Credit Risk and Dividend Irrelevance

Dan Galai and Zvi Wiener

School of Business Administration

The Hebrew University of Jerusalem

Jerusalem, 91905

Israel

May 13, 2015

Abstract

We show how, in a Merton-type model with bankruptcy, the dividend policy impacts the values of

equity and debt as well as credit risk. The recent financial crisis has emphasized the fact that

excessive dividends can lead to financial distress. When dividends are paid from assets (including

cash), there is a potential for a conflict of interest between shareholders and debtholders. The

model presented allows for a quantitative setting of restrictions on dividends and gives a useful tool

to support dividend payments or preclude a distribution when such could otherwise jeopardize the

firm. We show the implications of our approach compared to the implications of the Signaling

Approach, and the Smoothing Approach. It is shown that the Miller-Modigliani irrelevance of

dividends theorem must rely on more assumptions than in the original paper. In this paper, we

highlight the role of dividends (and stock repurchases) to possibly mitigate the potential conflict of

interests between shareholders and debtholders. The emphasis is on the credibility of the dividend

policy.

JEL Classification Numbers: G12; G13; G15

Keywords: credit spread, foreign debt, dividend policy, Merton’s model

Author’s E-Mail Address: dan.galai@huji.ac.il, zvi.wiener@huji.ac.il

We wish to thank Zvi Bodie, Kose John, Neri Bukspan and Avri Ravid for their insights and helpful suggestions and

fruitful discussions, as well as the participants of the seminar at the University of Auckland, the University of New

South Wales, University of Melbourne, the University of Western Australia, New York University, Yeshiva University

and International Conference on Quantitative Finance, Insurance and Risk Management, Morocco. We acknowledge

financial support from the Israeli Science Foundation (ISF) the Zagagi Center and the Krueger Center at the Hebrew

University. Part of Dan Galai work was done while being a Visiting Professor at MBS, Melbourne, Australia. Galai serves

as the Dean of The Sarnat School of Management, College for Academic Studies, Or Yehuda.

1

Credit Risk and Dividend Irrelevance

I. Introduction

The contingent claim approach (CCA) to pricing corporate securities was initially suggested

by Black and Scholes (1973) in their seminal paper. It was followed by Merton (1974) who applied

the option pricing model to pricing corporate bonds and by Galai and Masulis (1976) who applied

the approach to pricing equities. The initial model was based on a simplified firm with a zero

coupon, fixed maturity debt, and no dividends during the term of the debt. It was shown that, under

the simplifying assumptions, the equity of a levered firm can be priced as a European call option on

the firm’s assets. The zero-coupon bond can be priced as a riskless debt minus the European put

option. The exercise price in this case is the face value of the debt at maturity, which includes both

the principal amount and the accrued interest payments. In this framework, the credit risk of the

bond is contained, or priced, in the put option (see Merton (1974), and Crouhy, Galai, Mark (1998)).

The original Merton model assumes that bankruptcy can occur only at the maturity of the debt.

Since then many papers were published using CCA to price various types of securities issued

by corporations (e.g. warrants, convertible bonds, and more, see the reference list). Also, extensive

research was directed toward changing some of the simplifying assumptions. Black and Cox (1976)

extended the model to include senior and junior debt instruments. They also allowed for early

bankruptcy during the term of the debt instruments. Francois and Morellec (2004) introduced

different bankruptcy rules to measure their effect on the credit risk premiums. This work was

extended by Galai, Raviv and Wiener (2007) for various legal systems of bankruptcies. Cox and

Ross (1976) also applied the CCA to price coupon paying bond and equity with constant dividend

payouts.

We introduce the dividend policy to the Merton model initially under the simplifying

assumptions. We assume that dividends are paid continuously at a fixed rate, by selling assets of the

firm. We address in the CCA framework the issue of dividend policy as a contingent claim by itself,

and its effect on the valuation of corporate debt and hence, on the credit risk of the corporation.1 We

1 Garbade (2001), in his book considers discrete-time dividends as contingent claims of the

corporations. He does not directly addresses the assessment of credit risk of the firm.

2

derive the probability of default (PD) endogenously in the model (both in risk neutral terms as well

as in terms of the economic probability).

It was observed by many researchers that firms smooth their dividend payments and try to

maintain a stable dividend payout ratio, (see, for example, Lintner (1956), DeAngelo et al. (1992)).

If according to M&M, dividend policy is irrelevant why firms actively manage their dividends?

Many possible explanations are provided in the academic literature, including tax considerations,

signaling via dividends, and more (see, for example, Kalay (1980, 1982), Lambrecht and Myers

(2012), Berk and DeMarzo (2007) chapter 17, Van Horne (2002), chapter 11, and Guttman et. al.

(2010)).

Black in his “Dividend Puzzle” paper (1976) says “The harder we look at the dividend

picture, the more it seems like a puzzle with pieces that just don’t fit together”. He checks the issues

of taxes, transaction costs and more. Black’s conclusion is that stock repurchase may be a more

efficient way to make a distribution to shareholders. In this paper we do not separate between the

two types of distribution. Black also raises the issue of the potential conflict of interest between the

stockholders and bondholders but dismisses it as too small in many cases, and, “… if the effects are

large, the company can negotiate with the creditors”.

Our model provides another explanation which is based on the shareholders-bondholders

conflict of interests. By making the dividend policy known in advance, the shareholders are

extracting (an expected) value from the bondholder. If the policy is stable, it makes it easier for the

bondholders to monitor the policy and assure that it is consistent with the covenants, expectations,

and the acceptable range of probabilities of default. If a profitable, levered firm is not paying

dividends (or repurchases shares), it actually enhances the value of the debt by reducing the

probability of default. If dividends were expected but are not being paid out, there is a transfer of

wealth from equity to debt holders. Dividends are, therefore, a means of extracting value to

shareholders. However, making this policy known and stable reduces the cost of debt as it stabilizes

the credit risk of the firm and makes it more predictable. The model has important implications for

corporate governance and regulation of dividend policy and distributions to shareholders. Bond

covenants can be set in order to protect in a more rational way the debt holders of a corporation.

