managerial compensation and capital structurespiegel/papers/bis.pdf · 554...

Managerial Compensation andCapital Structure

Elazar BerkovitchThe Interdisciplinary Center Herzliya Israel

email elibidcacil

Ronen IsraelThe Interdisciplinary Center Herzliya Israel and

University of Michigan Business SchoolAnn Arbor MI

email risraelidcacil

Yossef SpiegelBerglas School of Economics

Tel Aviv UniversityRamat Aviv Tel Aviv 69978 Israel

email Spiegelposttauacil

We investigate the interaction between nancial structure and managerialcompensation and show that risky debt affects both the probability of man-agerial replacement and the managerrsquos wage if he is retained by the rm Ourmodel yields a rich set of predictions including the following (i) The marketvalues of equity and debt decrease if the manager is replaced moreover theexpected cash ow of rms that retain their managers exceeds that of rmsthat replace their managers (ii) Managers of rms with risky debt outstand-ing are promised lower severance payments (golden parachutes) than man-agers of rms that do not have risky debt (iii) Controlling for rmrsquos sizethe leverage managerial compensation and cash ow of rms that retaintheir managers are positively correlated (iv) Controlling for the rmrsquos sizethe probability of managerial turnover and rm value are negatively cor-related (v) Managerial pay-performance sensitivity is positively correlatedwith leverage expected compensation and expected cash ows

For their comments we thank Patrick Bolton Yaniv Grinstein Denis Gromb Chris-tian Laux Fausto Panunzi John Persons Raphael Repullo Harald Uhlig Yoram WeissAmir Yaron two anonymous referees and a coeditor and seminar participants at Ben-Gurion University Carnegie Mellon University CEMFI The Hebrew University ofJerusalem Tel Aviv University Tilburg University Universite des Sciences Socialesde Toulouse the 8th GIF Meeting on Frontier Aspects in Economic Research inMannheim the 7th World Congress of the Econometric Society in Tokyo the fall 1995INFORMS meetings in New Orleans the fth annual meeting of Colloquia in EconomicResearch in Milano and CEPR workshops in Lisbon and in Naples

copy 2000 Massachusetts Institute of TechnologyJournal of Economics amp Management Strategy Volume 9 Number 4 Winter 2000 549ndash584

550 Journal of Economics amp Management Strategy

1 Introduction

Financial structure and managerial compensation are crucial for gen-erating value to shareholders because of their inuence on manage-rial quality and incentives Practitioners have long recognized thatthe two are interdependent for instance in the leveraged buyout(LBO) wave of the 1980s nanciers used high levels of debt andperformance-sensitive compensation packages to motivate managersDespite this apparent interdependence economists have by and largestudied nancial structure and managerial compensation in isolationFor example the principle-agent literature (eg Mirrlees 1976 Harrisand Raviv 1979 Holmstrom 1979) studies the design of managerialcompensation contracts but abstracts from nancial structure consid-erations Likewise agency models of capital structure (eg Jensen andMeckling 1976 Grossman and Hart 1982) do not consider managerialcompensation explicitly1

This paper develops a theory of managerial compensation andcapital structure that explicitly allows for their interdependence Tothis end we consider a three-period model In period 0 the rm isestablished and a manager is hired In period 1 the manager takesactions that boost the future cash ow of the rm but also makethe rm more dependent on his ability For example the managerselects workers organizes production chooses the rmrsquos strategy inthe product market etc We model this activity as a choice of an unob-servable effort level that together with managerial ability determinesthe cash ow of the rm in period 2 After taking his actions (butbefore the cash ow is realized) the manager and the shareholdersreceive a common signal that perfectly reveals the period 2 cash owunder his control At this point shareholders may replace the managerwith a new manager whose ability is yet unknown However if theincumbent manager is replaced the rm loses the extra cash ow thathis actions may have generated this in turn enables the manager todemand more compensation Anticipating this demand shareholdersselect the managerrsquos compensation contract and the nancial structureof the rm to provide him with appropriate incentives while limitinghis ability to demand a higher wage This framework enables us toaddress important questions that were not addressed before for exam-ple Do highly levered rms tend to pay their managers higher wagesthan rms with low or moderate debt levels Do they replace their

1 Another branch of the literature considers the role of external forces such as themarket for corporate control or competition in the product market in ensuring manage-rial quality and effort (eg Grossman and Hart 1980 Hart 1983 Scharfstein 1988a b)Again this literature generally ignores the effect of the rmrsquos nancial structure onmanagerial incentives and quality

Managerial Compensation and Capital Structure 551

managers more often And do their securities tend to have highermarket values

The choices of managerial compensation and capital structureare driven in our model by two effects First when the rm is lever-aged replacing a manager whose ability is known with a new man-ager whose ability is yet unknown shifts value from debtholders toshareholders Consequently risky debt credibly commits the share-holders to an overly aggressive replacement policy and this may moti-vate the manager to exert more effort ex ante in order to promote hischances to keep his job2 We refer to this effect as the job-security effectThis effect is positive only if the marginal productivity of the man-ager is increasing at the critical cash ow below which the manageris replaced (the replacement rule) Otherwise raising the replacementrule has an adverse effect on managerial effort3 When this is the casethe rm may restore managerial incentives by offering the manager agolden parachute that softens the replacement rule by making it morecostly to re the manager Second committing debt payments to out-siders reduces the free cash ow of the rm and limits the compen-sation that the manager can demand We refer to this effect of debtas the free-cash-ow effect This effect always discourages managerialeffort since it implies that the manager captures a smaller fractionof his marginal contribution to the rmrsquos cash ow Moreover thiseffect may decrease managerial quality because it induces the rm toadopt an ex post inefcient replacement rule The net impact of thefree-cash-ow effect on the ex ante value of the rm is positive onlyif the manager captures a sufciently large fraction of the free cashow and the rmrsquos performance is not too sensitive to managerialincentives and quality4

Our model yields several interesting and as far as we knownovel empirical predictions The rst prediction concerns the relation-ship between severance payments (golden parachutes) and debt

Firms that issue risky debt do not offer their managers a goldenparachute

2 In other words all else equal the shareholders of a leveraged rm prefer to takea gamble and hire a new manager in the hope that the cash ow under him will exceedthat under the incumbent manager (ie engage in asset substitution) Anticipating thisincentive the manager may work harder in order to generate enough cash ow tomake the gamble too costly for shareholders (see Berkovitch and Israel 1996) Notehowever that debtholders are not duped the shareholdersrsquo behavior is anticipated bythe debtholders and reected in the pricing of debt when it is issued

3 This implies that setting a high standard provides incentives only if the standardis ldquorealisticrdquo If the standard is already high raising it further is counterproductive

4 Although we focus attention on the job-security and free-cash-ow effects thereare obviously other factors that drive the rmrsquos internal policy decisions including thermrsquos investment opportunity set (Smith and Watts 1992) diversication (Rose andShepard 1997) and regulatory and political constraints (Joskow et al 1996)


This prediction may seem counterintuitive at rst glance since goldenparachutes are typically thought of as means of insuring managersagainst the risk of losing their jobs given that risky debt raises thisrisk it might be thought that golden parachutes and risky debt willbe offered simultaneously However in our model all agents are risk-neutral and more importantly the rm uses risky debt and goldenparachutes as means to motivate the manager to exert more effortWhen the marginal productivity of the manager is increasing at theefcient replacement rule the current replacement rule is too softso the rm motivates the manager by issuing risky debt that makesthe replacement rule more aggressive When the marginal productiv-ity of the manager is decreasing at the efcient replacement rule thereplacement rule is already too aggressive Therefore the rm offersthe manager a golden parachute that softens the replacement rule andthereby motivates the manager to work harder5

A second empirical prediction concerns the impact of manage-rial replacement on the market values of debt and equity and on thefuture cash ow of the rm Intuitively when the rm issues riskydebt the replacement rule becomes overly aggressive in the sense thatthe critical level of the period 2 cash ow below which the manager isreplaced exceeds the average cash ow under an alternative managerTherefore on average rms that retain their managers have a highercash ow than rms that replace their managers Moreover since theprice of equity and debt in period 0 reect both low and high real-izations of the period 2 cash ow managerial replacement conveysbad news to the market whereas managerial retention conveys goodnews This leads to the following predictions

The market values of equity and debt fall if the manager is replacedMoreover the expected cash ow of rms that retain their managersexceeds that of rms that replace their managers

In Section 4 below we argue that these predictions are consistent withempirical evidence

Another implication of our model is that if the manager isretained his wage represents a fraction of his incremental contribu-tion to earnings over and above the contribution of an alternative managerThis implies that the managerrsquos wage could be a small fraction ofthe rmrsquos overall cash ow even if on the margin the manager cap-tures a large fraction of the cash ow This may shed light on Jensen

5 It should be emphasized that in practice rms may have additional reasons forissuing debt and offering golden parachutes beyond those that are considered in ourmodel In a more general setting this prediction suggests a negative correlation betweenleverage and golden parachutes


and Murphyrsquos (1990) estimate that the pay-performance sensitivity forCEOs of publicly owned corporations is quite small (about $325 per$1000 change in shareholders wealth) Jensen and Murphy argue thattheir estimate is too low to provide CEOs with meaningful incentivesOur theory suggests that their estimate may be low simply becauseit measures the average pay-performance sensitivity which could bequite low even if the marginal pay-performance sensitivity is largeenough to provide CEOs with strong incentives

A third type of empirical predictions concerns the choice of debtthe managerial effort the managerial compensation the managerialturnover the expected cash ow conditional on the manager beingretained and the value of the rm Due to the complexity of ourmodel we derive these predictions from numerical simulations Con-trolling for rm size these simulations yield inter alia the followingpredictions

