principles_of_corporate_finance_unit_g_lectures.pdf

Capital Structure What Is Capital Structure? • Capital structure refers to the mix of financing instruments (eg, shares, preferred stock, bonds, warrants, etc) a firm uses to fund its investments (assets). • We can think of a firm’s capital structure as broadly being composed of debt and equity. •...

Capital Structure What Is Capital Structure? • Capital structure refers to the mix of financing instruments (eg, shares, preferred stock, bonds, warrants, etc) a firm uses to fund its investments (assets). • We can think of a firm’s capital structure as broadly being composed of debt and equity. • Can be summarised by the debt (or leverage) ratio: Debt ratio = Debt Debt + Equity • Or the debt-to-equity ratio: Debt-equity ratio = Debt Equity Debt and Equity Equity • An equity/stock/share-holding confers an ownership stake in a firm (voting rights). • Equity holders are residual claimants to a firm’s cash flows, entitled but not obligated to receive payments (ie, dividends) from after-tax profits. • Shareholders in corporations are protected by limited liability. Debt: • Many types: loans, bonds, notes. • Creditors/debtholders typically receive legally obligated interest payments (fixed or floating rates), and repayment of principal at maturity. • Interest payments are generally paid out of pre-tax profits. The End What Does Leverage Do? What Does Debt Do? An Example MacBeth Spot Removers is considering moving from being “unlevered” (ie, no debt) to having equal proportions of debt and equity (ie, D/E = 0 to D/E = 1). Consider the consequences of that leverage-increasing (ie, debt-increasing) transaction: Unlevered firm Data Number of shares Price per share Market value of shares 1,000 $10 $10,000 Expected outcome Outcomes Operating income Earnings per share Return on shares (%) A $500 $0.5 5% B 1,000 1.00 10 C 1,500 1.50 15 D 2,000 2.00 20 Example: MacBeth Spot Removers Levered firm (50% debt @ 10% interest) Data Number of shares Price per share Market value of shares Market value of debt 500 $10 $5,000 $5,000 Outcomes Operating income Interest Equity earnings Earnings per share Return on shares (%) A $500 $500 $0 $0 0% B 1,000 500 500 1 10 C 1,500 500 1,000 2 20 D 2,000 500 1,500 3 30 Example: MacBeth Spot Removers (cont.) 3 Unlevered Levered 2.5 EPS ($) 2 1.5 1 0.5 0 0 500 1,000 1,500 2,000 Operating income ($) The Effect of Leverage Leverage (more debt): • Boosts expected EPS and the expected return to equity, as long as the cost of debt is lower than the firm’s expected return on invested capital, But • Also increases the risk of equity (even when the debt is risk-free!) The End MM Capital Structure Irrelevance Agenda 1. MM Proposition I 2. Home-made leverage 3. MM and risky debt Enter M&M Modigliani and Miller (1958) showed that under the following conditions (“perfect capital markets”): 1. Investment is held constant 2. No transactions costs 3. Efficient capital markets 4. Managers maximise shareholders’ wealth 5. No taxes (or no differential tax treatment between equity and debt) 6. No bankruptcy costs (new one) The value of the firm and the wealth of the shareholders does not change when you change capital structure. MM Intuition: The Firm as a Pie Equity Equity Debt In perfect capital markets, changing the capital structure changes how the stream of cash flows generated by a firm’s assets is divided amongst debt and equity holders but does not change the total cash flow going to all investors. Merton Miller on MM Proposition I “I have a simple explanation [for the first Modigliani-Miller proposition]. It’s after the ball game, and the pizza man comes up to Yogi Berra and he says, ‘Yogi, how do you want me to cut this pizza, into quarters?’ Yogi says, ‘No, cut it into eight pieces, I’m feeling hungry tonight’.” — Merton H. Miller, from his testimony in Glendale Federal Bank’s lawsuit against the US government, December 1997 MM Capital Structure Irrelevance MM demonstrated that: • When there are no taxes and capital markets function well, it makes no difference whether the firm borrows or individual shareholders borrow. • Shareholders can borrow (and make their returns riskier) on their own (“home-made leverage”), so will not pay more to invest in an otherwise identical levered firm. • Therefore, the market value of a company does not depend on its capital structure. Example: Applying MM’s Argument to MacBeth Suppose MacBeth decides to remain unlevered, but you prefer the equity pay-off from the levered firm (50% debt). You can lever up yourself and replicate the levered firm’s return. • Suppose you have $10 to buy one share. • You could borrow $10 and buy two shares. Outcomes Earnings on two shares Less: Interest @ 10% Net earnings on investment Return on $10 investment (%) A $1 $1 $0 0% B 2 1 1 10 C 3 1 2 20 D 4 1 3 30 This strategy costs $10 of your own money to create (the same price as an unlevered MacBeth share), so you should not pay any more to invest in a 50% levered MacBeth share. MM Proposition I: Sketch of Proof, Part I Two firms, U and L, are identical in all ways except capital structure. Firm U is unlevered, Firm L is levered. • Strategy: Take a 1% stake in the unlevered firm. Dollar investment 0.01 × VU Dollar return 0.01 × Profits • Alternative strategy: Purchase 1% of both the debt and equity of Firm L. Debt: Equity: Total: Dollar investment 0.01 × DL 0.01 × EL 0.01 × (DL + EL ) = 0.01 × VL Dollar return 0.01 × Interest 0.01 × (Profits − Interest) 0.01 × Profits MM Proposition I: Sketch of Proof, Part II Both strategies produce the same dollar return: 0.01 × Profits. Therefore, in the absence of arbitrage opportunities, the costs of the two strategies (the dollar investment) must be the same. We must have: 0.01 × VU = 0.01 × VL That is: VU = VL MM Proposition I: Sketch of Proof, Part III • Strategy: Take a 1% stake in the equity of the levered firm. Dollar investment 0.01 × EL = 0.01 × (VL − DL ) Dollar return 0.01 × (Profits − Interest) • Replication strategy: Borrow 1% of the debt of L and purchase 1% of equity of U. Borrowing: Equity: Total: Dollar investment −0.01 × DL 0.01 × VU 0.01 × (VU − DL ) Dollar return −0.01 × Interest 0.01 × Profits 0.01 × (Profits − Interest) • Therefore, 0.01 (VL − DL ) = 0.01 (VU − DL ) → VU = VL . Risk-Free Debt or Risky Debt: MM Irrelevance Holds Risk-free debt All-equity firm Equity Debt Total to all investors: Good state 10 Bad state 4 10 4 Firm with debt (Promised payment: 4) Good state Bad state 6 0 4 4 10 4 Risky debt All-equity firm Equity Debt Total to all investors: Good state 10 Bad state 4 10 4 Firm with debt (Promised payment: 5) Good state Bad state 5 0 5 4 10 4 Summary: MM Proposition I • If capital markets are doing their job, firms cannot increase value by changing their capital structure. • Firm value is independent of the debt ratio. • Capital structure is irrelevant, even if that debt is risky. The End Modelling 1: Home-made Leverage Quick Question • Ms Kraft owns 50,000 shares of the common stock of Copperhead Corporation with a market value of $2 per share. • The company has issued 8 million shares in total. • Copperhead now announces that it is replacing $1 million of short-term debt with an issue of common stock. • What action can Ms Kraft take to ensure that she is entitled to exactly the same proportion of profits as before? Answer to Quick Question • Ms Kraft owns (50,000/8,000,000) = 0.625% of the firm. • Copperhead proposes to increase common stock by $1 million to $17 million (= $2 × 8m + $1m) and reduce debt by the same amount. • Ms Kraft can lever up on her own by: • Borrowing 0.625% × 1, 000, 000 = $6, 250 and • Using that money to buy more Copperhead stock Answer to Quick Question (cont.) • Copperhead Corporation issues $1 million of equity to retire a short-term debt. Ms Kraft, who owns α = 0.625% of pre-issue equity, wants to maintain her pre-restructure equity cash flows. • Assets are unaffected by the restructure, so MM holds. VApre = VApost D pre + E pre = D post + E post D pre + E pre = Dpre − 1 + E post