The optimal long term dividend policy should be characterized by credibility. There is a

major difference in the dividend policy implications from the shareholder’s point of view between

an “end of game” policy and the “long term” policy, when the debt should be rolled over again and

3

again. This credible policy implies that the shareholders should not harm the interests of the

bondholders over time, while assuring the equityholders to receive any excess value due to future

“good” performance of the firm. In other words, if debt was issued with a given credit quality, the

equityholders may have no incentive to increase the credit quality in good states, and may prefer

paying a dividend while maintaining the credit quality. If they need to issue a new debt they may

prefer to pay less dividends if their credit rating will improve. The equityholders are entitled to get

all the excess residual value. However, in bad states the dividend policy should be such that the

decrease in assets' value is being shared. The dividend policy should be constrained in such a way

that the value of equity cannot increase while the value of debt decreases and all the loss is solely

incurred by debtholders.

In this paper, we highlight the role of dividends (and stock repurchases) as a mitigation

instrument in the potential conflict of interests between shareholders and debtholders. The idea is

that increases in dividends (or repurchases) increase the credit risk of debtholders and potentially

can affect the credit spreads.2 To mitigate the potential widening of credit spreads, the shareholders

may be advised to employ a credible dividend policy. Unstable, uncertain and incredible dividend

policy may cost shareholders via the cost of raising future debt. Therefore, “end-of-game” policy is

an extreme case, and may lead to different conclusions than the “ongoing”, levered firm.

In Section II we summarize prior research on dividend policy. We present the CCA model

with options in Section III. In Section IV we confront the Irrelevance Theorems of Modigliani and

Miller with the measurement of credit risk to show the effects of the potential conflict of interest

between shareholders and debtholders. This is illustrated with an example using the Binomial model

to show the impact of unexpected change in dividend policy. The implications of our approach are

different from the conclusions of the Signaling Approach as explained in Section V. Section VI

shows how the potential conflict of interest can be mitigated also by means of dividend smoothing

2 It was recently announced (see Reuters, January 20, 2015) that Microsoft, which is an AAA rated company, is

considering a stock repurchase plan of 40B dollars, to be financed mainly by a new debt. As a market value of equity of

approximately 340B, the repurchase plan translates to a dividend payout of around 12%. The new debt will more than

double the existing long term debt. According to Reuters, the rating agencies will probably downgrade Microsoft. “It is

very conceivable that our net debt-to-Ebitda ratio would go somewhere in between the 2.0 and 2.5 range," said the

CFO of Microsoft - John Stephens on the earnings call. "We will let the debt rating agencies deal with it as they see fit.

But we are comfortable with where we are going and we understand the implications."

http://www.reuters.com/article/2015/01/30/microsoft-ratings-idUSL1N0V82JF20150130

4

policy. In Section VII we indicate the consistency of many empirical findings with our approach.

Section VIII concludes.

II. Prior research

The topic of dividend policy attracted the attention of many academic researchers. Lintner

(1956) was the first to draw the attention to the observed policy of smoothing dividends. Miller and

Modigliani (1961) showed, however, that in a perfect capital market (PCM) dividend policy should

be irrelevant. Black (1976) raised the issue of the dividend puzzle due to its tax disadvantage.

Brennan and Thakor (1990) show that despite the preferential tax treatment of capital gains

for individual investors, the majority of shareholders may support a cash dividend payment for small

distributions. Shareholders may prefer open market stock repurchases for larger distributions. The

basic contention of this paper is that in order for share repurchase to be qualified for favorable tax

treatment, they cannot be on a pro-rata basis. In such a case the less informed shareholders may be

vulnerable to expropriation by the better informed. Brennan and Thakor focus on the potential

conflict of interest between informed and uninformed shareholders. Their model completely ignores

the potential conflict of interest with the bondholders.

Benartzi, Michaeli and Thaler (1997) find very limited support to the claim that changes in

dividends have information content about the future earning of the firm. Increases (decreases) in

dividends are correlated with increases (decreases) of earnings in the same year and the year before,

but do not explain future unexpected earnings increases (decreases).

Kalay (1980, 1982) looks at the potential conflict of interest between the stock and bond

holders, and argues that bond covenants usually prevent stockholders from shifting values away

from bondholders. He shows empirically that, in any case, the shareholders did not distribute the

maximum possible for distribution at each year; dividend distributions stayed below the constraints

imposed by the covenants.

In a more recent study by Brav et al. (2005) the authors surveyed 384 financial executives

and what determined their dividend policies. In general they find little support for agency, signaling

and clientele hypothesis of payout policies. They find that perceived stability of dividends is

important; however the link between dividends and earnings has weakened since Lintner (1956)

found that firms manage their dividends to show stability over time.

5

Various researchers suggested introducing the dividend payout to the contingent claim

analysis of debt and equity (e.g. Cox and Ross (1976), Black and Cox (1976)). Fan and Sundaresan

(2000) model the value of corporate debt and optimal dividend policy in a game-theoretic setting

with varying bargaining powers between debt holders and equity holders. Delianedis and Geske

(2001) used the dividend payout policy trying to explain the observed credit spreads, for a sample of

firms in the US from November 1991 to December 1998. They accrue all dividends during the life

of the bond to its maturity. The empirical evidence, again, shows only partial explanation of the

observed credit spreads.

In a provocative paper DeAngelo and DeAngelo (2006) argue against the dividend

irrelevance Theorem of M&M, and claim that payout policy is not irrelevant. They argue that “…

M&M “equivalence principle” – that the discounted value of cash flows from investment must be

equal the discounted value of dividends – is not a universal property, but holds only for optimal

payout policies.” Their claim is that a necessary condition for stockholders wealth maximization is

to distribute the full present value of all free cash flow (FCF) to currently outstanding shares. For

them dividend policy matters in determining the equity value. This claim will be further discussed

below.

Smith and Warner (1979) raise the issue of the potential conflict of interests between

debtholders and shareholders and how it affects the financial contracting of the corporation. They

conclude that dividend and financial policy restrictions are written to give stockholders incentives to

follow a firm-value maximizing production/investment policy. The major dividend covenant is a

limit on distributions to stockholders by defining an inventory of funds (accounting or economic

earnings) available for distribution over the life of the bond. This inventory is a function of a few

variables. They also state that “The price which bondholders pay for the issue will be lower to

reflect the possibility of subsequent wealth transfer to stockholders”. In this paper we highlight this

later point and show how it can be priced in.

III. The Model

A. Pricing of Debt and Equity when the Company Does Not Pay Dividends.

Merton (1974) showed how corporate bonds can be priced as riskless government bonds for

the same duration (T) minus the price of a put option on the value of the firm, V, with a strike price

6

equal to the face (par) value of the bond (F), which is the promised payment due at T, including the

principal and the cumulative interest.