Leverage managerial compensation and cash ow of rms thatretain their managers are positively correlatedProbability of managerial turnover and rm value are negativelycorrelatedManagerial pay-performance sensitivity is positively correlated withleverage expected compensation and expected cash ows

Our premise that capital structure is important for discipliningand monitoring managers has been made earlier by Grossman andHart (1982) In their model the managerrsquos goals are not fully alignedwith those of shareholders To overcome this problem the rm issuesdebt which increases the probability of bankruptcy Because the man-ager is effectively assumed to lose his job if the rm goes bankruptdebt induces him to come closer to prot maximization But fromGrossman and Hart it is unclear why the manager should lose hisjob because the agency problem in their paper is one of moral haz-ard so ex post the manager is as good as any other manager that therm can hire Indeed one contribution of our paper is that it providesa mechanism through which debt credibly commits the rm to replaceits manager if prots are not sufciently high

More recently Dewatripont and Tirole (1994) and Berkovitch andIsrael (1996) examined the role of capital structure in disciplining man-agers in settings that are closer to the present one The focus of thesepapers however is on the allocation of control rights rather thanthe interaction between capital structure and managerial compensa-tion Similarly to these papers Dessi (1997) shows that short-termdebt triggers creditorsrsquo intervention when the rm is underperform-ing In addition she shows that long-term debt induces the managerto exert effort by curtailing his ability to raise funds in the future


Like our paper Holmstrom and Tirole (1993) also examine the interac-tion between capital structure and managerial compensation but theirfocus is on equity nancing They show that by issuing outside equityinsiders increase the liquidity of the rmrsquos stock and thereby encour-age speculators to monitor managerial performance This improvesthe information content of the stock price and allows the rm todesign a more efcient managerial compensation contract Garveyand Swan (1992) also study the interaction between capital structureand incentive schemes but in their model the incentive schemes areoffered to a group of workers rather than to the rmrsquos manager Theirtheory predicts lower debt levels and more compressed pay scales ascooperation between workers becomes more important

The rest of the paper is organized as follows In Section 2 wepresent the model and in Section 3 we solve it and characterize theequilibrium In Section 4 we provide empirical predictions regardingprice reactions and changes in the expected cash ow of the rmfollowing its decision on whether or not to replace its manager InSection 5 we solve the model numerically and derive cross-sectionalempirical predictions We conclude in Section 6 All proofs appear inthe Appendix

2 The Model

A rm is established in period 0 and operates in periods 1 and 2The sequence of events is described in Figure 1 In period 0 afterthe rm is established the shareholders hire a manager to run it andissue debt to be repaid at the end of period 2 and possibly additionalequity to outsiders The proceeds from issuing the new securities areeither invested in the rm or paid out as a dividend In period 1 themanager chooses a nonveriable effort level e that affects the cashow of the rm in period 2 For example e can represent a long-terminvestment in RampD or in a new line of business that materializes onlyin period 2 Apart from effort the period 2 cash ow of the rm is alsoaffected by the managerrsquos ability to run the rm which at the timethe manager is hired is as yet unknown either to the shareholdersor to the manager To reect the uncertainty regarding the managerrsquosability we assume that given an effort level e the period 2 cash owis represented by a random variable y distributed on Acirc1 according toa distribution function H (y | e) We assume that H (y | e) satises thelinear distribution function condition (LDFC) (Hart and Holmstrom1987) so H (y | e) 5 eH1(y) 1 (1 e)H2(y) where H1(y) and H2(y) aretwice continuously differentiable distributions with H1(y) pound H2(y)for all y and a strict inequality for some y This implies that H1(y)


FIGURE 1 THE SEQUENCE OF EVENTS

dominates H2(y) in the rst-order stochastic dominance sense Den-ing D (y) ordm H2(y) H1(y) sup3 0 we can write

H (y | e) 5 H2(y) e D (y) (1)

The density function of y is h(y | e) 5 h2(y) e D cent (y) where D cent (y) ordmh2(y) h1(y) Our formulation implies that the managerrsquos effort deter-mines a convex combination of two xed distributions each of whichcaptures the managerrsquos unknown productivity by exerting more effortthe manager increases the probability that the cash ow in period 2will be drawn from the better distribution H1(y) The parameter D (y)represents the marginal productivity of managerial effort Followingthe neoclassical tradition we assume that D (y) is unimodal whichimplies that the managerrsquos average ldquoproduction functionrdquo has aninverted U-shape6 In addition we assume that limynot ` y D (y) 5 0This assumption is satised for example when the support of y isnite

In period 1 after the manager has exerted effort he and theshareholders observe a common nonveriable signal S about theperiod 2 cash ow under his control To avoid unnecessary complica-tions we assume that S perfectly reveals the period 2 cash ow underthe incumbent manager Having observed S shareholders decidewhether to retain the current manager or replace him with an alterna-tive manager The latter is drawn from a large pool of potential man-agers We assume that the market for managers is competitive andnormalize the reservation utility of managers (including the incum-bent manager) from alternative jobs to 07 In addition we assume

6 This assumption is weaker than the assumption that the distribution function Hhas the monotone likelihood-ratio property and it is satised by most smooth distribu-tions for example the assumption holds when H1 and H2 are two exponential normallognormal uniform or logistic distributions

7 The assumption that the reservation utility of the incumbent manager froman alternative job is 0 implies that the signal S reveals information only about themanagerrsquos productivity in his current job (rm-specic human capital) not about hisproductivity in other jobs (general human capital) Moreover the assumption that themanagerial labor market is competitive means that a new manager has no bargainingpower vis-a-vis the rm


that the cash ow under an alternative manager is distributed on Acirc1

according to a distribution function H3(y) 8 The mean cash ow inperiod 2 under an alternative manager is Aringy 5 H `

0 yh3(y) dy SinceH3(y) is independent of e it follows that managerial effort is idiosyn-cratic in the sense that it affects the rmrsquos cash ow only if the incum-bent manager is retained

Having described the information structure we turn to the wagecontract that the manager gets in period 0 Since the managerrsquos effortlevel and the signal S are nonveriable to a third party the wage con-tract can be conditioned in principle only on the period 2 cash owwhich is veriable and on whether the manager stays with the rmquits his job or is red (but not on managerial effort and the signal)In practice however it is often difcult to determine unambiguouslywhether a manager left a rm voluntarily or was forced to resign (iewas red)9 To reect this difculty we assume that the events that ledto the managerrsquos departure are not veriable This means that a wagecontract is a pair (w0 w1) where w0 is the managerrsquos compensation ifhe either quits his job or is being red and w1 is his compensation ifhe stays with the rm10 Since the period 2 cash ow is independentof the incumbent managerrsquos effort once he leaves the rm the wayin which w0 is paid (equity options bonds cash etc) is immaterial11

For convenience we shall assume that w0 is paid in the form of asenior bond and refer to it as a golden parachute

8 Although we do not put restrictions on H3(y ) it is natural to assume that H3(y ) 5H2(y) since this implies that ex ante all managers are the same The incumbent managerthen has an advantage in that only he can exert effort in period 1 and affect the period 2cash ow We do not require that H3(y) 5 H2(y) in order to emphasize that our resultshold for any distribution function H3(y) provided that its support is Acirc1

9 See for instance Weisbach (1988) or Denis et al (1997) A similar situation arisesin professional sports where often there are controversies regarding the events that ledto the departure of a head coach (who is an a sense like a CEO of a company) fromhis position For example when Bora Miltanovich left his position as the head coachof the US soccer team he claimed to have been red while the US olympic committeeclaimed that he quit at his will Similarly when Pat Riley left the New York Knicks in1995 there was a controversy regarding the events that led to his departure

10 Agrawal and Knoeber (1998) examine a sample of 446 rms that appeared on theForbes magazine list of the 500 largest US rms in (1987) (excluding public utilities)and nd that 51 of the CEOs in the sample had golden parachutes (provisions forcertain cash and other benets if the CEO is red is demoted or resigns within acertain time period) They also nd that only 12 of the CEOs had a written assuranceof job security andor income protection for a specied number of years and only2 had both written assurances and golden parachutes The small incidence of writtenassurances of job security is consistent with our assumption that it may be very hardto specify unambiguously the events that lead to a change in control

11 In other words once the manager leaves the rm the ability of the rm to pay w0depends only on the cash ow under the alternative manager which is independent ofthe incumbent managerrsquos effort Therefore only the expected value of w0 is importantfor our analysis


Unlike w0 the managerrsquos wage when he stays with the rm w1depends on the period 2 cash ow which in turn depends on the man-agerrsquos effort level Our model differs from standard principal-agentmodels in that here the employment relationship can be terminatedat any time with the court being unable to determine unambiguouslywhich party is responsible for this termination Therefore if the man-ager believes that he can extract from the rm more than w1 he canthreaten to quit unless w1 is renegotiated Likewise if the sharehold-ers believe that it is possible to cut w1 they can threaten to re themanager unless w1 is renegotiated The ability of both parties to forcea wage renegotiation in period 1 once they observe S implies that theperiod 0 wage contract is meaningful only if it prescribes the expectedoutcome that would be attained under wage renegotiation12 We post-pone the description of the renegotiation process until the next sec-tion but note that it yields an expected wage that depends on theperiod 2 cash ow w

1 (y) Since the shareholders fully anticipate thewage renegotiation process they will offer the manager in period 0 arenegotiation-proof contract (w0 w

1(y))Apart from a monetary compensation whoever runs the rm in

period 2 (either the incumbent or a new manager) draws nontrans-ferable benets of control B We assume that B is sufciently large toensure that both the incumbent and an alternative manager will agreeto work for the rm in period 2 even without monetary compensa-tion The incumbent managerrsquos cost of effort w (e) is an increasingand convex function with w cent (0) 5 0 In addition we assume that allagents are risk-neutral and we normalize the intertemporal discountrate to zero

