1. Review: Risk, Return, Capital Structure Valuation Fin 615 Winter A 2005 Ross School of Business University of Michigan © Sugato Bhattacharyya. Please do not distribute without written permission.

2. Princeton Spring 2004 Sugato Bhattacharyya Recap  Up to now, we have primarily dealt with the case of certain cash flows  But, we have started talking about uncertain cash flows and risk  From basic Micro principles, we have seen that an expected payoff-variance representation may characterize risk and risk-return trade-offs

3. Princeton Spring 2004 Sugato Bhattacharyya Opportunity Cost  Certainty: Best alternative matched on maturity period – explicitly or implicitly  Our Aim: Best alternative matched on maturity period AND riskiness  To do that, we have to define Risk Measure(s) properly AND figure out the Market Price of Risk (expected return per unit of risk-measure)

4. Princeton Spring 2004 Sugato Bhattacharyya Mean-Variance  Higher Mean is Better  Lower Variance is Better  Returns can be used as measures  Investors are non-satiated  Investors are risk-averse Investors must expect higher returns on a portfolio with higher variance

5. Princeton Spring 2004 Sugato Bhattacharyya Evidence

6. Princeton Spring 2004 Sugato Bhattacharyya Diversification  The empirical evidence shown pertained to portfolios. What about individual securities?  Principle: Rational, risk-averse investors will diversify to reduce risk  Diversification serves to “wipe out” risk, provided component securities in portfolio don’t “move together” much

7. Princeton Spring 2004 Sugato Bhattacharyya Schematically.. # of Securities in Portfolio Undiversifiable Risk 1151,00030 Risk of Portfolio

8. Princeton Spring 2004 Sugato Bhattacharyya Implication  Because investors dislike variance, they diversify  Because they diversify, variance of individual securities is not the relevant measure of risk for them  What matters is how much variance each security contributes to the whole portfolio

9. Princeton Spring 2004 Sugato Bhattacharyya CAPM  With symmetric information, everybody should hold the same risky portfolio the Market Portfolio  Therefore, the relevant measure of risk is the covariance with the market portfolio.  This measure, standardized by the variance of the market portfolio, is denoted by beta.

10. Princeton Spring 2004 Sugato Bhattacharyya CAPM contd The beta gives a measure of how sensitive the stock price is to economy-wide factors.

11. Princeton Spring 2004 Sugato Bhattacharyya The Market Model Alternative Interpretation: If the market portfolio can represent the economy-wide risk, then we can use it to write down the Market Model:

12. Princeton Spring 2004 Sugato Bhattacharyya Firm-specific Risk  The larger is the more important is firm-specific risk in the actual realized price of the security.  Total risk of a security may be decomposed into “priced” and “non- priced” risk as

13. Princeton Spring 2004 Sugato Bhattacharyya Systematic vs. Idiosyncratic  Two stocks with same total risk may have very different levels of priced risk  Two stocks with same level of priced risk may have very different levels of total risk

14. Princeton Spring 2004 Sugato Bhattacharyya CAPM The CAPM shows that, for a properly defined risk measure, the relationship between risk and (expected) return is linear: The relationship is also called the Security Market Line

15. Princeton Spring 2004 Sugato Bhattacharyya Implementing the CAPM  What to take as the Market Portfolio? A diversified stock portfolio?  What to take as the Risk-free Rate? How to account for term-structure?  How to get Expected Return on Market Portfolio? Use historical record? If so, how long? Should one use Arithmetic or Geometric Mean?

16. Princeton Spring 2004 Sugato Bhattacharyya Definitions of Means  Arithmetic Mean of Returns:  Geometric Mean of Returns

17. Princeton Spring 2004 Sugato Bhattacharyya Playing with Equations

18. Princeton Spring 2004 Sugato Bhattacharyya Playing with Equations - 2 CEQ

19. Princeton Spring 2004 Sugato Bhattacharyya Introduction  A firm's Capital Structure refers to the mix of the firm’s liabilities.  We will start with the most basic question of capital structure: the mix between debt and equity.  General lessons will apply to more complex capital structures.  To say a firm is Financially Leveraged just means that the firm uses debt in its capital structure. (The British term is Gearing)

20. Princeton Spring 2004 Sugato Bhattacharyya A Levered Firm  Three concepts: Value of the Firm (Enterprise Value) Value of Equity Value of Debt = D + EV Note: A “$500 M Firm” does not refer to any of these