PFeD rT −= − (V, F, r, T, σ) (1)

where σ is the standard deviation of the rate of return of V. Based on Black-Scholes and Merton the

value of the Put option P is given by

P= ( ) ( )21 dNeFdNV rT −⋅⋅+−⋅− −

(2)

where N(d) is the cumulative standard normal distribution up to point d, r is the continuous riskless

interest rate and

TddT

TFe

V

drT

σσ

σ−=

+

=−

12

2

1 ,2

1ln

Hence, the value of the bond is

( ) ( )( ) ( ) ( )1221 dNVdNeFdNeFdNVFeD rTrTrT −⋅+⋅⋅=−⋅⋅+−⋅−−= −−−

(3)

Galai and Masulis (1976) showed that under these assumptions, the value of equity, S, is priced as a

call option on the value of the firm, V.

Hence,

S = ( ) ( )21 dNeFdNV rT ⋅⋅−⋅ −

(4)

and, of course, S+B = V as is dictated by the Modigliani-Miller (1958) Theorem I.

When the Merton model was empirically tested, it was found that the realized spreads are

higher in practice as compared to the model prices. This phenomenon means that bond market

7

prices are lower than the model prediction. Various reasons were suggested to explain the gap

between model prices and market prices. See for example Elton et al (2001).

We can show that paying dividends is similar to paying junior debt before the maturity of the

senior debt. Dividends behave like a short maturity junior debt, in terms of increasing the credit risk

of long maturity senior debt.

By constructing a model for credit risk on senior debt when dividends are being paid, we can

construct debt covenants so that the probability of default will be below a given level, or we can

restrict the dividend policy to maintain a desired credit rating by constructing quantitative characters

for credit rating levels using averages (like spread or PD) published by rating agencies. In

subsection B, the assumption is that there is a firm commitment to such a dividend policy during the

term of the debt. In subsection C we study a more realistic assumption, that dividends are discrete

(say, quarterly) and the board has discretion to stop or reduce the dividend payments, in the case of

adverse economic conditions.

B. Pricing of Debt and Equity when the Company Pays Dividends.

We make the traditional assumption of Black and Scholes (1973) and Merton (1973, 1974).

We assume that the firm is financed by equity, S, and a plain-vanilla zero coupon bond B, with

notional value, F, to be paid at time T. In addition, we assume the firm V, pays a continuous

dividend, δ, to the shareholders, and dividend rate is known and constant. It is also implicitly

assumed that all dividends are distributed by "selling" part of the existing assets, V, and not by

raising additional equity or debt.

In Merton (1973), the pricing of a European call option was extended to the case of

continuous dividends, over the life of the option, to which the option holders are not entitled. In our

case, the shareholders in the levered firm can be regarded as having a call option on the firm’s assets

and in addition they are entitled to get the dividend. The dividends paid to the shareholders reduce

the value of the firm V, by the rate δ, and hence, the value of the put option, which reflects the credit

risk, is affected by the dividend stream. Let us denote by PEX

the value of the put option on V, with

strike F and maturity T, when continuous dividends at a rate δ, are paid to the shareholders:

( ) ( )EXrTEXTEX dNFedNVeP 21 −+−−= −−δ (5)

where

8

T

T

Fe

VeLn

d

rT

T

EX

σ

σδ

2

2

1

+

=−

−

TddEXEX σ−= 12

It can be noticed that 0≥∂∂δ

EXP, or, the value of the put increases with the increase in the dividend

payout. Denote the price of the bond, when dividends are paid by BEX, then

EXrTEX PFeB −= −

( ) ( )[ ]EXrTEXTrT dNFedNVeFe 21 −+−−= −−− δ (6)

( ) ( )EXTEXrT dNVedNFe 12 −+= −− δ

It can be shown that BBEX < and hence BVSBVS EXEX −=>−= .

Now we can describe the probability of default for the bond over its life when faced with a

continuous dividend rate δ. Based on Boness (1964) and Galai (1978), it can be shown that the true

PD (for the period T) is:

( )truedNPD 2−=

Where

T

TFe

VeLn

dRT

T

true

σ

σδ

2

2

2

1−

=−

−

(7)

and R is the expected rate of return on the firm’s assets. Note that the risk neutral PD is given by

( )EXdN 2− .

Black and Cox (1976) extend equation (6) for the case that the bond has safety covenants. In

particular they show (p. 356) the contingent value of the bond when, the firm’s reorganization takes

place as soon as )( tTr

t FeV−−≤ . This is the stopping boundary in a form of a trigger for bondholders

to take over the firm. Introducing such a barrier does not change the basic results, and the value of

the bond, B, is still an increasing function of V and T and a decreasing function of σ, r and δ.

Introducing the barrier increases the value of B while reducing the value of equity, S, and also

increases the probability of bankruptcy while reducing the loss given default (LGD).

9

C. The effect of a single period dividend on the credit risk.

The model in subsection C depicts the standpoint of the board members who must approve the next

period dividend, while the model in subsection B describes the perspective of the debtholders who

take into consideration today the expected dividend stream over the whole term of the debt.

Equation (7), in this case, becomes

τσ

τσδτ

τ

2

,2

2

1−

=−

−

RT

true Fe

VeLn

d (7’)

where τ < T is the end of the single dividend period approved by the board of directors and thus the

impact of the dividend stream on V is during the period τ only. ( )truedN τ,2− is the true probability of

default of the firm given the next period dividend only, while ignoring the expected future dividend

stream. This model recognizes that the dividend policy, δ, for the period up to τ is a firm

commitment, while all future dividends beyond τ must be approved by the board of directors, based

on the information available to the firm and its decision makers after the end of period τ. Clearly

the probability of default from the board perspective given the single period dividend policy may

differ from the probability of default estimated by debtholders, since )()( 2,2

truetrue dNdN −≤− τ .

Of course, an investor who considers purchasing a bond at present, facing a deterministic

decision to pay dividends during period τ, cannot ignore, in pricing the bond, the future contingent

dividend decisions beyond τ. While the board can change the dividend policy after τ, subject to

bond covenants, and considering the potentially conflicting interests of debtholders and

shareholders, the value of corporate securities at present, must reflect the possible decisions

regarding future dividend policy. This issue will be further discussed below.

IV. Credit risk and dividend irrelevance

In their seminal paper Miller and Modigliani (1961) (M&M) showed the irrelevance of the

dividend policy. This irrelevance was shown under the assumption of PCM and given the

investment policy of the firm, which determines the current value of the firm V. This last

assumption is critical to the irrelevance theorem, since it separates the effect of the investment

decision from the decision concerning how it is financed.