At the end of period 2 after the cash ow has been realized therm needs to repay its debt and compensate the manager accordingto his wage contract If the cash ow falls short of the nancial obli-gations of the rm the rm declares bankruptcy and its cash ow isdistributed to debtholders and the manager according to their respec-tive claims The shareholderrsquos payoff in this case is zero

3 Equilibrium Characterization

We solve the model by backward induction First conditional on theincumbent manager being retained and given the signal S we solvefor the wage that the manager can obtain by insisting that his wage

12 Alternatively the parties can specify in the contract an arbitrary w1 with theunderstanding that it will be renegotiated in period 1 However in our model thispossibility gives the parties no advantage and to the extent that renegotiation is costlythe parties are better off writing an initial contract that is immune to renegotiation Formodels in which the parties write an ex ante contract with the intention of renegotiatingit later once they have more information see Chung (1991) Aghion et al (1994) andMatthews (1995)


contract be renegotiated This allows us to determine w 1(y) which is

the compensation that a renegotiation-proof wage contract must spec-ify if the manager stays with the rm Given the capital structure ofthe rm and the wage contract we solve for the optimal replacementrule and show that it can be summarized by a critical signal AtildeS suchthat the manager is replaced whenever S is below AtildeS and is retainedotherwise Then given AtildeS and the wage contract we solve for themanagerrsquos effort level Finally we solve for the optimal capital struc-ture of the rm and the severance payment w

0 that will be speciedin the wage contract

31 The Replacement Rule and ManagerialCompensation

Since the period 0 wage contract is renegotiation-proof it must guar-antee the manager the same expected wage that he would obtainthrough wage renegotiation We therefore begin the analysis by con-sidering the bargaining game that will take place in period 1 if eitherparty wish to renegotiate the original contract At the start of thisgame nature selects either the manager (with probability c ) or theshareholders (with probability 1 c ) to make a take-it-or-leave-it offerIf the offer is rejected the manager leaves the rm and a new manageris hired If the offer is accepted the manager retains his job and getsthe proposed wage To simplify matters we assume that the managerhas no private funds so wage offers must be nonnegative13

Let F be the face value of the debt that the rm issues in period 0Given F and w0 the expected payoff of shareholders if the incumbentmanager is replaced is

V r 5 H`

w0 1 F(y w0 F)h3(y) dy (2)

This expression represents the expected cash ow of the rm in period2 under an alternative manager net of w0 and F conditional on therm being solvent Recalling that the manager receives w0 before debtis due the expected payoff of the manager when he is replaced is

U r 5 Hw0

0yh3(y) dy 1 H

`

w0

w0h3(y) dy (3)

Using equations (2) and (3) we prove the following lemma

13 Alternatively it can be assumed as in Hart (1983) that the managerrsquos utility frommonetary compensation is given by U (w) 5 w for w sup3 0 and U(w) 5 ` otherwise


Lemma 1 (i) In equilibrium w0 is set such that U r lt B(ii) In a renegotiation-proof wage contract

w 1 (y) 5 c y AtildeS AtildeS ordm V r 1 F (4)

Part (i) of the lemma implies that the manager is always betteroff staying with the rm as his benets of control exceed his expectedseverance payment To interpret w

1 (y) note that y AtildeS is the differencebetween the net cash ow under the current manager y F andthe net expected cash ow under an alternative manager V r Hencey AtildeS represents the incumbent managerrsquos incremental contribution tothe net cash ow over and above the contribution of an alternativemanager Equation (4) indicates that the managerrsquos wage when hekeeps his job is a fraction c of his incremental contribution to the netcash ow Therefore the parameter c can be thought of as a measureof the managerrsquos ldquobargaining powerrdquo

Next we consider the replacement policy Sequential rationalityrequires shareholders to replace the manager if and only if doing soenhances the expected value of equity If the manager is replaced theexpected value of equity is V r Since the value of equity if the manageris retained is y F w

1 (y) 5 y F c y AtildeS shareholders retain themanager if and only if y F c y AtildeS gt V r or equivalently y gt AtildeSHence

Lemma 2 In equilibrium shareholders retain the manager if and only ify gt AtildeS

Lemma 2 denes AtildeS as the critical value of the signal below whichthe incumbent manager is replaced in what follows we shall refer toAtildeS as the replacement rule Since AtildeS plays a crucial role in the analysiswe now study its properties Using equation (2) and recalling that Aringy 5H `

0 yh3(y) dy is the mean cash ow in period 2 under an alternativemanager the replacement rule can be written as

AtildeS ordm V r 1 F 5 Aringy w0 1 Hw0 1 F

0(w0 1 F y)h3(y) dy (5)

Ex post efciency requires the manager to be replaced if and only if thecash ow under him is below Aringy That is the ex post efcient replace-ment rule is AtildeS 5 Aringy Equation (5) however shows that in general thereplacement rule will be ex post inefcient As a result the incumbentmanager may sometimes be replaced even if the cash ow under him


exceeds Aringy or conversely be retained even if the cash ow under himis below Aringy Differentiating AtildeS with respect to F and w0 reveals that

AtildeSF

5 H3(F 1 w0) gt 0AtildeSw0

5 [1 H3(F 1 w0)] lt 0 (6)

The reason why AtildeS decreases with increasing w0 is straightforwardthe higher w0 is the more costly it is to re the manager Henceshareholders adopt a ldquosofterrdquo replacement rule The reason why thereplacement rule increases with F is more subtle and is due to theasset substitution effect (Jensen and Meckling 1976) When the rmis leveraged replacing a manager whose ability is known with amanager whose ability is yet unknown shifts value from debtholdersto shareholders Consequently as the rm becomes more leveragedshareholders become more aggressive and replace the manager moreoften14 As we show below issuing debt in order to commit to anex post inefcient replacement rule may give shareholders a strategicadvantage vis-a-vis the manager15

32 Managerial Effort

Anticipating the replacement rule and given his wage contract themanager chooses an effort level at the beginning of period 1 withthe objective of maximizing his expected payoff Since the managerrsquospayoff is B 1 w

1 (y) when he is retained and U r when he is replacedand since replacement occurs whenever y gt AtildeS the expected payoff ofthe manager net of his cost of effort is given by

U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)

where h(y | e) 5 h2(y) e D cent (y) Let e be the effort level that max-imizes this expression Differentiating U (e) substituting for w

1(y)

14 Put differently the more leveraged the rm becomes the higher is the probabilityof default Since shareholders receive a zero payoff in the event of default they havean incentive to take a gamble in period 1 by hiring a new manager in the hope that hisability will be higher than the ability of the incumbent manager so that the rmrsquos cashow will exceed S

15 The idea that debt may confer a strategic advantage on the rm by commit-ting it to an ex post inefcient decision has been also used by eg Berkovitch andIsrael (1996) in the context of internal control Israel (1991) in the context of takeoversSpiegel (1996) in the context of procurement contracts Bronars and Deere (1991) andSarig (1998) in the context of bargaining with a labor union and Novaes and Zingales(1998) in the context of corporate bureaucracy In John and John (1993) a leveragedrm uses managerial compensation as a way to commit to minimize the agency costof debt


from equation (4) integrating by parts and using the assumption thatlimynot ` y D (y) 5 0 the rst-order condition for e is

U r(e ) 5 (B U r) D (AtildeS) 1 c H`

AtildeSD (y) dy w cent (e ) 5 0 (8)

The assumptions that w cent cent gt 0 and w cent (0) 5 0 ensures that e is positiveand unique To interpret equation (8) note that B U r represents theeffective benets of control that the manager gets when he is retainedHence the rst term in the equation captures the positive effect ofeffort on the probability that the incumbent manager will be retainedand realize his benets of control The second term captures the posi-tive effect of effort on the expected wage of the manager conditionalon his being retained Combined the rst two terms represent themarginal benet of effort and at the optimum they must be equal tothe marginal cost of effort w cent (e )

Recalling that U r is a function of w0 and AtildeS is a function of Fand w0 equation (8) denes the optimal effort level e as an implicitfunction of F and w0 To study how these variables affect e we rstdifferentiate equation (8) with respect to F and e use equation (6) andrearrange terms to obtain

e

F5

e

AtildeSAtildeSF

5

(B U r) D cent (AtildeS) c D (AtildeS)

w cent cent (e )

H3(w0 1 F) (9)

Equation (9) shows that debt has two distinct effects on e The rstis a job-security effect captured by the rst term inside the squarebrackets To see how it works note that an increase in F increasesthe critical signal below which the manager is replaced and loseshis effective benets B U r This may induce the manager to exerteither more or less effort depending on the sign of D cent (AtildeS) which deter-mines whether the marginal productivity of managerial effort D (AtildeS) increases or decreases in AtildeS To illustrate consider Figure 2 whichshows the rst-order condition for the managerrsquos problem assumingthat c 5 0 (ie only the job-security effect matters) If the replace-ment rule is initially at a point like AtildeS1 where D cent ( AtildeS1) gt 0 and the rmraises it slightly by issuing debt then the managerial benet of effortincreases As a result the horizontal line in Figure 2(A) shifts upwardand the manager exerts more effort In contrast if the replacementrule is initially at a point like AtildeS2 where D cent (AtildeS1) lt 0 then raising itslightly by issuing debt leads to a downward shift in the horizontalline in Figure 2(A) so the manager exerts less effort


