- The author David Durand contradicts the findings of Franco Modigliani and Merton Miller (MM) on the cost of capital and the irrelevance of capital structure. - Durand argues MM's assumptions, including the unrealistic foundations that arbitrage is always possible and risk is minor, do not reflect real world markets which have imperfections and restrictions. - Durand provides examples showing how MM's propositions would not hold in cases involving growth, retained earnings, or margin restrictions - violating the equivalence of securities needed for their theory. Real world markets do not achieve the long-run equilibrium assumed by MM.

1. David Durand, “The Cost of Capital,
Corporation Finance, and the Theory
of Investment: Comment”

2. Purpose of the paper
• The author David Durand contradict with the findings
of *Franco Modigliani; Merton H. Miller, “The Cost of
Capital, Corporation Finance, and the Theory of
Investment: Comment”, American Economic Review,
June 1958, 48,261-97] (hereafter) MM.
• The difficulties associated of using their findings to
support "An operational definition of the cost of capital
and a workable theory of investment”
• MM main assumption “The value of a firm is
unaffected by how that firm is financed”
• capital structure irrelevance principle

3. Proposition I Foundation Devices
• Equation (3)
• ρk constant capitalization factor for all “firms “in class k
"equivalent return“.
• For Proposition I to hold, Foundations
– Arbitrage is possible between securities in an equivalent return
class (Not arbitrage “switch”)
– “Firm” hybrid “not a corporation”
• Marketable securities like a corporation
• Proration of income like a partnership
• Allocation of financial responsibility like neither
– Exclude risk. (Risk in minor Uncertainties)
– Long-run equilibrium (stocks sell at book value)
• Unrealistic Foundations

4. I. Proposition I and Arbitrage: An
Illustrative Example
• Petrolease earns $10 per share on the average, all of
which it pays out in dividends.
• Leverfund open-end investment trust
– Assets consist solely of Petrolease shares
– 1 share of Petrolease = 1 Share of Stock and $100 bond at
Interest rate 0.05.
– Incurs no expenses and pays out all earnings
– open-end fund
• Issue 1 share + 1 bond = adding 1 share Petrolease
• Demand 1 share + 1 bond = subtract 1 share Petrolease
– No loading charge (Same Price)
– Trade without commission in Open Market

5. Arbitrage
• MM “Upon equivalence in exchange between
a share of Petrolease and a bond and share of
Leverfund, not upon equivalence of income”.
• MM Arbitrage = “Perfect substitute"
• In fact share of Petrolease is not a perfect
substitute for a bond and share of Leverfund
• Leverfund to closed-end trust (Closecorp)
• Exchange of securities in no longer possible
(No Arbitrage.)

6. Enforcing the Arbitrage
• Hedge position, to provide income without investment.
– But this sort of transaction may be hard to arrange
• Switching of investment
– from comparatively unattractive issues into others that
seem to offer a higher return for the same risk
– Require the active cooperation of a large body of investors
• MM [11, p. 270+ “levered companies cannot command
a premium over unlevered companies because
investors have the opportunity of putting the
equivalent leverage into their portfolio [sic] directly by
borrowing on personal account."

7. HEDGE Example
• If Closecorp sells at a 5 per cent premium (additional value
original value + 5 per cent ).
• an operator might short selling (sell what he don’t have)
100 bonds and shares,
• investing the proceeds in 105 shares of Petrolease;
• then, since the income from 100 shares of Petrolease
would suffice exactly to cover interest and dividend
requirements on his short position
• he would derive as net income the dividends from 5 shares
of Petrolease. But this sort of transaction may be hard to
arrange, owing to the many restrictions on short selling;
and it exposes the operator to numerous risks-including the
risk of being caught in a corner

8. Switching Example

9. Theory failure
• Proposition I can be no more than an inequality for
Petrolease and Closecorp
• Closecorp securities enjoy a wider market than does
Petrolease stock
• Closecorp to command a premium
– Stocks has a special appeal to risk-takers
– Bonds has a special appeal both to the safety-minded and
to those barred from buying Stock
• In the long run Closecorp can expand
– issuing more bonds
– high-leverage share
• MM neglected the financial operations of corporation

10. II. Market Imperfections: Restrictions
of Margin Buying
• MM ”Those who hold the current view-whether
they realize it or not-must assume not merely
that there are lags and frictions in the
equilibrating process-a feeling we certainly
share, claiming for our propositions only that
they describe the central tendency around
which observations will scatter-but also that
there are large and systematic imperfections in
the market which permanently bias the
outcome.”

