AFM 371 Winter 2008 Chapter 16 - Capital Structure: Basic Concepts

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1 AFM 371 Winter 2008 Chapter 16 - Capital Structure: Basic Concepts 1 / 24

2 Outline Background Capital Structure in Perfect Capital Markets Examples Leverage and Shareholder Returns Corporate Taxes 2 / 24

3 Background capital structure is the firm s mix of financing instruments we will consider a highly simplified context with only straight debt and common shares let B denote the market value of the firm s debt and let S denote the market value of the firm s equity firm value V = B + S the pie: B S two questions: 1. What happens to the cost of various sources of funds if the firm changes its capital structure? 2. Is there an optimal capital structure? ackground 3 / 24

4 Cost of Capital Review the cost of equity r S is the expected return on the firm s common shares in the CAPM r S = r f + β [E(r M ) r f ] note that this return can be in the form of dividends, capital gains, or both the cost of debt r B is the expected return on the firm s debt, i.e. the rate of interest paid the weighted average cost of capital is given by r WACC = S B + S r S + B B + S r B note that we are ignoring (for now) the tax deductibility of interest payments read over chapters 11 and 13 to review these concepts ackground 4 / 24

5 The Objective of Management since management is (in principle) controlled by the shareholders, we normally assume that management seeks to maximize the value of the firm s equity however, as long as there are no costs of bankruptcy, maximizing equity value S is equivalent to maximizing firm value V example: a firm has 10,000 shares; share price is $25 debt has a market value of $100,000 firm value V = B + S = $100,000 + $25 $10,000 = $350,000 suppose the firm borrows another $50,000 and pays it immediately as a special dividend the value of debt increases to $150,000, but how are shareholders affected? Background 5 / 24

6 The Objective of Management Cont d consider three possible outcomes: V $380,000 V $350,000 V $320,000 S $230,000 $200,000 $170,000 Dividend $50,000 $50,000 $50,000 Capital gain/loss -$20,000 -$50,000 -$80,000 Net gain/loss $30,000 $0 -$30,000 the change in capital structure benefits the shareholders if and only if the value of the firm increases managers should choose the capital structure that they believe will have the highest firm value (i.e. make the pie as big as possible) ackground 6 / 24

7 Perfect Capital Markets we will begin by assuming perfect capital markets: information is free and available to everyone on an equal basis no transaction costs no taxes no costs of bankruptcy we will also assume (for simplicity) that all cash flows are perpetuities (just to make the calculations easier) two famous names: Modigliani and Miller (MM) MM Proposition I (No Taxes): The market value of any firm is independent of its capital structure let V U be the value of an unlevered firm (i.e. all equity financing) and let V L be the value of an otherwise identical levered firm (i.e. some debt financing) MM Proposition I (No Taxes) then simply says V U = V L Capital Structure in Perfect Capital Markets 7 / 24

8 Proof of MM Proposition I (No Taxes) let X be the identical income stream generated by each firm (i.e. U and L); V U = S U be the value of the unlevered firm; and V L = S L + B L be the value of the levered firm consider an investor who owns some fraction α (e.g. 5%) of the shares of U: Investment Return α of U s equity αs U = αv U αx this investor can get the same return by investing in L: Investment Return α of L s equity αs L = α(v L B L ) α(x rb L ) α of L s bonds αb L αrb L αv L αx if V U > V L the investor would not buy any shares in U since the same return is available on a smaller investment in L apital Structure in Perfect Capital Markets 8 / 24

9 Proof of MM Proposition I (No Taxes) Cont d consider an investor who owns α of L s equity: Investment Return α of L s equity αs L = α(v L B L ) α(x rb L ) this investor can get the same return by investing in U and borrowing on personal account: Investment Return α of U s equity αs U = αv U αx Borrow αb L -αb L -αrb L α(v U B L ) α(x rb L ) if V L > V U the investor would not buy any shares in L since the same return is available on a smaller investment in U we have shown that no-one would buy shares in U if V U > V L and that no-one would buy shares in L if V L > V U therefore V U = V L is the only solution consistent with market equilibrium apital Structure in Perfect Capital Markets 9 / 24

10 Some Observations MM s result is based on a no-arbitrage argument: if two investments give the same future returns, they must cost the same today a key (implicit) assumption is that individuals can borrow as cheaply as corporations one way to do this is through buying stock on margin with a margin purchase, the broker lends the investor a portion of the cost (e.g. to buy $10,000 of stock on 40% margin, put up $6,000 of your own money and borrow $4,000 from the broker) since the broker holds the stock as collateral, brokers generally charge relatively low rates of interest firms, on the other hand, often borrow using illiquid assets as collateral (and get charged higher rates) the same arguments apply to more complicated capital structures the same arguments apply if cash flows are not perpetuities Capital Structure in Perfect Capital Markets 10 / 24

11 Example #1 given V U = $100M, X = $10M, r = 5%, B L = $50M, then MM Proposition I S L = $50M suppose S L = $40M: suppose S L = $60M: xamples 11 / 24

12 Example #2 suppose a firm has the following all equity capital structure: Original Capital Structure: All Equity Number of shares 1,000 Share price $10 Market value of shares $10,000 operating income differs across economic states as follows: Expected State Value Probability Operating income $500 $750 $1,500 $2,250 $2,500 $1,500 EPS $0.50 $0.75 $1.50 $2.25 $2.50 $1.50 ROE 5% 7.5% 15% 22.5% 25% 15% Examples 12 / 24

