# 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
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
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

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