# Chapter 15 Debt and Taxes

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1 hapter 15 Debt and Taxes Pelamed Pharmaceutcals has EBIT of \$325 mllon n In addton, Pelamed has nterest expenses of \$125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net ncome? b. What s the total of Pelamed s 2006 net ncome and nterest payments? c. If Pelamed had no nterest expenses, what would ts 2006 net ncome be? How does t compare to your answer n part (b)? d. What s the amount of Pelamed s nterest tax sheld n 2006? a. Net Income = EBIT Interest Taxes = ( ) ( 0.40 ) = \$120 mllon. b. Net ncome + Interest = = \$245 mllon c. Net ncome = EBIT Taxes = 325 ( 0.40 ) = \$195 mllon. Ths s = \$50 mllon lower than part (b). d. Interest tax sheld = % = \$50 mllon Grommt Engneerng expects to have net ncome next year of \$20.75 mllon and free cash flow of \$22.15 mllon. Grommt s margnal corporate tax rate s 35%. a. If Grommt ncreases leverage so that ts nterest expense rses by \$1 mllon, how wll ts net ncome change? b. For the same ncrease n nterest expense, how wll free cash flow change? a. Net ncome wll fall by the after-tax nterest expense to \$ ( 0.35 ) = \$20. mllon. b. Free cash flow s not affected by nterest expenses Suppose the corporate tax rate s 40%. onsder a frm that earns \$00 before nterest and taxes each year wth no rsk. The frm s captal expendtures equal ts deprecaton expenses each year, and t wll have no changes to ts net workng captal. The rsk-free nterest rate s 5%. a. Suppose the frm has no debt and pays out ts net ncome as a dvdend each year. What s the value of the frm s equty? b. Suppose nstead the frm makes nterest payments of \$500 per year. What s the value of equty? What s the value of debt? c. What s the dfference between the total value of the frm wth leverage and wthout leverage? d. The dfference n part (c) s equal to what percentage of the value of the debt?

2 194 Berk/DeMarzo orporate Fnance, Second Edton a. Net ncome = 00 ( 40% ) = \$600. Thus, equty holders receve dvdends of \$600 per year wth no rsk. 600 E = = \$12, 000 5% 300 b. Net ncome = ( ) ( 0.40 ) = \$300 E = = \$6000. Debt holders receve nterest 5% of \$500 per year D = \$,000 c. Wth leverage = 6,000 +,000 = \$16,000 Wthout leverage = \$12,000 Dfference = 16,000 12,000 = \$4000 4,000 d. = 40% = corporate tax rate, Braxton Enterprses currently has debt outstandng of \$35 mllon and an nterest rate of 8%. Braxton plans to reduce ts debt by repayng \$7 mllon n prncpal at the end of each year for the next fve years. If Braxton s margnal corporate tax rate s 40%, what s the nterest tax sheld from Braxton s debt n each of the next fve years? Year Debt Interest Tax Sheld Your frm currently has \$0 mllon n debt outstandng wth a % nterest rate. The terms of the loan requre the frm to repay \$25 mllon of the balance each year. Suppose that the margnal corporate tax rate s 40%, and that the nterest tax shelds have the same rsk as the loan. What s the present value of the nterest tax shelds from ths debt? Year Debt Interest Tax Sheld PV \$ Arnell Industres has just ssued \$ mllon n debt (at par). The frm wll pay nterest only on ths debt. Arnell s margnal tax rate s expected to be 35% for the foreseeable future. a. Suppose Arnell pays nterest of 6% per year on ts debt. What s ts annual nterest tax sheld? b. What s the present value of the nterest tax sheld, assumng ts rsk s the same as the loan? c. Suppose nstead that the nterest rate on the debt s 5%. What s the present value of the nterest tax sheld n ths case? a. Interest tax sheld = \$ 6% 35% = \$0.21 mllon b. \$0.21 PV(Interest tax sheld) = = \$3.5 mllon 0.06

