Chapter 15: Debt and Taxes

Chapter 15: Debt and Taxes-1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt 2. Personal taxes => equty ncome s usually taxed at a lower rate than nterest ncome => ncentve to fund the frm wth equty II. Corporate Income Taxes A. Interest Tax Sheld Ex. Assume you are startng a frm that wll generate a pre-tax cash flow of $100,000 per year. What are your after-tax cash flows f you call your nvestment equty and f you call your nvestment a loan? Assume the corporate tax rate s 35% and that your frm pays out all of ts cash flows ether as dvdends or nterest. Let: If pad as a dvdend: 100,000.35(100,000) = $65,000 If pad as nterest: $100,000 => extra $35,000 per year f call nvestment a loan Q: Where does the $35,000/year come from? Q: If we only consder corporate taxes, how should frms be funded? CF L = cash flows to nvestors wth leverage CF U = cash flows to nvestors wthout leverage (unlevered) C = corporate tax rate => CF L = CF U + Interest Tax Sheld => nterest tax sheld = reducton n taxes because ssue debt = τ nterest expense Ex. CF L = 65,000 +.35(100,000) = 100,000 c

Chapter 15: Debt and Taxes-2 B. Interest Tax Sheld and Frm Value Let: V L = value of levered frm (frm wth debt) V U = value of unlevered frm (frm wth no debt) V L = V U + PV(Interest Tax Sheld) (15.2) C. The Interest Tax Sheld wth Permanent Debt 1. Assumptons: 1) Frm plans to keep a constant dollar amount of debt forever 2) Frm s margnal tax rate s fxed 2. PV of Tax Sheld of Permanent Debt PV(Interest Tax Sheld) = PV(C x Future Interest Payments) = τ c PV(Future Interest Payments) Interest Payment = τ c r r D = τ c r = τ c D (15.4) where: r = nterest rate on debt D = market value of frm s outstandng debt => V L = V U + CD (15.A) Ex. Assume frm s currently funded wth 100% equty and has a market value of $500,000. What wll the frm be worth f the corporate tax rate s 35%, and the frm ssues $200,000 of permanent debt and uses the proceeds to repurchase stock? V L = 500,000 +.35(200,000) = 570,000 => U.S. corporate tax code gves frms an ncentve to ssue debt Q: Where does the extra $70,000 come from?

Chapter 15: Debt and Taxes-3 D. The Weghted Average Cost of Captal wth Taxes From Chapter 14: E = market value of frm s outstandng equty D = market value of frm s outstandng debt re = cost of captal for levered equty rd = cost of captal for frm s debt Basc dea: tax savngs reduce the cost of borrowng r => rat = rd(1-c) (15.B) where: rat = after-tax cost of borrowng W ACC Note: Equaton 15.B can also be used to calculate the after-tax returns for nvestors f use the nvestor s tax rate rather than C E D re rd C (15.5) E D E D Ex. Assume that the market value of a frm s equty s $300,000 and that the market value of ts debt s $200,000. Assume also that the cost of equty s 12%, that the cost of debt s 5%, and that the corporate tax rate s 35%. What s the cost of captal for the frm f nterest s not tax deductble and f t s? r WACC r WACC 300, 000 200, 000 500, 000 500, 000 300, 000 200, 000. 12. 05 1-. 35 500, 000 500, 000 not tax deductble. 12. 05. 092 tax deductble. 085. 6. 12. 4. 0325 Q: What happens to the value of the frm today f the cost of captal s lower? Increases III. Personal Income Taxes A. Personal Taxes and the Interest Tax Sheld => man ssue for captal structure: personal taxes are usually lower for equty ncome than debt ncome => as corporate debt rses, personal taxes ncrease

Chapter 15: Debt and Taxes-4 B. Valung the Interest Tax Sheld wth Personal Taxes V L = V U + D (15.8) where: c e 1 (15.7) 1 = effectve tax advantage of debt c = tax rate on corporate ncome e = tax rate on personal equty ncome, = tax rate on personal nterest ncome Note: see Chapter 15 supplement for proof Ex. Assume that C =.35, =.3, and e =.3 1 5 5 => V L = V U +.35D Note: f e = : personal taxes cancel out Q: How should we fund the frm? Ex. Assume that C =.35, =.3, and e =.15 1 5. 15 107 => V L = V U +.2107D Q: How should we fund the frm? Note: f > e: addtonal taxes at personal level reduces tax beneft at corporate level Note: Dffcult to calculate for several reasons 1. nvestors don t have to realze captal gans and can offset gans wth losses 2. mx of dvdends and captal gans vares by frm 3. returns on retrement accounts untaxed 4. tax rates vary across nvestors

