M170 Corporate Finance Handout 1

M170 Corporate Finance Handout 1
Flavio Toxvaerd 9 two-hour session Office hours: By appointment Office: Room 32, 2. floor

Main texts: Berk and DeMarzo: Corporate Finance *
Grinblatt and Titman: Financial Markets and Corporate Strategy * Brealey and Myers: Principles of Corporate Finance Tirole: The Theory of Corporate Finance Amaro de Matos: Theoretical Foundations of Corporate Finance

Handout 1 Capital Structure, Modigliani-Miller, Taxes, Bankruptcy
Berk and DeMarzo chapters 14, 15

Chapter Outline 14.1 Equity versus Debt Financing
14.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value 14.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital 14.5 MM: Beyond the Propositions

Learning Objectives Define the types of securities usually used by firms to raise capital; define leverage. Describe the capital structure that the firm should choose. List the three conditions that make capital markets perfect. Discuss the implications of MM Proposition I, and the roles of homemade leverage and the Law of One Price in the development of the proposition.

Learning Objectives (cont'd)
Calculate the cost of capital for levered equity according to MM Proposition II. Illustrate the effect of a change in debt on weighted average cost of capital in perfect capital markets. Calculate the market risk of a firm’s assets using its unlevered beta. Illustrate the effect of increased leverage on the beta of a firm’s equity.

Compute a firm’s net debt. Discuss the effect of leverage on a firm’s expected earnings per share. Show the effect of dilution on equity value. Explain why perfect capital markets neither create nor destroy value.

14.1 Equity Versus Debt Financing
Capital Structure The relative proportions of debt, equity, and other securities that a firm has outstanding

Financing a Firm with Equity
You are considering an investment opportunity. For an initial investment of $800 this year, the project will generate cash flows of either $1400 or $900 next year, depending on whether the economy is strong or weak, respectively. Both scenarios are equally likely.

Table 14.1 The Project Cash Flows

Financing a Firm with Equity (cont'd)
The project cash flows depend on the overall economy and thus contain market risk. As a result, you demand a 10% risk premium over the current risk-free interest rate of 5% to invest in this project. What is the NPV of this investment opportunity?

The cost of capital for this project is 15%. The expected cash flow in one year is: ½($1400) + ½($900) = $1150. The NPV of the project is:

If you finance this project using only equity, how much would you be willing to pay for the project? If you can raise $1000 by selling equity in the firm, after paying the investment cost of $800, you can keep the remaining $200, the NPV of the project NPV, as a profit.

Unlevered Equity Equity in a firm with no debt Because there is no debt, the cash flows of the unlevered equity are equal to those of the project.

Table 14.2 Cash Flows and Returns for Unlevered Equity

Shareholder’s returns are either 40% or –10%. The expected return on the unlevered equity is: ½ (40%) + ½(–10%) = 15%. Because the cost of capital of the project is 15%, shareholders are earning an appropriate return for the risk they are taking.

Financing a Firm with Debt and Equity
Suppose you decide to borrow $500 initially, in addition to selling equity. Because the project’s cash flow will always be enough to repay the debt, the debt is risk free and you can borrow at the risk-free interest rate of 5%. You will owe the debt holders: $500 × 1.05 = $525 in one year. Levered Equity Equity in a firm that also has debt outstanding

Financing a Firm with Debt and Equity (cont'd)
Given the firm’s $525 debt obligation, your shareholders will receive only $875 ($1400 – $525 = $875) if the economy is strong and $375 ($900 – $525 = $375) if the economy is weak.

Table 14.3 Values and Cash Flows for Debt and Equity of the Levered Firm

What price E should the levered equity sell for? Which is the best capital structure choice for the entrepreneur?

Modigliani and Miller argued that with perfect capital markets, the total value of a firm should not depend on its capital structure. They reasoned that the firm’s total cash flows still equal the cash flows of the project, and therefore have the same present value.

