Debt and Taxes Chapter 15 PDF

CH APTE R Debt and Taxes 15 IN A PERFECT CAPITAL MARKET, THE LAW OF ONE PRICE IMPLIES THAT NOTATION all financial transactions have an NPV of zero...

CH APTE R Debt and Taxes 15 IN A PERFECT CAPITAL MARKET, THE LAW OF ONE PRICE IMPLIES THAT NOTATION all financial transactions have an NPV of zero and neither create nor destroy Int interest expense value. Consequently, in Chapter 14, we found that the choice of debt versus PV present value equity financing does not affect the value of a firm: The funds raised from issu- r f       risk-free interest rate ing debt equal the present value of the future interest and principal payments the firm will make. While leverage increases the risk and cost of capital of the firm’s D market value of debt equity, the firm’s weighted average cost of capital (WACC), total value, and share rE        equity cost of capital price are unaltered by a change in leverage. That is, in a perfect capital market, a τ c      marginal corporate firm’s choice of capital structure is unimportant. tax rate This statement is at odds, however, with the observation that firms invest E market value of equity significant resources, both in terms of managerial time and effort and investment rwacc         weighted average cost banking fees, in managing their capital structures. In many instances, the choice of of capital leverage is of critical importance to a firm’s value and future success. As we will rD debt cost of capital show, there are large and systematic variations in the typical capital structures for U V  value of the unlevered different industries. For example, in March 2022, Vertex Pharmaceuticals, a bio- firm technology company, had debt of $967 million, cash of $7.5 billion, and equity V L  value of the firm with worth nearly $64 billion, giving the firm a market debt-equity ratio of 0.015, with leverage negative net debt (debt minus cash). In contrast, Ford Motor Company had a debt- τ i      marginal personal tax rate equity ratio of 2.1, and American Airlines’s debt-equity ratio was 4.3. Auto manu- on income from debt facturers and airlines typically have much higher debt ratios than biotechnology τ e       marginal personal tax rate and drug companies. If capital structure is unimportant, why do we see such con- on income from equity sistent differences in capital structures across firms and industries? Why do manag- τ *        effective tax advantage ers dedicate so much time, effort, and expense to the capital structure choice? of debt As Modigliani and Miller made clear in their original work, capital structure τ ex*        effective tax advantage on does not matter in perfect capital markets. Recall from Chapter 14 that a perfect interest in excess of EBIT capital market exists under the following assumptions: 1. Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows. 555 M15_BERK6318_06_GE_C15.indd 555 26/04/23 7:11 PM  556 Chapter 15 Debt and Taxes 2. There are no taxes, transaction costs, or issuance costs associated with security trading. 3. A firm’s financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them. Thus, if capital structure does matter, then it must stem from a market imperfection. In this chapter, we focus on one such imperfection—taxes. Corporations and investors must pay taxes on the income they earn from their investments. As we will see, a firm can enhance its value by using leverage to minimize the taxes it, and its investors, pay. 15.1 The Interest Tax Deduction Corporations must pay taxes on the income that they earn. Because they pay taxes on their profits after interest payments are deducted, interest expenses reduce the amount of corporate tax firms must pay. This feature of the tax code creates an incentive to use debt. Let’s consider the impact of interest expenses on the taxes paid by Macy’s, Inc., a retail de- partment store. Macy’s had earnings before interest and taxes of approximately $2.8 billion in 2014, and interest expenses of about $400 million. Given Macy’s marginal corporate tax rate of 35%,1 the effect of leverage on Macy’s earnings is shown in Table 15.1. TABLE 15.1   Macy’s Income with and without Leverage, Fiscal Year 2014 ($ million) With Leverage Without Leverage EBIT $2800 $2800 Interest expense −400 0 Income before tax 2400 2800 Taxes (35%) −840 −980 Net income $1560 $1820 As we can see from Table 15.1, Macy’s net income in 2014 was lower with leverage than it would have been without leverage. Thus, Macy’s debt obligations reduced the income available to equity holders. But more importantly, the total amount available to all investors was higher with leverage: With Leverage Without Leverage Interest paid to debt holders 400 0 Income available to equity holders 1560 1820 Total available to all investors $1960 $1820 With leverage, Macy’s was able to pay out $1960 million in total to its investors, versus only $1820 million without leverage, representing an increase of $140 million. 