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The Miller & Modigliani theorem
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The Miller & Modigliani theorem

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  1. The Miller & Modigliani theorem

  2. Turning to capital structure The two key questions in corporate finance: • Valuation: How do we distinguish between good investment projects and bad ones? • Financing: How should we finance the investment projects we choose to undertake? • We now turn to the second question.

  3. Some facts about capital structure • Firms finance themselves through retained earnings (internal financing) and selling securities in the market (external financing) • Internal financing (retained earnings) biggest source of financing for firms • Firms in countries with less developed financial markets use particularly little external financing 3. The external financing is done by issues of debt, equity and hybrid securities (such as convertible debt and preferred equity)

  4. 4. External financing is raised both in private and public markets • Private sources: Private equity, bank debt, private placements of bonds and equity • Public sources: IPOs, Seasoned equity issues; public bond issues 5. Sources of financing vary over time and over business cycle • Equity issues increase when stock market returns have been high for some period of time • Debt/borrowing issues less cyclical

  5. 4. Capital structures vary across different industries and countries • High leverage industries: Utilities, airlines, cars • Low leverage industries: biotech, software/internet, hardware • High leverage countries: Korea, Thailand, Indonesia, India • Low leverage countries: UK, Australia, US

  6. Industries Vary in Their Capital Structures *D/(D+E), Debt in book value, Equity in market value U.S. data

  7. Debt vs. equity • Equity and debt (and other corporate securities) differ along two dimensions: • Division of value - Debt is senior to equity → get the value of the firm until debt paid off • Equity gets whatever is left after debt has been paid (2) Division of control • Equity holders control firm as long as not bankrupt • Debt holders control firm when firm is bankrupt

  8. Equity is a call option • Equity gets max (0, V - D), i.e. a call option with strike D • Debt gets V – max (0. V – D) = min (V,D) E(V) Payment to debt holders, D(V). Payment to Equity holders, E(V). V=D(V)+E(V) Face of debt D(V) V Face of debt

  9. Questions we will try to answer: • Is there an “optimal” capital structure, i.e., an optimal mix between debt and equity? • More generally, can you ad value to existing owners (equity and debt holders) through decisions on the RHS of the balance sheet? • If yes, does the optimal financial policy depend on the firm’s operations (Real investment policy), and how?

  10. The Miller and Modigliani (MM) capital structure irrelevance theorem • MM (1958) maybe the most important paper in finance • Not only for corporate finance, but also for investments Black Scholes option pricing, for example, relies on arbitrage arguments introduced in this paper • One way to thing about it: what role does capital structure have in a neoclassical fully competitive model with frictionless markets • Like the CAPM • Answer: None!

  11. Why is MM so important? • We don’t believe it, literally • Since markets are not perfect, frictionless, and fully competitive • Strength of theorem is that by showing when capital structure is irrelevant, it also implies when it is relevant.

  12. To get some perspective: pre-MM views • Typical pre-MM view: debt is typically cheaper than equity • Interest rate on debt is lower than the investors’ required return on equity • Equity issues are dilutive: decrease earnings per share, which hurts shareholders • But we can’t have too much debt, because then we go bankrupt → Optimal capital structure

  13. The MM theorem shows that such arguments are flawed • The value of the firm is given by expected cash flows and the investors discount rate (or required rate of return) for these cash flows • V = E(FCF) / (1+R) • In “efficient markets” (i.e. the MM assumptions) capital structure affects neither of these.

  14. V = E(FCF)/(1+R) • Capital structure is just one way of splitting cash flows between different investors, but the total value of the firm remains the same • Although the required returns of debtholders and equityholders may differ, the weighted average cost of capital to the firm will always equal R

  15. The Miller Modigliani Irrelevance Proposition • Suppose the NPV of a new issue is zero. • Suppose the free cash flow to a levered firm is the same as to an all equity financed firm. • Then, financing does not matter! Value is maximized by taking all +NPV as before.

  16. Intuition: (Yogi Berra). • The firm finances its projects by promising free cash flow from operations to different types of investors (debt and equity holders). • The size of the pie is the sum of the free cash flows – it depends on the investment policy, not the way the pizza is divided between investors. When is it true that financing is irrelevant?

  17. Original MM (1958) home-made leverage proof: • “Twin” firms A and B with identical cash flows of CF • A is all-equity financed, value of equity = EA = VA • B has debt of D, value of equity = EB; VB = EB + D, • Miller and Modigliani claim that VA = VB, otherwise there would be an arbitrage opportunity

  18. Suppose debt D is risk less. If buy all of B’s equity, you get: • CR – D(1 + RD) = company’snet profits after interest • This costs you EB. • Instead suppose you buy all of A’s equity, but borrow on own account D of the purchase pries. • So cost to you is EA – D. • You get CF – D(1+RD) = company’s whole cash flow less personal interest you owe. • Since strategies yield same net cash flow to you, must cost the same to assemble: EB = EA – D, of VB = VA. • Otherwise there would be an arbitrage opportunity.

