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## The Cost of Capital, Corporation Finance & The Theory of Investment

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**The Cost of Capital, Corporation Finance & The Theory of**Investment American Economic Review Miller & Modigliani, 1958 Presented by Marc Fuhrmann February 1, 2007**Agenda**• Unique Contributions • Model Overview • Propositions I & II • Extensions of Propositions I & II • Proposition III • Implications • 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/pk, expected return of firm j denoted by xj • Then, we have: and pk 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 V2 > V1 • Suppose further an investor owns s2 dollars in firm 2 • Return Y2 is a fraction α of X – rD2: • Now suppose the investor sells the share and acquires instead s1=α(X- rD2). The new portfolio thus yields: • Since V2 > V1, we must have Y1 > Y2 => 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**Expected yield of a share of stock in firm j Debt/Equity Ratio Capitalization rate p for pure equity stream in class k Spread between p and r**Proof**Simple algebra: by definition of ij by Proposition I Substitute and simplify to obtain:**Extensions**Allow for: • Corporate taxation with deductible interest payments • Multiple types of bonds and interest rates • Market imperfections**Extension I: Taxation**Results: Proposition 1 becomes: Proposition 2 becomes: Taxable income Shareholders’ expected net income Average corporate tax rate**Extension II: Plurality of Bonds**• Proposition I remains unaffected • Proposition II has to be modified**Proof of Case 1**• Recall thatand • 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