The Cost of Capital, Corporation Finance & The Theory of Investment American Economic Review Miller & Modigliani, 1958 Presented by Marc Fuhrmann February 1, 2007

Agenda 1.Unique Contributions 2.Model Overview 3.Propositions I & II 4.Extensions of Propositions I & II 5.Proposition III 6.Implications 7.Limitations & Extensions Omitted: Relation to “Current” Doctrines, Empirics

Unique Contributions First formal use of no-arbitrage arguments Assumptions led to thorough examination of financial environment: –Taxes –Agency problems –Transactions and bankruptcy costs Framework widely used in practice (“WACC”) Simple analytical technique, easily understood

Model: Overview (I) Simple model to value uncertain returns: –All-equity firms belonging to homogeneous risk classes k (only expected returns vary across firms) –Then there must be a proportionality factor that relates stock price to expected return –Factor denoted by 1/p k, expected return of firm j denoted by x j –Then, we have: and p k can be thought of as the required rate of return.

Model: Overview (II) Debt Financing –Assumptions All debt cash flows are certain Bonds are traded in a perfect market  All bonds are perfect substitutes  Bonds sell at the same price per dollar of expected return

Proposition I Or, equivalently:  The average cost of capital is independent of its capital structure

Proof (Sketch) No-arbitrage argument: –2 firms, with identical expected return – Firm 1 all-equity, Firm 2 has some debt Suppose V 2 > V 1 Suppose further an investor owns s 2 dollars in firm 2 Return Y 2 is a fraction α of X – rD 2 : Now suppose the investor sells the share and acquires instead s1=α(X- rD 2 ). The new portfolio thus yields: Since V 2 > V 1, we must have Y 1 > Y 2 => Levered firms cannot command a premium over unlevered firms. Note: Key assumption is that investors can borrow at the same rate as firm

Proposition II Capitalization rate p for pure equity stream in class k Spread between p and r Debt/Equity Ratio Expected yield of a share of stock in firm j

Proof Simple algebra: by definition of i j by Proposition I Substitute and simplify to obtain:

Extensions Allow for: 1.Corporate taxation with deductible interest payments 2.Multiple types of bonds and interest rates 3.Market imperfections

Extension I: Taxation Average corporate tax rate Shareholders’ expected net income Taxable income Results: Proposition 1 becomes: Proposition 2 becomes:

Extension II: Plurality of Bonds Proposition I remains unaffected Proposition II has to be modified

Proof of Case 1 Recall that and Now, let the firm borrow I dollars for an investment yielding p*. It follows that: And therefore we have: and and finally

Implications The source of funds is irrelevant with respect to the question of whether or not an investment is worthwhile. There remain other reasons to prefer one type of financing over another: –Asymmetric information –Tax considerations –Management interest (not always in conflict with owners)

Limitations & Extensions The model provides a framework for capital-structure and investment decisions It can be extended in many directions –more realistic assumptions –general equilibrium context Empirical testing is needed  Countless extensions and tests over the past 50 years  1826 citations according to Google Scholar