# U + PV(Interest Tax Shield)

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1 CHAPTER 15 Debt and Taxes Chapter Synopsis 15.1 The Interest Tax Deduction A C-Corporation pays taxes on proits ater interest payments are deducted, but it pays dividends rom ater-tax net income. Thus, the tax code provides an incentive or the use o debt inancing. An interest tax shield is the amount a irm would have paid in taxes i it did not have interest expense. The size o the interest tax shield equals interest expense the tax rate Valuing the Interest Tax Shield The dierential taxing o interest and dividends represents a market imperection not considered in the original MM propositions. Given the availability o an interest tax shield, MM Proposition I can be restated in the presence o corporate taxes such that: The total value o the levered irm exceeds the value o the irm without leverage due to the present value o the tax savings rom debt: V = V U + PV(Interest Tax Shield) I a irm has a permanent, constant amount o debt, D, a marginal tax rate o τ c,and a riskree debt cost o capital o r = r then the interest tax shield equals: D, τ τ τ c Interest c (r D) (r = = = c D) PV(Interest Tax Shield) = τ r r r c D The tax deductibility o interest lowers the eective cost o debt inancing or the irm. I the interest on debt is tax deductible, then an interest rate r is equivalent to an eective ater-tax rate o r (1 τ c ). To account or the beneit o the interest tax shield, the WACC can be restated to account or the ater-tax cost o debt:

2 174 Berk/DeMarzo Corporate Finance, Second Edition E D rwacc = re + rd(1 τ C). E+ D E + D 15.3 Recapitalizing to Capture the Tax Shield Consider a irm that has 20 million shares outstanding, a stock price o \$15, no debt, and a 35% tax rate. The irm has had consistently stable earnings and management believes that they can borrow as much as \$100 million. They are considering a leveraged recapitalization in which they would use the borrowed unds to repurchase \$100 million/\$15 = 6.67 million shares. They expect that the tax savings rom this transaction will boost the stock price and beneit shareholders. Without leverage, the irm s market value is the value o its unlevered equity. Assuming the current stock price is the air price or the shares without leverage: U V = (20 million shares) (\$15) = \$300 million. With \$100 million in permanent debt, the present value o the irm s uture tax savings is τ c D = 0.35(\$100 million) = \$35 million and the levered irm value is: V = V U + PV(Interest Tax Shield) = \$300 million + \$35 million = \$335 million. The equity value, net o the \$100 million o debt, is: \$235 million E = V D= \$335 million \$100 million = \$235 million P = = \$ Since the shares were repurchased at \$15, the million remaining shareholders get all o the \$35 million tax shield, which equals \$35 million/13.33 million = \$2.625 per share. More realistically, once investors know the recap will occur, the share price will rise immediately to a level that relects the \$35 million value o the interest tax shield that the irm will receive, \$235 million/20 million = \$16.75 per share. The beneit o the interest tax shield now goes to all 20 million o the original shares outstanding or a total beneit o \$1.75/share 20 million shares = \$35 million Personal Taxes Personal taxes may oset the corporate tax beneits o leverage. Investors are generally taxed on interest income rom debt and dividend income rom a stock; they are also taxed on capital gains when they sell a stock but may delay incurring those taxes indeinitely. Every \$1 received ater taxes by debt holders rom interest payments costs equity holders \$1 (1 τ * ) on an ater tax basis, in which τ *, the eective tax advantage o debt, equals: τ τ τ τ τ τ * (1 i ) (1 c )(1 e ) (1 = c )(1 e ) = 1 (1 τi) (1 τi) whereτ e is the personal tax rate on equity income and τ i is the personal tax rate on interest * income. Now, the tax shield in a year is τ interest expense, and the value o a levered irm with permanent debt is V = V U + τ * D.

