1. Capital Structure. Introduction How are projects and firms financed? This choice determines the capital structure Capital structure is mix of types of securities issued by the firm mix of types of securities issued by the firm mix of claims that investors have on the firm’s cash flows mix of claims that investors have on the firm’s cash flows Why is it important? Capital structure affects the cost of capital, i.e. the discount rate which we use in valuation Capital structure affects the cost of capital, i.e. the discount rate which we use in valuation What are the determinants of the optimal (“target”) capital structure? Optimal c.s. should minimize the cost of capital (i.e. maximize the market value of the firm) Optimal c.s. should minimize the cost of capital (i.e. maximize the market value of the firm)

2. Modigliani and Miller proposition: in the absence of taxes, costs of financial distress and capital market imperfections capital structure is irrelevant! Why does the irrelevance result not hold in the real world? MM proposition is obtained under several strong assumptions. Any of the following factors can kill the irrelevance result: Taxes (corporate and personal) – Modified MM theory Taxes (corporate and personal) – Modified MM theory Costs of financial distress Costs of financial distress Transaction costs Transaction costs Agency costs Agency costs Asymmetric information Asymmetric information We will discuss them

3. Sources of Long Term finance Internal financing (retained earnings) But firms often spend more than they generate internally. The deficit is financed by new sales of debt & equity But firms often spend more than they generate internally. The deficit is financed by new sales of debt & equity Types of instruments Equity Equity Debt Debt Leases Leases

4. Equity Can be publicly traded or not Types: Common Stock - claim on the share of profits (after tax and payments to creditors) Common Stock - claim on the share of profits (after tax and payments to creditors) may have different voting rights Preferred Stock – paid after tax and payment to creditors too, but is normally a fixed claim (similarity to debt) Preferred Stock – paid after tax and payment to creditors too, but is normally a fixed claim (similarity to debt) No voting rights in normal times Dividend is paid before dividend on common stock Warrants Warrants Call options on a firm’s shares

5. Can be publicly traded or not Fixed claim (not a share of profits!) Interest payments occur before payments to preferred and common stockholders and before taxes, i.e. tax deductible No control (voting) rights in normal times Control rights in case of default Can be convertible into stock upon realization of some conditions Debt

6. Debt differs by Maturity Maturity Liquidity Liquidity public bonds - liquid public bonds - liquid bank loans or private placements - illiquid bank loans or private placements - illiquid Security (for bonds) Security (for bonds) secured (by an asset) secured (by an asset) Mortgage bonds, collateral bonds Mortgage bonds, collateral bonds unsecured ordinary unsecured ordinary Debentures, notes (“backed” by the earning power of the firm, no collateral) Debentures, notes (“backed” by the earning power of the firm, no collateral) unsecured subordinated unsecured subordinated Subordinated debentures (Least protected. Holders of such bonds are paid after all other creditors) Subordinated debentures (Least protected. Holders of such bonds are paid after all other creditors)

7. Leases Borrowing an asset in exchange for future fixed repayments (similar to debt) Types of leases Operating lease Operating lease Usually short term and the asset is returned Usually short term and the asset is returned Capital (investment) lease Capital (investment) lease Usually lasts for the entire life of the asset and the asset can sometimes be acquired at the end by the lessee at low price Usually lasts for the entire life of the asset and the asset can sometimes be acquired at the end by the lessee at low price

8. Financing patterns In the US, on average, 60-80% of the investment expenditures is financed with internal funds. In other countries reliance on internal funds is generally lower but still 40-60%. New sales of debt strongly prevail over new equity issues Large variations between types of firms and industries (e.g. for startups equity financing strongly prevails) Capital structure: in the US, average market value debt- equity ratio is 0.5 (very roughly). Large variations between industries: from 0.08 in biotech to 3 in financial sector.

9. Pie model of the firm As long as D is fixed, maximizing E is equivalent to maximizing the whole pie (i.e. the total firm value). But D is not fixed if debt is risky D E F D E V default

10. Modigliani – Miller without taxes Irrelevance of capital structure (MM I) Cost of levered equity as a function of capital structure (MM II)

11. Financing a firm with equity Entrepreneur has an investment opportunity Investment needed: $800 The project cash flows: Prob(strong)=Prob(weak)=1/2Suppose: Risk free interest rate = 5% Risk free interest rate = 5% The appropriate risk premium for this investment = 10% The appropriate risk premium for this investment = 10% Hence, the cost of capital (return investors require) is 15% Hence, the cost of capital (return investors require) is 15% NPV = -800 + (½*1400 + ½*900)/1.15 = $200 > 0

12. Imagine, in order to finance the project entrepreneur sells 100% of shares of this project to outside investors – the project will be all-equity financed How much would he raise? Fair price for 100% of shares is (½*1400 + ½*900)/1.15 = 1000 He would invest 800 and keep 200. Hence, his gain is exactly NPV In fact he could sell 80% of shares and keep 20% for himself. Then investors would provide 800 and he would get 0.2*1000 = 200, i.e. the same