1 Macy’s paid an average tax rate of approximately 36.2% in 2014, after accounting for other credits and deferrals. Because we are interested in the impact of a change in leverage, Macy’s marginal tax rate—the tax rate that would apply to additional taxable income—is relevant to our discussion. M15_BERK6318_06_GE_C15.indd 556 26/04/23 7:11 PM  15.1 The Interest Tax Deduction 557 It might seem odd that a firm can be better off with leverage even though its earnings are lower. But recall from Chapter 14 that the value of a firm is the total amount it can raise from all investors, not just equity holders. Because leverage allows the firm to pay out more in total to its investors—including interest payments to debt holders—it will be able to raise more total capital initially. Where does the additional $140 million come from? Looking at Table 15.1, we can see that this gain is equal to the reduction in taxes with leverage: $980 million − $840 million = $140 million. Because Macy’s does not owe taxes on the $400 million of earnings it used to make interest payments, this $400 million is shielded from the corporate tax, providing the tax savings of 35% × $400 million = $140 million. In general, the gain to investors from the tax deductibility of interest payments is re- ferred to as the interest tax shield. The interest tax shield is the additional amount that a firm would have paid in taxes if it did not have leverage. We can calculate the amount of the interest tax shield each year as follows: Interest Tax Shield = Corporate Tax Rate × Interest Payments (15.1) EXAMPLE 15.1 Computing the Interest Tax Shield Problem Shown below is the pro-forma forecasted income statement for D.F. Builders (DFB). Given its marginal corporate tax rate of 25%, what is the amount of the interest tax shield for DFB in years 2023 through 2026? DFB Income Statement (+ million) 2023 2024 2025 2026 Total sales $3369 $3706 $4077 $4432 Cost of sales −2359 −2584 −2867 −3116 Selling, general, and administrative −226 −248 −276 −299 expense Depreciation −22 −25 −27 −29 Operating income 762 849 907 988 Other income 7 8 10 12 EBIT 769 857 917 1000 Interest expense −50 −80 −100 −100 Income before tax 719 777 817 900 Taxes (25%) −180 −194 −204 −225 Net income $539 $583 $613 $675 Solution From Eq. 15.1, the interest tax shield is the tax rate of 25% multiplied by the interest payments in each year: ($ million) 2023 2024 2025 2026 Interest expense −50 −80 −100 −100 Interest tax shield 12.5 20 25 25 ( 25% × interest expense ) Thus, the interest tax shield enabled DFB to pay an additional $82.5 million to its investors over this period. M15_BERK6318_06_GE_C15.indd 557 26/04/23 7:11 PM  558 Chapter 15 Debt and Taxes CONCEPT CHECK 1. With corporate income taxes, explain why a firm’s value can be higher with leverage even though its earnings are lower. 2. What is the interest tax shield? 15.2 Valuing the Interest Tax Shield When a firm uses debt, the interest tax shield provides a corporate tax benefit each year. To determine the benefit of leverage for the value of the firm, we must compute the present value of the stream of future interest tax shields the firm will receive. The Interest Tax Shield and Firm Value Each year a firm makes interest payments, the cash flows it pays to investors will be higher than they would be without leverage by the amount of the interest tax shield:  Cash Flows to Investors   Cash Flows to Investors   Interest   with Leverage  = without Leverage  +  Tax Shield        Figure 15.1 illustrates this relationship. Here you can see how each dollar of pretax cash flows is divided. The firm uses some fraction to pay taxes, and it pays the rest to investors. By increasing the amount paid to debt holders through interest payments, the amount of the pretax cash flows that must be paid as taxes decreases. The gain in total cash flows to investors is the interest tax shield. Because the cash flows of the levered firm are equal to the sum of the cash flows from the unlevered firm plus the interest tax shield, by the Law of One Price the same must be true for the present values of these cash flows. Thus, letting V L and V U represent the value of the firm with and without leverage, respectively, we have the following change to MM Proposition I in the presence of 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: V L = V U + PV (Interest Tax Shield) (15.2) FIGURE 15.1 1000 Taxes 900 Taxes Interest The Cash Flows of the Pretax Tax Unlevered and Levered 800 Cash Flow Shield (EBIT) Firm Levered 700 By increasing the cash Earnings 600 Cash Flow flows paid to debt ­holders through ­interest ­payments, 500 a firm ­reduces the amount 400 Unlevered paid in taxes. Cash flows Earnings paid to ­investors are shown 300 Interest in blue. The increase in on Debt 200 total cash flows paid to investors is the interest 100 tax shield. (The figure 0 shows a 20% marginal Assets Unlevered Firm Levered Firm corporate tax rate.) M15_BERK6318_06_GE_C15.indd 558 26/04/23 7:11 PM  15.2 Valuing the Interest Tax Shield 559 Pizza and Taxes In Chapter 14, we mentioned the pizza analogy that ­Merton payment. But when debt holders get a slice, there is no tax. Miller once used to describe the MM Propositions with perfect Thus, by allocating more slices to debt holders rather than capital markets: No matter how you slice it, you still have the