Because the cash flows of the debt and equity sum to the cash flows of the project, by the Law of One Price the combined values of debt and equity must be $1000. Therefore, if the value of the debt is $500, the value of the levered equity must be $500. E = $1000 – $500 = $500.

Because the cash flows of levered equity are smaller than those of unlevered equity, levered equity will sell for a lower price ($500 versus $1000). However, you are not worse off. You will still raise a total of $1000 by issuing both debt and levered equity. Consequently, you would be indifferent between these two choices for the firm’s capital structure.

The Effect of Leverage on Risk and Return
Leverage increases the risk of the equity of a firm. Therefore, it is inappropriate to discount the cash flows of levered equity at the same discount rate of 15% that you used for unlevered equity. Investors in levered equity will require a higher expected return to compensate for the increased risk.

Table 14.4 Returns to Equity with and without Leverage

The Effect of Leverage on Risk and Return (cont'd)
The returns to equity holders are very different with and without leverage. Unlevered equity has a return of either 40% or –10%, for an expected return of 15%. Levered equity has higher risk, with a return of either 75% or –25%. To compensate for this risk, levered equity holders receive a higher expected return of 25%.

The relationship between risk and return can be evaluated more formally by computing the sensitivity of each security’s return to the systematic risk of the economy.

In summary: In the case of perfect capital markets, if the firm is 100% equity financed, the equity holders will require a 15% expected return. If the firm is financed 50% with debt and 50% with equity, the debt holders will receive a return of 5%, while the levered equity holders will require an expected return of 25% (because of their increased risk).

In summary: Leverage increases the risk of equity even when there is no risk that the firm will default. Thus, while debt may be cheaper, its use raises the cost of capital for equity. Considering both sources of capital together, the firm’s average cost of capital with leverage is the same as for the unlevered firm.

Textbook Example 14.1

Textbook Example 14.1 (cont'd)

Alternative Example 14.1 Problem
Suppose the entrepreneur borrows $700 when financing the project. According to Modigliani and Miller, what should the value of the equity be? What is the expected return?

Alternative Example 14.1 (cont'd)
Solution Because the value of the firm’s total cash flows is still $1000, if the firm borrows $700, its equity will be worth $300. The firm will owe $700 × 1.05 = $735 in one year. Thus, if the economy is strong, equity holders will receive $1400 − 735 = $665, for a return of $665/$300 − 1 = %. If the economy is weak, equity holders will receive $900 − $735 = $, for a return of $165/$300 − 1 = −45.0%. The equity has an expected return of

Solution Note that the equity has a return sensitivity of % − (−45.0%) = %, which is %/50% = % of the sensitivity of unlevered equity. Its risk premium is 38.33% − 5%= 33.33%, which is approximately % of the risk premium of the unlevered equity, so it is appropriate compensation for the risk.

14.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value
The Law of One Price implies that leverage will not affect the total value of the firm. Instead, it merely changes the allocation of cash flows between debt and equity, without altering the total cash flows of the firm.

14.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value (cont'd)
Modigliani and Miller (MM) showed that this result holds more generally under a set of conditions referred to as perfect capital markets: Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows. There are no taxes, transaction costs, or issuance costs associated with security trading. A firm’s financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them.

14.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value (cont'd)
MM Proposition I: In a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.

MM and the Law of One Price
MM established their result with the following argument: In the absence of taxes or other transaction costs, the total cash flow paid out to all of a firm’s security holders is equal to the total cash flow generated by the firm’s assets. Therefore, by the Law of One Price, the firm’s securities and its assets must have the same total market value.

Homemade Leverage Homemade Leverage
When investors use leverage in their own portfolios to adjust the leverage choice made by the firm. MM demonstrated that if investors would prefer an alternative capital structure to the one the firm has chosen, investors can borrow or lend on their own and achieve the same result.

Homemade Leverage (cont'd)
Assume you use no leverage and create an all-equity firm. An investor who would prefer to hold levered equity can do so by using leverage in his own portfolio.