3 Berk/DeMarzo orporate Fnance, Second Edton 195 c. Interest tax sheld = \$ 5% 35% = \$0.175 mllon. \$0.175 PV = = \$3.5 mllon Ten years have passed snce Arnell ssued \$ mllon n perpetual nterest only debt wth a 6% annual coupon, as n Problem 6. Tax rates have remaned the same at 35% but nterest rates have dropped so Arnell s current cost of debt captal s 4%. a. What s Arnell s annual nterest tax sheld? b. What s the present value of the nterest tax sheld today? a. Soluton Interest tax sheld = \$ 6% 35% = \$0.21 mllon \$0.21 b. Soluton PV(Interest tax sheld) = = \$5.25 mllon Alternatvely, new market value of debt s D = (.06)/.04 = \$15 mllon. Tc D = 35% 15 = \$5.25 mllon Bay Transport Systems (BTS) currently has \$30 mllon n debt outstandng. In addton to 6.5% nterest, t plans to repay 5% of the remanng balance each year. If BTS has a margnal corporate tax rate of 40%, and f the nterest tax shelds have the same rsk as the loan, what s the present value of the nterest tax sheld from the debt? Interest tax sheld n year 1 = \$30 6.5% 40% = \$0.78 mllon. As the outstandng balance declnes, so wll the nterest tax sheld. Therefore, we can value the nterest tax sheld as a growng perpetuty wth a growth rate of g = -5% and r = 6.5%: \$0.78 PV = = \$6.78 mllon 6.5% + 5% Safeco Inc. has no debt, and mantans a polcy of holdng \$ mllon n excess cash reserves, nvested n rsk-free Treasury securtes. If Safeco pays a corporate tax rate of 35%, what s the cost of permanently mantanng ths \$ mllon reserve? (Hnt: what s the present value of the addtonal taxes that Safeco wll pay?) D = -\$ mllon (negatve debt) So PV(Interest tax sheld) = Tc D = -\$3.5 mllon. Ths s the present value of the future taxes Safeco wll pay on the nterest earned on ts reserves Rogot Instruments makes fne Volns and ellos. It has \$1 mllon n debt outstandng, equty valued at \$2 mllon, and pays corporate ncome tax at rate 35%. Its cost of equty s 12% and ts cost of debt s 7%. a. What s Rogot s pretax WA? b. What s Rogot s (effectve after-tax) WA? E D 2 1 = r + r (1 ) = =.33% E + D E + D 3 3 a. rwacc E D τ c E D 2 1 = r + r (1 ) = 12+ 7(.65) = 9.52% E + D E + D 3 3 b. rwacc E D τ c

4 196 Berk/DeMarzo orporate Fnance, Second Edton Rumolt Motors has 30 mllon shares outstandng wth a prce of \$15 per share. In addton, Rumolt has ssued bonds wth a total current market value of \$150 mllon. Suppose Rumolt s equty cost of captal s %, and ts debt cost of captal s 5%. a. What s Rumolt s pretax weghted average cost of captal? b. If Rumolt s corporate tax rate s 35%, what s ts after-tax weghted average cost of captal? a. E = \$15 30 = \$450 mllon. D = \$150 mllon. Pretax WA = % + 5% = 8.75% WA = % + 5% 35% = % b. ( ) Summt Bulders has a market debt-equty rato of 0.65 and a corporate tax rate of 40%, and t pays 7% nterest on ts debt. The nterest tax sheld from ts debt lowers Summt s WA by what amount? D E+ D = 1.65 =. Therefore, WA = Pretax WA.394(7%)(.40) = Pretax WA 1.% So, t lowers t by 1.1% NatNah, a bulder of acoustc accessores, has no debt and an equty cost of captal of 15%. Suppose NatNah decdes to ncrease ts leverage and mantan a market debt-to-value rato of 0.5. Suppose ts debt cost of captal s 9% and ts corporate tax rate s 35%. If NatNah s pretax WA remans constant, what wll ts (effectve after-tax) WA be wth the ncrease n leverage? D rd Pretax Wacc 15% % E+ D τ = = Restex mantans a debt-equty rato of 0.85, and has an equty cost of captal of 12% and a debt cost of captal of 7%. Restex s corporate tax rate s 40%, and ts market captalzaton s \$220 mllon. a. If Restex s free cash flow s expected to be \$ mllon n one year, what constant expected future growth rate s consstent wth the frm s current market value? b. Estmate the value of Restex s nterest tax sheld = 12% + 7% 0.40 = 8.42% L FF V = E+ D = = 407 = = WA g g g = = 5.96% 407 a. WA ( ) b pretax WA = 12% + 7% = 9.70% FF = = = \$267 mllon pretax WA g PV Interest Tax Sheld = = \$140 mllon U V ( )