3 Berk/DeMarzo Corporate Finance, Second Edition 175 * When there are no personal taxes, or when τ e = τ i, thenτ = τ C. However, when τ e < τ i, as it is today, then τ * < τ C and there is a tax beneits o leverage Optimal Capital Structure with Taxes In recent years, U.S. irms have shown a clear preerence or debt as a source o external inancing. In act, the overall net equity issues has been negative, meaning that the value o shares that irms have bought back is greater than the value o the shares they have issued. Even though irms have not issued new equity, the market value o equity has risen over time such that average irm s debt as a raction o the irm s value has remained reasonably stable at 35% to 40%. In 2005, debt accounted or about 36% o U.S irms capital structures; however, the use o debt varied signiicantly by industry. Firms in growth industries like high technology carry very little debt, whereas airlines, automakers, and utilities, have high leverage ratios. There is no corporate tax beneit rom incurring interest payments that exceed EBIT. In act, because interest payments constitute a tax disadvantage at the investor level whenτ i > τ e, investors will pay higher individual taxes with excess leverage, making them worse o. Thus, it is optimal to borrow until interest equals EBIT to take ull advantage o the corporate tax deduction o interest, but avoid the tax disadvantage o excess leverage at the personal level. Since there are other provisions in the tax laws or deductions and tax credits, such as depreciation, investment tax credits, and operating loss carryorwards, some irms rely less heavily on the interest tax shield. However, even ater considering alternate tax shields, irms have ar less leverage than theory would predict at this point in the analysis. In the next chapter, actors that may help explain such apparently suboptimal behavior, such as bankruptcy costs, are considered. Selected Concepts and Key Terms Interest Tax Shield The amount that a irm would have paid in taxes i it did not have interest expense. The size o the interest tax shield each period equals interest expense the tax rate. Concept Check Questions and Answers With corporate income taxes, explain why a irm s value can be higher with leverage even though its earnings are lower. A irm can be better o even though its earnings are lower because the total amount available to all investors is higher with leverage. The value o a irm is the total amount it can raise rom all investors, not just equity holders. So, i the irm can pay out more in total with leverage, it will initially be able to raise more total capital What is the interest tax shield? The interest tax shield is the gain to investors rom the tax deductibility o interest payments. It is the additional amount that a irm would have paid in taxes i it did not have leverage.

4 176 Berk/DeMarzo Corporate Finance, Second Edition With corporate taxes as the only market imperection, how does the value o the irm with leverage dier rom its value without leverage? The total value o the levered irm exceeds the value o the irm without leverage due to the present value o the tax savings rom debt How does leverage aect a irm s weighted average cost o capital? Corporate taxes lower the eective cost o debt inancing, which translates into a reduction in the weighted average cost o capital. The magnitude o the reduction in the WACC is proportional to the amount o debt inancing. The higher the irm s leverage, the more the irm exploits the tax advantage o debt, and so the lower its WACC How can shareholders beneit rom a leveraged recap when it reduces the total value o equity? Although a leveraged recap reduces the total value o equity, shareholders capture the beneits o the interest tax shield upront. The stock price rises at the announcement o the recap How does the interest tax shield enter into the market value balance sheet? The total market value o a irm s securities must equal the total market value o the irm s assets. In the presence o corporate taxes, we must include the interest tax shield as one o the irm s assets on the market value balance sheet Under current law (in 2009), why is there a personal tax disadvantage o debt? Just like corporate taxes, personal taxes reduce the cash lows to investors and diminish irm value. Personal taxes thus have the potential to oset some o the corporate tax beneits o leverage. Currently, in the United States and many other countries, interest income is taxed more heavily than capital gains rom equity How does the personal tax disadvantage o debt change the value o leverage or the irm? Personal taxes oset some o the corporate tax beneits o leverage and thus reduce the value o leverage or the irm How does the growth rate o a irm aect the optimal raction o debt in the capital structure? The optimal raction o debt, as a proportion o a irm s capital structure, declines with the growth rate o the irm Do irms choose capital structures that ully exploit the tax advantages o debt? The empirical results o international leverage indicate that irms do not ully exploit the tax advantages o debt because the interest expense o the average irm is well below its taxable income Examples with Step-by-Step Solutions Solving Problems Problems using this chapter s ideas oten involve calculating the ater-tax cost o debt, the ater-tax weighted-average cost o capital, the interest tax shield, and inding the present value o the interest tax shield and the value o a levered irm. Applications include considering the consequences on shareholder value o a leveraged recapitalization, which