FIGURE 2 (A) THE OPTIMAL CHOICE OF MANAGERIAL EFFORT(B) THE MARGINAL PRODUCTIVITY OF THE MANAGER

The second effect of debt on managerial effort captured by thesecond term inside the square brackets in equation (9) is a free-cash-ow effect It arises because w

1 (y) is lower when the rm has less freecash ow (ie cash ow that was not committed to debtholders) Thiseffect always discourages managerial effort because an increase in Flowers the free cash ow of the rm and hence the manager cancapture a small fraction of his contribution to earnings

To study the effect of w0 on managerial effort we differentiateequation (8) with respect to w0 and e use equation (6) and rearrangeterms to obtain

e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0

5[(B U r ) D cent (AtildeS) c D (AtildeS)][1 H3(w0 1 F)] D (AtildeS)[1 H3(w0)]

w cent cent (e ) (10)


The job-security and free-cash-ow effects are also present inequation (10) although now they have the opposite signs to thosein equation (9) because w0 lowers AtildeS rather than increases it like F In addition w0 has a negative effect on managerial effort because anincrease in effort means that the manager is less likely to be replacedand receive the expected payoff U r Using equations (9) and (10) weestablish the following result

Proposition 1 The managerrsquos effort level e is increasing in F if andonly if the job-security effect is positive and large enough to outweigh the(negative) free-cash-ow effect ie (B U r ) D cent (AtildeS) gt c D (AtildeS) When thiscondition holds e is decreasing in w0

Proposition 1 implies that a necessary condition for debt to inducemanagerial effort is that the marginal productivity of the managerincreases with AtildeS Moreover the proposition shows that when debtboosts managerial effort the golden parachute w0 lowers it

33 The Choice of Debt and the Golden Parachute

Next we consider the shareholdersrsquo problem in period 0 Assumingthat the capital market is perfectly competitive new investors mustbreak even in expectation so the entire expected cash ow of the rmnet of managerial compensation accrues to the existing shareholdersTherefore the expected payoff of the shareholders at the beginning ofperiod 0 is given by

V 5 HAtildeS

0( Aringy U r)h(y | e ) dy 1 H

`

AtildeSy w

1 (y) h(y | e ) dy (11)

The rst term in this expression corresponds to states of nature inwhich the manager is replaced Then the mean cash ow is Aringy andshareholders receive all of it net of the severance payment to theincumbent manager either directly or through the pricing of debtThe second term corresponds to states of nature in which the incum-bent manager is retained in which case the period 2 net cash ow isy w

1(y) The shareholdersrsquo problem is to choose the golden parachute

w0 the face value of debt F and possibly the amount of equity to beissued to outsiders with the objective of maximizing V Equation (11)shows that F affects V only through its effect on the replacementrule AtildeS The golden parachute w0 affects V through AtildeS but in addi-tion it also has a direct effect on V through U r and an indirect effect


through e Using the rst-order conditions for the shareholdersrsquo prob-lem we prove the following result

Proposition 2 F gt 0 implies w 0 5 0 Hence a necessary condition for

the rm to offer the incumbent manager a golden parachute is that F 5 0

Taken literally Proposition 2 says that leveraged rms shouldnot offer their managers golden parachutes The reason is that bothdebt and golden parachutes are used to inuence the replacementrule that the rm adopts Since the two instruments have the oppositeeffect on the replacement rule the rm would never use both of themsimultaneously In practice however debt and golden parachutes maycoexist because rms are likely to use them for reasons that are nottaken into account in our model Therefore Proposition 2 suggeststhat in a more general setting we should expect to nd a negativecorrelation between leverage and golden parachutes

Using equation (5) Proposition (2) implies that if F gt 0 thenAtildeS gt Aringy implying that the replacement rule is more ldquoaggressiverdquo thanthe ex post efcient rule On the other hand if F 5 0 and w

0 gt 0 thenAtildeS lt Aringy so the replacement rule is ldquosofterrdquo than the ex post efcientrule and if F 5 w

0 5 0 then AtildeS 5 Aringy so the replacement rule is ex postefcient Hence leveraged rms may replace their manager even ifhis productivity is above the average productivity of an alternativemanager whereas rms who offer their manager a golden parachutemay retain the manager even if his productivity is below that of analternative manager

Equation (11) indicates that the value of the rm depends on Fand w0 in a rather complex manner To facilitate the analysis we breakdown the overall effect of F and w0 on V into a job-security effect anda free-cash-ow effect To disentangle these effects we consider rstthe case where c 5 0 so the free-cash-ow effect disappears

Proposition 3 Suppose that c 5 0 Then

(i) If D cent ( Aringy) gt 0 then Aringy lt AtildeS lt ` 0 lt F lt ` and w 0 5 0 so the rm

issues debt but does not offer the manager a golden parachute(ii) If D cent ( Aringy) pound 0 then F 5 0 Now the rm may set w

0 gt 0 provided thatB is sufciently large

The intuition behind Proposition 3 is as follows When c 5 0 therm issues debt only if this induces the manager to exert more effortThis scheme works because it commits shareholders to an overlyaggressive replacement rule such that AtildeS gt Aringy When the marginalproductivity of the manager is increasing at the efcient replacementrule ie D cent ( Aringy) gt 0 raising the replacement rule above Aringy motivates the


manager to work harder16 Hence shareholders choose F by tradingoff the benet from boosting e against the loss from distorting thereplacement rule In contrast when D cent ( Aringy) pound 0 shareholders do notbenet from issuing debt because it discourages managerial effortconsequently F 5 0 Now shareholders may offer the manager agolden parachute in order to make it even less attractive to replacehim later on If B is sufciently large the extra protection againstdismissal induces the manager to exert more effort so offering hima golden parachute may be optimal for shareholders if the result-ing increase of cash ow outweighs the cost of offering a goldenparachute

Next we isolate the free-cash-ow effect in order to study itseffect on the capital structure of the rm To this end we assume thatH1 5 H2 in which case D (y) 5 0 for all y so the cash ow in period 2is affected only by the managerrsquos ability and not by his effort Thisassumption eliminates the job-security effect because the manager hasno way to promote his chances to retain his job implying that e 5 0Hence the rm chooses F by trading off the benet from limitingthe managerrsquos compensation against the loss from adopting an ex postinefcient replacement rule17

Proposition 4 Suppose that H1 5 H2 so that D (y) 5 0 for all y Thenfor all c gt 0 one has AtildeS gt Aringy F gt 0 and w

0 5 0 Moreover F increaseswith c

Proposition 4 is in the spirit of Jensenrsquos (1986) free-cash-owhypothesis the rm issues debt in order to restrict the cash ow thatcan accrue to the manager However unlike in Jensen here the benetfrom issuing debt must be traded off against the distortion of thereplacement rule

4 Price Reactions and Expected Cash Flow

In this section we examine the implications of our theory for theimpact of managerial replacement on the prices of the rmrsquos secu-rities and on its future cash ow

16 For instance D cent ( Aringy) gt 0 whenever H1 and H2 are two exponential normal orlogistic distributions In contrast when H1 and H2 are two lognormal uniform orgamma distributions D cent ( Aringy) may be either positive or negative depending on the spe-cic parameters of the distributions for example when the two distributions are log-normal with parameters (1 1 t 2) and (1 2) respectively D cent ( Aringy) gt 0 if and only if t lt 4[with D cent ( Aringy) gt 0 when t 5 4]

17 Another way to eliminate the job-security effect is to assume that B 5 0 Thenprovided that Y cent (e) Y cent cent (e) is increasing in e (ie the cost of effort is sufciently convex)we get the same result as in Proposition 4


Proposition 5 (i) The market values of equity and debt and the value ofthe rm decrease if the manager is replaced and increase if the manageris retained

(ii) The expected cash ow of leveraged rms that retain their managerexceeds that of rms that replace their manager

Proposition 5 has several empirical implications First since theprices of equity and debt in period 0 reect both low realizations ofS for which the manager is replaced and high realizations for whichthe manager is retained managerial replacement should convey badnews to the capital market and be associated with negative price reac-tions This prediction is consistent with Khanna and Poulsen (1995)who nd that changes in top management lead to a negative pricereaction especially in rms that end up ling for bankruptcy underChapter 1118

Second to the extent that earnings are serially correlated cur-rent earnings can serve as a proxy for the signal S Since managerialreplacement is associated with low realizations of S Proposition 5implies that lower current earnings are associated with a higher prob-ability of managerial replacement This result is consistent with thending of Hermalin and Weisbach (1988) Warner et al (1988)Weisbach (1988) Kaplan and Minton (1994) and Blackwell et al (1994)

Third since the manager is replaced whenever S lt AtildeS and sinceAtildeS exceeds the average cash ow under an alternative manager Aringy whenever F gt 0 it follows that all else equal rms that retaintheir managers have on average a higher cash ow than rms thatreplace their managers This prediction is consistent with Murphyand Zimmerman (1993) who nd that the market-adjusted growthrates of sales decline signicantly prior to CEO departures and remainnegative for several years following the departure The prediction isalso consistent with Kang and Shivdasani (1997) who nd in a sam-ple of nonnancial Japanese rms that the industry-adjusted returnon assets (ratio of pretax operating income to total assets) was neg-ative in the three years prior to a nonroutine managerial turnover

18 In contrast with Khanna and Poulsen Warner et al (1988) do not nd signicantstock price reactions to announcements on managerial turnover Their nding howevermay be due to the fact that the announcements were anticipated by the market fromthe poor performance of the rms prior to the announcement For example Denis andDenis (1995) nd a signicant negative cumulative abnormal return over the 250 dayspreceding the turnover announcement ( 1714 in the case of forced resignations of topmanagement in large corporations) but not in the two days prior to the announcementitself Similarly Furtado and Rozeff (1987) nd a 37 average two-day-announcement-period abnormal return for forced dismissals but argue that ldquoThe evidence appears tobe consistent with a market that is already aware of negative performance associatedwith management and regards the dismissal as good news and a sign that the problemmay be remediedrdquo (pp 155ndash156) For additional evidence on the stock price reactionsto announcements of managerial turnover see the survey of Furtado and Karan (1990)


