Topics in Financial Economics Term 2, Lecture 2

1. Topics in Financial Economics Term 2, Lecture 2 Readings Asset types Leverage Modigliani-Miller - Irrelevance of corporate financial structure in complete perfect markets MM and rates of return – risk offsets return MM in imperfect markets (taxes, bankruptcy) – market failures restore relevance of structure Weighted cost of capital – an alternative view of optimal leverage [Details optional, for the adventurous] incompleteness – the general equilibrium approach The depressing results MM in the (real) world

2. Readings for Lect 1-2, (S = suggested – read at least 1) Copeland, Weston and Shastri, Financial Theory and Corporate Policy, Chaps. 14-15 (some terms explained in ch 13). Myers (2001) “Capital Structure” The Journal of Economic Perspectives, Vol. 15, No. 2. (Spring, 2001), pp. 81-102. Allen, F. and D. Gale, (1988) “Optimal Security Design,” Review of Financial Studies 1, 229-263. Arrow, K. (1964) “The Role of Securities in the Optimal Allocation of Risk-Bearing,” Review of Economic Studies 31, 91-96. Ekern, S. and R. Wilson (1974) “On the Theory of the Firm in an Economy with Incomplete Markets” Bell Journal of Economics 5, 171-80. Grossman, S. and O. Hart (1979) “A Theory of Competitive Equilibrium in Stock Market Economies,” Econometrica 47, 293-329. Hart, O. (1975) “On the Optimality of Equilibrium when the Market Structure is Incomplete,” Journal of Economic Theory 11, 418-43. Hellwig, M. (1981) “Bankruptcy, Limited Liability, and the Modigliani-Miller Theorem,” American Economic Review 71, 155-70. Merton, R. (1990) “The financial system and economic performance,” Journal of Financial Services Research 4, 263-300. Stiglitz, J. (1969) “A Re-Examination of the Modigliani-Miller Theorem,” American Economic Review 59, 784-93.

3. Growth and value revisited The firm described by the EBIT formula is separated into a no-growth component and the PV of a stream of future investments. But the assets are only valuable for their returns r, not as assets in themselves – suppose ku = 10%: Firm 1 invests £10000, gets 20% return (£2000), value grows by £9090 Firm 2 invests £30000, gets 10% return (£3000), value unchanged Firm 3 invests £100000, gets 5% return (£5000), value falls by £45454 So maximising earnings growth may reduce (minimise) value. Note also that the formula takes no account of where the firm’s earnings go (dividends, interest payments, share repurchases, etc.)

4. An unlevered firm with perpetual growth Suppose firm reinvests a% of free cash flow for return r – forever.

5. We can’t have r > ku forever…

6. Types of security Common stock – ‘real’ owners, with pre-emptive rights to any value the company wishes to distribute and to control (subject to voting rights, and not in bankruptcy) Long term debt – stipulated future stream of payments (interest/face value) that must be paid to avoid default. ‘Junk’ bonds are very high yield (value varies inversely with interest) Preferred stock - stipulated future stream of dividends paid before common stock Note: in liquidation, priority is: bank debt, bonds, preferred stock, common stock [pecking order] Overall amount: debt (80%) > equity (15%) > preferred (5%), but some recent movement. Convertible securities – e.g. bonds convertible to common stock, or warrants giving time-limited right to buy equity at set price, options, etc.

7. Payment to asset holders

8. Gearing (debt/equity combinations) I Example: Promgaz is reviewing its structure – it pays no taxes, has access to perfect capital markets and faces a 10% interest rate. It has 100 shares outstanding at £20 per share and no debt. Business plan envisages 3 scenarios: Scenario: 1 (pr 1/8) 2 (pr 1/2) 3(pr 3/8) Operating income £100 £250 £300Earnings/share £1 £2.5 £3Return on equity 5% 12.5% 15% The firm has no leverage and pays out all income as dividends. Expected earnings are 250. Actual Earnings per Share (EPS) could be more or less than £2.5. Expected return on equity = EPS/P = £2.5/ £20 = 12.5%.

9. Gearing (debt/equity combinations) II The CEO has concluded that the shareholders would benefit if the company had equal proportions of debt and equity, and prepares to issue £1000 of debt at the risk-free rate (10%), using the money raised to repurchase 50 shares Scenario: 1 2 3 .Operating income £100 £250 £300Interest £100 £100 £100Equity earnings £0 £150 £200EPS £0 £3 £4Return on equity 0% 15% 20%

10. The leverage decision “If income > £200, leverage raises EPS, so financing decision depends on expected income” Does this make sense to you?