10

These assumptions are also underlying their other seminal paper, Modigliani and Miller

(1958), which shows the irrelevance of the capital structure on the value of the firm. It is assumed

that each claim holder can perfectly protect his interest in the firm. The major implicit assumption

behind both M&M papers is that the potential conflict between the old and new shareholders and

bondholders is resolved by negotiations and bondholders are protected from decisions of the

shareholders by debt covenants. Also, all contingent claims are fairly priced in the PCM.

Miller and Modigliani (1961) in their dividend paper deal with a pure equity firm. Hence,

higher dividends today must be accompanied by lower dividends per share in the future, such that

the present value of the dividend stream will be consistent, and will be equal to the present value of

the firm. The additional financing may come from issuing new shares. Modigliani and Miller (1958)

deal with the irrelevance of capital structure but since there are no dividends they ignore in this

paper the potential conflict of interests between shareholders and bondholders arising from a

dividend policy. Our paper is also based on the basic M&M framework and assumptions. We show

above how, in this framework, equity and debt can be priced to reflect different dividend policies

while protecting the interests of each claim holder.

The basic dividend irrelevance of M&M is simple to prove. It is assumed that the

investment policy is given and hence V, the present value of the firm's assets can be determined.

Since the firm is an all equity firm, then, under PCM, it must be that S=V. Therefore, the present

value of expected dividends to initial shareholders must be equal to S=V. For simplicity, let us

assume that all investments were made already with the initial equity and no future investments are

expected. This assumption implies that all future free cashflow must be distributed to the

shareholders. New equity can be issued only to retire existing equity, and if fairly priced, cannot

create value. It should be noticed that since it is an ex ante model, under uncertainty, and not based

on realization, also new equity is planned at the base time and the relevant pricing of future new

equity is the current pricing.

This discussion helps to resolve the statements made by DeAngelo and DeAngelo (2006).

They show the relevance of dividend policy only if they deviate from the above assumptions, for

example, if they allow for accumulating cash, it means changing the investment policy, and may be

even destroying value (see also a paper by Handley (2008)).

Our approach follows the spirit of M&M. In our model and discussion, the starting point is

that V is given (as well as its distribution over time). We introduce both capital structure and

11

dividend policies. The policies must be known in advance and must be fully credible in order to

price equity and debt and prove the irrelevance. If policies are not credible, debtholders will pay less

for new debt than the benchmark which is based on the indicated (but not credible) dividend policy,

and charge higher risk premium.

In the next section we deal with the issue of dividend policy from corporate governance

perspective. While in the PCM assumptions all corporate claims are well protected and financial

policies are credible, in the analysis below we deal with potential deviations from the “full

protection” assumption. It is also important, in this context, to separate the “end-of-game” scenario

from the case of a perpetual firm that operates for a long horizon and finds it efficient to maintain its

reputation and credibility.

Having a declared policy of not paying dividends (or repurchasing shares for that matter)

cannot be an optimal policy in the long run for a levered firm (if the number of profitable projects is

limited). Actually, not paying dividends, if dividends are expected, means that the value of debt is

increasing at the expense of shareholders. On the other hand, paying too high dividends for a levered

firm, leads to an increase of its credit risk, and is also non-optimal since the cost of raising new debt

can be excessive.

The optimal policy depends on dividend expectations, debt covenants and the possibility of

free and costless negotiation among stakeholders of the firm. Between the two extremes we find that

a stable, consistent dividend policy, that is targeted to keep the probability of default stable, within a

narrow range, is the best policy. It is consistent with M&M as well as with the empirical evidence.

In this context, we can add to the roles of the independent board of directors the periodic

monitoring of the dividend policy, in order to enhance the credibility of the dividend policy. The

independent board is not necessarily committed to long term dividend policy. The board must

approve any dividend distribution. Hence, they must consider the conflicting interests and long-term

welfare of the firm and its stakeholders.

The Binomial Example

Let us illustrate the dividend case with a Binomial distribution example. In Figure 1 we

show a firm with initial assets of V=100, following a 2-period stationary distribution either

expanding by a factor of U=1.1, or declining by a factor D=0.9. The riskless interest rate is 1% per

period. The firm issued a “plain vanilla” zero coupon bond with a face value of K=90. Figure 1

12

shows the equilibrium values of the bond (B) and equity (S) at each time period and state of nature.

This is the case of the firm with no dividend. In the case that the firm will decline successively over

two periods, and hence the value of the firm will reach V23=81, the firm will be bankrupt and

B23=81 and S23=0. Since all participants know that there is a possibility that the firm will go

bankrupt, the current bond value B=86.44 (and S=13.56) will fully reflect this information. The

riskless 2-period bond, with a face value of 90 is worth 88.23, and the difference of 1.79 fully

reflects the present cost of the credit risk. At 86.44 the corporate bond is fairly priced.

Now, let us assume that if the company’s value is increasing in the first period and the value

of assets reaches V11=110, the shareholders decide to pay out a dividend of div11=11. Figure 2

depicts such a case. Since the ex-dividend value of remaining assets will be V22 - div11 = 99 is only

conditional on Up-state in period 1, therefore at time 2 the value of assets can reach either

V21=99x1.1=108.9 or V22=99x0.9=89.1. The dividend payout leads to a new state that did not exist

for the no-dividend case, where the firm is bankrupt and all assets belong to the debtholders. This

state is caused by paying dividends at a high rate of 11 at time 1, contingent on the firm increasing

in value. Note that with a dividend of, say, 10 or below, the bond will be fully paid at time 2 given

that it went up at time 1, and it’s current value should stay at 86.44. It should be noted that the

dividend effect on the bond value is not due to paying higher dividend than the Up factor. For

example, if we change the face value of debt to F2=95, it can be shown with the above parameters

that any dividend above 5 will reduce the value of debt, while shifting value to the shareholders.

See more details in the Appendix A.

Solving the binomial tree as described in Figure 2, shows that the current value of the debt is

now BEX=86.22 (the stock value is SEX=13.78, where 5.990 is the present value of the expected

dividends and 7.788 is the present value of the stock without the dividend). The difference of 0.22

(=86.44-86.22) reflects the “loss” of value to the bondholders due to the dividend policy of the firm.

Paying dividend of 10 or less at time 1 would have left the values of both equity and debt unchanged

from the no-dividend case.

