Capital Structure Value

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UV3929Rev. Jun. 30, 2011

This technical note was prepared by Associate Professor Marc Lipson. Copyright 2009 by the University ofVirginia Darden School Foundation, Charlottesville, VA. All rights reserved. To order copies, send an e-mail [email protected] part of this publication may be reproduced, stored in a retrieval system,used in a spreadsheet, or transmitted in any form or by any meanselectronic, mechanical, photocopying,

recording, or otherwisewithout the permission of the Darden School Foundation.

CAPITAL STRUCTURE AND VALUE

The underlying principle of valuation is that the discount rate must match the risk of thecash flows being valued. Furthermore, when we include the possibility that cash flows arefinanced with debt capital, valuations must acknowledge the tax deductibility of interestpayments. This note presents a series of calculations that illustrate these two essential points andthe relations between them. The results provide important insights into the following capitalstructure questions: How does debt financing affect equity holders? Does debt financing createvalue for a firm? What is the right amount of debt financing?

The context for this analysis is a very simple firm valuation in which the firm experiencesno growth and lasts indefinitely. In other words, we assume that the firms operating cash flowsare a perpetuityan infinite stream of identical cash flows. This allows for an extremelytractable valuation calculationthe value of a perpetuity is the cash flow divided by the discountrate.1This simple context is chosen to focus on the underlying principles, though these principlesare quite general. We will focus on the value of the whole firm, which is the sum of debt andequity values and is referred to as enterprise value.

The analysis is divided into four parts. First, we examine the effects of debt financing onequity cash flow variability. The analysis justifies a common calculation, which is to adjustcapital asset pricing model (CAPM) betas for leverage. The term leverage, in this context, refersto the use of debt financing (financial leverage). Second, the note considers the effects of debtfinancing where there are no taxes. While unrealistic, this analysis establishes an importantbenchmark that makes later results easier to understand. Third, the note calculates enterprisevalue using a variety of methods. The use of differing methods helps illustrate underlying

1This is a simplification of the ubiquitous constant growth formula shown below, but with zero growth. In theconstant growth formula, V0is the value now (time zero), CF1is the cash flow one period in the future (time one), kis the discount rate per period, andgis the growth rate of cash flows from time one onward.

gk

CFV

10

With zero growth, the formula reduces to V0= CF k, where there is no longer a need to subscript CFsince all cashflows are the same. To understand this formulas logic, consider the case where you put $100,000 in a bank account

that pays 5% forever. You will receive 0.05 $100,000 = $5,000 a year, every year. Now turn this around: If yourdiscount rate were 5%, and you were promised $5,000 a year forever, that would be the same as having $100,000 inthe bank today. In other words, at a 5% discount rate, $5,000 a year is worth $5,000 0.05 = $100,000.


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principles. Finally, the note considers explicitly how a financing change would affect stockprices. This last analysis demonstrates quite clearly how the benefits associated with debtfinancing (the tax deductibility of interest payments) benefit shareholders.


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Financial Risk

Our simple firm generates an expected EBIT of $104,000 a year, every year; however,

this cash flow is not certain. The calculation below explores the effects of a 20% decrease inEBIT on the cash flow to equity holders. Consider this effect when the firm has zero debt andwhen the firm has debt equal to $380,000 on which it pays 6.0%. Assume furthermore that thefirm pays taxes of 30%. Fill out the table below. Note that given the simple structure of the firm,net income will be paid each year to equity holders.

No DebtBase Case 20% Decrease

EBIT 104,000 83,200

Interest 0 0

Earnings Before Tax 104,000 83,200Tax 31,200

Net Income 72,800

Percentage Change in Net Income

Debt Equal to $380,000Base Case 20% Decrease

EBIT 104,000 83,200

Interest

Earnings Before TaxTax

Net Income

Percentage Change in Net Income

Given the resulting changes in equity cash flows, it is clear that the existence of debtfinancing magnifies changes in equity cash flows. As you might expect, this variation alsoinfluences the beta of a firms equity. In fact, we can describe that effect with Equation 1, whichyou will use for the remainder of these calculations:

L= U(1 + (1 t) D E) (1)

where L is the leveraged beta (beta given debt financing), U is the unleveraged beta (beta offirm without debt, also called an asset beta), tis the marginal corporate tax rate,Dis the marketvalue of debt, andEis the market value of equity.


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Valuation without TaxesWeighted Average Cost of Capital (WACC) Approach

To better understand the effects of debt, which are related to the existence of tax deductibility,

it is useful to consider first a world with a zero marginal tax rate. The usual formulas still apply, butthe tax rate is set to zero. We will assume that given the risks of our simple firm, and assuming thefirm was entirely financed with equity, the beta of the equity would equal 0.80. This is theunleveraged beta referred to in Equation 1. Furthermore, we will assume the risk-free rate of return isequal to 6.0%. This is the same as the interest rate on debt, which implies that the debt is riskless.2Finally, assume that the market risk premium is equal to 5.5%.