13. Imagine, entrepreneur had invested 400 from his own money and had raised only 400 as outside equity. He had to sell exactly 40% to outside investors and would keep 60%. His payoff would be 0.6*1000 – 400 = 200, e.g. as before Hence, observation: in a perfect market (no transaction cost, asymmetric info problems, moral hazard) it does not matter whether to finance a firm internally or by raising external funds

14. Adding Debt Suppose entrepreneur decides to finance the project partially through debt. He sells bonds for $500. If they are risk free, the required return is 5%, hence he will pay $525 in a year. Since 525 < 900, debt is indeed risk-free. He wants to sell then 100% of equity (now it would be levered equity). How much would investors pay for it now? Modigliani – Miller: E = $500

15. Modigliani – Miller Proposition I In a perfect capital market a firm’s total market value is equal to the market value of the total cash flows generated by its assets and is independent of its capital structure: U = A = E + D A – market value of assets, U – market value of unlevered equity, E – market value of levered equity, D – market value of debt. A – market value of assets, U – market value of unlevered equity, E – market value of levered equity, D – market value of debt. Perfect capital market: No taxes No taxes No costs of financial distress No costs of financial distress No transaction and issuance costs No transaction and issuance costs No asymmetric information No asymmetric information The firms' financing and operating decisions are independent. In particular, no agency costs (managers maximize firm value) The firms' financing and operating decisions are independent. In particular, no agency costs (managers maximize firm value) Individuals can undertake the same financial transactions as the firms and at the same prices (e.g. borrow at the same interest rate) Individuals can undertake the same financial transactions as the firms and at the same prices (e.g. borrow at the same interest rate)

16. Intuition If the way we divide cash flows from an asset among different claims (securities) does not affect these cash flows, the total market value of these claims must be independent of the way we divide the cash flows (We need some more for this result to hold: any division is costless, all investors know the same as insiders, i.e. do not treat a particular division as any signal of firm value, investors can freely trade at the same terms as firms) (We need some more for this result to hold: any division is costless, all investors know the same as insiders, i.e. do not treat a particular division as any signal of firm value, investors can freely trade at the same terms as firms) MM I holds not only for a split into debt and equity, but for any combination of any securities

17. Proof by arbitrage argument Consider firm 1 and firm 2. At t=1,2,...., both firms generate the same (random) earnings (EBIT) X > 0. But they differ in their cap. structure: Firm 1 has equity and debt (risk free and perpetual for simplicity) Firm 1 has equity and debt (risk free and perpetual for simplicity) Firm 2 has no debt Firm 2 has no debt Firm 1 pays annual interest r f, which is equal to the return on safe debt in the market market value of firm i's debt: D i market value of firm i's equity: E i total market value of firm i: U i = E i + D i Hence, at t: firm 1's debtholders receive: r f D 1 firm 1's debtholders receive: r f D 1 firm 1's equityholders receive: X- r f D 1 firm 1's equityholders receive: X- r f D 1 firm 2's equityholders receive: X firm 2's equityholders receive: X

18. Step 1: It cannot be that U ₂ >U ₁. Proof: Suppose U ₂ >U ₁ and consider an investor holding a fraction α of firm 2's shares. At t, he would receive αX. Instead, he could: Sell the shares for αU ₂ Sell the shares for αU ₂ Buy in a fraction αU ₂ /U ₁ of firm 1's debt and equity as: αU ₂ = (αU ₂ /U ₁ ) ⋅ D ₁ +(αU ₂ /U ₁ ) ⋅ E ₁ Buy in a fraction αU ₂ /U ₁ of firm 1's debt and equity as: αU ₂ = (αU ₂ /U ₁ ) ⋅ D ₁ +(αU ₂ /U ₁ ) ⋅ E ₁ At t, the investor would receive: At t, the investor would receive: (αU ₂ /U ₁ ) r f D 1 + (αU ₂ /U ₁ ) ⋅ (X- r f D 1 ) = (αU ₂ /U ₁ )X > αX for all X Hence, there is an arbitrage opportunity. Intuition: Arbitrageurs can "undo firm 1's leverage" by buying its debt and equity in proportions such that interest paid and received cancel.

19. Step 2: It cannot be that U ₁ >U ₂. Proof: Suppose U ₁ >U ₂ and consider an investor holding a fraction α of firm 1's shares. At t, he would receive X- r f D 1. Instead, he could: Sell the shares for αE 1 Sell the shares for αE 1 Borrow αD 1 Borrow αD 1 Invest the total in a fraction α(U ₁ /U ₂ ) of firm 2's shares:αE ₁ +αD ₁ = α(U ₁ /U ₂ )U ₂ Invest the total in a fraction α(U ₁ /U ₂ ) of firm 2's shares:αE ₁ +αD ₁ = α(U ₁ /U ₂ )U ₂ At t, the investor would get α(U ₁ /U ₂ )X and pay interests r f D 1 : α(U ₁ /U ₂ )X - r f D 1 > α(X- r f D 1 ) for all X. At t, the investor would get α(U ₁ /U ₂ )X and pay interests r f D 1 : α(U ₁ /U ₂ )X - r f D 1 > α(X- r f D 1 ) for all X. Hence, there is an arbitrage opportunity. Intuition: Arbitrageurs can "lever up" firm 2 by borrowing on individual accounts (homemade leverage).