The story of the potential conflict of interest between share and bond holders can be easily

illustrated with the binomial example:

(1) If the bondholders expected the dividends to be 10 or less at time 1 in the Up state, they would

price the debt at 86.44. But if at time 1, the firm surprises the debtholders and decides to pay

dividends of 11 (or more), there is a shift of value from bondholders to shareholders of 0.22 (or

13

more). By increasing dividends unexpectedly at time 1 from 10 to 11 the credit risk of debt has

increased, in present value terms, by 0.22, and benefited the shareholders.

(2) If bondholders knew in advance that the dividend is 11, they would price the bonds at 86.22,

which is the fair value of such bonds, and at time 1 if it is an up-market the fair value of the bonds

is B11=88.71 (rather than 89.11).

(3) If bondholders expected dividends to be 11 and hence priced debt at 86.22; but when the Up-

market is realized, they try to prevent the payment of dividends claiming that it can drive the firm to

bankruptcy (which can, under certain circumstances, be a correct statement), and, say, demand to

restrict D11 to 10. In such a case there is a wealth transfer from shareholders to bondholders. The

bond price is expected to be B11=89.11 rather than 88.71 and 0.40 is lost by shareholders at time 1 to

the bondholders (which translates to 0.22 wealth transfer in present value terms).

M&M assume that once the dividend policy is known, the prices of shares and bonds will

fully reflect such a policy. But, if there is any deviation from the pre-determined policy, there are

good chances that there is a wealth transfer one way or another. Since the shareholders decide

dynamically on such a policy, there are better chances of transferring wealth away from

bondholders. Unexpected decisions are not built in the M&M propositions, and the leverage effect is

not treated in the 1961 paper. M&M propositions are actually based on known contingent decisions

for any future state of nature so that current prices reflect all uncertainties including these future

decisions.

However, in real life, if bondholders suspect that the shareholders may act, via the dividend

policy to harm their interests, they will price it and it will be reflected in the risk premium they are

demanding. The major implication of this analytics is that firms have to pay higher interest on debt

than predicted by their current capital structure, the riskiness of their assets and their current

dividend policy. This effect is indeed empirically observed.

In order to reduce the cost of debt the shareholders must maintain a credible dividend policy.

For example, a constant dividend payout, in absolute terms or relative to earnings may be consistent

with the concerns described above. It is also easy to monitor such a policy by all parties. Constant

proportional dividends per share may be easier to sustain under different economic environments as

contrasted with the absolute one. Such a policy is consistent with the well-known “dividend

smoothing” practice.

14

Debt covenants usually provide protection to debtholders in “Down” states, by not allowing

dividend distribution in case when earnings are negative or low. However, the covenants may not be

sufficient in protecting the debtholders in “Up” states, especially for highly levered firms with

volatile assets as highlighted by the binomial example.

The conclusion from this section is that dividend’s uncertainty implies higher credit spread

than those predicted by “rational” models based on current parameters. As mentioned above, there is

ample empirical evidence supporting this claim. In economic terms, shareholders have an implicit

option to shift value from bondholders to shareholders. Shareholders can opt to reduce the value of

such an option by reducing the volatility of their dividend policy by proving credible dividend

policy. This hidden option is priced in an efficient market, but these values are, so far, being ignored

by the traditional models such as the CAPM and the contingent claim approach.

V. Dividend policy and the Signaling Approach

We have shown that by increasing the dividend payout beyond what was expected in the

marketplace, the value of equity may increase and the value of debt may decrease (thus increasing

the credit risk of the firm). This effect will be stronger for highly levered companies than for firms

with low leverage, everything else the same.

This result can be contrasted with the Signaling Approach (SA) suggested by Ross (1977)

and tested by Kalay (1980, 1982). According to the signaling approach, a firm that increases the

dividend payout signals to the market that it expects improved results in the future. In order for the

SA to work the new signal should be above and beyond what the market already expects and what is

already reflected in stock prices. The SA should equally work, if valid, for firms regardless of their

leverage and for negative news as well as positive news. It should be noted that the signaling, if

valid, should affect both the value of equity and debt in the same direction.

In our model dividends are also expected to increase with increased profitability. The

purpose of the dividend increase in such a case is not necessarily to signal to the market the “good

news”, but simply to align the interests of the stakeholders and maybe to keep the PD (close to)

constant. Not increasing the dividend payout when profitability is higher than initially expected,

may lead to decrease in PD and to improving the welfare of the bondholders beyond what they

perceived. The increased dividends in good states may prevent or mitigate wealth transfer to

debtholders.

15

It should be emphasized that in our model current dividend is not necessarily the important

measure for valuing corporate securities. What determines the value of equity, debt and the credit

spreads is the dividend stream over the life of the bond. So, even when current dividends are

temporarily down, for example during recessionary times, it may have small effect if they are

expected to increase during expansion period. The important factor is the present value of the

dividends, which are also treated as a contingent claim on the corporation.

VI. How to mitigate the potential conflict of interest?

Kalay (1982) highlighted the issue of the potential conflict of interests between the

shareholders and bondholders. He focused on the constraints on dividend payments in the bond

covenants, in order to mitigate “… the potential to transfer wealth from the bondholders (i.e.,

payments which are financed by new debt issues or reduced investments).” He showed that “… the

empirical evidence suggests that these constraints are not binding – i.e., stockholders do not pay

themselves as much dividends as they are allowed to.” Kalay argued that the dividend constraints

plus the “reservoir” for future dividends reduces the likelihood of overinvestment in negative NPV

projects.

We argue that the constraints and the "reservoir" can be explained by shareholders

establishing the credibility of their dividend policy. They try to mitigate the potential credit risk in

the future, especially in bad states. Thus, the initial cost of debt can be decreased, compared to the

situations where no constraints are imposed. We can explain the rationality of constraints as well as

of the reservoir not in terms of mitigating overinvestments but simply in terms of reducing credit

risk.

So, instead of talking about an optimal dividend policy the firm must think in terms of

credible dividend policy. An efficient way to minimize the potential conflict of interest between

shareholders and bondholders is therefore to determine a dividend policy in advance. The “smooth”

dividend policy (i.e. fixed per share rate) maybe a reasonable one for stable firms with sufficient

equity capital. Another option is to set dividend policy as a certain proportion (say δ) of V as long as

V is above a minimal threshold.

Let us set the objective function governing the dividend policy as follows:

16

c1 ≤ PD≤ c2

where ( )truedNPD 2−= as defined in (7).

For example, for a one-year horizon, c1=0.03% and c2=0.06%, are consistent with AA+

rating. This objective function can be translated to a dividend payout policy consistent with a certain

credit rating. Nevertheless, the probability of default depend on other variables as well, such as the

leverage ratio rT

Fe

V−

and the volatility, σ. Changes in these parameters can affect the PD and, as a

result, the dividend policy.