(the companyrsquos president did not remain on the board of directors)It should be pointed out though that this prediction is cross-sectionaland compares rms that replace their managers with rms that donot In particular the prediction does not rule out the possibility thatthe performance of a given rm may improve after its manager isreplaced because the expected cash ow prior to the replacement

H AtildeS

0 yh(y | e )dy might well fall short of Aringy which is the expected cashow under a new manager (this is especially true if AtildeS is not too muchabove Aringy)19

5 Comparative-Statics Results AndCross-Sectional Predictions

Having examined the job-security and free-cash-ow effects in isola-tion we now show that putting them together yields a rich set ofempirical predictions regarding the choices of debt managerial effortmanagerial compensation managerial turnover expected return oninvestment and value of the rm The two effects however may workin opposite directions since the free-cash-ow effect always discour-ages managerial effort while the job-security effect may induce eithermore or less managerial effort depending on the sign of D cent (AtildeS) Conse-quently the interaction between the two effects is in general intractableTo derive cross-sectional empirical predictions when both effects arepresent we therefore impose more structure on the model and runnumerical simulations

To facilitate the numerical simulations we assume that the dis-utility from managerial effort is w (e) 5 ke2 and the distribution ofthe cash ow in period 2 is a weighted sum of two exponential dis-tributions H1(y) 5 1 e ym l and H2(y) 5 H3(y) 5 1 e y (m 1 t) l where k m t and l are positive constants20 Note that D (y) ordmH2(y) H1(y) sup3 0 for all y sup3 0 and D (y) increases with t so highervalues of t are associated with a higher marginal productivity of effortThe mean cash ow in period 2 under an alternative manager isAringy 5 l (m 1 t) while the mean cash ow under the incumbent man-

ager is a weighted average of Aringy and l m Since the mean cash ow

19 Indeed Denis and Denis (1995) nd a large improvement in the performance ofrms that replace their managers

20 We choose w (e) to be quadratic because then the rst-order condition for themanagerrsquos problem is linear in e The coefcient k is chosen to guarantee that the man-agerrsquos problem has an interior solution ie 0 pound e pound 1 (since e represents effort it mustbe nonnegative moreover since H is a weighted average of two distributions e hasto be less than 1) The distribution functions H1 and H2 were chosen to be exponentialbecause this allows us to solve the model numerically (we also tried normal lognormallogistic and gamma distributions but were unable to obtain numerical solutions)


under both managers increases with l we interpret l as a measure ofrm size

Based on the numerical simulations we report in Section 51comparative-statics results on the effects of changes in the exogenousvariables of the model on the various endogenous variables of inter-est The primary reason for reporting these results is to clarify andillustrate the interaction between the job-security and free-cash-oweffects In practice though it might be difcult to nd good proxiesfor the exogenous variables in our model so the results in Section 51may be hard to test directly Hence in Section 52 we exploit the factthat proxies for the endogenous variables in our model are readilyavailable to derive testable hypotheses based on the predicted corre-lations between the endogenous variables in our model We believethat these hypotheses provide at least a preliminary guide for futureempirical research on the interaction between capital structure andmanagerial compensation

51 Comparative-Statics Results

In this subsection we examine how variations in exogenous parame-ters affect the equilibrium values of debt managerial effort manage-rial compensation rm value expected cash ow and probability ofmanagerial turnover (henceforth called simply managerial turnover)Since the job-security effect is mainly driven by B while the free-cash-ow effect is mainly driven by c we x the values of l m t and kand study the impact of changes in B and c In Figure 3 we x thevalues of l at 1 of m and t at 05 and of k at 10 (setting k 5 10 ensuresthat the managerrsquos problem has an interior solution) and describe thevarious endogenous variables of interest as a function of c for threevalues of B 0 10 and 40 In Figure 4 we repeat this exercise for thecase where l 5 40 To ensure that the managerrsquos problem still hasan interior solution we increased k to 30 Changes in m t and k didnot yield new insights so we do not report comparative-statics resultswith respect to these variables Moreover running the exercise withadditional values of B (ie raising B from 0 to 40 by smaller incre-ments) and with additional values of l did not make a big differenceso we do not report these results either

511 The Face Value of Debt We computed F usingequation (A-5) in the Appendix The results are shown in Figures 3(A)and 4(A) When B 5 c 5 0 the manager does not get any bene-ts of control so shareholders cannot exploit the job-security effect


FIGURE 3 SIMULATION RESULTS UNDER THE ASSUMPTIONTHAT l 5 1 m 5 t 5 05 k 5 10 (A) FACE VALUE OF DEBT (B)MANAGERIAL EFFORT (C) MANAGERIAL COMPENSATION (D)MANAGERIAL TURNOVER (E) EXPECTED CASH FLOW CONDI-TIONAL ON THE MANAGERrsquoS BEING RETAINED (F) VALUE OFTHE FIRM

moreover the manager has no bargaining power so there is no needto issue debt to limit his compensation Hence F 5 0 Moving awayfrom the origin F increases monotonically with both B and c Intu-itively the higher is B the more effective the job security effect becomesso the rm issues more debt to exploit this effect Similarly as c

increases the free-cash-ow problem becomes more severe so there isgreater need to restrict the managerrsquos compensation by issuing debt



Figure 4(A) shows that when l 5 40 (while k is raised to 30 to ensurethat e remains between 0 and 1) the face value of debt is higher thanin the case where l 5 1 reecting the fact that the job-security andfree-cash-ow effects are now stronger21

21 Raising k to 30 when l 5 1 did not change the results but had the disadvantagethat the debt levels as functions of c for different values of B were all clustered becausea large k implies a high disutility of effort and hence a low e consequently debt hasa very small effect on e


512 Managerial Effort We computed e using equation(8) Figure 3(B) shows that e increases monotonically with B andincreases monotonically with c when B is small but has an invertedU-shape when B is large Intuitively an increase in B makes it moreimportant for the manager to keep his job and hence he works harderAs c increases the manager captures a larger fraction of the rmrsquos freecash ow Now it might be thought that this would imply a highere but since the rm issues more debt when c increases the rmhas less free cash ow so the overall effect on e may be negativeFigure 4(B) shows that when l increases from 1 to 40 the negativeeffect of debt on e is ameliorated so e increases monotonically withboth B and c

513 Managerial Compensation Our measure of manage-rial compensation is the expected value of w

1 (y) conditional on themanager being retained Using equation (4) this expression is givenby

Ew 5H `

AtildeS c (y AtildeS )h(y | e )dy

1 H (AtildeS | e ) (12)

In general Ew is affected by AtildeS which determines the size of thermrsquos free cash ow and by e which affects the probability that thecash ow will be large As Figures 3(c) and 4(c) show Ew increasesmonotonically with both B and c Intuitively an increase in B magni-es the job-security effect and as we saw earlier the resulting posi-tive effect on e outweighs the negative effect due to the increase in AtildeS hence the overall effect of B on Ew is positive Although an increasein c affects AtildeS more than it affects e the overall effect on Ew isstill positive due to the increase in the fraction of the free cash owthat accrues to the manager The only difference between Figures 3(c)and 4(c) is that when l 5 40 the effect of B on Ew is much weakerthan in the case where l 5 1

514 Managerial Turnover The equilibrium probabilitythat the manager is replaced (ie managerial turnover) is given byH (AtildeS | e ) and was computed by substituting for AtildeS and e intoequation (1) A priori it is not clear whether an increase in B andc should have a positive or a negative effect on H (AtildeS | e ) becausethe rm issues more debt and hence AtildeS is higher But since e mayincrease as well the manager may have a better chance to reach AtildeS

and save his job Figure 3(D) shows that when B increases the positiveeffect of e dominates so there is less managerial turnover When c


increases the negative effect of the increase in AtildeS dominates so thereis more managerial turnover Figure 4(D) shows that when l 5 40H (AtildeS | e ) still decreases in B but now it may also decrease in c if c

is small This is because the increase of l to 40 means that the marginalproductivity of effort D (S) is higher so e has a stronger effect onthe rmrsquos cash ow Hence when c is small the positive effect of theincrease in e dominates the associated negative effect of the increasein AtildeS so H (AtildeS | e ) decreases with increasing c When c is large theopposite may hold

515 Expected Cash Flow Conditional on the ManagerrsquosBeing Retained The expected cash ow when the manager isretained is given by

CF1(e ) 5H `

AtildeS yh(y | e )dy

1 H (AtildeS | e ) (13)

Figure 3(E) shows that when l 5 1 both AtildeS and e increase with B andc thus leading to higher expected cash ow When l 5 40 e maydecrease with increasing c if c is large but as Figure 4(E) shows thecorresponding increase in AtildeS dominates so overall CF1(e ) increaseswith B and c throughout

516 The Value of the Firm Equation (11) shows that thevalue of the rm V is positively affected by e negatively affectedby w

1(y) and holding e and w 1 (y) constant it is negatively affected

by managerial turnover H (AtildeS | e ) As we saw earlier an increase inc leads to an increase in w

1(y) and in general it has an ambiguouseffect on e and on H (AtildeS | e ) Figure 3(F) shows that when l 5 1 thenegative effect of c through its effect on w

1 (y) and H (AtildeS | e ) domi-nates the positive effect of c through the increase in e so V decreaseswith increasing c In contrast when l 5 40 H (AtildeS | e ) decreases withincreasing c for low c while e increases and as Figure 4(F) showsthese positive effects outweigh the negative effect due to the increasein w