5 Berk/DeMarzo Corporate Finance, Second Edition 177 involves issuing debt which is then used to repurchase shares. Problems may also involve considering the eects o personal taxes. Examples 1. You are trying to decide whether your irm should use debt inancing under dierent assumptions regarding the amount o debt in its capital structure. The irm s assets will generate an expected EBIT o \$800,000 per year (beginning one year rom today) in perpetuity. The irm will make no new capital or working capital investments and all assets are ully depreciated. The assets have a beta o 1.5, the risk-ree rate is 5%, and the market risk premium is 10%. You can issue bonds at par paying an annual coupon at a 5% annual rate. The corporate tax rate is 50%, and the irm has 100,000 shares outstanding. [A] What is the value o the irm with no debt? What is the stock value per share? What is the value o the irm i it issues \$1.5 million o debt and uses the proceeds to repurchase 75,000 shares or \$20 (75,000 \$20 = \$1.5 million)? What is the stock value per share? Should the irm issue the debt? Step 1. Determine the unlevered equity cost o capital. The equity cost o capital is ER [ ] = r + β ( ER [ ] r ) = 5% + 1.5(10%) = 20%. i Mkt i Step 2. Determine the ree cash lows o the unlevered irm. Since the irm will make no new investments and has no depreciation, FCF = NI each year. EBIT \$800,000 50% 400,000 Net income 400,000 Step 3. Determine the value o the unlevered irm. FCF \$400,000 Since the cash lows are a perpetuity, PV = = = \$2 million r 0.20 Step 4. Determine the value per share. U V \$2,000,000 Value per share = = = \$20 Shares Outstanding 100,000 Step 5. Determine the value o the levered irm. U Dr ( D)( τ C) V = V + PV(Tax shield) = \$2,000,000 + rd \$1,500,000(0.05)(0.50) = \$2,000,000 + = \$2,750, Step 6. Determine the equity value per share. The total equity value is V D = \$2,750,000 \$1,500,000, and the number o shares repurchased is \$1,500,000/\$20=75,000, so: 2,750,000 1,500,000 Value per share = = \$ ,000 75,000 Mkt

6 178 Berk/DeMarzo Corporate Finance, Second Edition Thus, the irm should issue the debt based on these assumptions because it leads to an \$50 \$20 increase in the share price o = 150%. \$20 2. Wrigley Inc. had \$1 billion in EBITDA in The irm is unlevered and has a market value o equity o \$12 billion and a tax rate o 40%. Consider the eect on the value o the irm o the ollowing debt issuances. Assume that all proceeds will be used to buy back stock. [A] Issuing \$6 billion o 8% coupon rate 5-year bonds which repay the principal in 5 years. Issuing \$6 billion o 8% coupon rate permanent bonds. [C] Issuing \$6 billion o 8% coupon rate bonds, with amount o bonds increasing by 5% every year orever. Step 1. Determine the value o the levered irm or the 5-year bonds. Since annual interest is 0.08(\$6 billion) = \$480 million, the annual tax shield is \$480 million 0.40 = \$192 million or ive years. V U 1 1 = V + PV(Interest Tax Shield) = \$12 billion + \$192million (1.08) = \$12 billion + \$0.8 billion = \$12.8 billion Step 2. Determine the value o the levered irm or the permanent bonds. Now, the \$192 million tax shield is a perpetuity. U \$192 million V = V + PV(Interest Tax Shield) = \$12 billion +.08 = \$12 billion billion = \$14.4 billion Step 3. Determine the value o the levered irm or the bonds that increase by 5% every year orever. Now, the \$14 million tax shield is the irst cash low in a growing perpetuity. U \$192million V = V + PV(Interest Tax Shield) = \$12 billion = \$12billion billion = \$18.5 billion 3. Best Buy is equally likely to have EBIT this coming year o \$1 billion, \$1.5 billion, or \$2 billion. Its corporate tax rate is 35%, and investors pay a 15% tax rate on income rom equity and a 30% tax rate on interest income. [A] What is the eective interest tax shield (considering both personal taxes and corporate taxes) i interest expense is \$500 million this year? At what level o interest expense does the eective tax advantage o debt disappear? Step 1. Determine the eective tax rate i all o the interest will be used to shield taxes. ( 1 τc)( 1 τe) ( )( ) τ* = 1 = 1 = 21.1% 1 τ i Step 2. Determine the eective tax shield i interest expense is \$500,000. Tax shield = τ * Interest expense = \$500,000 = \$105,357