21. Princeton Spring 2004 Sugato Bhattacharyya Leverage: Classical View  Debt is senior to Equity.  Hence it is less risky (less sensitive to shocks to the firm’s prospects)  Hence, the expected return of debt is less than that of equity  Conclusion: Issuing cheaper debt should increase the value of the Firm  Caveat: Issuing too much debt makes it likely for the firm to default

22. Princeton Spring 2004 Sugato Bhattacharyya Leverage: Classical View  Thus, according the classical view, there should be some kind of optimal capital structure which trades off The cheaper cost of debt with The costs associated with default  This classical view is often seen in the pronouncements of less financially sophisticated executives

23. Princeton Spring 2004 Sugato Bhattacharyya Benchmark Scenario Perfect Capital Markets 1.no taxes; 2.no bankruptcy costs; 3.no transaction costs (buying, selling or issuing securities) or bid-ask spreads; 4.equal access to the markets (symmetric information, size is irrelevant, same borrowing and lending rates to all, etc..); 5.Competitive security markets. Firms are price takers.

24. Princeton Spring 2004 Sugato Bhattacharyya In perfect capital markets, capital structure is irrelevant to firm value V L = V U Debt level Leveraged Firm value, V L VUVU VLVL Modigliani-Miller: Proposition I

25. Princeton Spring 2004 Sugato Bhattacharyya The Pizza Hut Intuition: Since production decisions are fixed, the total cash flow is unchanged; Capital Structures are merely different ways of splitting the same total. $100 $40 $60 $80 $20 M&M Proposition I

26. Princeton Spring 2004 Sugato Bhattacharyya The Portfolio Argument: Owning 10% shares in unlevered firm gives you same cash flows as owning 10% of debt and 10% of equity in levered firm with same gross cash flows. M&M Proposition I 0.1 x Profit 0.1 x Interest + 0.1 x (Profit – Interest) = 0.1 x Profit vs.

27. Princeton Spring 2004 Sugato Bhattacharyya The Home-made Leverage Argument:  All players face the same interest rate  Holding 10% of equity in levered firm gives you same cash flows as borrowing 10% of its debt and buying 10% of equity of the unlevered firm M&M Proposition I 0.1 x (Profit – Interest) - 0.1 x Interest + 0.1 x Profit = 0.1 x Profit vs.

28. Princeton Spring 2004 Sugato Bhattacharyya Value of the Firm For a perpetual firm with constant expected cash flows, Value must be the constant expected cash flows of the firm divided by some required rate of return: where E(R a ) is the required (expected) rate of return on the assets of the firm.

29. Princeton Spring 2004 Sugato Bhattacharyya Debt and Cost of Capital  Since V L = V U, it must be that E(R a ) remains constant as the capital structure changes.  But, the required rate of return to holding the levered firm’s securities must be: where E(R d ) is the required rate of return on debt and E(R L e ) is the required rate of return on the levered equity of the firm. Weighted Average Cost of Capital (WACC)

30. Princeton Spring 2004 Sugato Bhattacharyya Debt and Cost of Capital WACC = = The Weighted Average Cost of Capital is invariant to changes in Capital Structure

31. Princeton Spring 2004 Sugato Bhattacharyya Modigliani-Miller Proposition II If WACC doesn’t change, what does? Proposition II (no taxes) The expected rate of return on equity of a levered firm increases in proportion to the debt-equity ratio (D/E), expressed in market values:

32. Princeton Spring 2004 Sugato Bhattacharyya Proof of Prop II

33. Princeton Spring 2004 Sugato Bhattacharyya M&M Proposition II: Graphically Rate of return (%) ELEL rArA WACC DLDL rfrf rErE rDrD Debt is risky Debt is not risky

34. Princeton Spring 2004 Sugato Bhattacharyya When we use the SML to estimate the systematic risk of a stock, the estimated beta reflects not only the risk of the assets in the firm (its business risk), but also the financial risk (or the risk associated with the use of debt by the firm). Thus, the risk of equity consists of both business risk and financial risk. Business Risk and Financial Risk

35. Princeton Spring 2004 Sugato Bhattacharyya The Business Risk of a Firm is, presumably, inherent to its type of business. The Financial Risk of the Firm’s Equity is, ultimately, a decision variable at the management’s discretion. The formula in MM Prop II allows us to disentangle these two sources of risk. Business Risk and Financial Risk

36. Princeton Spring 2004 Sugato Bhattacharyya Bottom Line  Should the firm issue “Cheaper Debt”?  Issuing Cheaper Debt does increase the Expected Cash Flows to Equity (and EPS)  But it also increases its Riskiness  MM Prop I says “it’s all a wash”