Table 14.6 Replicating Levered Equity Using Homemade Leverage

If the cash flows of the unlevered equity serve as collateral for the margin loan (at the risk-free rate of 5%), then by using homemade leverage, the investor has replicated the payoffs to the levered equity, as illustrated in the previous slide, for a cost of $500. By the Law of One Price, the value of levered equity must also be $500.

Now assume you use debt, but the investor would prefer to hold unlevered equity. The investor can re-create the payoffs of unlevered equity by buying both the debt and the equity of the firm. Combining the cash flows of the two securities produces cash flows identical to unlevered equity, for a total cost of $1000.

Table 14.7 Replicating Unlevered Equity by Holding Debt and Equity

In each case, your choice of capital structure does not affect the opportunities available to investors. Investors can alter the leverage choice of the firm to suit their personal tastes either by adding more leverage or by reducing leverage. With perfect capital markets, different choices of capital structure offer no benefit to investors and does not affect the value of the firm.

Suppose there are two firms, each with date 1 cash flows of $1400 or $900 (as shown in Table 14.1). The firms are identical except for their capital structure. One firm is unlevered, and its equity has a market value of $1010. The other firm has borrowed $500, and its equity has a market value of $500. Does MM Proposition I hold? What arbitrage opportunity is available using homemade leverage?

Solution MM Proposition I states that the total value of each firm should equal the value of its assets. Because these firms hold identical assets, their total values should be the same. However, the problem assumes the unlevered firm has a total market value of $1,010, whereas the levered firm has a total market value of $500 (equity) + $500 (debt) = $1,000. Therefore, these prices violate MM Proposition I.

Solution Because these two identical firms are trading for different total prices, the Law of One Price is violated and an arbitrage opportunity exists. To exploit it, we can buy the equity of the levered firm for $500, and the debt of the levered firm for $500, re-creating the equity of the unlevered firm by using homemade leverage for a cost of only $500 + $500 = $1000. We can then sell the equity of the unlevered firm for $1010 and enjoy an arbitrage profit of $10.

Date 0 Date 1: Cash Flows Cash Flow Strong Economy Weak Economy Buy levered equity -$500 $875 $375 Buy levered debt $525 Sell unlevered equity $1,010 $1,400 -$900 Total cash flow $10 $0 Note that the actions of arbitrageurs buying the levered firm’s equity and debt and selling the unlevered firm’s equity will cause the price of the levered firm’s equity to rise and the price of the unlevered firm’s equity to fall until the firms’ values are equal.

14.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital
Leverage and the Equity Cost of Capital MM’s first proposition can be used to derive an explicit relationship between leverage and the equity cost of capital.

14.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital (cont'd)
Leverage and the Equity Cost of Capital E Market value of equity in a levered firm. D Market value of debt in a levered firm. U Market value of equity in an unlevered firm. A Market value of the firm’s assets.

Leverage and the Equity Cost of Capital MM Proposition I states that: The total market value of the firm’s securities is equal to the market value of its assets, whether the firm is unlevered or levered.

Leverage and the Equity Cost of Capital The cash flows from holding unlevered equity can be replicated using homemade leverage by holding a portfolio of the firm’s equity and debt.

Leverage and the Equity Cost of Capital The return on unlevered equity (RU) is related to the returns of levered equity (RE) and debt (RD):

Leverage and the Equity Cost of Capital Solving for RE: The levered equity return equals the unlevered return, plus a premium due to leverage. The amount of the premium depends on the amount of leverage, measured by the firm’s market value debt-equity ratio, D/E.

Leverage and the Equity Cost of Capital MM Proposition II: The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio. Cost of Capital of Levered Equity

Leverage and the Equity Cost of Capital Recall from above: If the firm is all-equity financed, the expected return on unlevered equity is 15%. If the firm is financed with $500 of debt, the expected return of the debt is 5%.