to equity holders, more pizza will be available to investors. same amount of pizza. While the total amount of pizza does not change, there is We can extend this analogy to the setting with taxes, but more pizza left over for investors to consume because less the story is a bit different. In this case, every time equity pizza is consumed by Uncle Sam in taxes. holders get a slice of pizza, Uncle Sam gets a slice as a tax Clearly, there is an important tax advantage to the use of debt financing. But how large is this tax benefit? To compute the increase in the firm’s total value associated with the inter- est tax shield, we need to forecast how a firm’s debt—and therefore its interest p ­ ayments— will vary over time. Given a forecast of future interest payments, we can determine the interest tax shield and compute its present value by discounting it at a rate that corresponds to its risk. EXAMPLE 15.2 Valuing the Interest Tax Shield without Risk Problem Suppose DFB restructures its existing debt, and will instead pay $80 million in interest each year for the next 10 years, and then repay the principal of $1.6 billion in year 10. These payments are risk free, and DFB’s marginal tax rate will remain 25% throughout this period. If the risk-free interest rate is 5%, by how much does the interest tax shield increase the value of DFB? Solution In this case, the interest tax shield is 25% × $80 million = $20 million each year for the next 10 years. Therefore, we can value it as a 10-year annuity. Because the tax savings are known and not risky, we can discount them at the 5% risk-free rate: 1 1− 1  PV (Interest Tax Shield) = $20 million ×   0.05 1.0510  = $154 million The final repayment of principal in year 10 is not deductible, so it does not contribute to the tax shield. The Interest Tax Shield with Permanent Debt In Example 15.2, we know with certainty the firm’s future interest payments and associ- ated tax savings. In practice, this case is rare. Typically, the level of future interest payments varies due to changes the firm makes in the amount of debt outstanding, changes in the interest rate on that debt, and the risk that the firm may default and fail to make an interest payment. In addition, the firm’s marginal tax rate may fluctuate due to changes in the tax code and changes in the firm’s income bracket. Rather than attempting to account for all possibilities here, let’s consider the special case in which the firm issues debt and plans to keep the dollar amount of debt constant forever.2 2 We discuss how to value the interest tax shield with more complicated leverage policies in Chapter 18. M15_BERK6318_06_GE_C15.indd 559 26/04/23 7:11 PM  560 Chapter 15 Debt and Taxes For example, the firm might issue a perpetual consol bond, making only interest payments but never repaying the principal. More realistically, suppose the firm issues short-term debt, such as a five-year coupon bond. When the principal is due, the firm raises the money needed to pay it by issuing new debt. In this way, the firm never pays off the principal but simply refinances it whenever it comes due. In this situation, the debt is effectively permanent. Many large firms have a policy of maintaining a certain amount of debt on their balance sheets. As old bonds and loans mature, new borrowing takes place. The key assumption here is that the firm maintains a fixed dollar amount of outstanding debt, rather than an amount that changes with the size of the firm. Suppose a firm borrows debt D and keeps the debt permanently. If the firm’s marginal tax rate is τ c , and if the debt is riskless with a risk-free interest rate r f , then the interest tax shield each year is τ c × r f × D , and we can value the tax shield as a perpetuity: τ c × Interest τ c × ( r f × D ) PV (Interest Tax Shield) = = rf rf = τc × D The above calculation assumes the debt is risk free and the risk-free interest rate is c­onstant. These assumptions are not necessary, however. As long as the debt is fairly priced, no arbitrage implies that its market value must equal the present value of the future interest payments:3 Market Value of Debt = D = PV (Future Interest Payments) (15.3) If the firm’s marginal tax rate is constant,4 then we have the following general formula: Value of the Interest Tax Shield of Permanent Debt PV (Interest Tax Shield) = PV ( τ c × Future Interest Payments) = τ c × PV (Future Interest Payments) = τc × D (15.4) This formula shows the magnitude of the interest tax shield. Given a 21% corporate tax rate, it implies that for every $1 in new permanent debt that the firm issues, the value of the firm increases by $0.21. The Weighted Average Cost of Capital with Taxes The tax benefit of leverage can also be expressed in terms of the weighted average cost of capital. When a firm uses debt financing, the cost of the interest it must pay is offset to some extent by the tax savings from the interest tax shield. For example, suppose a firm 3 Equation 15.3 holds even if interest rates fluctuate and the debt is risky. It requires only that the firm never repay the principal on the debt (it either refinances or defaults on the principal). The result follows by the same argument used in Chapter 9 to show that the price of equity should equal the present value of all future dividends. 