David Durand, “The Cost of Capital, Corporation Finance, and the Theory

of Investment: Comment”

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

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

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

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.)

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."

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

Switching Example

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

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.”

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.

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.

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."

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

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

Switching Example

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”

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.

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.

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)

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

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

Cont.

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

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

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

Thank You