E pre = −1 + E post αE pre = −1α + αE post The End MM Proposition II Leverage and Returns MM Proposition I states that: A = VU = VL = D + EL • • • • • A: market value of the firm’s assets VU : market value of equity if the firm is unlevered VL : market value of the firm if levered D: market value of debt if the firm is levered EL : market value of equity if the firm is levered We can think of firm’s assets as a portfolio of the debt and equity securities used to fund them. Leverage and Returns (cont.) We know that the expected return on a portfolio is a weighted average of the expected returns of its components, so that: rA = rU = wD × rD + wE × rE And since portfolio weights are the proportion of the total market value of a portfolio that is invested in each security, we have:  rA = rU = D D+E   × rD + E D+E  × rE The RHS is known as the company cost of capital, also as the (pre-tax) weighted average cost of capital (WACC). MM Proposition II Rearranging the WACC expression to make the expected return on levered equity, rE , the subject of the formula, we get: rE = rU + D (rU − rD ) E MM Proposition II: The expected rate of return on the common stock of a levered firm increases in proportion to the debt-equity ratio (D/E). Any increase in expected return is exactly offset by an increase in risk. • This is why leverage does not affect value. MM Proposition II: WACC With Risk-Free Debt r rD rA rE rE = expected return on equity rA = expected return on assets rA = rU = WACC rD rD = expected return on debt D/E MacBeth Revisited • Back to the MacBeth example • We can use MM Proposition II to understand the effect of leveraging up to 50% debt on the cost of equity • Unlevered firm: rU = rA = Expected operating income 1, 500 = = 0.15 Market value of all securities 10, 000 • Levered firm: ! 5, 000 rE = 0.15 + (0.15 − 0.10) = 0.2 or 20% 5, 000 MM Proposition II in CAPM Betas If the CAPM is true, then these changes in expected return produced by leverage should correspond to changes in CAPM betas. βA = βU = βD D D+E ! + βE E D+E Rearranging: ! D βE = βU + (βU − βD ) E ! MM Proposition II: WACC With Risky Debt 1 1 Source: Brealey, Myers, and Allen Example: WACC With Risky Debt Assume the following market value balance sheet: Assets 100 Asset value 100 Debt (D) Equity (E) Firm value (V) 30 70 100 • rD = 7.5%, rE = 15%, and overall cost of capital (WACC) is:     D E rA = × rD + × rE D+E D+E     30 70 = × 0.075 + × 0.15 100 100 rA = 12.75% Example: WACC With Risky Debt (cont.) The firm issues additional 10 of debt and uses cash to repurchase 10 of its equity: Assets 100 Asset value 100 40 60 100 Debt (D) Equity (E) Firm value (V) As total cash flows do not change, rA = 12.75%, however, suppose more debt increases rD to, say, 7.875%:  40 0.1275 = 100 → rE = 16%   × 0.07875 + 60 100  × rE Summary of MM Propositions I and II • Financial leverage does not affect: • Risk or expected return on the firm’s assets • Firm value • Financial leverage does affect: • Risk and expected return on the firm’s common stock • Financial leverage may affect: • The risk or expected return on debt, depending on the amount of leverage and the nature of the default The End Applying MM Capital Structure Example, Part I Consider an all-equity firm • Cash = $60 • The firm has only one project that requires an investment of $60 and will generate an uncertain cash flow of $60 or $100 (equally likely) • Market price of risk = 8.4% • Risk-free rate = 6.6% • Beta of the assets = 1 First two questions 1. What is the required return on assets? (Use CAPM) 2. What is the value of the firm? Capital Structure Example, Part II 1. Required return on assets: rA = rf + βA (E(rM ) − rf ) = 6.6 + 1 × 8.4 = 15% 2. Firm value: NPVProject = −60 + Therefore: VFirm 0.5 × 100 + 0.5 × 60 80 = −60 + = 9.6 1 + 0.15 1.15 80 = 60 + −60 + 1.15 ! = 69.6 Capital Structure Example, Part III The firm issues $30 of bonds. • The beta of the debt is 0. • The risk-free interest rate is 6.6%. • So repayment of bonds requires 30 × 1.066 ≈ $32. The firm distributes $30 of dividends. • Therefore, the size of the firm is unchanged. Question: What is the value and expected return of the firm’s equity? Capital Structure Example, Part IV Today Next year Bad state Good state Expected CF 0 60 100 80 CF to debt -30 32 32 32 CF to equity 30 28 68 48 Total CF Capital Structure Example, Part V Approach 1: MM Proposition I • By MM Proposition I: the assets of the firm are unaffected, therefore the value of the firm is unchanged; VFirm = 69.6 • Value of debt: D = 30 • Therefore, EL = VFirm − D = 69.6 − 30 = 39.6 • The expected cash flow to equity is 48 • Therefore, to find the expected return on equity, we solve: 39.6 (1 + rE ) = 48 • rE = (48/39.6) − 1 = 21.4% Capital Structure Example, Part