20. Example: arbitrage for our firm

22. Changing a capital structure does not change stock price Example: leveraged recapitalization Harrison Industries is currently all-equity with 50 mln shares traded at $4 per share. Hence, its assets market value = equity value = 200 Harrison Industries is currently all-equity with 50 mln shares traded at $4 per share. Hence, its assets market value = equity value = 200 Harrison plans to borrow $80 mln and use the money to repurchase stock Harrison plans to borrow $80 mln and use the money to repurchase stock How much would the stock cost after the transaction? How much would the stock cost after the transaction? Imagine after the announcement the stock price would be $x. The firm can repurchase 80 mln/x shares. The stock price after the transaction must be equal $x too (investors are forward looking) Imagine after the announcement the stock price would be $x. The firm can repurchase 80 mln/x shares. The stock price after the transaction must be equal $x too (investors are forward looking) 50 mln – 80 mln/x has left. Their total value should be assets market value – debt market value = 200 – 80 =120 50 mln – 80 mln/x has left. Their total value should be assets market value – debt market value = 200 – 80 =120 x(50 – 80/x) = 120  x = 4 – did not change! x(50 – 80/x) = 120  x = 4 – did not change!

23. Market value balance sheet after each stage of Harrison’s leveraged capitalization Note: this was a zero-NPV transaction. Non-zero NPV transaction would change the stock price, but choosing whether to use debt or equity for financing does not matter for the stock price

24. Returns to equity with and without leverage Levered equity has higher expected return than levered. Why? Because it’s more risky. Leverage increases both return and risk of equity

25. Modigliani – Miller Proposition II In fact, the following relationship is true: Return (expected) on all firm’s assets r A = return on unlevered equity r U = (E/(E+D))r E + (D/(D+E))r D Here r E – return (expected) on equity in a levered firm, r D – return (expected) on debt Here r E – return (expected) on equity in a levered firm, r D – return (expected) on debt Hence, MM II: Firm’s return on equity (cost of equity) increases with leverage

26. Cost of capital for a firm: r WACC – weighted average cost of capital (we will use it for valuation of projects and firms)

27. As the fraction of the firm financed with debt increases, both the equity and the debt become riskier and their cost of capital rises. Yet, because more weight is put on the lower-cost debt, the weighted average cost of capital remains constant.

28. Levered and Unlevered Betas Since, these formulas are consistent with MM II When debt is risk free its beta = 0, and then

31. Cash, Net Debt and Enterprise Value Very often Enterprise Value is used as a market value of a business EV = Equity + Net Debt Net Debt = Debt – Cash and Risk-Free Securities EV – market value of assets excluding cash MM I for EV: In a perfect capital market a firm’s EV is equal to the market value of the total cash flows generated by its assets excluding cash and is independent of the combination of Equity, Debt and Cash (or of the combination of Equity and Net Debt) MM II is the same, but r U, r D and D have slightly different meanings

32. Cash reduces market risk of equity (effect opposite to the one of debt)

33. Note: here D is Net Debt and beta U is beta of assets net of cash

34. Is the following statement true?: Leverage can increase expected earnings per share. If it does, it should increase stock price. Wrong. Stock price does not change as we saw. Even if EPS increase they become more volatile with leverage. Example: Levitron Industries (LVI) is currently all-equity. Its expected next year EBIT = $10 mln. Levitron Industries (LVI) is currently all-equity. Its expected next year EBIT = $10 mln. It has 10 mln shares outstanding, traded at $7.50 per share It has 10 mln shares outstanding, traded at $7.50 per share LVI wants to do leveraged recapitalization: borrowing $15 million at interest rate 8% and using the proceeds to repurchase 2 mln shares at $7.50 (we know such transaction should not change the stock price) LVI wants to do leveraged recapitalization: borrowing $15 million at interest rate 8% and using the proceeds to repurchase 2 mln shares at $7.50 (we know such transaction should not change the stock price) Let’s show that EPS will become more volatile Let’s show that EPS will become more volatile

35. Currently Net Income = EBIT = $10 mln Hence EPS = $10 mln/10 mln = $1 Hence EPS = $10 mln/10 mln = $1 With the debt, annual interest payment = $15 mln * 0.08 = $1.2 mln Hence, NI = EBIT – i = $8.8 mln Hence, NI = EBIT – i = $8.8 mln Hence EPS = $8.8 mln/8 mln = $1.10 > $1 Hence EPS = $8.8 mln/8 mln = $1.10 > $1 But $10 mln is expected EBIT. Imagine EBIT = either $4 or $16 (each with prob. ½) In an unlevered firm EPS would be either $0.4 or $1.6 In an unlevered firm EPS would be either $0.4 or $1.6 In a levered firm EPS would be either $0.35 or $1.85. More volatility (hence, more risk) In a levered firm EPS would be either $0.35 or $1.85. More volatility (hence, more risk)

36. The sensitivity of EPS to EBIT is higher for a levered firm than for an unlevered firm. Thus, given assets with the same risk, the EPS of a levered firm is more volatile.