11. A counter-argument “Leverage does help shareholders if income is above £200 – but the shareholders can borrow for themselves.” Suppose one borrows £20 and buys 2 unleveraged shares of Promgaz common stock, paying only £20 of her own money. Scenario: 1 2 3Share earnings £2 £5 £6Less interest @ 10% £2 £2 £2Net equity earnings £0 £3 £4Return on £20 invest. 0% 15% 20% These are exactly the same as the returns to buying one share in the leveraged firm, whose shares must therefore sell for 2 * £20 - £20 = £20. Thus adding leverage does not let the shareholders do anything they can’t already do and so cannot add value. This is the argument behind the Modigliani-Miller theorem.

12. Modigliani-Miller - informal treatment The expected return on a firm’s assets, rA, equals the ratio of expected operating income to the firm’s total value. If it differs from the firm’s securities’ total market value, there would be arbitrage opportunities. The firm’s operating income is not affected by its financial posture (is this true?), so rA isn’t either. If one person holds all a firm’s debt and equity, the interest cancels out, the person simply receives the operating income and the expected return is rA. The expected return on a basket of assets is a weighted average of the expected returns on each, so rA = drD + (1-d)rE, where d is the proportion of the firm’s assets held in debt. Modigliani-Miller’s ‘second proposition’ – rE = rA + g(rA-rD), where g is the ratio of D to E

13. Graphical illustration Assumes bonds are essentially riskless at low debt levels – rD is independent of D/E and rE is linear in D/E. As D/E increases, so does the risk of default and risk transfers from shareholders to bondholders and the firm has to pay more interest on debt. According to the Proposition, when this happens the line flattens out.

14. MM I: more carefully Firm's market value is independent of its capital structure if: Investors only care about risk and return All investors have a common-knowledge view of returns Capital markets are perfect: Price-taking Same rate for borrowing and lending (rB) Equal access to all relevant information Unlimited short sales allowed No transactions (issue, bankruptcy) costs or taxes Proof A proportion s of stock of an unlevered firm with earnings I will earn sI An otherwise-identical firm with debt B and equity E is worth VL = E + B If the firm pays D to debt holders, dividends I-D > 0 (assumes no default): equity share s is worth s(I-D)

15. Proof of MMI, continued Homemade leverage: Borrow on margin to buy s at a cost sVU paying annual dividends of sI Assume loans make up s share of the total debt of the levered firm If investor and leveraged firm pay same interest rate, annual interest on the loan will also be sI Net income from the joint investment will be s(I-D), same as that on s of unleveraged firm If arbitrage is possible, the market must value both income flows (which are identical) at the same price. Net investment under joint strategy is sVU - sB, investing in s of leveraged firm’s equity costs sE, so  E = VU – B and VU = E + B – VL If not, there will be arbitrage: If leveraged firm is worth more, a portfolio with 0 cash flow but positive market value would result from buying stock in unleveraged firm, borrowing on margin and selling short stock in leveraged firm. If unleveraged firm is worth more, buy stock and debt in leveraged firm and sell short equity in unleveraged firm

16. First argument: a firm's borrowing does not affect its value. Second argument: rate of return on equity increases as leverage increases. Isn’t this contradictory? Risk increases with leverage. The firm's beta is a weighted average of the betas of the individual securities: So earnings per share and return to equity are not important in determining optimal financial structure – they can always be increased by borrowing, but added risk offsets added return. Therefore, we must look to market imperfections, bankruptcy and taxes for guidance. MM and rates of return

17. break

18. Taxes In many countries, interest is deductible as a cost of doing business while dividends are taxed as income – this ‘tax shield’ obviously favours debt financing (note structure of returns in private equity deals) The firm’s policy depends on shareholder interests – if personal taxes treat interest and dividend income symmetrically previous results hold. Firm’s choice: if interest is deductible, PV = PV(all equity) + PV(tax shield) This should lead firms to maximise borrowing to capture tax advantage – but they don’t borrow very much (30-40%). Obviously, they are worried about something – perhaps bankruptcy and the agency costs (Merton 1990) associated with the possibility of bankruptcy (distress costs) Now, PV = PV(all equity) + PV(tax shield) – PV(distress costs) If cost levels are fixed, higher debt means greater probability of distress, which is traded off against tax savings