5 Berk/DeMarzo orporate Fnance, Second Edton Acme Storage has a market captalzaton of \$0 mllon and debt outstandng of \$40 mllon. Acme plans to mantan ths same debt-equty rato n the future. The frm pays an nterest rate of 7.5% on ts debt and has a corporate tax rate of 35%. a. If Acme s free cash flow s expected to be \$7 mllon next year and s expected to grow at a rate of 3% per year, what s Acme s WA? b. What s the value of Acme s nterest tax sheld? a. L FF 7 V = E+ D = 140 = =. Therefore WA = 8%. WA g WA 3% 40 WA = WA + D rd 8% 7.5% % E+ D τ = = b. Pre-tax ( )( ) U FF 7 V = = = \$122 mllon pretax WA g L U PV Interest Tax Sheld = V V = = \$18 mllon ( ) Mlton Industres expects free cash flow of \$5 mllon each year. Mlton s corporate tax rate s 35%, and ts unlevered cost of captal s 15%. The frm also has outstandng debt of \$19.05 mllon, and t expects to mantan ths level of debt permanently. a. What s the value of Mlton Industres wthout leverage? b. What s the value of Mlton Industres wth leverage? a. U 5 V = = \$33.33 mllon 0.15 L U b. V = V + τ D = = \$40 mllon Suppose Mcrosoft has 8.75 bllon shares outstandng and pays a margnal corporate tax rate of 35%. If Mcrosoft announces that t wll payout \$50 bllon n cash to nvestors through a combnaton of a specal dvdend and a share repurchase, and f nvestors had prevously assumed Mcrosoft would retan ths excess cash permanently, by how much wll Mcrosoft s share prce change upon the announcement? Reducng cash s equvalent to ncreasng leverage by \$50 bllon. PV of tax savngs = 35% 50 = \$17.5 bllon, or 17.5/ 8.75 = \$2.00 per share prce ncrease Kurz Manufacturng s currently an all-equty frm wth 20 mllon shares outstandng and a stock prce of \$7.50 per share. Although nvestors currently expect Kurz to reman an all-equty frm, Kurz plans to announce that t wll borrow \$50 mllon and use the funds to repurchase shares. Kurz wll pay nterest only on ths debt, and t has no further plans to ncrease or decrease the amount of debt. Kurz s subject to a 40% corporate tax rate. a. What s the market value of Kurz s exstng assets before the announcement? b. What s the market value of Kurz s assets (ncludng any tax shelds) just after the debt s ssued, but before the shares are repurchased? c. What s Kurz s share prce just before the share repurchase? How many shares wll Kurz repurchase? d. What are Kurz s market value balance sheet and share prce after the share repurchase? a. Assets = Equty = \$ = \$150 mllon b. Assets = 150 (exstng) + 50 (cash) + 40% 50 (tax sheld) = \$220 mllon