4 The tax rate may not be constant if the firm’s taxable income fluctuates sufficiently to change the firm’s tax bracket (we discuss this possibility further in Section 15.5). M15_BERK6318_06_GE_C15.indd 560 26/04/23 7:11 PM  15.2 Valuing the Interest Tax Shield 561 The Repatriation Tax: Why Some Cash-Rich Firms Borrowed In April 2013, Apple Inc. borrowed $17 billion in what was Many firms adopted this strategy of holding cash over- then the largest U.S. corporate bond issuance of all time. But seas and borrowing at home to delay paying the repatria- why would a firm with over $100 billion in cash on hand need tion tax. The chart below shows the cash and debt positions to borrow money? The answer is that while Apple indeed had of the ten firms with the largest overseas cash positions plenty of cash, the vast majority of that cash was overseas, at that time. With the exception of GE, these firms were and bringing it back to the United States would trigger a tax primarily borrowing against their foreign holdings, where liability in excess of 20% that Apple wanted to avoid. most of their cash resided. Also shown is the growth in the Apple’s situation was not uncommon. When U.S. firms aggregate amount held overseas by U.S. corporations, which earn profits overseas, those profits are subject to the foreign exceeded $2.8 trillion by the end of 2017. corporate tax of the country in which they are earned. Prior to To encourage firms to repatriate funds and invest more 2018, if the profits were then “repatriated” by bringing them at home, Congress enacted a one-time “tax holiday” in 2004, back to the United States, the firm would owe the difference but the effect was temporary. Congress decided to enact a between the foreign tax paid and the U.S. corporate tax rate. more permanent fix as part of the 2017 TCJA. As of the Because foreign corporate tax rates are often very low—for end of the 2017 tax year, all cash held overseas was “deemed example, 12.5% in Ireland versus 35% in the United States at repatriated” and subject to a one-time tax of up to 15.5%. the time of Apple’s transaction—this so-called repatriation As a result, foreign income can now be returned to the tax was significant. Rather than bear this cost, many firms United States with no additional repatriation tax, and so the chose to hold the funds abroad in the form of bonds or other incentive to hoard cash overseas and borrow at home no short-term investments and raise the cash they needed in the longer exists. The policy had the intended effect, and in the United States by borrowing domestically. In Apple’s case, the Federal Reserve reports that in 2018 alone, $850 billion of $17 billion it borrowed was used to conduct share repurchases. this overseas cash was repatriated. 2017 Cash and Debt ($ billion) Apple Microsoft Cisco Systems Alphabet Oracle Johnson & Johnson General Electric Amgen Cash Held Overseas Domestic Cash Gilead Sciences Total Debt Qualcomm $0 $50 $100 $200 $250 $300 Total Overseas Cash Holdings of U.S. Firms 3,000 2,500 2017 Overseas Cash ($ billion) TCJA 2,000 1,500 2004 Repatriation 1,000 ”Tax Holiday” 500 0 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 M15_BERK6318_06_GE_C15.indd 561 26/04/23 7:11 PM  562 Chapter 15 Debt and Taxes with a 21% tax rate borrows $100,000 at 10% interest per year. Then its net cost at the end of the year is Year-End Interest expense r × $100,000 = $10,000 Tax savings −τ c × r × $100,000 = −2,100 Effective after-tax cost of debt r × ( 1 − τ c ) × $100,000 = $7,900 The effective cost of the debt is only $7,900 $100,000 = 7.90% of the loan amount, rather than the full 10% interest. Thus, the tax deductibility of interest lowers the effective cost of debt financing for the firm. More generally,5 With tax-deductible interest, the effective after-tax borrowing rate is r ( 1 − τ c ). In Chapter 14, we showed that without taxes, the firm’s WACC was equal to its u­ nlevered cost of capital, which is the average return that the firm must pay to its investors (equity hold- ers and debt holders). The tax-deductibility of interest payments, however, lowers the effective after-tax cost of debt to the firm. As we discussed in Chapter 12, we can account for the benefit of the interest tax shield by calculating the WACC using the effective after-tax cost of debt: Weighted Average Cost of Capital (After Tax)6 E D rwacc = rE + rD ( 1 − τ c ) (15.5) E+D E+D The WACC represents the effective cost of capital to the firm, after including the benefits of the interest tax shield. It is therefore lower than the pretax WACC, which is the a­ verage r­eturn paid to the firm’s investors. From Eq. 15.5, we have the following relationship ­between the WACC and the firm’s pretax WACC: E D D rwacc = rE + rD − rD τ c ¸˚˝˚˛ ¸˚+˚˝˚ E + D E + D E D ˚˛ (15.6) Pretax WACC Reduction Due to Interest Tax Shield As we will show in Chapter 18, even in the presence of taxes, a firm’s target leverage ratio does not affect the firm’s pretax WACC, which equals its unlevered cost of capital and depends only on the risk of the firm’s assets.7 Thus, the higher the firm’s leverage, the more the firm exploits the tax advantage of debt, and the lower its WACC is. Figure 15.2 illustrates this decline in the WACC with the firm’s leverage ratio. The Interest Tax Shield with a Target Debt-Equity Ratio Earlier we calculated the value of the tax shield assuming the firm maintains a constant level of debt. In many cases this assumption is unrealistic—rather than maintain a constant 5 We derived this same result in Chapter 5 when considering the implications of tax-deductible interest for individuals (e.g., with a home mortgage). 