11. Cont.
• In Proposition I Whenever the market deviates
from equilibrium (economic the price is fixed
demand equal supply) shift in the price
– Investors exclusive rights to profit by giving them full
responsibility to correct deviations from equilibrium
• Speed
• adequate volume
• MM suggested that Market imperfections prevent
corporations from issuing or redeeming securities as fast
as investors can switch account.

12. Restrictions
• Switching operations by investors faced by
• margin restrictions
• brokers' commissions
• tax considerations
• and other institutional limitations at that time
– institutional restrictions limit the volume of switching operations
that investors can arrange on short notice-especially switching
from high-leverage stocks held outright into low-leverage stocks
on margin
• The switch is insufficient in volume to maintain the
market anywhere near equilibrium.

13. III. The Risks of Margin Buying
• MM[11, p. 268]:"All bonds (including any
debts assumed by households for the purpose
of carrying shares) are assumed to yield a
constant income per unit of time, and this
income is regarded as certain by all traders
regardless of the issuer.“
• MM[11, p. 269]: "one income stream for
another stream, identical in all relevant
respects but selling at a lower price."

14. Cont.
• But this argument does not apply to corporate
stockholders in a world of high risk, and in a
world where yield are really uncertain.
• MM had such safety in mind

15. Example
• If Petrolease earnings were absolutely certain to
remain above $5 per share
• Petrolease Income = Closecorp Income
– neither the margin lender nor the Closecorp
bondholder would run any risk of default
• Petrolease income may fall below $5 per share.
(oil wells run dry)
• Clasecorp specially chartered as a limited
partnership or joint venture with pro-rata
allocation of responsibility

16. Switching Example

17. IV. The Problem of Retention and
Growth
• MM “As will become clear later, as long as
management is presumed to be acting in the
best interests of the stockholders, retained
earnings can be regarded as equivalent to a
fully subscribed, pre-emptive issue of
common stock. Hence, for present purposes,
the division of the stream between cash
dividends and retained earnings in any period
is a mere detail”

18. Example
• C1, C2 has equally assets as A
• C1, C2 earnings on regular basis on assets A = p*
• No profit, all gone as dividends so they will still
have same assets A and earning of = Ap*.
• C1 and C2 belong to the same class j.
• C2 started to retain earnings, reinvest in assets B.
• C2 will have more earnings than C1
• C2 level up to new class.

19. Cont.
• pre-emptive stock issue will not avoid this
difficulty unless stocks sell at book value.
– first, to maintain earnings per share unchanged
and thus keep the corporation in the same class;
– second, to provide a genuine equation between
the amount retained and the hypothetical stock
issue.

20. Cont.
• Company Earning (Started to expand) = Aρ*
• N # of shares so, Aρ*/N = earning per share
• Book Value Bo = A/N
• ρk Market capitalizing rate
• Stock Price Po = Aρ*/ ρk N
• Price to Book ratio Po/Bo = ρ*/ ρk
• Company retains and reinvests I = Aρ*X at Yield =
ρ*.
• earn = Aρ* (1 + ρ*X)

21. Cont.
• When ρ*= ρk and Po=Bo no change in the
price Po, but what P1 can’t meet both
requirement.
– ρ*= ρk and Po=Bo
– provide a genuine equation between the amount
retained and the hypothetical stock issue
• For example to P1 = Bo the corporation must
issue new share

22. Cont.
• 1 numbering of new shares
• 2 add them to the old N of shares
• When ρ*≠ ρk and Po ≠ Bo can’t determine P1
because of the entire future growth of the
corporation

23. Cont.
• In the operating world stocks do not sell at
book value not even approximately

24. Problems of Empirical Analysis
• The difficulty of assembling a sample of
corporations capable of supporting a
comparative, or cross-section, type of analysis
• The empirical analyst will be unable to assemble
any sample meeting the rigid requirements of
MM's equivalent class.
• samples that are reasonably homogeneous in
most respects, and yet show enough variation in
growth rate, capital structure, and the like to
bring out the influence of these factor

25. Conclusion
• MM have cut out for themselves the
extremely difficult, if not impossible, task of
being pure and practical at the same time.
– Risk affords
– Equilibrium mechanism in an imperfect market
– The difficulty of having an equivalent return class

26. Thank You