37. Princeton Spring 2004 Sugato Bhattacharyya Possible Departures  In the real-world, we have corporate taxes; interest on debt is tax advantaged  In the real-world, we have personal taxation of income; income from holding debt is tax disadvantaged  In the real-world, costs of bankruptcy are not zero  In the real-world, managers may not maximize value of the firm  In the real-world, investment policy may be impossible to decouple from capital structure

38. Princeton Spring 2004 Sugato Bhattacharyya Corporate Taxes  If interest payments are tax- advantaged, and debt and equity are both on the SML, then debt is, indeed, “cheaper” from the firm’s point of view  This may give rise to a preference for debt in capital structure

39. Princeton Spring 2004 Sugato Bhattacharyya Intuition # 1 As debt increases, the government share of the given pie decreases.  The figures below assume pre-tax value of $100; thus, with t c = 34%, V U = $66 (first figure on left). $34 $66 $50 $17 $33 $80 $7 $13 V U = $66V L = $50 + $33 = $83 V L = $80 + $13.2 = $93.2

40. Princeton Spring 2004 Sugato Bhattacharyya Intuition # 2  Investors cannot get a tax break on personal borrowing and, therefore, are willing to pay a premium for firms to take leverage on their behalf.  Comparable to the growth of auto leasing after 1986 tax reform act when non-mortgage interest deductions were eliminated.

41. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm  Consider an infinitely lived firm with a particular investment policy  Each year, its before tax and interest cash flows are denoted by with a mean value of  We will sometimes call this figure Earnings before Interest and Taxes (EBIT) and assume away, for now, issues of Depreciation, Changes in Working Capital, Investment etc

42. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm contd.  If this firm is financed entirely by equity, its expected after-tax cash flows each period would be  What would be the value today of this firm?  We know that we can use two lessons: The perpetuity valuation formula The opportunity cost argument

43. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm contd.  Utilizing these lessons, we can write  Where value is calculated at time 0 and the discount rate corresponds to the expected return associated with an investment of equal level of riskiness

44. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm contd.  Now, assume that this firm has, instead debt of Face Value F and coupon rate c. Also assume that the interest on the debt is always fully deductible for taxes (that is, there’s enough cash flows always)  Then, value of its equity can be written as:

45. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm contd.  Also, the value of its bonds can be written as:  Finally, the total cash flows to all security holders can be written as:  What is the value of this set of perpetual cash flows?

46. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm contd.  To get the value, remember that each set of cash flows has to be discounted at its own appropriate risk-adjusted discount rate  Clearly, the discount rate for the first set is the one we used for the all-equity firm, while the discount rate for the second set is that for debt cash flows  Then, discounting and adding values would give us the following relationship

47. Princeton Spring 2004 Sugato Bhattacharyya Value of Levered Firm contd.  Thus, we have established the following relationship Value of a Levered Firm = Value of the Unlevered Firm + PV of Interest Tax Shields

48. Princeton Spring 2004 Sugato Bhattacharyya Lesson  With tax deductibility of interest (and our various assumptions up to this point), it is always advantageous to have debt  So, how much debt maximizes the value of the firm?  Answer: As much as the firm’s cash flows can support for tax deductibility

49. Princeton Spring 2004 Sugato Bhattacharyya Reality Check  But, we don’t see most firms borrowing to the hilt. And we do see firms paying considerable federal taxes.  So, what gives?  Maybe Personal tax disadvantages of debt negate the corporate tax advantage Maybe costs associated with default act as a brake against too much leverage

50. Princeton Spring 2004 Sugato Bhattacharyya Leverage and Personal Taxes  Suppose income from debt is taxed at a rate t p, the ordinary income rate and that from equity is taxed at a rate t pE  Note that, due to differential rates of taxation, the second rate is likely to be smaller than the first rate. That is, debt is tax disadvantaged from the personal taxes point of view.

51. Princeton Spring 2004 Sugato Bhattacharyya Leverage and Personal Taxes  Then, total cash flow to security holders is: CF from Unlevered FirmCF from Debt

52. Princeton Spring 2004 Sugato Bhattacharyya Leverage and Personal Taxes  Translating into Values, we now have:  Bottom Line: With reasonable parameters, the tax advantage to debt stays, but is reduced in magnitude  BM estimate marginal value to be to be 13%, about a third of the value we’d get without considering personal taxes.

53. Princeton Spring 2004 Sugato Bhattacharyya What Limits Leverage?  Companies do not seem to want to borrow according to the theories we have developed up to now.  In fact, there are corporations like Microsoft and Pfizer who do not borrow at all (essentially)  Are all corporations leaving money on the table or are there costs to borrowing that we haven’t dealt with?