6 We will derive this formula in Chapter 18. See Chapter 12 for methods of estimating the cost of debt (and Eqs. 12.12 and 12.13 on page 467 in the context of the WACC). 7 Specifically, if the firm adjusts its leverage to maintain a target debt-equity ratio or interest coverage ratio, then its pretax WACC remains constant and equal to its unlevered cost of capital. See Chapter 18 for a full discussion of the relationship between the firm’s levered and unlevered costs of capital. M15_BERK6318_06_GE_C15.indd 562 26/04/23 7:11 PM  15.2 Valuing the Interest Tax Shield 563 FIGURE 15.2 35% The WACC with and without Corporate Taxes 30% We compute the WACC as a function of the firm’s target debt-to-value ratio using 25% Equity Cost of Capital rE Eq. 15.5. As shown in Cost of Capital Figure 14.1, the firm’s 20% unlevered cost of capital or pretax WACC is constant, Pretax WACC ru 15% reflecting the required return of the firm’s investors based WACC with Taxes rwacc on the risk of the firm’s 10% assets. However, the WACC, which represents the after- Debt Cost of Capital rD 5% tax cost to the firm, declines with leverage as the ­interest After-Tax Debt Cost of Capital rD (1 2 tc ) tax shield grows. The ­figure 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% assumes a marginal ­corporate income tax rate of τ c = 20%. % Debt Financing (D/(E 1 D)) level of debt, many firms target a specific debt-equity ratio instead. When a firm does so, the level of its debt will grow (or shrink) with the size of the firm. As we will show formally in Chapter 18, when a firm adjusts its debt over time so that its debt-equity ratio is expected to remain constant, we can compute its value with lever- age, V L , by discounting its free cash flow using the WACC. The value of the interest tax shield can be found by comparing V L to the unlevered value, V U , of the free cash flow discounted at the firm’s unlevered cost of capital, the pretax WACC. EXAMPLE 15.3 Valuing the Interest Tax Shield with a Target Debt-Equity Ratio Problem Western Lumber Company expects to have free cash flow in the coming year of $4.25 million, and its free cash flow is expected to grow at a rate of 4% per year thereafter. Western Lumber has an equity cost of capital of 10% and a debt cost of capital of 6%, and it pays a corporate tax rate of 21%. If Western Lumber maintains a debt-equity ratio of 0.50, what is the value of its interest tax shield? Solution We can estimate the value of Western Lumber’s interest tax shield by comparing its value with and without leverage. We compute its unlevered value by discounting its free cash flow at its pretax WACC: E D 1 0.5 Pretax WACC = rE + rD = 10% + 6% = 8.67% E+D E+D 1 + 0.5 1 + 0.5 M15_BERK6318_06_GE_C15.indd 563 26/04/23 7:11 PM  564 Chapter 15 Debt and Taxes Because Western Lumber’s free cash flow is expected to grow at a constant rate, we can value it as a constant growth perpetuity: 4.25 VU = = $91 million 8.67% − 4% To compute Western Lumber’s levered value, we calculate its WACC: E D WACC = rE + rD ( 1 − τ c ) E+D E+D 1 0.5 = 10% + 6% ( 1 − 0.21 ) = 8.25% 1 + 0.5 1 + 0.5 Thus, Western Lumber’s value including the interest tax shield is 4.25 V L = = $100 million 8.25% − 4% The value of the interest tax shield is therefore PV (Interest Tax Shield) = V L − V U = 100 − 91 = $9 million CONCEPT CHECK 1. With corporate taxes as the only market imperfection, how does the value of the firm with leverage differ from its value without leverage? 2. How does leverage affect a firm’s weighted average cost of capital? 15.3 Recapitalizing to Capture the Tax Shield When a firm makes a significant change to its capital structure, the transaction is called a ­recapitalization (or simply a “recap”). In Chapter 14, we introduced a leveraged recapi- talization in which a firm issues a large amount of debt and uses the proceeds to pay a special dividend or to repurchase shares. Leveraged recaps were especially popular in the mid- to late-1980s, when many firms found that these transactions could reduce their tax payments. Let’s see how such a transaction might benefit current shareholders. Midco Industries 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 21% tax rate. Management plans to borrow $100 million on a permanent basis through a leveraged recap in which they would use the borrowed funds to repurchase outstanding shares. Their expectation is that the tax savings from this transaction will boost Midco’s stock price and benefit shareholders. Let’s see if this expectation is