It is easy to see in the expression for the PD the tradeoff between the expected rate of return

on the firm’s assets and the dividend rate. What determines the PD is the difference between the two

parameters δ−R (for a given volatility). Hence a policy of maintaining a stable probability of

default can be translated to adjusting the dividend rate to the expected rate of return. Hence the

volatility of the firm’s rate of return plays also a major role in setting a dividend policy. Low

volatility firms can afford to pay higher dividend yield for the same R in order to achieve a certain

PD.

Actually, the issue raised here is much broader than the dividend policy only. The credit risk

of a firm, and the value of its debt and equity is determined by the interaction of the parameters as

set in equations (6). The model is based on a set of fixed parameters. Dynamic changes of these

parameters are not allowed. We assume that the dividend policy δ is set and also the amount of debt

F to be paid back at time T.

The M&M framework does not take into account future, strategic management decisions that

affect δ, F and σ. In such a case the bondholders, which are “in the hands” of the shareholders,

should assume the worst case scenario in determining the value of debt. This case is not described

by equation (6).

VII. Supporting Empirical Evidence and Testable Hypotheses

Empirical research on credit risk spreads showed consistently that actual spreads are greater

than predicted by the CCA or other models. This is especially true for higher rated bonds, when

measuring the relative (and not absolute) deviation of the actual yield from the predicted one. Jones,

17

Mason and Rosenfeld (1984) estimated the default spread based on Merton’s approach and found it

was less than observed credit spread. Elton et al. (2001) were able to explain about half of the spread

differential by credit risk parameters, and attributed the additional premium to unobservable

variables such as taxation, liquidity, and more. Similar results are also reported by Huang and

Huang (2012), who can explain only 2% of the observed spread for Aaa bonds and 94.8% for B

rated bonds.

We hypothesize that the seemingly under-pricing of corporate bonds may be due to ignoring

the dividend policies of the firms. Many of the public companies however follow a fixed dividend

policy. By paying dividends the credit risk of the bonds is increased. From the bondholders

perspective this is similar to reducing the value of the firm and hence increasing the value of the put

option, which represents the credit risk. In other words, expected dividends (or repurchases), which

are ignored by the original Merton model, can explain (at least part of) the overpricing of bonds

values and the under-estimation of the risk premium of corporate bonds.

In Appendix B we provide a table with simulation results for a representative, levered firm.

We consider a firm with total current value of V=100, and a pure discount bond promising to pay

F=90 in 3 years. When the assets' volatility is 20% per annum and the riskless rate is 5%, the credit

spread is 1.8% when no dividends are expected. But, if the firm expects to pay a continuous

dividend yield of 5% with no restrictions, the credit spread should be priced at 3.07%. At 10%

dividend yield the spread is 4.92%. Hence, ignoring dividends during the life of the bond implies

over-estimation of bond prices (and under-estimation of credit spreads) that can be substantial. Also,

if bondholders believe the firm will pay 5% but are surprised by a 10% payout, it means that they

under charged by almost 2% per year.

Huang and Huang (2012) assume in their base case that dividend yield is 6%, and in Table 9

they conduct a sensitivity tests for the case when the dividend yield is either 0% or 8%. They show

that for the base case with maturity of debt equal to 4 years, they can explain 94.8% of the actual

credit spreads with the CCA for B rated bonds but only 2.1% for Aaa rated bonds with a payout

ratio assumption of 10% for B rated bonds 96.2% of the credit spread can be explained. The effect

of the change in dividend ratio for Aaa bonds is negligible, as the PD for Aaa bonds is hardly

affected if the dividend payout is 0, 6% or 8%.

It can be noted in Table 9 of Huang and Huang (2012) that for Aaa, Aa and A rated bonds,

the ratio of the model credit spread to the observable credit spreads is not more than 15%. But, the

18

highly rated companies have a substantial capacity to pay dividends or repurchase their shares.

Recall the recent news about Microsoft corporation (see footnote 2 above). They are able and

willing to raise about 25B dollars of new long term debt to finance a stock repurchase program of

40B dollars, even at a threat of being downgraded. This major distribution to shareholders has an

impact on the credit risk of Microsoft.

This option is usually reserved to highly rated companies, with low leverage, and is not

available for companies with lower rating which often have a much higher leverage. This option, to

change drastically the distribution policy to shareholders, is probably priced in the credit risk of

highly rated companies.

Kalay (1980, 1982) demonstrates that companies in his sample did not pay all the allowable

dividends, which is consistent with our approach. Paying all the way to the allowed limit may be

costly in terms of future borrowing costs. In Appendix B we also show how constrained dividends,

when the firm is not performing well, can reduce the credit spread. For example, if the policy is to

distribute always 5% of Vt, the expected credit spread is 3.07%, but it can be reduced to 2.57% if the

firm has a credible policy of stopping dividend payments once the firm value falls below 80. It will

fall to 2.26% if the policy is to stop the payments when the firm's value falls below 90. Again, the

point estimates are under the assumptions of PCM and full credibility. Kalay in his papers, did not

investigate the possible effect of distribution up to the limit on the credit risk of the firm.

We find supporting evidence to our approach in the ample evidence on dividend smoothing.

This is very much consistent with our view of establishing credibility. Hence, the more frequent and

more stable dividend distribution helps to establish credibility and we expect credit spreads to be

lower for companies with credible dividend policy.

Therefore, empirical test of the CCA approach in levered firms must consider two factors

related to the dividend policy: first, the expected dividend stream over the life of the debt must be

taken into account. Second, the expected deviations from the dividend policy should be considered.

The expected deviations should be close to zero for the most credible firms. It is difficult to

measure the degree of non-credibility of firms and we expect that investors treat less credible firms

by assuming higher dividend payout bordering the limits set by the covenants. Testing our approach

directly is complicated by the fact that future dividends can be funded by new debt or equity, while

the basic model described above was based on the assumption that dividends are distributed from V,

i.e. from sales of assets. It is obvious that when dividends are fully finance by new equity, the credit

19

risk is not affected. By modeling dividends from sales of assets we focus on the direct effect of

dividend policy on the value of equity, debt and credit risk.

VIII. Conclusions

The topic of dividend policy of corporations attracted a lot of attention in the academic

literature. The issues were why to pay dividends (e.g. Black (1976))? Are dividends affecting the

value of the firm (e.g. Miller and Modigliani (1961))? Are dividends used for signaling purposes

(e.g. Ross (1977))? Are dividends distributed to reduce the agency problem of managers with excess

free cashflow (e.g. Jensen (1986))? Why, empirically, firms try to smooth their dividends (e.g.