54. Princeton Spring 2004 Sugato Bhattacharyya Bankruptcy  Classical View: Borrowing too much risks bankruptcy; therefore limit borrowing  But if default brings about either restructuring or liquidation, only ownership pattern changes; value doesn’t  So, why should prospect of Bankruptcy matter in leverage decisions?

55. Princeton Spring 2004 Sugato Bhattacharyya Bankruptcy Costs  There are costs associated with being bankrupt that are dissipative  Direct Bankruptcy Costs:  Payments to third parties - Lawyers - Consultants  Dead-weight costs - "wasted" time and effort

56. Princeton Spring 2004 Sugato Bhattacharyya Bankruptcy Costs  If there are significant costs associated with going bankrupt, then the expected costs go up with leverage  When firms are making their leverage decision, they should take into account the increase in expected bankruptcy costs as leverage increases  Then, we have a tradeoff.

57. Princeton Spring 2004 Sugato Bhattacharyya Tax Benefits vs. Expected Costs of Leverage Debt Market Value of The Firm Value of unlevered firm PV of interest tax shields Expected bankruptcy costs Value of levered firm Optimal amount of debt Maximum value of firm

58. Princeton Spring 2004 Sugato Bhattacharyya Direct Costs of Bankruptcy  Estimates are of the order of 3% of total book value of assets before entering bankruptcy  Comparing with the tax benefits of debt, these don’t seem high  Especially when the probability of bankruptcy is taken into account  Conclusion: There must be other costs associated with “Financial Distress”

59. Princeton Spring 2004 Sugato Bhattacharyya Costs of Financial Distress  Indirect Bankruptcy Costs  impaired ability to conduct business  suppliers may demand cash payment  customers may be cautious  Value may be sacrificed by a firm about to default. This dissipation of value would be anticipated and hurt firm value when debt is increased

60. Princeton Spring 2004 Sugato Bhattacharyya Agency Costs  When we incorporate the fact that managers act in the interest of stockholders, we encounter situations in which such interest may conflict with firm value maximization  Such situations may arise when a firm is highly leveraged

61. Princeton Spring 2004 Sugato Bhattacharyya Risk Shifting  Suppose that you have debt due of $100 tomorrow but your assets are worth $50 today  Assume that default triggers liquidation and the proceeds are distributed by APR  Ignore, for simplicity, the time value of money, direct costs of bankruptcy and risk aversion

62. Princeton Spring 2004 Sugato Bhattacharyya Risk Shifting  In this situation, if default occurs, the stockholders anticipate getting $0  Suppose they can take the firm’s assets, liquidate and get $50 today with which they go to Las Vegas and take the following gamble: -$50 $200 $0 0.1 0.9 Expected Value = $ 20 Will they play this game?

63. Princeton Spring 2004 Sugato Bhattacharyya Risk Shifting Contd.  Clearly, they have nothing to lose.  Thus, they are willing to take on a negative NPV project, provided it is risky enough (total risk)  If this is anticipated by debt holders, then they will charge more for debt upfront if the firm attempts to lever up  This will reduce the attractiveness of debt and act as a brake

64. Princeton Spring 2004 Sugato Bhattacharyya Underinvestment  Now, consider the same situation as before and say a project opportunity arises that involves an investment of $10 that will, for sure, give a payback of $30.  Clearly, this is positive NPV  Will shareholders be willing to contribute to take on this investment?

65. Princeton Spring 2004 Sugato Bhattacharyya Underinvestment  If they do, they are out of $10 but are sure of not getting back anything – all the money goes to debtholders  Thus, they pass up on positive NPV projects if they are not risky enough  Such opportunity costs would also be anticipated by debtholders ex ante and limit the attractiveness of leverage

66. Princeton Spring 2004 Sugato Bhattacharyya More Agency Costs of Debt  Would you fly an airline which is in financial distress? Why not?  Would you buy a car from a company that is likely to go bankrupt?  Would you put your money in a bank that is about to go under if it promises to pay you a high interest rate?

67. Princeton Spring 2004 Sugato Bhattacharyya Agency Advantage of Debt?  Are there any advantages to debt beside tax deductibility?  Debt may reduce overinvestment incentives on the part of a manager who is not acting in the shareholder interest  High debt obligations may limit wasteful investment.  LBOs?

68. Princeton Spring 2004 Sugato Bhattacharyya Commitment Advantage of Debt  Consider a steel plant with high sunk costs and low variable costs  If equity financed, its subject to hold-up by unionized workers who might bargain for higher wages once investment is sunk  Debt may act as a commitment device to limit such bargaining power