realistic. The Tax Benefit First, we examine the tax consequences of Midco’s leveraged recap. Without leverage, Midco’s total market value is the value of its unlevered equity. Assuming the current stock price is the fair price for the shares without leverage: V U = ( 20 million shares ) × ( $15 share ) = $300 million M15_BERK6318_06_GE_C15.indd 564 26/04/23 7:11 PM  15.3 Recapitalizing to Capture the Tax Shield 565 With leverage, Midco will reduce its annual tax payments. If Midco borrows $100 million using permanent debt, the present value of the firm’s future tax savings is PV (Interest Tax Shield) = τ c D = 21% × $100 million = $21 million Thus, the total value of the levered firm will be V L = V U + τ c D = $300 million + $21 million = $321 million This total value represents the combined value of the debt and the equity after the recapi- talization. Because the value of the debt is $100 million, the value of the equity is E =V L − D = $321 million − $100 million = $221 million While total firm value has increased, the value of equity dropped after the recap. How do shareholders benefit from this transaction? Even though the value of the shares outstanding drops to $221 million, don’t forget that shareholders will also receive the $100 million that Midco will pay out through the share repurchase. In total, they will receive the full $321 million, a gain of $21 million over the value of their shares without leverage. Let’s trace the details of the share repurchase and see how it leads to an increase in the stock price. The Share Repurchase Suppose Midco repurchases its shares at their current price of $15 per share. The firm will repurchase $100 million ÷ $15 per share = 6.667 million shares, and it will then have 20 − 6.667 = 13.333 million shares outstanding. Because the total value of equity after the transaction is $221 million, the new share price is $221 million = $16.575 13.333 million shares The shareholders who keep their shares earn a capital gain of $16.575 − $15 = $1.575 per share, for a total gain of $1.575 share × 13.333 million shares = $21 million In this case, the shareholders who remain after the recap receive the benefit of the tax shield. However, you may have noticed something odd in the previous calculations. We assumed that Midco was able to repurchase the shares at the initial price of $15 per share, and then demonstrated that the shares would be worth $16.575 after the transaction. Why would a shareholder agree to sell the shares for $15 when they are worth $16.575? No Arbitrage Pricing The previous scenario represents an arbitrage opportunity. Investors could buy shares for $15 immediately before the repurchase, and they could sell these shares immediately after- ward at a higher price. But this activity would raise the share price above $15 even before the repurchase: Once investors know the recap will occur, the share price will rise i­mmediately to a level that reflects the $21 million value of the interest tax shield that the firm will receive. That is, the value of the Midco’s equity will rise immediately from $300 million to $321 million. With 20 million shares outstanding, the share price will rise to $321 million ÷ 20 million shares = $16.05 per share Midco must offer at least this price to repurchase the shares. M15_BERK6318_06_GE_C15.indd 565 26/04/23 7:11 PM  566 Chapter 15 Debt and Taxes With a repurchase price of $16.05, the shareholders who tender their shares and the shareholders who hold their shares both gain $16.05 − $15 = $1.05 per share as a result of the transaction. The benefit of the interest tax shield goes to all 20 million of the original shares outstanding for a total benefit of $1.05 share × 20 million shares = $21 million. In other words, 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. EXAMPLE 15.4 Alternative Repurchase Prices Problem Suppose Midco announces a price at which it will repurchase $100 million worth of its shares. Show that $16.05 is the lowest price it could offer and expect shareholders to tender their shares. How will the benefits be divided if Midco offers more than $16.05 per share? Solution For each repurchase price, we can compute the number of shares Midco will repurchase, as well as the number of shares that will remain after the share repurchase. Dividing the $221 million total value of equity by the number of remaining shares gives Midco’s new share price after the transaction. No shareholders will be willing to sell their shares unless the repurchase price is at least as high as the share price after the transaction; otherwise, they would be better off waiting to sell their shares. As the table shows, the repurchase price must be at least $16.05 for shareholders to be willing to sell rather than waiting to receive a higher price. Repurchase Price Shares Repurchased Shares Remaining New Share Price ($/share) (million) (million) ($/share) PR R = 100 PR N = 20 − R PN = 221 N 15.00 6.67 13.33 $16.58 15.55 6.43 13.57 16.29 16.05 6.23 13.77 16.05 16.55 6.04 13.96 15.83 17.05 5.87 14.13 15.64 If Midco offers a price above $16.05, then all existing shareholders will be eager to sell their shares, because the