7 Berk/DeMarzo Corporate Finance, Second Edition 179 Step 3. Determine when the eective tax rate is negative by considering dierent levels o interest expense. Interest expense Probability o NI > 0 E[ τ C ] τ * \$500,000, \$1,000,000, \$1,500,000, \$2,000,000, So or an interest expense up to \$1.5 billion, there is a tax advantage. For interest expense over \$1.5 billion, there is an expected eective tax disadvantage or debt inancing. Questions and Problems 1. A irm expects ree cash low o \$10 million each year. Its corporate tax rate is 35%, and its unlevered cost o capital is 10%. The irm also has outstanding debt o \$35 million, and it expects to maintain this level o debt permanently. [A] What is the irm s value without leverage? What is the irm s value with the \$35 million o debt? 2. A irm is considering permanently adding \$100 million o debt to its capital structure. The corporate tax rate is 35%. [A] Absent personal taxes, what is the value o the interest tax shield rom the new debt? I investors pay a tax rate o 40% on interest income, and a tax rate o 20% on income rom dividends and capital gains, what is the value o the interest tax shield rom the new debt? 3. An unlevered irm has 50 million shares outstanding and a stock price o \$20. The irm plans to unexpectedly announce that it will issue \$500 million in 10% coupon rate debt inancing and use the proceeds to repurchase shares. The debt level is expected to remain at this level. The tax rate is 35%. [A] What is the irm s market value beore the announcement? [C] What is the market value o the irm ater the repurchase? What is the share value ater the repurchase assuming that the shares can be repurchased at \$20 per share? 4. Suppose the corporate tax rate is 35%, and investors pay a tax rate o 15% on income rom dividends or capital gains and a tax rate o 28% on interest income. Your irm plans to issue \$1 billion in perpetual 10% coupon bonds. The irm has historically paid all net income out as dividends; however, in order to pay this interest expense, the irm will cut its dividend. [A] How much will bondholders receive ater paying taxes on the interest they earn? By how much will the irm need to cut its dividend each year to pay this interest expense? [C] By how much will this cut in the dividend reduce equity holders annual ater-tax income? [D] How much less will the government receive in total tax revenues each year? [E] What is the eective tax advantage o debt with this amount o leverage? 5. Your unlevered irm will have a certain EBIT every year o \$80 million. Every year it will spend \$10 million on capital expenditures, invest \$10 million in net working capital, and have \$28 million in depreciation. The corporate tax rate is 35%, and the irm s cost o capital is 11%. [A] I the irm s ree cash low is expected to grow by 5% per year, what is the value o its equity today?

8 180 Berk/DeMarzo Corporate Finance, Second Edition I the debt cost o capital is 10%, what amount o borrowing would maximize the value o the irm? What would the value o the irm be then? Solutions to Questions and Problems 1. [A] U 10 V = = \$100 million 0.10 U V = V + τ D = = \$110.5 million C 2. [A] PV(Interest Tax Shield) = τ C D = 35% 100 = \$35 million. ( )( ) τ* = 1 = 13.33% PV(Interest Tax Shield) = τc D = 13.33% 100 = \$13.33 million 3. [A] V U = \$20 50 million = \$1 billion V = V U + PV(Tax Shield) = \$1 billion + \$500 million(0.10)(0.35) =\$175 million 0.10 = \$1.175 billion. [C] E = V D = \$1.175 billion \$500 million = \$675 million 500 million They will repurchase \$ = 25 millionshares. \$20 \$1.175 billion 500 million The share price is thus = =\$ million 25 million 4. [A] \$100 million (1.28) = \$72 million each year An interest expense o \$100 million per year reduces net income by 100(1.35) = \$65 million ater corporate taxes. So, dividends will be \$65 million less. [C] [D] \$65 million dividend cut \$65 (1.15) = \$55.25 million per year. Interest taxes = million = \$28 million ess corporate taxes = million= \$35 million ess dividend taxes = million = \$9.75 million Government tax revenues change by = \$16.75 million ( )( ) [E] τ* = 1 = 23.3% [A] FCF = EBIT ( 1 τ ) + Dep Capex Δ NWC = 80 ( ) = \$60 U 60 V = E = = \$1 billion The irm can pay \$80 million in interest, so it can borrow: \$80 million = \$800 million at 10% \$800 million(0.10)(0.35) V = \$1 billion + = \$1.28 billion 0.10

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