Lintner (1956))?

In this paper, we highlight the role of dividends (and stock repurchases) to possibly mitigate

the potential conflict of interests between shareholders and debtholders. The paper has two

interrelated objectives. First, we incorporate the dividend policy of the firm in the contingent claim

approach (CCA) to price corporate securities, and especially to assess credit risk. Second, we offer

an explanation for a stable dividend policy as an important tool to monitor and manage credit risk of

corporate bonds. Bond covenants cannot ignore the dividend policy and we highlight how the

potential conflict of interest between share and bond holders can be mitigated. Third, we highlight

the role of the board in periodically evaluating and setting the dividend policy of the firm in a way

that can take into consideration the conflicting interests of its stakeholders.

In a perfect capital market as assumed in Miller and Modigliani (1961), Modigliani and

Miller (1958), Sharpe (1963) and Lintner (1956), dividend policy may be a matter of indifference. If

all securities are held by all investors in their market value weighted ratios, the investors are

indifferent to transfer of wealth from one class of assets to another. Also, the “me first” rule (see

Fama and Miller (1973)), assumes full protection against shifting of values. However, we know that

investors usually do not hold the market portfolio. Also, strict application of the “me first” rule will

restrict the investment policies of the firm. We live in a world where the potential for conflict of

interests among claimholders is a fact of life.

If the shareholders keep the dividend policy opaque, or chaotic, new debt-holders will reduce

the price they will be willing to pay for the bond, to reflect the adverse effect on them of such a

policy. So, in order to prove M&M dividend irrelevance when facing default risk we need to set not

20

only the investment policy but also the dividend policy. If not - shareholders will have an incentive

to distribute high dividends even when facing high probability of default.

21

Appendix A

In this Appendix we show the conditions for the binomial case, when a dividend payout at time 1 in

the up-state can cause a reduction in the value of the bond. See the notations of “The Binomial

Example”.

Define EXEX

EX

VDV

divVV

2211

1111

=⋅

−=.

Now, it can be shown that if KV EX ≥22 there is no change in the current value of debt and equity and

0000 , SSBB EXEX == . In such a case dividends have no effect on equity value.

divD

KVKDdivVKDVKV

EXEX ≥−⇔≥⋅−⇔≥⋅⇔≥ 11111122 )(

In the numerical example: div≥=−9.0

4

9.0

95110 .

If KV EX <22 , the equity’s value sill increase with dividends:

divD

KVKV

EX ≥−⇔< 1122

The economic reason is that if D

KVdiv −> 11 , there is a greater chance of bankruptcy (i.e. another

“new” state of bankruptcy), which reduces the value of the bond while increasing the value of

equity.

22

Figure 1: The Binomial Tree with no dividends: V=100, U=1.1, D=0.9, r=1%, F2=90,

B2i=Min (F2,V2i).

V21 = 121

B21 = 90

V11 = 110 S21 = 31

B11 = 89.11

Asset V=100 S11 = 20.89 V22 = 99

Bond B=86.44 B22 = 90

Stock S=13.56 V12 = 90 S22 = 9

B12 = 85.1

S12 = 4.9 V23 = 81

B23 = 81

S23 = 0

2

23

2

22

2

210

)1()1(2

R

SQSQQQSS

⋅−+⋅−⋅⋅+⋅= ,

DU

DRQ

−−

= , DU

RUQ

−−

=−1 .

23

Figure 2: The Binomial Tree with dividends: div11=11 and div12=0.

V21 = 108.9

B21 = 90

S21 = 18.9

V11 + div11= 99 + 11

B11 = 88.708 V22 = 89.1

S11 = 10.292 B22 = 89.1

Asset V = 100 S22 = 0

Bond B = 86.222

Stock S = 13.778 = 7.788+5.990 V23 = 99

V12 = 90 B23 = 90

B12 = 85.1 S23 = 9

S12 = 4.9

V24 = 81

B24 = 81

S24 = 0

24

Appendix B: Simulation results under alternative dividends payout and

constraints

Parameters: V = 100, F = 90, T = 3, r = 5%, σV = 20%.

We considered the following cases: δ = 0, 3%, 5%, 10% and the dividend boundary V*=0 (no

boundary), V* = 80, V* = 90.

The results for 40,000 paths with semi-annual time steps.

Value of stock (standard error is reported in parenthesis):

V* = 0 V* = 80 V* = 90

δ = 0% 26.95 (0.16) 26.95 (0.16) 26.95 (0.16)

δ = 3% 28.46 (0.15) 27.90 (0.15) 27.54 (0.15)

δ = 5% 29.67 (0.14) 28.60 (0.14) 27.94 (0.14)

δ = 10% 33.46 (0.11) 30.45 (0.11) 28.97 (0.13)

Value of bond (standard error is reported in parenthesis):

V* = 0 V* = 80 V* = 90

δ = 0% 73.39 (0.04) 73.39 (0.04) 73.39 (0.04)

δ = 3% 71.87 (0.05) 72.42 (0.05) 72.79 (0.04)

δ = 5% 70.65 (0.05) 71.72 (0.05) 72.38 (0.05)

δ = 10% 66.83 (0.06) 69.84 (0.05) 71.33 (0.05)

Credit spread:

V* = 0 V* = 80 V* = 90

δ = 0% 1.80% 1.80% 1.80%

δ = 3% 2.50% 2.24% 2.07%

δ = 5% 3.07% 2.57% 2.26%

δ = 10% 4.92% 3.45% 2.75%

PD:

V* = 0 V* = 80 V* = 90

δ = 0% 28.52% 28.52% 28.52%

δ = 3% 36.25% 35.05% 33.27%

δ = 5% 41.67% 39.68% 36.40%

δ = 10% 56.36% 51.48% 44.61%

PV of the expected credit loss:

V* = 0 V* = 80 V* = 90

δ = 0% 14.27 14.27 14.27

δ = 3% 15.44 14.38 14.04

δ = 5% 16.36 14.47 13.97

δ = 10% 18.87 14.80 13.75

25

Bibliography

Acharya, V., J. Huang, M.G. Subrahmanyam, and R.K. Sundaram, 2000, Costly Financing, Optimal

Payout Policies, and the Valuation of Corporate Debt, Working Paper, NYU Working Paper No.

FIN-01-043.