shares will have a lower value after the transaction is completed. In this case, Midco’s offer to repurchase shares will be oversubscribed and Midco will need to use a lottery or some other rationing mechanism to choose from whom it will repurchase shares. In that case, more of the benefits of the recap will go to the shareholders who are lucky enough to be selected for the repurchase. Analyzing the Recap: The Market Value Balance Sheet We can analyze the recapitalization using the market value balance sheet, a tool we devel- oped in Chapter 14. It states that the total market value of a firm’s securities must equal the total market value of the firm’s assets. In the presence of corporate taxes, we must include the interest tax shield as one of the firm’s assets. We analyze the leveraged recap by breaking this transaction into steps, as shown in Table 15.2. First, the recap is announced. At this point, investors anticipate the future ­interest tax shield, raising the value of Midco’s assets by $21 million. Next, Midco issues $100 million in new debt, increasing both Midco’s cash and liabilities by that amount. Finally, Midco uses the cash to repurchase shares at their market price of $16.05. In this step, Midco’s cash declines, as does the number of shares outstanding. M15_BERK6318_06_GE_C15.indd 566 26/04/23 7:11 PM  15.4 Personal Taxes 567 TABLE 15.2            Market Value Balance Sheet for the Steps in Midco’s Leveraged Recapitalization Market Value Balance Step 1: Step 2: Step 3: Sheet ($ million) Initial Recap Announced Debt Issuance Share Repurchase Assets Cash 0 0 100 0 Original assets ( V U ) 300 300 300 300 Interest tax shield 0 21 21 21 Total assets 300 321 421 321 Liabilities Debt 0 0 100 100 Equity = Assets − Liabilities 300 321 321 221 Shares outstanding (million) 20 20 20 13.77 Price per share $15.00 $16.05 $16.05 $16.05 Note that the share price rises at the announcement of the recap. This increase in the share price is due solely to the present value of the (anticipated) interest tax shield. Thus, even though leverage reduces the total market capitalization of the firm’s equity, sharehold- ers capture the benefits of the interest tax shield up front.8 CONCEPT CHECK 1. How can shareholders benefit from a leveraged recap when it reduces the total value of equity? 2. How does the interest tax shield enter into the market value balance sheet? 15.4 Personal Taxes So far, we have looked at the benefits of leverage with regard to the taxes a corporation must pay. By reducing a firm’s corporate tax liability, debt allows the firm to pay more of its cash flows to investors. Unfortunately for investors, after they receive the cash flows, they are generally taxed again. For individuals, interest payments received from debt are taxed as income. Equity investors also must pay taxes on dividends and capital gains. What are the consequences to firm value of these additional taxes? Including Personal Taxes in the Interest Tax Shield The value of a firm is equal to the amount of money the firm can raise by issuing securities. The amount of money an investor will pay for a security ultimately depends on the benefits the investor will receive—namely, the cash flows the investor will receive after all taxes have been paid. Thus, just like corporate taxes, personal taxes reduce the cash flows to investors and diminish firm value. As a result, the actual interest tax shield depends on the reduction in the total taxes (both corporate and personal) that are paid.9 8 We are ignoring other potential side effects of leverage, such as costs of future financial distress. We discuss such costs in Chapter 16. 9 This point was made most forcefully in yet another pathbreaking article by Merton Miller, “Debt and Taxes,” Journal of Finance 32 (1977): 261–275. See also M. Miller and M. Scholes, “Dividends and Taxes,” Journal of Financial Economics 6 (1978): 333–364. M15_BERK6318_06_GE_C15.indd 567 26/04/23 7:11 PM  Key Points and Equations 581 Employee Stock Options The typical employee stock option allows employees of a as Microsoft, Cisco Systems, Dell, and Qualcomm, had no firm to buy the firm’s stock at a discounted price (often, the taxable income—using the stock option deduction, they price of the stock when they started employment). When an were able to report a loss for tax purposes.* A study by Pro- employee exercises a stock option, the firm is essentially selling fessors J. Graham, M. Lang, and D. Shackelford reported shares to the employee at a discount. If the discount is large, the that in 2000, stock option deductions for the entire Nasdaq employee can exercise the option and earn a large profit. 100 exceeded aggregate pretax earnings.