Capital Structure Decisions: Modigliani and Miller 1958 JF

Who are Modigliani and Miller (MM)? They published theoretical papers that changed the way people thought about financial leverage. They won Nobel prizes in economics because of their work. MM’s papers were published in 1958 and 1963. Miller had a separate paper in 1977. The papers differed in their assumptions about taxes.

The State of the Literature c. 1950s Economic theorists have made detrimental simplifications e.g. physical assets (bonds) could be assumed to give known, sure streams The cost of capital is therefore the rate of interest on bonds The firm will invest until marginal yield = marginal interest

The State of the Literature c. 1950s Under certainty, two criteria of rational managerial decision-making are prevalent: The maximization of profits The maximization of market value Under both, the cost of capital = interest rate on bonds

The State of the Literature c. 1950s Some attempts had been made to deal with uncertainty: A risk discount subtracted from expected yield A risk premium added to the market rate of interest This works for macro generalization models, but not for macro indicators or micro concerns

The State of the Literature c. 1950s Profit maximization from the certainty model had led to utility maximization of managers/owners i.e. the decision-making application was subjective Another option: market value maximization

Market Value Max. Offers an application function for the cost of capital, pk Yields a functional theory of investment However, capital structure theory and knowledge of how structural variability affects market value were both lacking

Primary Questions Does capital structure matter in determining the market value of a firm? (page 268) What is the nature of the market price of a share? i.e. “cost of capital” (page 271) Does the type of security used to finance an investment matter? (page 288)

Assumption 1 To analyze the problem within the M&M structure, initially assume: (1) Perfect capital markets. By a perfect capital market, we mean: (a) no transaction costs - to allow for costless short sales and long purchases, (b) no taxes, (c) no bankruptcy costs.

Assumption 2 There exists a group of homogeneous firms which have assets that yield a perpetual stream of uncertain cash flows: yearly cash flows are random drawings from the same distribution, i.e., no growth, and individuals have homogeneous expectations concerning the expected cash flows. The only permitted difference in these firms is that the random cash flow from one firm in the portfolio can be equal to the random cash flow for some other firm in the portfolio, times a constant. Therefore, since all firms have the same cash flows (or cash flows times a constant) in every state of nature, then these firms will also have the same risk and therefore the same expected return, ρk.

Assumptions 3, 4, 5 (3) These firms can either be all equity or part debt and part equity. (4) Equity of the firms is risky. Debt is risk free, paying a constant interest rate, r, over time. Investors can also borrow at the risk-free rate. Implicit in these assumptions: (5) The investment decision is unaffected by the financing decision. Thus, the distribution of the cash flows from the asset is the same whether the firm is unlevered or levered.

Assumptions 6,7,8 (6) Managers always work to maximize shareholder wealth. This implies that there are no conflicts of interest between managers and stockholders. Stockholder / bondholder conflicts are assumed away because the debt is risk free. (7) Corporate insiders and outsiders have the same information - this prevents insiders from signaling their private information by choosing a particular capital structure (8) 100% dividend payout ratio.

rsL = rsU + (rsU - rd)(D/S) rA: return on asset, or WACC MM with Zero Taxes (1958) Proposition I: VL = VU. Proposition II: rsL = rsU + (rsU - rd)(D/S) Or rsL = rA + (rA - rd)(D/S) rA: return on asset, or WACC

The Basic Propositions: Proposition I “The market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate pk appropriate to its class” (268) i.e. a firm with pure equity financing and one with leveraged financing will have the same market value

The Basic Propositions: Proposition II “the expected yield of a share of stock is equal to the appropriate capitalization rate pk for a pure equity stream in the class, plus a premium related to financial risk equal to the debt-to-equity ratio times the spread between pk and r” (271) i.e. the cost of equity is a linear function of the firm’s debt to equity ratio. The higher the debt, the higher the required return on equity

rsL = rsU + (rsU - rd)(D/S) Graph the MM relationships between capital costs and leverage as measured by D/S. Without taxes Cost of Capital (%) 26 20 14 8 rsL = rsU + (rsU - rd)(D/S) Rs WACC, Rsu, or RA Rd Debt/Stock Ratio (%) 0 20 40 60 80 100

The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost. Although rd remains constant, rs increases with leverage. The increase in rs is exactly sufficient to keep the WACC constant.

Graph value versus leverage. Value of Firm, V (%) 4 3 2 1 VU VL Firm value ($3.6 million) 0 0.5 1.0 1.5 2.0 2.5 Debt (millions of $) With zero taxes, MM argue that value is unaffected by leverage.

With corporate taxes added, the MM propositions become: Find V, S, rs, and WACC for Firms U and L assuming a 40% corporate tax rate. With corporate taxes added, the MM propositions become: Proposition I: VL = VU + TD. Proposition II: rsL = rsU + (rsU - rd)(1 - T)(D/S).

Notes About the New Propositions 1. When corporate taxes are added, VL ¹ VU. VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. 2. rsL increases with leverage at a slower rate when corporate taxes are considered.

MM relationship between capital costs and leverage when corporate taxes are considered. Cost of Capital (%) rs 26 20 14 8 WACC rd(1 - T) Debt/Value Ratio (%) 0 20 40 60 80 100

MM relationship between value and debt when corporate taxes are considered. Value of Firm, V (%) 4 3 2 1 VL TD VU Debt (Millions of $) 0 0.5 1.0 1.5 2.0 2.5 Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.

What does capital structure theory prescribe for corporate managers? 1. MM, No Taxes: Capital structure is irrelevant--no impact on value or WACC. 2. MM, Corporate Taxes: Value increases, so firms should use (almost) 100% debt financing. 3. Miller, Personal Taxes: Value increases, but less than under MM, so again firms should use (almost) 100% debt financing.

What does capital structure theory prescribe for corporate managers? Miller, Personal Taxes: Value increases, but less than under MM, so again firms should use (almost) 100% debt financing. B: bond; Tc: corporate tax rate; Tps:personal capital gain tax rate; Tpb: personal interest income tax rate

Do firms follow the recommendations of capital structure theory? Firms don’t follow MM/Miller to 100% debt. Debt ratios average about 40%. However, debt ratios did increase after MM. Many think debt ratios were too low, and MM led to changes in financial policies.

Do firms follow the recommendations of capital structure theory? Firms don’t follow MM/Miller to 100% debt. Debt ratios average about 40%. However, debt ratios did increase after MM. Many think debt ratios were too low, and MM led to changes in financial policies. Reference: HOW DO CFOS MAKE CAPITAL BUDGETING AND CAPITAL STRUCTURE DECISIONS? by John Graham and Campbell Harvey, http://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P76_How_do_CFOs.pdf

Example: with corporate tax

With corporate tax example

With bankruptcy costs

With bankruptcy costs