  19. NOTE: We have not assumed anything about how NPV is calculated. • MM does not rely, for example, on CAPM being true. • What is essential is that there are no arbitrage opportunities (financial markets are competitive and complete). • Does all this seem a bit esoteric…? • Capital structure arbitrage is currently a popular hedge fund strategy.

  20. MM and the cost of capital • We have seen that when a firm levers up (finances with debt), it increases the risk ness of its equity. The weighted average cost of capital remains the same: • In our example: • D/(D+E)*rD + E/(D+E)*rE = rA • (10/11)*(10%)+(1/11)*(100%)= 18.18% • It is true that debt requires a lower return. • However, when you lever up, the equity becomes riskier and requires an even higher return. These two effects exactly cancel.

  21. Effect of leverage on returns in the MM world return on assets • Return on equity (“MM proposition II”): rE = rA + (D/E)(rA-rD) • Risk of equity: βE = βA + (D/E)(βA – βD)

  22. Returns and leverage Expected Returns rE rA rD Debt becomes risky Debt/Equity

  23. Do we believe the MM assumptions? • MM irrelevance theorem holds if • NPV of a new issue of debt or equity is zero. • The free cash flow to a levered firm is the same as to an all equity financed firm. • Do we believe that these assumptions are true in the real world? • If not, this gives us a role for capital structure!

  24. (A) Is new issuance zero NPV? • There are 3 conditions for this to be true. • The first two are: • Financial markets are competitive. • New investors just demand fair return on their investment. • Financial markets are complete: • Investors can choose any consumption pattern by borrowing, lending, and hedging. • If not, the firm may be able to make money by offering a cash flow stream with attractive risk characteristics to certain clientele.

  25. For a typical corporation, these two conditions probably hold • It is hard to think that a corporation could make money by issuing some new, eotic security that did not exist before • There are close substitutes available for any security that a company can issue • Making profits from pure financial engineering is better left to the investment banks than regular corporations!

  26. But there is a third condition as well: 3. Prices reflect all existing information (strong form efficiency) • BUT: if the manager has private information about prospects of the firm, MM does not hold! → Could potentially issue misvalued securities and make money!

  27. (2) Are FCF Levered = FCF All Equity? • The assumptions for this to be true are: • No taxes (or no asymmetric tax treatments) • There are no extra costs of financial distress. • There are no transaction costs from issuing securities (or the same costs for debt and equity) • Managers and employees always work to maximize the value of the firm • As we will see, all of these assumptions may not always hold in real world.

  28. Using M-M Sensibly • M-M is not a literal statement about the real world. It obviously leaves important things out. • But it gets you to ask the right question: How is this financing move going to change the size of the pie? • Helps you avoid making the wrong arguments, such as the cost of capital argument above. • Lets go back to some logical fallacies that MM can address.

  29. “Debt is cheaper than equity because it has a low interest rate” • What matters for the value of the firm is RA, the opportunity cost of capital for the firms assets • In an MM world, when you take on more leverage, your RE will increase to keep RA constant

  30. MM applies to all corporate finance decisions • M-M Theorem was initially meant for capital structure, but applies to all aspects of financial policy: • capital structure is irrelevant. • long-term vs. short-term debt is irrelevant. • dividend policy is irrelevant. • buying back shares is irrelevant. • risk management is irrelevant. • purely diversifying acquisitions are irrelevant. • etc. • Indeed, the proof applies to all financial transactions because they are all zero NPV transactions.

  31. (dividends) – (net proceeds from new financing) = (cash flow from operations) – (new investment) • In other words: think about the choice of whether to pay a dividend or not. • If we increase our dividend we can always issue new equity (or debt) to offset this shortfall • If we decrease our dividend we can always repurchase some shares (or pay down some debt) to offset. • We know that value is given by discounting the right hand side Free Cash Flows • LHS does not matter for value, if RHS given

  32. As long as excess cash retained earns a market return, net payments to financial markets do not matter. • $ 100 of excess cash today is worth $ 100 regardless of whether pay out now or later. • Although the return on the firm’s assets may go down if you keep cash on your balance sheet, required return also goes down since firm cash flows become less risky • Total payout policy does not matter either under MM, as long as retained cash flow earns a fair market return and is paid out at some future point.

  33. Essentially the payout policy argument is the same as the debt irrelevance argument. • Important principle: Deciding how much debt to take on and deciding how much cash to pay out is essentially the same decision Cash = Negative debt! • This is why we should consider Net Debt = Debt – Excess Cash when we evaluate capital structure and unlever betas.

  34. Bottom line • Using the MM theorem, we can understand what does (and doesn’t) matter for financial policy. • To understand capital structure and payout policy in the real world we will now see what happens when we relax some of the MM assumptions: • What if there are corporate and personal taxes? • Costs of financial distress? • Conflicts of interest among managers, equity holders, and debt holders? • Managers are better informed than investors?