1(y) hence V increases with c As c increases H (AtildeS | e ) beginsto increase c so together with the increase in w

1(y) it outweighs thepositive effect of the increase in e so V begins to decrease in c Figures 3(F) and 4(F) also show that V increases in B reecting thepositive effect of B on e and on the probability of turnover

517 The Pay-Performance Sensitivity of ManagerialCompensation Equation (4) indicates that when the incumbentmanager retains his job he receives a fraction c of his incremental


contribution to the net cash ow Hence the parameter c measuresin our model the pay-performance sensitivity of the managerrsquos wagecontract22 Using the latter as a proxy for the managerrsquos bargainingpower it follows from Figures 3 and 4 that leverage expected com-pensation and expected cash ow are all positively correlated withmanagerial pay-performance sensitivity Interestingly Figure 3 and 4indicate that the probability of a managerial turnover and the valueof the rm are not correlated with the pay-performance sensitivity ofthe managerrsquos contract as we explained earlier this is because thejob-security and free-cash-ow effects work in opposite directions

52 Correlations Between Endogenous Variables

Although the comparative-statics analysis reported in the previoussubsection is very useful for understanding the various forces thatshape the equilibrium in our model it has a drawback in that in prac-tice B and c are either unobservable or hard to estimate This makes itdifcult to test our predictions directly In this section we exploit thefact that proxies for the endogenous variables in our model are readilyavailable to derive testable hypotheses based on the predicted corre-lations between these variables To this end we conduct the followingexperiment We x the values of k t m and l and independentlydraw at random 100 pairs of B and c from the square [0 40] acute [0 1]For each pair we solve the model numerically and obtain 100 equilib-rium outcomes Using these outcomes we are then able to observe thepairwise correlations between the equilibrium values of the endoge-nous variables that are driven by variations in B and c Figure 5 showsour ndings when l 5 1 m 5 t 5 05 and k 5 10 and Figure 6shows similar ndings for l 5 40 m 5 t 5 05 and k 5 30 (k wasraised to 30 to ensure an interior solution for the managerrsquos problem)Figure 5 therefore corresponds to ldquosmall rmsrdquo (l 5 1) while Figure 6corresponds to ldquolarge rmsrdquo ( l 5 40) In each case we run linearregressions between the equilibrium values of the endogenous vari-ables and show in each box the tted regression line and the value ofR2 This procedure produces predictions about the cross-section corre-lations between easy-to-measure endogenous variables that are drivenby variations in the underlying values of B and c

Several interesting predications emerge from Figures 5 and 6First controlling for rm size the face value of debt and manage-rial compensation are strongly positively correlated This predictionis consistent with Gaver and Gaver (1993) who nd a positive corre-lation between debtequity ratios (both book and market values) and

22 We thank an anonymous referee for suggesting this interpretation of c


FIGURE 5 SIMULATIONS RESULTS FOR A RANDOM SELECTIONOF 100 PAIRS OF B AND GAMMA ASSUMING THAT l 5 1 m 5T 5 05 AND k 5 10 (THE SOLID LINES IN EACH FRAMEARE FITTED LINEAR REGRESSIONS) (A) DEBT AND MANAGE-RIAL COMPENSATION (B) MANAGERIAL TURNOVER AND FIRMVALUE (C) DEBT AND EXPECTED CASH FLOW (D) MANAGE-RIAL COMPENSATION AND EXPECTED CASH FLOW (E) MAN-AGERIAL TURNOVER AND DEBT (F) MANAGERIAL TURNOVERAND EXPECTED COMPENSATION

the average cash compensation of the ve most highly paid executivesin each rm and with Berger et al (1997) who nd a positive corre-lation between net increases in leverage (net debt issued minus equityissued plus equity repurchased over total assets) and increases in theCEOrsquos holdings of exercisable stock options It should be emphasized


FIGURE 6 SIMULATIONS RESULTS FOR A RANDOM SELECTIONOF 100 PAIRS OF B AND GAMMA ASSUMING THAT l 5 40 m 5t 5 05 AND k 5 30 (THE SOLID LINES IN EACH FRAMEARE FITTED LINEAR REGRESSIONS) (A) DEBT AND MANAGE-RIAL COMPENSATION (B) MANAGERIAL TURNOVER AND FIRMVALUE (C) DEBT AND EXPECTED CASH FLOW (D) MANAGE-RIAL COMPENSATION AND EXPECTED CASH FLOW (E) MAN-AGERIAL TURNOVER AND DEBT (F) MANAGERIAL TURNOVERAND EXPECTED COMPENSATION

that the intuition for this result in our model is subtle since both debtand compensation are determined endogenously Hence cross-rmvariations in debt and compensation are driven by variations in theunderlying values of B and c The positive correlation between debtand compensation is a direct consequence of the analysis in Section 51that shows that F and Ew are both increasing in B and c


Second Figure 5(B) reveals that in the case of small rms rmvalue and managerial turnover show a strong negative correlationThis suggests that rms that replace their managers more often haveon average lower values The strong negative correlation reects ourndings in Section 51 that the probability of turnover increases inc and decreases in B while the value of the rm decreases in c

and increases in B Figure 6(B) shows that in the case of large rmsthe negative correlation between the two variables is weaker Thisis because now managerial turnover is a U-shaped function of c while rm value is an inverted U-shaped function of c Moreoverthe respective extrema are attained at different values of c The nega-tive correlation is weakest when c is low since then the value of therm is relatively high while managerial turnover is relatively low

Third both the face value of debt and managerial compensationare positively correlated with the expected cash ow conditional onthe manager being retained This reects our ndings in Section 51that all three variables increase with B and c The positive correlationis much stronger in the case of large rms (see the respective R2 ineach box) because all three variables are less sensitive to changes inB when l 5 40 than when l 5 1 This implies that highly levered rmsgenerate on average a high cash ow and pay their managers highwages especially when the rm is large

Fourth the face value of debt and managerial compensationare weakly positively correlated with managerial turnover Unlike theprevious results a priori it is unclear whether the correlation betweendebt and managerial turnover should be positive or negative becausethe face value of debt increases with B and c whereas managerialturnover increases in B but decreases in c As Figures 5(E) and 6(E)show when the two effects are taken together a weak but positivecorrelation between the face value of debt and managerial turnoveremerges Similarly the weak correlation between managerial com-pensation and turnover reects the conicting predictions regardingcross-sectional variations in B and in c while managerial compensa-tion increases in B managerial turnover decreases in B Consequentlywhen rms differ only with respect to the benets of control of theirmanagers our model predicts a negative correlation between man-agerial turnover and compensation This negative correlation becomesweaker however when rms also differ with respect to c since man-agerial compensation and turnover are both increasing in c whenl 5 1 whereas managerial compensation increases with c but man-agerial turnover is a U-shaped function of c when l 5 40


6 Conclusion

In this paper we have examined the role of compensation contractsand capital structure in disciplining and monitoring managers andshown that studying them jointly yields new insights and empiricalpredictions In particularly we showed that the simultaneous choiceof compensation and capital structure is driven by two effects Therst which we call the job-security effect arises because risky debtand golden parachutes induce the rm to adopt an ex post inef-cient replacement rule which in turn motivates the manager to exertmore effort in attempt to secure his job When the manager meets thegoal that the rm has chosen keeping him creates a surplus and thisenables the manager to demand a fraction of his incremental contri-bution to the cash ow over and above the contribution of an alterna-tive manager Debt can now benet the shareholders by limiting thefree cash ows that the manager can capture Thus the combinationof performance-sensitive compensation and optimally chosen capitalstructure implements a better incentive and control system

Our theory enables us to derive a rich set of empirical predic-tions regarding the impact of managerial replacement on the pricesof equity and debt and on the expected cash ow of the rm Wealso obtain results on the interaction between capital structure man-agerial compensation managerial turnover rm value Some of theseresults are consistent with existing evidence while others are yet to betested

Our theory reveals that there is a systematic and rather complexrelationship between managerial compensation and capital structureThis suggests that in empirical cross-section studies on the determi-nants of managerial compensation and its effects on rm performancecapital structure should not be used merely as a control variableLikewise empirical research on nancial structure should not viewmanagerial compensation as a simple control variable Rather com-pensation and capital structure should be studied jointly Althoughthe theoretical underpinnings of how rms choose their capital struc-ture and managerial compensation are still not sufciently developedwe believe that our paper provides at least a preliminary guide forfuture empirical research on these topics

Although our theory has focused exclusively on internal incen-tives external forces such as competition in the product market or inthe market for corporate control are also very important for disciplin-ing and monitoring managers Therefore in a more general settingthe choices of capital structure and managerial compensation willhave to take into account external incentives as well For instancedebt may lower the likelihood of a takeover (Israel 1991) and hence


interfere with external incentives to exert effort Golden parachuteson the other hand may have a positive effect on managerial qualitybecause they weaken the incentive of a manager to resist a takeover(Lambert and Larcker 1985) In addition to these theoretical consider-ations there is also empirical evidence that suggests that the interac-tion between internal and external forces is important For exampleDenis and Denis (1995) nd that in a sample of 88 rms that forcedtheir top managers to resign over the period 1985ndash1988 56 were thetargets of some corporate control activity (eg block investment in thermrsquos shares takeovers LBOs) in the two-year period following theresignation In future research it would be interesting to examine theinteraction between managerial compensation and capital structure ina setting where both internal and external incentives are present