Leverage and the Equity Cost of Capital Therefore, according to MM Proposition II, the expected return on equity for the levered firm is:

14.5 MM: Beyond the Propositions
Conservation of Value Principle for Financial Markets With perfect capital markets, financial transactions neither add nor destroy value, but instead represent a repackaging of risk (and therefore return). This implies that any financial transaction that appears to be a good deal may be exploiting some type of market imperfection.

Chapter Outline 15.1 The Interest Tax Deduction
15.2 Valuing the Interest Tax Shield 15.3 Recapitalizing to Capture the Tax Shield 15.4 Personal Taxes 15.5 Optimal Capital Structure with Taxes

Learning Objectives Explain the effect of interest payments on cash flows to investors. Calculate the interest tax shield, given the corporate tax rate and interest payments. Calculate the value of a levered firm. Describe the effect of a leveraged recapitalization on the value of equity. Describe the effect of personal taxes on the corporate tax benefits of leverage.

Given corporate and personal tax rates on equity and debt, calculate the tax benefit of debt with personal taxes. Discuss why the optimal level of leverage from a tax-saving perspective is the level at which interest equals EBIT. Describe the relationship between the optimal fraction of debt and the growth rate of the firm.

15.1 The Interest Tax Deduction
Corporations pay taxes on their profits after interest payments are deducted. Thus, interest expense reduces the amount of corporate taxes. This creates an incentive to use debt.

15.1 The Interest Tax Deduction (cont'd)
Consider Safeway, Inc. which had earnings before interest and taxes of approximately $1.85 billion in 2008, and interest expenses of about $350 million. Safeway’s marginal corporate tax rate was 35%. As shown on the next slide, Safeway’s net income in 2008 was lower with leverage than it would have been without leverage.

Table 15.1 Safeway’s Income with and without Leverage, 2008 ($ millions)

Safeway’s debt obligations reduced the value of its equity. But the total amount available to all investors was higher with leverage.

Without leverage, Safeway was able to pay out $1,202 million in total to its investors. With leverage, Safeway was able to pay out $1,325 million in total to its investors. Where does the additional $123 million come from?

Interest Tax Shield The reduction in taxes paid due to the tax deductibility of interest In Safeway’s case, the gain is equal to the reduction in taxes with leverage: $648 million − $525 million = $123 million. The interest payments provided a tax savings of 35% × $350 million = $123 million.

15.2 Valuing the Interest Tax Shield
When a firm uses debt, the interest tax shield provides a corporate tax benefit each year. This benefit is the computed as the present value of the stream of future interest tax shields the firm will receive.

The Interest Tax Shield and Firm Value
The cash flows a levered firm pays to investors will be higher than they would be without leverage by the amount of the interest tax shield.

Figure 15.1 The Cash Flows of the Unlevered and Levered Firm

The Interest Tax Shield and Firm Value (cont'd)
MM Proposition I with Taxes The total value of the levered firm exceeds the value of the firm without leverage due to the present value of the tax savings from debt.

Suppose ALCO plans to pay $60 million in interest each year for the next 8 years, and then repay the principal of $1 billion in year 8. These payments are risk free, and ALCO’s marginal tax rate will remain 39% throughout this period. If the risk-free interest rate is 6%, by how much does the interest tax shield increase the value of ALCO? 81

Alternative Example 15.2 Solution The annual interest tax shield is:
$1 billion × 6% × 39% = $23.4 million for 8 years. 82

The Interest Tax Shield with Permanent Debt
Typically, the level of future interest payments is uncertain due to changes in the marginal tax rate, the amount of debt outstanding, the interest rate on that debt, and the risk of the firm. For simplicity, we will consider the special case in which the above variables are kept constant.

The Interest Tax Shield with Permanent Debt (cont'd)
Suppose a firm borrows debt D and keeps the debt permanently. If the firm’s marginal tax rate is c , and if the debt is riskless with a risk-free interest rate rf , then the interest tax shield each year is c × rf × D, and the tax shield can be valued as a perpetuity.