19. Optimal financial structure with bankruptcy

20. Alternative view – weighted cost of capital Above, return on firm’s assets was: rA = (D/(D+E)) * return to debt + (E/(D+E)) * return to equity rA = opportunity cost of capital for projects with the same risk as the firm After tax cost of debt is (1-?c)rD*, where ?c is the corporate tax rate and rD* is adjusted to include distress costs and systematic risk – when the firm is in trouble, bondholders bear some costs – this makes them demand a higher return when debt is issued: rD* = rD + distress-risk premium The weighted cost of capital is: The net impact is to make rWA a u-shaped function of the debt ratio:

21. Reprise on WACC, 1

22. Reprise on WACC, 2

23. Graphical illustration, revisited Optimal debt ratio minimises weighted average cost of capital: same as where PV of firm is maximised. To see this, suppose firm makes £C/pd forever: PV = C/rWA, and smaller rWA implies bigger PV of firm.

24. The GE approach, 1 (blue slides optional) GE approach (Arrow, Debreu and McKenzie) uses complete markets for goods described by state, time and place. Trivial extension of Walrasian analysis at a cost: enormous numbers of markets. Within this framework, 3 main results: Value maximisation as the unanimous stakeholder choice of objective Efficient resource, etc. decisions can be decentralised using value maximisation Irrelevance of financial structure as consequence of budget constraint: value of claims on firm = value of production plan by the Law of One Price (arbitrage). Many of these markets are redundant and others fail to exist. ‘number’ uncountably infinite in continuous time (Merton, Black-Scholes, Harrison-Kreps) but the security space can be ‘spanned’ by continuous trading of a limited set of securities. Can sustain same allocations as complete model, but frequent (cts) trading is costly required level of rationality is (too) high Strong regularity assumptions, and at least one security for each ‘dimension’ of uncertainty Much literature assumes specific functional forms (log utility, Brownian motion) Agents need to ‘internalise’ full information: to implement spot trades, need to know other spot prices. The incomplete-markets extension (below) provides a useful counterexample: when markets are incomplete, stakeholders may disagree about the firm’s objectives, information may not be fully reflected in prices and financial innovation – the creation of complex financial structures and new instruments – may increase the firm’s value or the efficiency of incentives and risk allocation.

25. The GE approach, 2 Incompleteness is only part of the problem. We need to understand: Why some markets do not exist (e.g. fixed, transactions costs) Which markets do exist (e.g. path-dependence), and How existing markets behave (imperfect competition, multiple prices, intermediaries) Spanning lets managers infer security prices from arbitrage (look at prices of traded securities and ‘fill in’ prices of untraded ones) But they need to understand the set of traded securities (A in what follows) Which way to ‘construct’ a given security from traded ones gives the right price? In GE commodity prices tell managers enough to maximise profits (hence value) With incomplete markets, they must rely on conjecture about how decisions affect value. Spanning lets them form the conjectures by looking at the values of other firms. In general, may be strategic problems (simultaneous decisions by firms) or selection problems (need to consider marginal valuations by different types of investors). Result: complex objective functions, harder to decentralise among and within firms. Shareholder views The standard incomplete information model uses very large sets of producers and security types; owners can ‘sort themselves out’ so that they are unanimous per firm. Grossman-Hart (1979) allows differences, but is complex to use; changes in ownership lead to time inconsistency. There are not so many types of firm – but not so many types of investor either. The formation of ‘types’ and the ‘Tiebout process’ (sorting) are unresolved.

26. Back to general equilibrium… Need to reconsider production sets – without complete markets there may be ambiguity/disagreement about what firm should choose: so we assume each Yj is a single point {yj} To begin, assume that: firms do not trade securities (?j = 0); there are no ‘Arrow securities’ ?h, paying fixed amounts in given states Feasibility requires:Since firms have no decisions, equilibrium requires utility maximisation: Now let firms trade securities:

27. Definition and result… Note that the result is still feasible and utility still maximised Definition: equilibrium with incomplete markets (E.I.M.) is a feasible allocation a=((ai),(aj)) ? A and prices (q,v) ? RH x RJ s.t. Theorem: if (a,q,v) ? A x RH x RJ is an E.I.M. and (?j’) is an arbitrary allocation of firm portfolios, then there is an E.I.M. (a’,q,v’) s.t. a’ = ((ai’), (aj’)) ai’ = (xi,?i’, ?i’) aj’ = (yj,?j’) (The ‘real’ parts x, y are the same). Note the space of commodity bundles spanned by equity and securities is exogenous because we assumed the firm’s choice of production plan was exogenous. In other words no financial innovation.

