The Cost of Capital, Corporation Finance The Theory of Investment

							  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/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 X
   –   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
                  Capitalization                Ratio
                    rate p for     Spread
                   pure equity     between
                    stream in       p and r
                     class k
                     Proof
Simple algebra:
               by definition of ij

               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

   Results:
   Proposition 1 becomes:

Taxable
income
   Proposition 2 becomes:              Shareholders’
                         Average       expected net
                       corporate tax     income
                           rate
 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


                                      and finally




• And therefore we have:
                     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