If the debt is fairly priced, no arbitrage implies that its market value must equal the present value of the future interest payments.

If the firm’s marginal tax rate is constant, then:

15.3 Recapitalizing to Capture the Tax Shield
Assume that Midco Industries wants to boost its stock price. The company currently has 20 million shares outstanding with a market price of $15 per share and no debt. Midco has had consistently stable earnings, and pays a 35% tax rate. Management plans to borrow $100 million on a permanent basis and they will use the borrowed funds to repurchase outstanding shares.

The Tax Benefit Without leverage
VU = (20 million shares) × ($15/share) = $300 million If Midco borrows $100 million using permanent debt, the present value of the firm’s future tax savings is PV(interest tax shield) = cD = 35% × $100 million = $35 million

The Tax Benefit (cont'd)
Thus the total value of the levered firm will be VL = VU + cD = $300 million + $35 million = $335 million Because the value of the debt is $100 million, the value of the equity is E = VL − D = $335 million − $100 million = $235 million

The Tax Benefit (cont'd)
Although the value of the shares outstanding drops to $235 million, shareholders will also receive the $100 million that Midco will pay out through the share repurchase. In total, they will receive the full $335 million, a gain of $35 million over the value of their shares without leverage.

The Share Repurchase Assume Midco repurchases its shares at the current price of $15/share. The firm will repurchase 6.67 million shares. $100 million ÷ $15/share = 6.67 million shares It will then have million shares outstanding. 20 million − 6.67 million = million

The Share Repurchase (cont'd)
The total value of equity is $235 million; therefore the new share price is $17.625/share. $235 million ÷ million shares = $17.625 Shareholders that keep their shares earn a capital gain of $2.625 per share. $ − $15 = $2.625

The Share Repurchase (cont'd)
The total gain to shareholders is $35 million. $2.625/share × million shares = $35 million If the shares are worth $17.625/share after the repurchase, why would shareholders tender their shares to Midco at $15/share?

No Arbitrage Pricing If investors could buy shares for $15 immediately before the repurchase, and they could sell these shares immediately afterward at a higher price, this would represent an arbitrage opportunity.

No Arbitrage Pricing (cont'd)
Realistically, the value of the Midco’s equity will rise immediately from $300 million to $335 million after the repurchase announcement. With 20 million shares outstanding, the share price will rise to $16.75 per share. $335 million ÷ 20 million shares = $16.75 per share

With a repurchase price of $16.75, the shareholders who tender their shares and the shareholders who hold their shares both gain $1.75 per share as a result of the transaction. $16.75 − $15 = $1.75

The benefit of the interest tax shield goes to all 20 million of the original shares outstanding for a total benefit of $35 million. $1.75/share × 20 million shares = $35 million When securities are fairly priced, the original shareholders of a firm capture the full benefit of the interest tax shield from an increase in leverage.

15.4 Personal Taxes The cash flows to investors are typically taxed twice. Once at the corporate level and then investors are taxed again when they receive their interest or divided payment.

15.4 Personal Taxes (cont'd)
For individuals: Interest payments received from debt are taxed as income. Equity investors also must pay taxes on dividends and capital gains.

Including Personal Taxes in the Interest Tax Shield
The amount of money an investor will pay for a security depends on the the cash flows the investor will receive after all taxes have been paid. Personal taxes reduce the cash flows to investors and can offset some of the corporate tax benefits of leverage.

Including Personal Taxes in the Interest Tax Shield (cont'd)
The actual interest tax shield depends on both corporate and personal taxes that are paid. To determine the true tax benefit of leverage, the combined effect of both corporate and personal taxes needs to be evaluated.