Baker M., J. Wurgler “Dividends as Reference Points: A Behavioral Signaling Approach”, NBER

Working Paper No. 18242 Issued in July 2012 NBER Program(s): CF.

Benartzi, S., R. Michaely, and R. Thaler, 1997, Do changes in

dividends signal the future or the past? Journal of Finance 52, pp. 1007–1034.

Bensoussan A., M. Crouhy, and D. Galai, 1994, Stochastic equity volatility related to the leverage

effect, Applied Mathematical Finance, 1, pp. 63-85.

Bensoussan A., M. Crouhy, and D. Galai, 1995, Stochastic equity volatility related to the leverage

effect II: Valuation of European equity options and warrants, Applied Mathematical Finance, 2, pp.

43-59.

Bensoussan A., M. Crouhy, and D. Galai, 1995, Black-Scholes approximation of warrant prices,

Advances in Futures and Options Research, 8, pp. 1-14.

Berk J., and P. DeMarzo, Corporate Finance, Pearson Addison-Wesley, 2007.

Black, F., and J. Cox, 1976, Valuing corporate securities: some effects of bond indenture provisions,

Journal of Finance, 31, pp. 351-367.

Black, F., and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of

Political Economy, Vol. 81, No. 3, pp. 637-654.

Boness, J. A., 1964, Elements of a Theory of Stock-Option Value, Journal of Political Economy,

Vol. 72, No. 2, pp. 163-175.

Brealey, R., and S. Myers, Principles of Corporate Finance, McGraw Hill, 5th edition, (1996).

Brennan Michael J. and Anjan V. Thakor, 1990, Shareholder Preferences and Dividend Policy The

Journal of Finance ,Vol. 45, No. 4, pp. 993-1018.

26

Brickley, James A., 1983, Shareholder wealth, information signaling, and the specially designated

dividend: An empirical study, Journal of Financial Economics 12, pp. 187-209.

Cox, J. C., and S. A. Ross, 1976, The Valuation of Options for Alternative Stochastic Processes,

Journal of Financial Economics, 3, pp. 145-166.

Damodaran, A., Corporate Finance, Wiley 1997.

Damodaran, A., Damodaran on Valuation (2nd ed.), Wiley (2006), pp. 637-647.

DeAngelo H., and L. DeAngelo, 2006, The irrelevance of the MM dividend irrelevance theorem,

Journal of Financial Economics, 79, pp. 293-315.

Delianedis, G., and R. L. Geske, 2001, The Components of Corporate Credit Spreads: Default,

Recovery, Taxes, Jumps, Liquidity, and Market Factors, UCLA Anderson Working Paper NO. 22-

01.

Elton, E., Gruber, M., Agrawal, D., Mann, C., 2001, Explaining the rate spread on corporate bonds,

Journal of Finance 56, pp. 247–277.

Fan, H., and S. M. Sundaresan, 2000, Debt valuation, strategic debt service, and optimal dividend

policy. Review of Financial Studies 13, pp. 1057–1099.

Francois, P., and E. Morellec, 2004, Capital structure and asset prices: Some effects of bankruptcy

procedures, Journal of Business 77, pp. 387–411.

Galai D., 1978, On the Boness and Black-Scholes Models for Valuation of Call Options, Journal of

Financial and Quantitative Analysis, 13, pp. 15-27.

Galai D., and R. Masulis, 1976, The option pricing model and the risk factor of stock, Journal of

Financial Economics, 3, pp. 53-81.

Galai D., A. Raviv, and Z. Wiener, 2007, Liquidation triggers and the valuation of equity and debt,

Journal of Banking and Finance, 31, pp. 3604-3620.

27

Garbade K. D., Pricing Corporate Securities as Contingent Claims, MIT Press, 2001, 415 p.

Guttman, I., O., Kadan, and E. Kandel, 2010, Dividend stickiness and strategic pooling, Review of

Financial Studies, 23, pp. 4455-4495.

Handley, J. C., 2008, Dividend Policy, Reconciling DD with MM, Journal of Financial Economics,

Vol. 87:2, pp. 528-532

Huang, J., and M. Huang, 2012, How Much of Corporate-Treasury Yield Spread Is Due to Credit

Risk?: A New Calibration Approach. The Review of Asset Pricing Studies, 2 (2), pp. 153-202.

Jensen M. C., 1986, Agency Cost Of Free Cash Flow, Corporate Finance, and Takeovers

American Economic Review, Vol. 76 (2), pp. 323-329.

Jones E. P., S. P. Mason, and E. Rosenfeld, 1985, Contingent Claims Valuation of Corporate

Liabilities: Theory and Empirical Tests, in Corporate Capital Structures in the United States, ed. B.

M. Friedman, University of Chicago Press, pp. 239-264.

Kalay, A., 1980, Signaling, information content, and the reluctance to cut dividends, Journal of

Financial and Quantitative Analysis 15, pp. 855-873.

Kalay, A., 1982, Stockholder-bondholder conflict and dividend constraints, Journal of Financial

Economics 10, pp. 211-233.

Lintner, John V., 1956, Distribution of incomes of corporations among dividends, retained earnings,

and taxes, American Economic Review 46, pp. 97-113.

Lambrecht, B., M., and S. C. Myers, 2012, A Lintner Model of Payout and Managerial Rents,

Journal of Finance, 67:5, pp. 1761-1810.

Merton, R.C., 1974, On the pricing of corporate debt: The risk structure of interest rates, Journal of

Finance, 29, pp. 449-470.

Merton, R.C., 1973, Theory of rational option pricing, Bell Journal of Economics and Management

Science, 4, pp. 141-183.

28

Modigliani, F., and M. Miller, 1958, The Cost of Capital, Corporation Finance and the Theory of

Investment, American Economic Review 48 (3), pp. 261–297.

Miller, M., and F. Modigliani, 1961, Dividend Policy, Growth and the Valuation of Shares. Journal

of Business, 34, pp. 411-33.

Ross, S. A., 1977, The Determination of Financial Structure: The Incentive Signaling Approach.

The Bell Journal of Economics, Vol. 8, No. 1, pp. 23-40.

Smith C.W., and J.B. Warner, 1979, On Financial Contracting: An Analysis of Bond Covenants,

Journal of Financial Economics, 7, pp. 117-161.

Sundaram R., 2001, The Merton/KMV approach to Pricing Credit Risk, Extra Credit, pp. 59-68.

Watts, R. L., 1973, The Information Content of Dividends, The Journal of Business, Vol. 46, No. 2,

pp. 191-211.