VI Approach 2: MM Proposition II • We know that the value of the equity has to be discounted at the appropriate discount rate (levered firm), so: EL = 48 (1 + rE ) (1) • From MM Proposition II, we know that: rE = rU + D 30 (rU − rD ) = 15 + (15 − 6.6) EL EL • Two equations, two unknowns; solving for EL and rE : EL = 39.6 rE = 21.4% • Again, VFirm = EL + D = 39.6 + 30 = 69.6 (2) Capital Structure Example, Part VII Bottom line • Firm value has not changed. • Old shareholder’s wealth has not changed. • They now have a $30 dollar dividend and an equity stake worth $39.6, adding up to $69.6. The End MM Relevance Industry Debt Ratios 1 1 Source: Berk and DeMarzo M&M Relevance Look to the assumptions: 1. Investment is held constant 2. No transaction costs 3. No taxes 4. No bankruptcy costs 5. Efficient capital markets 6. Managers maximise shareholders’ wealth One or more of these assumptions must be false for capital structure choice to add value. The End The Interest Tax Shield Agenda 1. Interest tax shield (ITS) 2. The ITS and the cost of debt MM Assumptions 1. Investment is held constant 2. No transaction costs 3. No taxes 4. No bankruptcy costs 5. Efficient capital markets 6. Managers maximise shareholders’ wealth Corporate Tax and the Interest Tax Shield (ITS) Interest payments in many jurisdictions are treated as a cost of doing business and hence deducted from pre-tax income. This tax deductibility creates an interest tax shield. • Consider a firm with EBIT = $1,000 and τc = 40%. • If the firm has zero debt: • After-tax cash flow to equity = 1, 000 × (1 − 0.4) = $600 • If the firm has debt = $5,000 at a cost rD = 10%, then: • Interest payment = 10% × 5, 000 = $500 • After-tax cash flow to equity = (1, 000 − 500) × 0.6 = $300 • Total cash flow to all investors = 300 + 500 = $800 • The total cash flow to all investors (equity and debt) has increased by $200 (= 800 − 600). • This additional $200 comes from the $500 of EBIT that was shielded from tax, ie, 200 = 500 (interest) × 0.4 (tax rate). Interest tax shield (ITS) = (D × rD ) × τc Interest Tax Shield 1 1 Source: Berk and DeMarzo Interest Tax Shield and the Cost of Debt Another way to interpret the interest tax shield is that it effectively represents a government subsidy of the cost of debt. In our initial example: • Interest expense is $500, but in the presence of the debt, the firm’s tax bill is reduced by $200 (400 vs 200). • In effect, the firm only pays 500 − 200 = $300 in interest (ie, 60% = 1 − τc of the interest expense) and the taxpayer pays the remaining $200 (ie, 40% = τc ). • The effective cost of the debt for the firm on an after-tax basis is reduced to (300/5000) = 6% = 10% × 60% = rD × (1 − τc ). So, who benefits from the ITS – shareholders or debtholders? The End Accounting for the ITS in Valuation Agenda 1. Adjusted present value (APV) 2. Weighted average cost of capital (WACC) Adjusted Present Value (APV) APV = Base-case NPV + X PV of financing side effects • Financing effects enter through additional present value calculations. Each term explicitly measures how a particular financing factor adds or subtracts value. Financing side effects include: • Interest tax shield (+) • Issue costs of securities (−) • Subsidies by a supplier or government (+) • The APV method can be used to incorporate other benefits and costs arising from leverage when we relax more MM assumptions, eg, bankruptcy costs, agency costs. For now, we focus only on corporate taxes and the interest tax shield. Interest Tax Shield 1 1 Source: Berk and DeMarzo APV and the Interest Tax Shield Since, in any year: (CF to investors)L = (CF to investors)U + Interest tax shield By no-arbitrage, we must have: VL = VU + PV (Interest tax shield) To determine the levered firm/project value using APV, we need: 1. Firm/project value if unlevered 2. PV of the future stream of tax savings generated by leverage Permanent Debt • Assume a firm plans to keep a fixed dollar amount of debt, D, on its balance sheet permanently , at cost rD . • Interest payment each year: D × rD • Interest tax shield each year: Interest × τc = (D × rD ) × τc ITS: t 0 DrD τc DrD τc DrD τc 1 2 3 ... • Therefore, the present value of interest tax shields (ITS) is given by: PV(ITS) = D × rD × τc = D × τc rD • Questions • Why