13 Example #2 Cont d consider an alternative capital structure with 50% debt financing: Alternative Capital Structure: 50% Debt Number of shares 500 Share price $10 Market value of shares $5,000 Market value of debt $5,000 assuming an interest rate of 10%: Expected State Value Probability Operating income $500 $750 $1,500 $2,250 $2,500 $1,500 Interest $500 $500 $500 $500 $500 $500 Equity earnings $0 $250 $1,000 $1,750 $2,000 $1,000 EPS $0.00 $0.50 $2.00 $3.50 $4.00 $2.00 ROE 0% 5% 20% 35% 40% 20% xamples 13 / 24

14 Example #2 Cont d graphing EPS vs. operating income: EPS % debt All equity Operating income xamples 14 / 24

15 Example #2 Cont d since the expected ROE is higher under 50% debt, should the firm switch to this capital structure? not only have expected returns increased, but so has risk the MM argument is that is doesn t matter, because investors can effectively create the payoffs from the alternative capital structure themselves ( homemade leverage ) assume the firm stays with the original all equity capital structure but a particular investor prefers the alternative suppose the investor buys 10 shares (at a cost of $100), but finances this by investing $50 and borrowing $50: EPS $0.50 $0.75 $1.50 $2.25 $2.50 Earnings (10 shares) $5.00 $7.50 $15.00 $22.50 $25.00 Interest (10% on $50) -$5.00 -$5.00 -$5.00 -$5.00 -$5.00 Dollar returns $0.00 $2.50 $10.00 $17.50 $20.00 Percentage returns 0% 5% 20% 35% 40% (on $50 invested) xamples 15 / 24

16 How Does Leverage Affect Shareholder Returns? note that from the previous example that leverage increases the expected returns and risk for equity, even if there is no chance of bankruptcy recall the weighted average cost of capital formula r WACC = S B + S r S + B B + S r B MM Proposition I implies that the weighted average cost of capital is constant (i.e. independent of capital structure) in the previous example: everage and Shareholder Returns 16 / 24

17 MM Proposition II (No Taxes) define r 0 = cost of capital for all equity firm expected earnings for all equity firm = value of equity since r 0 = r WACC, we have r 0 = S B + S r S + B B + S r B this can be rearranged to yield MM Proposition II (No Taxes): r S = r 0 + B S (r 0 r B ) everage and Shareholder Returns 17 / 24

18 MM Proposition II (No Taxes) Cont d graphing MM Proposition II: Cost of capital (%) r S r WACC r 0 r B B/S everage and Shareholder Returns 18 / 24

19 Corporate Taxes so far we have ignored corporate taxes, but the tax deductibility of interest payments gives a big advantage to debt financing let T C be the corporate tax rate, and recall from chapter 13 that r WACC = S B + S r S + B B + S r B (1 T C ) a levered firm makes interest payments of r B B, and therefore has its corporate taxes reducted by r B B T C (the tax shield from debt) in an all equity firm, the after tax cash flow to the shareholders is EBIT (1 T C ) in a levered firm, the total after tax cash flow to the shareholders and bondholders is EBIT (1 T C ) + T C r B B orporate Taxes 19 / 24

20 MM Proposition I (Corporate Taxes) the value of an all equity (unlevered) firm is the present value of the after tax cash flow to the shareholders V U = EBIT (1 T C ) r 0 MM Proposition I (Corporate Taxes): V L = V U + PV(debt tax shield) assuming the amount borrowed is constant over time, we can calculate the present value of the debt tax shield by discounting the cash flow at the rate of interest to get: V L = EBIT (1 T C ) r 0 = V U + T C B + T C r B B r B orporate Taxes 20 / 24

21 Example #3 an investment project costs $100,000 and produces EBIT of $20,000 per year forever, T C = 36%. financing choices: U: all equity; L: $40,000 debt, r B = 5%, r 0 = 10% U L EBIT $20,000 $20,000 Interest 0 2,000 EBT 20,000 18,000 Tax 7,200 6,480 Net income 12,800 11,520 Total cash paid to investors $12,800 $13,520 suppose the firm chooses U and issues 10,000 shares. It would have the following market value balance sheet: Physical assets $128,000 Equity $128,000 (10,000 shares) orporate Taxes 21 / 24

22 Example #3 Cont d now the firm announces it will switch to L by issuing $40,000 of debt and repurchasing shares in an efficient market, the stock price will react immediately to this announcement the firm value will rise by the present value of the tax shield, so the market value balance sheet becomes Physical assets $128,000 Equity (10,000 shares) the firm then issues the debt and carries out the repurchase: Physical assets $128,000 Debt $40,000 Equity orporate Taxes 22 / 24

23 MM Proposition II (Corporate Taxes) how does leverage affect r S and r WACC? MM Proposition II (Corporate Taxes): r S = r 0 + B S (1 T C ) (r 0 r B ) orporate Taxes 23 / 24

24 MM Proposition II (Corporate Taxes) Cont d graphing MM Proposition II: Cost of capital (%) r S = r 0 + (B/S)(r 0 r B ) r S r 0 + (B/S)(1 T C )(r 0 r B ) r 0 r WACC = (S/V )r S + (B/V )(1 T C )r B r B B/S orporate Taxes 24 / 24

AFM 371 Practice Problem Set #2 Winter Suggested Solutions

AFM 371 Practice Problem Set #2 Winter 2008 Suggested Solutions 1. Text Problems: 16.2 (a) The debt-equity ratio is the market value of debt divided by the market value of equity. In this case we have