UV3929 Rev. Jun. 30, 2011
CAPITAL STRUCTURE AND VALUE The underlying principle of valuation is that the discount rate must match the risk of the cash flows being valued. Furthermore, when we include the possibility that cash flows are financed with debt capital, valuations must acknowledge the tax deductibility of interest payments. This note presents a series of calculations that illustrate these two essential points and the relations between them. The results provide important insights into the following capital structure questions: How does debt financing affect equity holders? Does debt financing create value 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 experiences no growth and lasts indefinitely. In other words, we assume that the firm’s operating cash flows are a perpetuity—an infinite stream of identical cash flows. This allows for an extremely tractable valuation calculation—the value of a perpetuity is the cash flow divided by the discount rate.1 This simple context is chosen to focus on the underlying principles, though these principles are quite general. We will focus on the value of the whole firm, which is the sum of debt and equity values and is referred to as enterprise value. The analysis is divided into four parts. First, we examine the effects of debt financing on equity cash flow variability. The analysis justifies a common calculation, which is to adjust capital asset pricing model (CAPM) betas for leverage. The term leverage, in this context, refers to the use of debt financing (financial leverage). Second, the note considers the effects of debt financing where there are no taxes. While unrealistic, this analysis establishes an important benchmark that makes later results easier to understand. Third, the note calculates enterprise value using a variety of methods. The use of differing methods helps illustrate underlying 1
This is a simplification of the ubiquitous constant growth formula shown below, but with zero growth. In the constant growth formula, V0 is the value now (time zero), CF1 is the cash flow one period in the future (time one), k is the discount rate per period, and g is the growth rate of cash flows from time one onward. CF1 V0 kg With zero growth, the formula reduces to V0 = CF ÷ k, where there is no longer a need to subscript CF since all cash flows are the same. To understand this formula’s 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 your discount rate were 5%, and you were promised $5,000 a year forever, that would be the same as having $100,000 in the bank today. In other words, at a 5% discount rate, $5,000 a year is worth $5,000 ÷ 0.05 = $100,000. This technical note was prepared by Associate Professor Marc Lipson. Copyright 2009 by the University of Virginia Darden School Foundation, Charlottesville, VA. All rights reserved. To order copies, send an e-mail to
[email protected]. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means—electronic, mechanical, photocopying, recording, or otherwise—without the permission of the Darden School Foundation.
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principles. Finally, the note considers explicitly how a financing change would affect stock prices. This last analysis demonstrates quite clearly how the benefits associated with debt financing (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 in EBIT on the cash flow to equity holders. Consider this effect when the firm has zero debt and when the firm has debt equal to $380,000 on which it pays 6.0%. Assume furthermore that the firm 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 Debt Base Case 20% Decrease EBIT Interest Earnings Before Tax Tax Net Income
104,000 0 104,000 31,200 72,800
83,200 0 83,200
Percentage Change in Net Income Debt Equal to $380,000 Base Case 20% Decrease EBIT Interest Earnings Before Tax Tax Net Income
104,000
83,200
Percentage Change in Net Income Given the resulting changes in equity cash flows, it is clear that the existence of debt financing magnifies changes in equity cash flows. As you might expect, this variation also influences the beta of a firm’s equity. In fact, we can describe that effect with Equation 1, which you will use for the remainder of these calculations: βL = βU (1 + (1 − t) D ÷ E)
(1)
where βL is the leveraged beta (beta given debt financing), βU is the unleveraged beta (beta of firm without debt, also called an asset beta), t is the marginal corporate tax rate, D is the market value of debt, and E is the market value of equity.
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Valuation without Taxes—Weighted 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, but the tax rate is set to zero. We will assume that given the risks of our simple firm, and assuming the firm was entirely financed with equity, the beta of the equity would equal 0.80. This is the unleveraged beta referred to in Equation 1. Furthermore, we will assume the risk-free rate of return is equal to 6.0%. This is the same as the interest rate on debt, which implies that the debt is riskless.2 Finally, 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, as described earlier, equal to $380,000. We will value the company using the WACC approach— discounting free cash flow by the WACC. To do this, you must have a measure of the proportion of debt financing based on market values, but the firm’s 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.
EBIT Tax NOPAT Change in Net PPE Change in NWC Free Cash Flow Unleveraged Beta Proportion of Debt Debt to Equity Leveraged Beta Cost of Equity (use CAPM)
No Debt
Debt = $380,000
104,000 0 104,000 0 0 104,000
104,000 0 104,000 0 0 104,000
0.80 0.00 0.00 0.80
0.80 0.38
WACC Enterprise Value Difference in Enterprise Values Calculate Ratio of Debt to Enterprise Value Provide an intuitive explanation for your results regarding the difference in enterprise values. 2
The 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 Taxes—WACC 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 first calculations, is equal to 30%.
EBIT Tax NOPAT Change in Net PPE Change in NWC Free Cash Flow Unleveraged Beta Proportion of Debt Debt to Equity Leveraged Beta Cost of Equity (use CAPM)
No Debt
Debt = $380,000
104,000 31,200 72,800 0 0 72,800
104,000 31,200 72,800 0 0 72,800
0.80 0.00 0.00 0.80
0.80 0.46683
WACC Enterprise 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 with no taxes. Provide an intuitive explanation for the results.
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Valuation with Taxes—Value 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 are reflected in the discount rate. But the central logic of valuation—discount cash flows at an appropriate rate—can be applied to more than just this one case. In fact, we can view the firm in a number of different ways and value the firm accordingly. In this section, rather than valuing the whole firm using the WACC approach, we will value each of the claims (debt and equity) on the firm separately. The sum of these claims will be equal to the enterprise value. In this analysis you will use the cost of equity from the prior calculations.
No Debt EBIT Interest Payments Income Before Taxes Tax Net Income (Cash to Equity)
104,000 0 104,000
Debt = $380,000 104,000
Cost of Equity Value of Equity Cash to Debt (Interest) Cost of Debt Value of Debt Enterprise Value
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Valuation with Taxes—Value 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. For our 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.
No Debt EBIT Tax NOPAT Change in Net PPE Change in NWC Free Cash Flow
104,000 31,200 72,800 0 0 72,800
Debt = $380,000 104,000 31,200 72,800 0 0 72,800
Beta of Operating Cash Flow Discount Rate Value of Operations Interest Payment Annual Taxes Shield Discount 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, of course, since it cannot matter how we slice up the firm. The value of the whole firm (WACC approach) must equal the sum of the claims on the firm (claims approach), which must equal the sum of the value of all assets (asset approach). Assuming debt is permanent and unchanging, and given that the appropriate discount rate would be the cost of debt (since it correctly reflects the risk of debt cash flows), a simple formula for the value of the tax shield is t × D.
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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 of adding debt? To understand the effects on equity holders, the following table examines the change in per share prices as our simple firm adds debt. In effect, we consider the same analysis as before, but we cast the results in terms of a recapitalization: The firm issues the debt and uses the proceeds to repurchase shares in the market. Fill out the table below, where the table is divided into a No Debt column (the market assumes the firm will have no debt) and a recapitalized column (the firm has competed the recapitalization). The analysis employs the asset valuation approach. The No Debt column asks you to calculate the price per share that reflects the anticipated value of the tax shield provided by 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 Free Cash Flow Discount rate for Operations Value of Operations
72,800
Recapitalized 72,800
Value of Tax Shield (t × D) Enterprise Value Debt 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 announcement that the firm will be issuing $380,000 in debt?
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