  35. Financial policy: Plan of Attack • Modigliani-Miller Irrelevance Proposition (1958): • In a world with out frictions, financial policy is completely irrelevant – does not change value of firm. • Now: How does the M world differ from the real world? • Taxes • Costs of financial distress • Other Frictions

  36. Relaxing the Assumptions of MM • New investors get zero NPV. • Financial markets are competitive. • Markets are strong form efficient. • Markets are complete. • The financial policy does not change the free cash flow from real investment policy. 4. No differential tax treatment. 5. No costs of financial distress. 6. No issuance costs. 7. Managers and employees do not have an incentive to deviate from +NPV rule. Almost true Not true

  37. The effect of corporate taxes • The importance of taxes was first noted by MM • Problem is not taxes per se, but that interest and dividends have a different tax treatment • In the U.S. (and for most other countries), the interest payments of corporations are tax-deductible, while dividends are not • Hence, there is a strict tax advantage to financing with debt rather than equity • As a matter of fact, implies firms should have 100% debt! • Which we clearly don’t observe…

  38. Example: Debt tax shield • A firm generates $ 100M in profits for sure every period in perpetuity. This is the only cash flow the firm has. • Risk-free rate is 10% • Corporate tax rate (TC) is 40%. • If the firm is 100% equity financed, what is the value of the firm?

  39. Every period, FCF = (1 – 0.40)*100= 60 • V = E = 60/0.10 = 600 • Now the firm takes of $ 500M of debt. What is the coupon of the debt?

  40. The debt is risk-free → debt holders require 10% → $ 50M coupon • What is the value of the equity? • Each period equity holders get the Net Income of the firm: (1-0.40)*(100–50) = 30 • Value of equity = 30 / 0.10 = 300

  41. Since the value of debt is $ 500, firm value is V = E + D = $ 500 + $ 300 = $ 800 • The firm value has increased by $ 200! • Another way to think about this: • VL = VU + PVTS • VL = value of the levered firm • VU = value of the unlevered firm • PVTS = PV of the Interest Tax Shield • In this case PVTS = $ 200M. Why?

  42. Each period the firm saves TC*I in taxes where TC is the corporate tax rate and I is the interest payment • I.e. yearly tax savings are 40%*$50 = $20M • Hence, the Present Value of the Tax Shield is PVTS - $ 20 / 0.10 = $ 200M.

  43. This is also equal to TC*D = 40%*$500 = $200 • the PVTS = TC*I/RD • But the interest payment I D*RD • The PVTS becomes TC*D*RD/RD=TC*D • PVTS = TC*D is a “back of the envelope” formula. It assumes that • D is constant (ta shield is a perpetuity) • Taz shield and debt payments have same systematic risk → can discount the tax shield at RD • What is the optimal level of debt for this company?

  44. Who gains from taking on the debt? • Say that the firm has 1000 shares outstanding • Before taking on any debt, each share is worth $600/100=$0.60/share • Now the firm takes on $500 of debt, and buys back $500 worth of shares • Think about this as happening in two steps:

  45. The firm raises $500 in debt. Firm now consist of the PV of future firm cash flows plus $500 in cash The value of firm is Cash + VU + PVTS= $500 + 600 + 200 = $1300 The value of equity is E = $1300 - $500 = $800 Share price increased from $0.60 to $0.80 →equity gets the whole $200 gain of the new debt tax shield!

  46. (2) Firm does a share repo of $500 → buys back $500/0.8 = 625 shares. Value of the firm is now $1300 - $500 = $800 E = V – D = $800 - $500 = $300 The equity market cap is lower, but equity holders wealth consist of $300 in stock + $500 in cash = $800

  47. Same argument applies to payout policy • Keeping excess cash of C in the company gives you a “negative” tax shield of t*C • Assume you keep $100 of excess cash in the firm and invests it in T-bonds @ 10%, say → Pre-tax profits increase by $10M/yr (perpetuity) if TC=40%, after tax profits are $6M/yr • What is the PV of this $100 T-bond investment?

  48. PV = CF/r = $6/0.1 = $60 → Keeping $100 of excess cash in the firm, rather than paying it out, reduces value of cash to $60! • if we keep excess cash of C in the firm rather than paying it out, this cash is only worth (1- TC)*C • I.e. cash has a “negative tax shield” of TC*C! • Here (and in general) keeping excess cash in firm is like having negative debt!

  49. Where do we stand now? • Adding corporate taxes to MM’s world suggest firms should be 100% debt financed and keep 0% excess cash! • Seems extreme: - Average debt ratio has been around 35% in last decades. - Many firms (Microsoft, Intel) hoard large amount of cash.  Either CFO’s are missing something, or something must be missing from our analysis. Firm’s value D/E

  50. In addition, most firms effectively pay less than the statutory rate in corporate taxes • Will not make profits every year • Net operating losses (NOLs) can be carried back and forward to offset profits in other years. • Some firms have large non-debt tax shields, such as depreciation, investment tax credits, etc.