Appendix

In this appendix we provide the proofs for Lemma 1 and Proposi-tions 1ndash5

Proof of Lemma 1 (i) Assume by way of negation that U r gt B andconsider the bargaining that takes place if any party wishes to rene-gotiate the original wage contract In what follows it is worth recall-ing that we assume that the contract renegotiation takes place afterthe rm has decided to retain the incumbent manager Hence theperiod 2 net cash ow under the incumbent manager y F mustbe sufciently large otherwise the rm will surely replace the incum-bent manager When the manager makes an offer he proposes a wagew

m that leaves shareholders indifferent between accepting in whichcase they get y F w

m and rejecting in which case they get V r Hence w

m 5 y F V r Likewise when the shareholders make anoffer they propose a wage w

s that leaves the manager indifferentbetween accepting and getting B 1 w

s and rejecting and getting anexpected payoff U r Hence w

s 5 U r B Since the manager makesan offer with probability c and the shareholders make an offer withprobability 1 c the managerrsquos monetary compensation is

w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)

Given w 1(y) shareholders retain the incumbent manager if and only

if their resulting expected payoff y F w 1 (y) exceeds their expected

payoff under a new manager V r Using (A-1) and recalling that Aringy 5H `

0 yh3(y)dy is the mean cash ow in period 2 under an alternative


manager it follows that the incumbent manager is retained if andonly if

y sup3 AtildeS ordm V r 1 U r 1 F B 5 Aringy Hw0 1 F

w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)

Given AtildeS w0 and w 1(y) the expected payoff of the manager as

a function of his effort is

U (e) 5 HAtildeS

0U r h(y | e) dy 1 H

`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`

AtildeSc (y AtildeS)h(y | e) dy w (e) (A-3)

where h(y | e) 5 h2(y) e D cent (y) Differentiating U (e) integrating byparts and using the assumption that limynot ` y D (y) 5 0 the rst-order condition for the optimal effort level e is

U cent (e ) 5 c H`

AtildeSD (y)dy w cent (e ) 5 0 (A-4)

From (A-2) it follows that AtildeS w0 5 H3(w0 1 F) H3(w0) gt 0 Hence ifthe rm raises w0 then AtildeS increases and as (A-4) shows e decreasesHence shareholders are better off lowering w0 to the point whereU r pound B as this saves them money and leads to more managerialeffort

(ii) To derive w 1(y) recall from part (i) of the proof that in the

renegotiation subgame the manager accepts any nonnegative wageoffer (he cannot accept negative wage offers because he has no per-sonal funds) and proposes a wage w

m 5 y AtildeS where AtildeS ordm V r 1 F Since the manager is willing to work even without monetary compen-sation the equilibrium strategy of shareholders is to offer him w

s 5 0and accept any offer not exceeding w

m In order to be renegotiation-proof the period 1 wage contract must specify the expected monetarycompensation that the manager can get from wage renegotiation sow

1(y) 5 c w m 5 c (y AtildeS) u

Proof of Proposition 1 Since D ( ) lt 0 the two comparative-staticsresults follow immediately from equations (9) and (10) u


Proof of Proposition 2 The rst-order conditions for the shareholderrsquosproblem are

VF

5V

AtildeSAtildeSF

5V

AtildeS H3(w0 1 F) pound 0 FVF

5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V

AtildeS [1 H3(w0 1 F)] H (AtildeS | e )(1 H3(w0))

( Aringy U r AtildeS) D (AtildeS) 1 (1 c ) H`

AtildeSD (y)dy

acuteD (AtildeS) (1 H3(w0) )

w cent cent (e )pound 0 w0

Vw0

5 0

(A-6)

whereV

AtildeS 5 ( Aringy U r AtildeS)h(AtildeS | e ) 1 c H`

AtildeSh(y | e )dy

1 ( Aringy U r AtildeS) D (AtildeS) 1 (1 c ) H`

AtildeSD (y)dy

acute


w cent cent (e )

(A-7)

The rst square-bracketed expressions on the third line of (A-6) andthe second line of (A-7) are obtained by integration by parts and usingthe assumption that limynot ` y D (y) 5 0 Since the last two terms onthe right side of (A-6) are negative it follows that w

0 gt 0 only ifV AtildeS lt 0 in which case (A-5) implies that F 5 0 When F gt 0(A-5) implies that V AtildeS 5 0 so from (A-6) it follows that w

0 5 0 u

Proof of Proposition 3 (i) Let c 5 0 and suppose that D cent ( Aringy) sup3 0Evaluating (A-7) at F 5 w0 5 0 and noting from equation (5) that inthis case AtildeS 5 Aringy we have

dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy

BD cent ( Aringy )w cent cent (e )

gt 0 (A-8)

This inequality implies that the rm would like to increase AtildeS above Aringy Equation (5) reveals that this can be done either by setting F gt 0 or by


setting w0 lt 0 The latter option is impossible however because themanager lacks personal funds Hence it must be the case that F gt 0so by Proposition 2 w

0 5 0 As AtildeS not ` the probability that theincumbent manager will be replaced approaches 1 so V not Aringy (recallthat w

0 5 0 implies that U r 5 0) But equation (11) evaluated at AtildeS 5 Aringy(and w0 5 0) indicates that V gt Aringy so the rm is better off issuing nodebt

(ii) Suppose that D cent ( Aringy) pound 0 Then (A-8) implies that the share-holders would like to set AtildeS pound Aringy so F 5 0 Evaluating (A-6) atc 5 F 5 w0 5 0 and noting from equation (5) that in this case AtildeS 5 Aringy we have

Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy

BD cent ( Aringy) 1 D ( Aringy)w cent cent (e )

H ( Aringy | e ) (A-9)

The shareholders would like to set w 0 gt 0 provided that the derivative

is positive A necessary condition for this is B gt D ( Aringy) D cent ( Aringy) u

Proof of Proposition 4 Suppose that H1 5 H2 Then D (y ) 5 0 ande 5 0 so (A-7) becomes

dV

dAtildeS 5V

AtildeS 1Vw

dw

dAtildeS 5 ( Aringy U r AtildeS)h2(AtildeS) 1 c H`

AtildeSh2(y)dy (A-10)

Noting from equation (5) that at F 5 0 the rst term on the right sideof (A-10) vanishes it follows that so long as c gt 0 it must be thecase that AtildeS gt Aringy and hence F gt 0 Proposition 2 implies in turn thatw

0 5 0 To examine the effect of c on F we differentiate equation(A-10) with respect to c and AtildeS to obtain

AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)

Since the numerator is positive by the second-order condition for amaximum it follows that AtildeS increases with c Equation (6) then impliesin turn that the rm needs to issue a higher F to implement thehigher AtildeS u

Proof of Proposition 5 (i) The value of equity in period 1 when themanager is replaced is given by

Er 5 V r (A-12)


The value of equity in period 1 conditional on the managerrsquos beingretained is given by

E1 5 V r 1(1 c ) H `

AtildeS (y AtildeS )h(y | e )dy

1 H (AtildeS ) (A-13)

Since the second term in the right side of (A-13) is positive E1 gt Er Moreover since the manager is replaced with probability H (AtildeS | e )and is retained with probability 1 H (AtildeS | e ) the value of equitybefore the replacement is made is E0 5 H (AtildeS | e )Er 1 [1 H (AtildeS | e )]E1Therefore Er lt E0 lt E1 implying that the value of equity decreaseswhen the manager is replaced and increases when the manager isretained

Similarly the value of debt in period 1 if the manager is replacedis given by

Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)

The value of debt in period 1 if the manager is retained is given by

D1 5 F (A-15)

Since the second term on the right side of (A-14) is negative D1 gt Dr Similarly to equity the value of debt before the replacement is made isgiven D0 5 H (AtildeS | e )Dr 1 [1 H (AtildeS | e )]D1 Hence Dr lt D0 lt D1 Theresults regarding rm value follow immediately because rm valueequals the sum of debt and equity values

(ii) When the manager is replaced the expected cash ow underan alternative manager is Aringy When the manager is retained the expectedcash ow is equal to the expected value of y conditional on y beingat least as large as AtildeS (otherwise the manager is replaced) But if therm is leveraged AtildeS gt Aringy so the expected cash ow exceeds Aringy u

REFERENCES

Aghion P M Dewatripont and P Rey 1994 ldquoRenegotiation Design with UnveriableInformationrdquo Econometrica 62 257ndash282

Agrawal A and C Knoeber 1998 ldquoManagerial Compensation and the Threat ofTakeoverrdquo Journal of Financial Economics 47 219ndash239

Berger P E Ofek and D Yermack 1997 ldquoManagerial Entrenchment and Capital Struc-ture Decisionsrdquo Journal of Finance 52 1411ndash1438

Berkovitch E and R Israel 1996 ldquoThe Design of Internal Control and Capital Struc-turerdquo The Review of Financial Studies 9 208ndash240


Blackwell DW J Brickley and M Weisbach 1994 ldquoAccounting Information and Inter-nal Performance Evaluation Evidence from Texas Banksrdquo Journal of Accounting andEconomics 17 331ndash358

Bronars S and D Deere 1991 ldquoThe Threat of Unionization The Use of Debt and thePreservation of Shareholders Wealthrdquo Quarterly Journal of Economics 16 231ndash254

Chung TY 1991 ldquoIncomplete Contracts Specic Investments and Risk SharingrdquoReview of Economic Studies 58 1031ndash1042

Denis D and D Denis 1995 ldquoPerformance Changes Following Top Management Dis-missalsrdquo Journal of Finance 50 1029ndash1057

and A Sarin 1997 ldquoOwnership Structure and Top Executive TurnoverrdquoJournal of Financial Economics 45 193ndash221

Dessi R 1997 ldquoImplicit Contracts Managerial Incentives and Capital Structurerdquo Finan-cial Markets Group Discussion Paper No 296 London School of Economics