6 198 Berk/DeMarzo orporate Fnance, Second Edton c. E = Assets Debt = = \$170 mllon. Share prce \$170 mllon = = \$ Kurz wll repurchase = mllon shares d. Assets = 150 (exstng) + 40% 50 (tax sheld) = \$170 mllon Debt = \$50 mllon E = A D = = \$120 mllon \$120 Share prce = = \$8.50 / share Rally, Inc., s an all-equty frm wth assets worth \$25 bllon and bllon shares outstandng. Rally plans to borrow \$ bllon and use these funds to repurchase shares. The frm s corporate tax rate s 35%, and Rally plans to keep ts outstandng debt equal to \$ bllon permanently. a. Wthout the ncrease n leverage, what would Rally s share prce be? b. Suppose Rally offers \$2.75 per share to repurchase ts shares. Would shareholders sell for ths prce? c. Suppose Rally offers \$3.00 per share, and shareholders tender ther shares at ths prce. What wll Rally s share prce be after the repurchase? d. What s the lowest prce Rally can offer and have shareholders tender ther shares? What wll ts stock prce be after the share repurchase n that case? 25 a. Share prce = = \$2.50 per share b. Just before the share repurchase: Assets = 25( exstng) + ( cash) + 35% ( tax sheld ) = \$38.5 bllon 28.5 E = 38.5 = 28.5Þshare prce = = \$2.85/ share. Therefore, shareholders wll not sell for \$2.75 per share. c. Assets = 25 (exstng) + 35% (tax sheld) = \$28.5 bllon E = 28.5 = 18.5 bllon 18.5 Shares = = bllon. Share prce = = \$2.775 share d. From (b), far value of the shares pror to repurchase s \$2.85. At ths prce, Rally wll have = 6.49 mllon shares outstandng, whch wll be worth 18.5 = \$2.85 after the repurchase. Therefore, shares wll be wllng to sell at ths prce Suppose the corporate tax rate s 40%, and nvestors pay a tax rate of 15% on ncome from dvdends or captal gans and a tax rate of 33.3% on nterest ncome. Your frm decdes to add debt so t wll pay an addtonal \$15 mllon n nterest each year. It wll pay ths nterest expense by cuttng ts dvdend. a. How much wll debt holders receve after payng taxes on the nterest they earn? b. By how much wll the frm need to cut ts dvdend each year to pay ths nterest expense?

7 Berk/DeMarzo orporate Fnance, Second Edton 199 c. By how much wll ths cut n the dvdend reduce equty holders annual after-tax ncome? d. How much less wll the government receve n total tax revenues each year? e. What s the effectve tax advantage of debt τ*? a. \$15 (1.333) = \$ mllon each year b. Gven a corporate tax rate of 40%, an nterest expense of \$15 mllon per year reduces net ncome by 15(1.4) = \$9 mllon after corporate taxes. c. \$9 mllon dvdend cut \$9 (1.15) = \$7.65 mllon per year. d. Interest taxes = = \$5 mllon Less corporate taxes = = \$6 mllon Less dvdend taxes =.15 9 = \$1.35 mllon e. Govt tax revenues change by = \$2.35 mllon (Note ths equals (a) (c)). ( 0.40)( 0.15) τ* = = 23.5% Apple orporaton had no debt on ts balance sheet n 2008, but pad \$2 bllon n taxes. Suppose Apple were to ssue suffcent debt to reduce ts taxes by \$1 bllon per year permanently. Assume Apple s margnal corporate tax rate s 35% and ts borrowng cost s 7.5%. a. If Apple s nvestors do not pay personal taxes (because they hold ther Apple stock n taxfree retrement accounts), how much value would be created (what s the value of the tax sheld)? b. How does your answer change f nstead you assume that Apple s nvestors pay a 15% tax rate on ncome from equty and a 35% tax rate on nterest ncome? a. \$1 bllon / 7.5% = \$13.33 bllon. b. To reduce taxes by \$1 bllon, Apple wll need to make nterest payments of 1/.35 = \$2.857 bllon, or ssue 2.857/.075 = \$38.1 bllon n debt. T = 1 (1 tc)(1 te)/(1 t) = 1 (.65)(.85)/.65 = 15% T D = 15% \$38.1 = \$5.71 bllon Markum Enterprses s consderng permanently addng \$0 mllon of debt to ts captal structure. Markum s corporate tax rate s 35%. a. Absent personal taxes, what s the value of the nterest tax sheld from the new debt? b. If nvestors pay a tax rate of 40% on nterest ncome, and a tax rate of 20% on ncome from dvdends and captal gans, what s the value of the nterest tax sheld from the new debt? a. PV = τ D = 35% 0 = \$35 mllon. b. ( 0.35)( 0.20) τ* = = 13.33% 0.40 PV = τ D = 13.33% 0 = \$13.33 mllon Garnet orporaton s consderng ssung rsk-free debt or rsk-free preferred stock. The tax rate on nterest ncome s 35%, and the tax rate on dvdends or captal gans from preferred