Figure 15.3 After-Tax Investor Cash Flows Resulting from $1 in EBIT

Table 15.3 Top Federal Tax Rates in the United States, 1971–2009

In general, every $1 received after taxes by debt holders from interest payments costs equity holders $(1 − *) on an after-tax basis, where: Effective Tax Advantage of Debt

When there are no personal taxes on debt income (i = 0) or when the personal tax rates on debt and equity income are the same (i = e ), the formula reduces to * = c. When equity income is taxed less heavily (e is less than i), then * is less than c.

Valuing the Interest Tax Shield with Personal Taxes
With personal taxes and permanent debt, the value of the firm with leverage becomes If * is less than c, the benefit of leverage is reduced in the presence of personal taxes.

15.5 Optimal Capital Structure with Taxes
Do Firms Prefer Debt? When firms raise new capital from investors, they do so primarily by issuing debt. In most years aggregate equity issues are negative, meaning that on average, firms are reducing the amount of equity outstanding by buying shares.

Figure 15. 5 Net External Financing and Capital Expenditures by U. S
Figure Net External Financing and Capital Expenditures by U.S. Corporations, 1975–2008 Source: Federal Reserve, Flow of Funds Accounts of the United States, 2009.

15.5 Optimal Capital Structure with Taxes (cont'd)
Do Firms Prefer Debt? While firms seem to prefer debt when raising external funds, not all investment is externally funded. Most investment and growth is supported by internally generated funds. Even though firms have not issued new equity, the market value of equity has risen over time as firms have grown. For the average firm, the result is that debt as a fraction of firm value has varied in a range from 30–45%.

Figure 15.6 Debt-to-Value Ratio [D / (E + D)] of U.S. Firms, 1975–2008
Source: Compustat and Federal Reserve, Flow of Funds Accounts of the United States, 2009.

15.5 Optimal Capital Structure with Taxes (cont'd)
Do Firms Prefer Debt? The use of debt varies greatly by industry. Firms in growth industries like biotechnology or high technology carry very little debt, while airlines, automakers, utilities, and financial firms have high leverage ratios.

Figure 15.7 Debt-to-Value Ratio [D / (E + D)] for Select Industries
Source: Capital IQ, 2009.

Limits to the Tax Benefit of Debt
To receive the full tax benefits of leverage, a firm need not use 100% debt financing, but the firm does need to have taxable earnings. This constraint may limit the amount of debt needed as a tax shield.

Table 15.4 Tax Savings with Different Amounts of Leverage

Limits to the Tax Benefit of Debt (cont'd)
From the previous slide: With no leverage, the firm receives no tax benefit. With high leverage, the firm saves $350 in taxes. With excess leverage, the firm has a net operating loss and there is no increase in the tax savings. Because the firm is already not paying taxes, there is no immediate tax shield from the excess leverage

No corporate tax benefit arises from incurring interest payments that exceed EBIT. Because interest payments constitute a tax disadvantage at the investor level, investors will pay higher personal taxes with excess leverage, making them worse off.

If the firm is not paying taxes, where c = 0, then the tax disadvantage of excess leverage is: Note: *ex is negative because (*e < i).

The optimal level of leverage from a tax saving perspective is the level such that interest equals EBIT. At the optimal level of leverage, the firm shields all of its taxable income and it does not have any tax-disadvantaged excess interest.

However, it is unlikely that a firm can predict its future EBIT (and the optimal level of debt) precisely. If there is uncertainty regarding EBIT, then there is a risk that interest will exceed EBIT. As a result, the tax savings for high levels of interest falls, possibly reducing the optimal level of the interest payment.

In general, as a firm’s interest expense approaches its expected taxable earnings, the marginal tax advantage of debt declines, limiting the amount of debt the firm should use.

Other Tax Shields There are numerous provisions in the tax laws for deductions and tax credits, such as depreciation, investment tax credits, carryforwards of past operating losses, etc. To the extent that a firm has other tax shields, its taxable earnings will be reduced and it will rely less heavily on the interest tax shield.

M170 Corporate Finance Handout 1

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