2%

Risky Debt.Using the promised yieldtimes one minus the corporate tax rate as the

cost of debt may be appropriate for relatively risk-free debt. Generally, however, this

after-tax yield is not the cost of debt capital for highly levered firms. For firms with

risky debt, the promised return on the debt (that is, the yield to maturity) is larger than

the debt’s expected return because of the possibility of default.

Expected rather than promised debt returns are the WACC inputs because the

WACC method, as a debt- and tax-based generalization of the risk-adjusted discount

rate method, is designed to discount expectedcash flows. As Chapter 11 noted, the risk-

adjusted discount rate method requires that expectedcash flows be discounted at

expectedrates of return.

The yield to maturity, a promised rather than an expected return for debt, over-

states the pretax cost of any debt financing with nonnegligible default risk. Partially

offsetting this, however, is the observation that the tax shields of highly levered firms

go unused when firms have insufficient taxable earnings. This makes the marginal cor-

porate tax rate overstate the appropriate input for T(and one less that tax rate under-

c

state the appropriate input for 1 T). Despite the fact that it would be a remarkable

c

coincidence if these two biases just offset one another, some practitioners use this

insight to rationalize the promised yield on debt and the corporate tax rate as WACC

inputs for firms with risky debt.

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478Part IIIValuing Real Assets

Let’s assume, however, that you are not this foolish and are using the expected

return on debt, rather than its promised yield, as your WACC input. In this instance,

the appropriate value to use for Tin the WACC formula may be higher or lower than

c

the corporate tax rate, depending on the relation between the promised yield of the debt,

the expected return of the debt, the frequency with which the firm is unprofitable, and

the likely timing of default.

In simple cases where the debt interest tax deduction is either fully used or fully

unused, and where the probability of full use is the same at any point in time in per-

petuity,the Tinput for the WACC is given by the equation

c

Corporate tax rateProbability of utilizationPromised yield to maturity

T(13.9)

^cr

D

The tax gain variable, T,is thus higher than the corporate tax rate if the product

c

of the probability of utilization and the promised yield to maturity exceeds r,and

D

lower otherwise. In these instances, one needs only to compute the numerator in the

preceding formula, which equals rT,and subtract it from rto obtain the after-tax

DcD

cost of debt r(1T).

Dc

For example, suppose the promised and expected yield on the debt is 14 percent

and the corporate tax rate is 34 percent. With a probability of .75, the firm enjoys the

full tax benefit of the 14 percent debt interest payment and with a probability of .25,

it enjoys no tax benefit from debt interest payments. In this case, each dollar of debt

has an expected tax benefit of 3.57 percent [.75(.34)14%]. Subtracting 3.57 percent

from ryields the after-tax cost of debt to the firm, r(1 T). When rexceeds 10.5

DDcD

percent, Tis less than the corporate tax rate of 34 percent, and if ris less than 10.5

cD

percent, Tis greater than the corporate tax rate.

c

In cases where the probability of utilizing the tax shield changes over time, Tmay

c

differ from the value given in equation (13.9). To illustrate this point, consider high-

yield debt. Firms that issue high-yield debt tend to have low default rates in the early

years after the debt is issued. In these early years, the tax deduction for profitable firms

issuing high-yield debt is based on the actual debt interest payments which early on

are likely to be larger than the promised interest payments of firms issuing safer debt.

Default for firms issuing high-yield debt reduces or even reverses the tax advantages

of debt (because of a possible taxable capital gain to the firm), but tends to occur many

years after issuance, and typically at a time when the firm’s tax bracket is zero. Thus,

for firms issuing high-yield debt, events that are relatively tax disadvantageous tend to

be deferred and the tax benefit of paying high coupons on the high-yield debt tends to

be immediate. The favorable timing of the debt tax benefit suggests that the appropri-

ate Tfor the WACC formula is greater than the Tgiven in equation (13.9).

cc

Of course, one also can generate cases for which the opposite is true. The com-

plexity of adjusting the WACC method to account for the timing of taxation punctu-

ates our reasons for preferring the APVmethod to analyze the debt tax shield in com-

plicated scenarios.

Computing the Expected Return of Risky Debt.Let us return now to the issue of

computing r,the expected return on debt, which the WACC method requires as the

D

pretax cost of debt. Two popular methods are used to identify expected returns on

risky debt and both tend to give similar values for r.The first method subtracts

D

expected losses owing to default from the promised yield (weighted by the no-default

probability) to generate the pretax cost of debt financing. For example, the promised

yield on a high-yield bond may be 14 percent; however, if 4 percent of these bonds

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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

479

default in a given year with the bondholders recovering about 60 percent of their

original investment (the 60% is known as therecovery rate),and thus losing 40 per-

cent, the expected return on the bonds is

.96(14%) .04(40%) 11.84%

The second method uses either the Capital Asset Pricing Model or APTto calcu-

late the expected return of the debt. Estimated betas for junk debt range from about .3

to about .5.¹²

Assuming a 6 percent risk premium on the market, the CAPM would pro-

ject a 1.8 percent (.3 6%) to 3 percent (.5 6%) spread between the expected

returns of a junk bond and a default-free bond.

Example 13.9 provides an estimate of the cost of debt capital that accounts for

default and the loss of tax benefits arising from negative net income and default.

Example 13.9:Calculating the Cost of Debt forHighly Levered Firms

RJR Nabisco has issued high-yield bonds to finance its LBO.Assume that the outstanding

bonds currently have a 14 percent per year yield to maturity, a beta of .5, and interest pay-

ments that are tax deductible with a probability of .75.If the risk-free rate is 8 percent per

year, the expected return of the market portfolio is 14 percent, and the corporate tax rate is

34 percent, what is the after-tax cost of debt to RJR Nabisco?

Answer:Using the CAPM, the expected return on the RJR bonds is

8% .5(14%8%) 11%

(To check whether this estimated default premium of 3 percent (14% 11%) is sensible,

see whether the product of the expected default rate and the recovery rate is 3 percent.)

To calculate the after-tax cost of debt, note that when RJR has sufficient income to take

advantage of the tax shield, it enjoys a tax savings of 4.76 percent (14% .34).With .75

as the probability of utilization, the expected tax savings per dollar of debt equals 3.57 per-

cent ( 4.76% .75), so RJR’s after-tax cost of debt is 7.43 percent (11% 3.57%).

Determining the Costs of Debt and Equity When the Project Is Adopted

For a firm, the relevant pretax cost of debt capital ror the cost of equity capital r

DE

is the expected rate of return of the respective sources of capital at the time the firm

decides to adopt the project rather than the actual cost that the firm incurred to obtain

the funds. Example 13.10 illustrates this distinction.

Example 13.10:Cost of Capital Is Based on Foregone Financial Market