28. Bankruptcy with complete markets Assume one firm (j=1), one production plan (y(w)>0) and one security (z(w)=1) Limited liability increases likelihood of default, debt risk. With complete markets Value of firm to original owners is the same as before:

29. Complete market default with > 1 firm A continuum of identical firms, with different levels of risky debt. There may be enough securities to span the whole (R?) commodity space. Assume y(?)=? and aj? = 1-? for ? = 1,…,|?| - then Since we can generate these securities for each state, we span the space: capital structure does not matter to the firm, but does matter to equilibrium.

30. Bankruptcy with incomplete markets Assume (for simplicity) that consumers can buy debt, but not issue their own debt or engage in short sales of the firm’s equity. Definition: An equilibrium with incomplete markets and bankruptcy (E.I.M.B.) is a feasible allocation and a price vector s.t.

31. Remarks… With incomplete markets, the valuation problem must be dealt with explicitly – market incompleteness means that people can disagree about security values, and only those who value them the most will hold positive amounts in equilibrium. This raises three questions: How much information is revealed by equilibrium prices (since those with ‘negative’ information may not be trading)? Will equilibrium exist at all? (if offers and acceptances signal information, learning is expensive and people may try to ‘free ride’) If equilibrium exists, can we get there? (if people learn from the willingness to trade, there may be no sequence of trades culminating in equilibrium where each step along the way is – conditionally on information revealed to that point – Pareto improving).

32. Remarks… Complete markets lead all shareholders to agree that value maximisation is the right objective function. However, in this case the firm’s choice of yj and ?j affects both Vj and the risk sharing effect of holding risky debt and shares. One way to restore unanimity: if firm j’s cash flow is spanned by other firms’ cash flows, the risk-sharing effect is redundant and only value of the firm matters (Eckern and Wilson (1974)). Another approach: if there are ‘enough’ firms, each customer can hold shares in a ‘version’ of the firm that optimises his own risk sharing needs (Hart (1975)). Without these shortcuts, the theory of the firm becomes very tricky. This is one reason why so much of general equilibrium theory does not have ‘real’ firms (pure exchange or only untraded (?) shares.

33. So what does this mean for MM? With ‘real’ incompleteness, consumers will have different marginal rates of substitution across states, and will disagree about security values: hence the value of the firm will reflect claims issued against the production plan. Example: firm chooses yj to sell to consumers of type i: equilibrium value of shares is volume * MRSi. No other type of customer would pay more for these shares. But it may be possible to decompose yj into ‘slices’ to be sold to different types (split-market) more profitably. As long as there are 2 types of customer who value different parts of the firm differently, this kind of arbitrage will proceed until markets are ‘completed’ – unless securities are costly to issue.

34. So what does this mean for MM? Consider 2 firms with different financial structures: 2 types of security; only common stock. If customers can make unlimited short sales, firms must have same value (otherwise arbitrage). If second security is costly, firms cannot have different structures either. Free-riding should force simplest (cheapest) structure. But unlimited short sales seems inconsistent with fixed issue costs. The problem is price-taking (perfect competition). With short sales, even a tiny firm can have a huge impact by issuing a security (a new market). Limiting short sales: limits the power of firms rescues the perfect competition assumption loses realism. The future lies with models of incomplete competition.

35. Summary of depressing results Negative propositions: Capital structure does not affect market value At any given moment, debt interest may seem to offer much more or less than equity EPS, so… Return on equity is a linear function of debt-equity ratio Can be used for valuation: measure WACC by looking at WACC of firms with similar risk profiles Dividend policy does not affect market value V (Cash flow – Dividend) + Value (Dividend) = Value (Cash flow) Individual investors do not affect financial policy Financial decisions matter in practice – why? Taxes, transactions bankruptcy and distress costs, incomplete markets, limits on short sales, asymmetric information, hidden actions and the conflict between share- and bond-holders when new debt is issued or the firm does riskier things