† For these firms, The amount of the discount is a cost for the firm’s equity there would have been no tax advantage associated with holders because selling shares at a price below their market debt—which may help explain why they used little to no value dilutes the value of the firm’s shares. To reflect this debt financing. cost, the IRS allows firms to deduct the amount of the dis- Since 2006, firms have been required to expense count from their earnings for tax purposes. ( The IRS taxes employee stock options. However, the rules for expensing employees on the gain, so the tax burden does not go away, the options are not the same as the tax deduction. Options but moves from the firm to the employees.) Unlike the are expensed based on their value when granted, but the tax interest tax shield, the tax deduction from employee stock deduction occurs and is based on the value when exercised. options does not add to the value of the firm. If the same As a consequence, stock options can create a significant dif- amounts were paid to employees through salary rather than ference between firms’ accounting income and their income options, the firm would be able to deduct the extra salary for tax purposes. For example, Mark Zuckerberg’s founding from its taxable income as well. options in Facebook led to an accounting expense of under During the stock market boom of the late 1990s, many $10 million, yet provided Facebook with a tax deduction technology firms and other firms that issued a large number exceeding $2 billion. of employee stock options were able to claim these deductions * See M. Sullivan, “Stock Options Take $50 Billion Bite Out of and lower their taxes relative to what one would naively have Corporate Taxes,” Tax Notes (March 18, 2002): 1396–1401. imputed from EBIT. In 2000, some of the most profitable † “Employee Stock Options, Corporate Taxes and Debt Policy,” Journal companies in the United States ( based on net income), such of Finance 59 (2004): 1585–1618. CONCEPT CHECK 1. How does the growth rate of a firm affect the optimal fraction of debt in the capital structure? 2. Do firms choose capital structures that fully exploit the tax advantages of debt? Key Points 15.1 The Interest Tax Deduction and Equations Because interest expense is tax deductible, leverage increases the total amount of income avail- able to all investors. The gain to investors from the tax deductibility of interest payments is called the interest tax shield. Interest Tax Shield = Corporate Tax Rate × Interest Payments(15.1) 15.2 Valuing the Interest Tax Shield When we consider corporate taxes, the total value of a levered firm equals the value of an unle- vered firm plus the present value of the interest tax shield. V L = V U + PV (Interest Tax Shield) (15.2) M15_BERK6318_06_GE_C15.indd 581 26/04/23 7:11 PM  582 Chapter 15 Debt and Taxes When a firm’s marginal tax rate is constant, and there are no personal taxes, the present value of the interest tax shield from permanent debt equals the tax rate times the value of the debt, τ c D. The firm’s pretax WACC measures the required return to the firm’s investors. Its effective after- tax WACC, or simply the WACC, measures the cost to the firm after including the benefit of the interest tax shield. The two notions are related as follows: E D rwacc = rE + rD ( 1 − τ c ) (15.5) E+D E+D E D D = rE + rD − rD τ c (15.6) E + D E + D   E +  D  Pretax WACC Reduction Due to Interest Tax Shield Absent other market imperfections, the WACC declines with a firm’s leverage. When the firm maintains a target leverage ratio, we compute its levered value V L as the pres- ent value of its free cash flows using the WACC, whereas its unlevered value V U is the present value of its free cash flows using its unlevered cost of capital or pretax WACC. 15.3 Recapitalizing to Capture the Tax Shield 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 Investors often face higher tax rates on interest income τ i than on income from equity τ e , off- setting the corporate tax benefit of leverage. The effective tax advantage of debt incorporating investor level taxes can be estimated as ( 1 − τ c )( 1 − τ e ) τ* = 1− (15.7) (1 − τ i ) 15.5 Optimal Capital Structure with Taxes The optimal level of leverage from a tax-saving perspective is the level such that interest equals the income limit for the tax deduction. In this case, the firm takes full advantage of the corporate tax deduction of interest, but avoids the tax disadvantage of excess leverage at the personal level. The optimal fraction of debt, as a proportion of a firm’s capital structure, declines with the growth rate of the firm. The interest expense of the average firm is well below its taxable income, implying that firms do not fully exploit the tax advantages of debt. Key Terms interest tax shield p. 557 repatriation tax p. 561 Further In their 1963 paper, “Corporate Income Taxes and the Cost of Capital: A Correction,” American Eco- Reading nomic Review 53 ( June 1963): 433–443, Modigliani and Miller adjusted their analysis to incorporate the tax benefits of leverage. Other classic works in how taxation affects the cost of capital and optimal capital structure include: M. King, “Taxation and the Cost of Capital,” Review of Economic Studies 41 (1974): 21–35; M. Miller, “Debt and Taxes,” Journal of Finance 32 (1977): 261–275; M. Miller and M. Scholes, “Dividends and Taxes,” Journal of Financial Economics 6 (1978): 333–364; and J. Stiglitz, “Tax- ation, Corporate Financial Policy, and the Cost of Capital,” Journal of Public Economics 2 (1973): 1–34. M15_BERK6318_06_GE_C15.indd 582 26/04/23 7:11 PM