8 200 Berk/DeMarzo orporate Fnance, Second Edton stock s 15%. However, the dvdends on preferred stock are not deductble for corporate tax purposes, and the corporate tax rate s 40%. a. If the rsk-free nterest rate for debt s 6%, what s cost of captal for rsk-free preferred stock? b. What s the after-tax debt cost of captal for the frm? Whch securty s cheaper for the frm? c. Show that the after-tax debt cost of captal s equal to the preferred stock cost of captal multpled by (1 τ*). a. Investors receve 6% (1.35) = 3.9% after-tax from rsk-free debt. They must earn the same after-tax return from rsk-free preferred stock. Therefore, the cost of captal for preferred stock s 3.9% 0.15% = 4.59%. b. After-tax debt cost of captal = 6% (1.40) = 3.60% s cheaper than the 4.59% cost of captal for preferred stock. ( 0.40)( 0.15) c. τ* = = 21.54% % (1.2154) = 3.60% Suppose the tax rate on nterest ncome s 35%, and the average tax rate on captal gans and dvdend ncome s %. How hgh must the margnal corporate tax rate be for debt to offer a tax advantage? ( )( e) τ* = > 0 f and only f τ < or equvalently: 1 τ e 0.65 τ > = = 27.8% Thus, there s a tax advantage of debt as long as the margnal corporate tax rate s above 27.8% Wth ts current leverage, Imp orporaton wll have net ncome next year of \$4.5 mllon. If Imp s corporate tax rate s 35% and t pays 8% nterest on ts debt, how much addtonal debt can Imp ssue ths year and stll receve the beneft of the nterest tax sheld next year? 4.5 Net ncome of \$4.5 mllon 0.35 = \$6.923 mllon n taxable ncome. Therefore, Arundel can ncrease ts nterest expenses by \$6.923 mllon, whch corresponds to debt of: \$ = mllon olt Systems wll have EBIT ths comng year of \$15 mllon. It wll also spend \$6 mllon on total captal expendtures and ncreases n net workng captal, and have \$3 mllon n deprecaton expenses. olt s currently an all-equty frm wth a corporate tax rate of 35% and a cost of captal of %. a. If olt s expected to grow by 8.5% per year, what s the market value of ts equty today? b. If the nterest rate on ts debt s 8%, how much can olt borrow now and stll have nonnegatve net ncome ths comng year? c. Is there a tax ncentve for olt to choose a debt-to-value rato that exceeds 50%? Explan. e

9 Berk/DeMarzo orporate Fnance, Second Edton 201 a. FF EBIT ( τ ) Dep apex NW ( ) = + Δ = = E = = \$450 mllon % 8.5% b. 15 Interest expense of \$15 mllon debt of \$ = mllon. c. No. The most they should borrow s mllon; there s no nterest tax sheld from borrowng more PMF, Inc., s equally lkely to have EBIT ths comng year of \$ mllon, \$15 mllon, or \$20 mllon. Its corporate tax rate s 35%, and nvestors pay a 15% tax rate on ncome from equty and a 35% tax rate on nterest ncome. a. What s the effectve tax advantage of debt f PMF has nterest expenses of \$8 mllon ths comng year? b. What s the effectve tax advantage of debt for nterest expenses n excess of \$20 mllon? (Ignore carryforwards.) c. What s the expected effectve tax advantage of debt for nterest expenses between \$ mllon and \$15 mllon? (Ignore carryforwards.) d. What level of nterest expense provdes PMF wth the greatest tax beneft? ( )( e) ( 0.35)( 0.15) a. τ* = = = 15% 0.35 b. For nterest expenses over \$20 mllon, net ncome s negatve so τ = 0. ( )( e) ( 0)( 0.15) Therefore, τ* = = = 31% 0.35 c. For nterest expenses between \$ mllon and \$15 mllon, there s a 2 3 chance that net ncome wll be postve. Therefore, the expected corporate tax savngs s 2 35% 23.3% 3 =. Thus, ( )( ) ( 0.23)( 0.15) e τ* = = = 0.3% d. There s a tax advantage up to an nterest expense of \$ mllon.

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