Fill out the table below, assuming first that there is no debt and then assuming debt, asdescribed earlier, equal to $380,000. We will value the company using the WACC approachdiscounting free cash flow by the WACC. To do this, you must have a measure of the proportionof debt financing based on market values, but the firms market value (enterprise value) is

unknown. A proportion is assumed below, and you will verify it is consistent with the results.You will also calculate the difference in enterprise values between the Debt and No Debt cases.

No Debt Debt = $380,000

EBIT 104,000 104,000

Tax 0 0

NOPAT 104,000 104,000

Change in Net PPE 0 0

Change in NWC 0 0

Free Cash Flow 104,000 104,000

Unleveraged Beta 0.80 0.80

Proportion of Debt 0.00 0.38

Debt to Equity 0.00

Leveraged Beta 0.80

Cost of Equity (use CAPM)

WACC

Enterprise Value

Difference in Enterprise ValuesCalculate Ratio of Debt to Enterprise Value

Provide an intuitive explanation for your results regarding the difference in enterprise values.

2The analysis can be adjusted to accommodate risky debt, but assuming riskless debt is another simplification

that allows a focus on underlying principals.


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Valuation with TaxesWACC Approach

In contrast to a world with no taxes, we now consider the more realistic case where the

firm pays taxes and interest payments are tax deductible. Assume that the tax rate, as in the firstcalculations, is equal to 30%.


EBIT 104,000 104,000

Tax 31,200 31,200

NOPAT 72,800 72,800


Change in NWC 0 0


Unleveraged Beta 0.80 0.80

Proportion of Debt 0.00 0.46683

Debt to Equity 0.00

Leveraged Beta 0.80

Cost of Equity (use CAPM)

WACCEnterprise Value

Difference in Enterprise Values

Calculate Ratio of Debt to Enterprise Value

The results above regarding the enterprise values are quite different from those in a world withno taxes. Provide an intuitive explanation for the results.


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Valuation with TaxesValue of Claims

It should be noted that the logic behind the WACC approach is that the operating

decisions of the firm are reflected in the cash flows, while all the financing decisions arereflected in the discount rate. But the central logic of valuationdiscount cash flows at anappropriate ratecan be applied to more than just this one case. In fact, we can view the firm ina number of different ways and value the firm accordingly.

In this section, rather than valuing the whole firm using the WACC approach, we willvalue each of the claims (debt and equity) on the firm separately. The sum of these claims will beequal to the enterprise value.

In this analysis you will use the cost of equity from the prior calculations.


EBIT 104,000 104,000

Interest Payments 0

Income Before Taxes 104,000

Tax

Net Income (Cash to Equity)

Cost of Equity

Value of Equity

Cash to Debt (Interest)

Cost of Debt

Value of Debt

Enterprise Value


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Valuation with TaxesValue of Assets

Another valuation approach would be to consider the firm as a collection of assets and to

value each of these assets separately. The sum of these assets would equal enterprise value. Forour simple firm, there are just two assets. The first is the operating capability of the firm(operating assets). The second is the tax shield provided by debt financing.


EBIT 104,000 104,000

Tax 31,200 31,200

NOPAT 72,800 72,800


Change in NWC 0 0


Beta of Operating Cash Flow

Discount Rate

Value of Operations

Interest Payment

Annual Taxes ShieldDiscount Rate

Value of Tax Shield

Enterprise Value

Note that in all three approaches, the value of the firm is identical. This must be the case, ofcourse, since it cannot matter how we slice up the firm. The value of the whole firm (WACCapproach) must equal the sum of the claims on the firm (claims approach), which must equal thesum of the value of all assets (asset approach). Assuming debt is permanent and unchanging, andgiven that the appropriate discount rate would be the cost of debt (since it correctly reflects therisk of debt cash flows), a simple formula for the value of the tax shield is tD.


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Per Share Effects

One striking result above is that the value of equity is markedly lower when we include

debt. This raises an important question: Are the equity holders better or worse off as a result ofadding debt? To understand the effects on equity holders, the following table examines thechange in per share prices as our simple firm adds debt. In effect, we consider the same analysisas before, but we cast the results in terms of a recapitalization: The firm issues the debt and usesthe proceeds to repurchase shares in the market.

Fill out the table below, where the table is divided into a No Debt column (the marketassumes the firm will have no debt) and a recapitalized column (the firm has competed therecapitalization). The analysis employs the asset valuation approach. The No Debt column asksyou to calculate the price per share that reflects the anticipated value of the tax shield providedby the new debt. For this analysis, assume the firm has 20,000 shares outstanding initially and

repurchases shares at a fair price when implementing the recapitalization.

No Debt Recapitalized


Discount rate for Operations

Value of Operations

Value of Tax Shield (tD)

Enterprise ValueDebt Outstanding

Equity Value

Price Without Tax Shield

Value of Tax Shield

Per Share Value of Tax Shield

Price Reflecting Value

Shares Repurchased

New Shares Outstanding

Price Post-Recapitalization

What does your analysis suggest would be the stock price (market) reaction to the announcementthat the firm will be issuing $380,000 in debt?

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Capital Structure Value