Chapter 15: Debt and Taxes-5 IV. Optmal Captal Structure wth Taxes A. Lmts to the Tax Beneft of Debt 1. Key => debt has a tax beneft to the frm only f have enough earnngs to deduct the nterest => f can t deduct the nterest and ncrease debt, taxes rse due to hgher personal taxes 2. Excess leverage: frm does not have enough earnngs to deduct the nterest 3. Tax mpact of excess leverage => corporate taxes are not reduced => c = 0 => ex 1 0 e e where ex = net tax dsadvantage of excessve debt => tax loss f ssue debt and e < B. Optmal Leverage wth Rsk-free Earnngs Before Interest and Taxes (EBIT) General dea: ssue debt as long as postve Example: Assume that a frm s rskless EBIT wll be $25,000 per year forever. Assume also that the corporate tax rate s 35%. Fnally, assume that the tax rate for ndvdual nterest ncome s 30% and that the tax rate on ndvdual equty ncome s 20%. (15.7) 1 c e => f nterest < $25,000 per year, 1 => f nterest > $25,000 per year, Q: What do these numbers tell us? ex 1 5. 0 25714. 1429

Chapter 15: Debt and Taxes-6 Optmal debt: set nterest equal to EBIT => no corporate taxes pad => optmal annual nterest n example = $25,000 C. Optmal Leverage wth Rsky Earnngs (EBIT) => as nterest expense ncreases, chance of deductng the nterest falls => use E(C) rather than C n equaton 15.7 E(C) = expected corporate tax savngs from nterest = probablty of usng tax sheld x C => 1 E c e (15.7B) Key: ssue debt as long as postve

Chapter 15: Debt and Taxes-7 Example: Assume that the corporate tax rate s 35%, that the personal tax rate s 30% on nterest ncome and 20% on equty ncome. Assume also the followng probablty dstrbuton for the frm s EBIT. (15.7B) 1 EBIT Prob. 10,000.05 15,000.10 20,000.10 25,000.15 30,000.20 35,000.20 40,000.10 45,000.10 E c e Q: What s the probablty of deductng nterest of: up to $10,000? 100% => can deduct even f have lowest possble EBIT (10,000) up to $15,000? 95% => 95% chance of havng EBIT of $15,000 or hgher =.1+.1+.15+.2+.2+.1+.1 = 1 -.05 up to $20,000? 85% => 85% chance of havng EBIT of $20,000 or hgher =.1+.15+.2+.2+.1+.1 = 1 -.05 -.1 up to $25,000? 75% =.15 +.2 +.2 +.1 +.1 = 1 -.05 -.1 -.1 up to $30,000? 60% up to $35,000? 40% up to $40,000? 20% up to $45,000? 10% more than $45,000? No chance snce hghest possble EBIT s $45,000 Q: What s E(C) and for nterest pad equal to: $0 to $10,000? => E(C) =.35 = 1 x.35 1 5 1 => 1 1 5714 Q: Issue debt f nterest currently less than $10,000? yes

Chapter 15: Debt and Taxes-8 $10,001 to $15,000? => E(C) =.95(.35) =.3325 1 325 1 => 1 3714 Q: Issue debt f nterest currently between $10,001 and $15,000? yes $15,001 to $20,000? => E(C) =.85(.35) =.2975 1 975 1 => 1. 19714 Q: Issue debt f nterest currently between $15,001 and $20,000? yes $20,001 to $25,000? => E(C) =.75(.35) =.2625 1 625 1 => 1. 14714 Q: Issue debt f nterest currently between $20,001 and $25,000? yes $25,001 to $30,000? => E(C) =.6(.35) =.21 1 1 1 => 1. 09714 Q: Issue debt f nterest currently between $25,001 and $30,000? yes $30,001 to $35,000? => E(C) =.14;. 01714 Q: Issue debt f nterest between $30,001 and $35,000? yes $35,001 to $40,000: E(C) =.07; =.06286 Q: Issue debt f nterest between $35,001 and $40,000? no

Expected Tax Savngs ($) per Year Chapter 15: Debt and Taxes-9 $40,001 to $45,000? E(C) =.035; = -.10286 Q: Issue debt f nterest between $40,001 and $45,000? no $45,001 or greater? E(C) = 0; = -.14286 = ex Q: Issue debt f nterest exceeds $45,000? no => optmal annual nterest = $35,000 Graph #2: Uncertan EBIT 10,000 5,000 0 0 10000 20000 30000 40000 50000 Interest Expense ($) D. Growth and Debt Note: Assume two frms have the same dstrbuton of possble earnngs (EBIT). Assume also that one frm s growng rapdly whle the other s not growng. 1) The tax-optmal debt for the frms wll be the same 2) The value of the hgh-growth frm s equty wll be hgher Result: The debt rato of the hgh growth frm wll be lower