do we discount at rD here? • What if the firm maintained a target debt ratio instead of a fixed dollar amount of debt? Example • Your company has no debt and is valued at $4 million. • The company’s annual profit is $900,000 before interest and taxes. • The corporate tax rate is 35%. • You have the option to exchange 50% of your equity for 5% perpetual bonds with a face value of $2 million. • Should you do this and why? Answer • Tax benefit = D × rD × τc = 2m × 0.05 × 0.35 = $35, 000 • PV of 35, 000 in perpetuity = 35, 000/0.05 = $700, 000 • That is, PV(Tax shield) = $2, 000, 000 × 0.35 = $700, 000 • Market value balance sheet Unlevered assets (VU ) PV(ITS) Firm value 4 0.7 4 + 0.7 = 4.7 Debt Equity Total liabilities 0+2=2 4 + 0.7 − 2 = 2.7 4 + 0.7 = 4.7 • Bottom line: The company just increased in value by 17.5% overnight (= 700K/4m)! Too easy! WACC Because the ITS reduces a firm’s effective cost of debt, we can alternatively incorporate the benefit it brings to firm and shareholder value into the firm’s cost of capital. We define a firm’s effective after-tax cost of capital, its WACC, as:     D E WACC = rD (1 − τc ) + rE V V Expanding this formula, we see its relationship with the company cost of capital (ie, before-tax WACC):     D E WACC = rD (1 − τc ) + rE V V       D E D = rD + rE − rD τc V V V   D WACC = WACCBT − rD τc V WACC (cont.) r rD (1 − τc ) rE rU WACC WACC rU rD (1 − τc ) D/E Quick Question • Gaucho Services starts life with all-equity financing and a cost of equity of 14%. • Suppose it refinances to the following market-value capital structure: • Debt: 45% at 9.5% • Equity: 55% • Gaucho pays taxes at a marginal rate of 40%. • Calculate Gaucho’s WACC. Answer • Initially, rE = rU = 14% • The leverage causes rE to increase to (using MM Proposition II): rE = rU + (D/E) (rU − rD ) = 0.14 + (45/55) × (0.14 − 0.095) = 17.68% • WACC:     D E + rE × V V = 0.095 × (1 − 0.40) × 0.45 + 0.1768 × 0.55 = 0.1229 WACC = 12.29% WACC = rD × (1 − τc ) × WACC and Valuation • If taxes are the only deviation from MM and • If the firm continuously rebalances its leverage to a target ratio, D/V then Discount FCF using the WACC If either assumption is violated, it is generally easier to use APV. The End Personal Taxes MM and Taxes MM with corporate taxes suggests firms should maximise borrowing capacity. So why do firms not borrow more? 1. You can only use interest tax shields if there will be future profits to shield. 2. Interest expense is not the only tax shield. 3. Consider investor/personal taxes. 4. Consider bankruptcy costs. Personal Taxes • In addition to corporate taxes (τc ) paid on the profit of the firm, the shareholders have to pay personal taxes on equity income (τpE ): • The dividends that they receive from the firm • Capital gains from the increase in market value of the firm • Although interest is not taxed at the corporate level, debt investors are taxed on their interest income, sometimes as ordinary income (τp ), which usually differs from τpE . • Taxation at the personal level can potentially reduce the tax advantage of debt found at the corporate level. Personal Taxes (cont.) Operating Income ($1.00) Or paid out as equity income Paid out as interest Corporate Tax None Tc Income after Corporate Tax $1.00 $1.00 – Tc Personal Taxes . Tp TpE (1.00 – Tc) Income after All Taxes $1.00 – Tp To bondholders $1.00–Tc–TpE (1.00 – Tc) =(1.00 – TpE)(1.00 – Tc) To stockholders Personal Taxes: Relative Advantage of Debt We can measure the relative advantage of debt (RAD) after all personal and corporate taxes have been deducted by comparing the after-tax amount that would be received by bondholders for each after-tax dollar received by stockholders: RAD = • If RAD > 1, issue debt • If RAD < 1, issue equity 1 − τp (1 − τpE )(1 − τc ) Example Interest Equity Income Income before tax Less corporate tax at Tc =.35 $1 0 $1 0.35 Income after corporate tax Personal tax at Tp = .3 and TpE = .105 1 0.3 0.65 0.068 $0.700 $0.582 Income after all taxes Advantage to debt= $ .118 Example (cont.) The relative advantage of debt: RAD = 0.7 (1 − 0.3) = = 1.2 > 1 (1 − 0.105)(1 − 0.35) 0.582 The relative advantage of debt remains even after accounting for personal taxes. So why are all companies not (close to) 100% debt-financed? The End