Dewatripont M and J Tirole 1994 ldquoA Theory of Debt and Equity Diversity of Secu-rities and Manager-Shareholder Congruencerdquo Quarterly Journal of Economics 1091027ndash1054

Furtado E and V Karan 1990 ldquoCauses Consequences and Shareholders Wealth Effectsof Managerial Turnover A Review of Management Turnoverrdquo Financial Management19 60ndash75

Furtado E and M Rozeff 1987 ldquoThe Wealth effects of Company Initiated ManagementChangesrdquo Journal of Financial Economics 18 147ndash160

Garvey G and P Swan 1992 ldquoManagerial Objectives Capital Structure and the Pro-vision of Worker Incentivesrdquo Journal of Labor Economics 10 357ndash379

Gaver J and K Gaver 1993 ldquoAdditional Evidence on the Association between theInvestment Opportunity Set and Corporate Financing Dividend and CompensationPoliciesrdquo Journal of Accounting and Economics 16 125ndash160

Grossman S and O Hart 1980 ldquoTakeover Bids the Free-Rider Problem and the Theoryof the Corporationrdquo Bell Journal of Economics 11 42ndash64

and 1982 ldquoCorporate Financial Structure and Managerial Incentivesrdquo inJ McCall ed The Economics of Information and Uncertainty Chicago University ofChicago Press 107ndash137

Harris M and Raviv 1979 ldquoOptimal Incentive Contracts with Imperfect InformationrdquoJournal of Economic Theory 20 231ndash259

Hart O 1983 ldquoThe Market Mechanism as an Incentive Schemerdquo Bell Journal of Eco-nomics 14 366ndash382

and B Holmstrom 1987 ldquoThe Theory of Contractsrdquo in T Bewley ed Advancesin Economic Theory Fifth World Congress Cambridge Cambridge University Press71ndash155

Hermalin B and M Weisbach 1988 ldquoThe Determinants of Board Compositionrdquo RANDJournal of Economics 19 589ndash606

Holmstrom B 1979 ldquoMoral Hazard and Observabilityrdquo Bell Journal of Economics 1074ndash91

and J Tirole 1993 ldquoMarket Liquidity and Performance Monitoringrdquo Journal ofPolitical Economy 101 678ndash709

Israel R 1991 ldquoCapital Structure and the Market for Corporate Control The DefensiveRole of Debt Financingrdquo Journal of Finance 46 1391ndash1410

Jensen M 1986 ldquoAgency Costs of Free Cash Flow Corporate Finance and TakeoversrdquoAmerican Economics Review 76 323ndash329

and W Meckling 1976 ldquoTheory of The Firm Managerial Behavior Agency Costsand Ownership Structurerdquo Journal of Financial Economics 3 305ndash360

and K Murphy 1990 ldquoPerformance Pay and Top-Management Incentivesrdquo Journalof Political Economy 98 225ndash264


John T and K John 1993 ldquoTop-Management Compensation and Capital StructurerdquoJournal of Finance 48 949ndash974

Joskow P N Rose and C Wolfram 1996 ldquoPolitical Constraints on Executive Com-pensation Evidence from the Electric Utility Industryrdquo Rand Journal of Economics27 165ndash182

Kang J-K and A Shivdasani 1997 ldquoFirm Performance Corporate Governance andTop Executive Turnover in Japanrdquo Journal of Financial Economics 38 29ndash58

Kaplan S and BA Minton 1994 lsquoAppointments of Outsiders to Japanese BoardsDeterminants and Implications for Managersrdquo Journal of Financial Economics 36225ndash258

Khanna N and A Poulsen 1995 ldquoManagers of Financially Distressed Firms Villainsor Scapegoatsrdquo Journal of Finance 50 919ndash940

Lambert R and D Larcker 1985 ldquoGolden Parachutes Decision-Making and Share-holders Wealthrdquo Journal of Accounting and Economics 7 179ndash203

Matthews S 1995 ldquoRenegotiation of Sales Contractsrdquo Econometrica 63 567ndash589Mirrlees J 1976 ldquoThe Optimal Structure of Incentives and Authority within an Orga-

nizationrdquo Bell Journal of Economics 7 105ndash131Murphy K and J Zimmerman 1993 ldquoFinancial Performance Surrounding CEO Turnoverrdquo

Journal of Accounting and Economics 16 273ndash315Novaes W and L Zingales 1998 ldquoBureaucracy as a Mechansim to Generate Informa-

tionrdquo httpgsblgzuchicagoeduRose N and A Shepard 1997 ldquoFirm Diversication and CEO Compensation Man-

agerial Ability or Executive Entrechmentrdquo Rand Journal of Economics 28 489ndash514Sarig O 1998 ldquoThe Effect of Leverage on Bargaining with a Corporationrdquo Financial

Review 33 1ndash16Scharfstein D 1988a ldquoProduct Market Competition and Managerial Slackrdquo Rand Jour-

nal of Economics 19 147ndash155 1988b ldquoThe Disciplinary Role of Takeoversrdquo Review of Economic Studies 55

185ndash199Smith C and R Watts 1992 ldquoThe Investment Opportunity Set and Corporate Financ-

ing Dividend and Compensation Policies Journal of Financial Economics 32 263ndash292Speigel Y 1996 ldquoThe Role of Debt in Procurement Contractsrdquo Journal of Economics and

Management Strategy 5 379ndash407Warner J R L Watts and K Wruck 1988 ldquoStock Prices and Top Management Changesrdquo

Journal of Financial Economics 20 431ndash460Weisbach M 1988 ldquoOutside Directors and CEO Turnoversrdquo Journal of Financial Eco-

nomics 20 461ndash492


1 Introduction

Financial structure and managerial compensation are crucial for gen-erating value to shareholders because of their inuence on manage-rial quality and incentives Practitioners have long recognized thatthe two are interdependent for instance in the leveraged buyout(LBO) wave of the 1980s nanciers used high levels of debt andperformance-sensitive compensation packages to motivate managersDespite this apparent interdependence economists have by and largestudied nancial structure and managerial compensation in isolationFor example the principle-agent literature (eg Mirrlees 1976 Harrisand Raviv 1979 Holmstrom 1979) studies the design of managerialcompensation contracts but abstracts from nancial structure consid-erations Likewise agency models of capital structure (eg Jensen andMeckling 1976 Grossman and Hart 1982) do not consider managerialcompensation explicitly1

This paper develops a theory of managerial compensation andcapital structure that explicitly allows for their interdependence Tothis end we consider a three-period model In period 0 the rm isestablished and a manager is hired In period 1 the manager takesactions that boost the future cash ow of the rm but also makethe rm more dependent on his ability For example the managerselects workers organizes production chooses the rmrsquos strategy inthe product market etc We model this activity as a choice of an unob-servable effort level that together with managerial ability determinesthe cash ow of the rm in period 2 After taking his actions (butbefore the cash ow is realized) the manager and the shareholdersreceive a common signal that perfectly reveals the period 2 cash owunder his control At this point shareholders may replace the managerwith a new manager whose ability is yet unknown However if theincumbent manager is replaced the rm loses the extra cash ow thathis actions may have generated this in turn enables the manager todemand more compensation Anticipating this demand shareholdersselect the managerrsquos compensation contract and the nancial structureof the rm to provide him with appropriate incentives while limitinghis ability to demand a higher wage This framework enables us toaddress important questions that were not addressed before for exam-ple Do highly levered rms tend to pay their managers higher wagesthan rms with low or moderate debt levels Do they replace their

1 Another branch of the literature considers the role of external forces such as themarket for corporate control or competition in the product market in ensuring manage-rial quality and effort (eg Grossman and Hart 1980 Hart 1983 Scharfstein 1988a b)Again this literature generally ignores the effect of the rmrsquos nancial structure onmanagerial incentives and quality

























2 The Model





H (y | e) 5 H2(y) e D (y) (1)































V r 5 H`

w0 1 F(y w0 F)h3(y) dy (2)


U r 5 Hw0

0yh3(y) dy 1 H

`

w0

w0h3(y) dy (3)














0(w0 1 F y)h3(y) dy (5)




AtildeSF


5 [1 H3(F 1 w0)] lt 0 (6)





U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)


1(y)









e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES








































































2 The Model





H (y | e) 5 H2(y) e D (y) (1)































V r 5 H`

w0 1 F(y w0 F)h3(y) dy (2)


U r 5 Hw0

0yh3(y) dy 1 H

`

w0

w0h3(y) dy (3)














0(w0 1 F y)h3(y) dy (5)




AtildeSF


5 [1 H3(F 1 w0)] lt 0 (6)





U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)


1(y)









e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES



















































H (y | e) 5 H2(y) e D (y) (1)































V r 5 H`

w0 1 F(y w0 F)h3(y) dy (2)


U r 5 Hw0

0yh3(y) dy 1 H

`

w0

w0h3(y) dy (3)














0(w0 1 F y)h3(y) dy (5)




AtildeSF


5 [1 H3(F 1 w0)] lt 0 (6)





U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)


1(y)









e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES










































































V r 5 H`

w0 1 F(y w0 F)h3(y) dy (2)


U r 5 Hw0

0yh3(y) dy 1 H

`

w0

w0h3(y) dy (3)














0(w0 1 F y)h3(y) dy (5)




AtildeSF


5 [1 H3(F 1 w0)] lt 0 (6)





U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)


1(y)









e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES



























































0(w0 1 F y)h3(y) dy (5)




AtildeSF


5 [1 H3(F 1 w0)] lt 0 (6)





U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)


1(y)









e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES


















































AtildeSF


5 [1 H3(F 1 w0)] lt 0 (6)





U (e) 5 HAtildeS

0U rh(y | e) dy 1 H

`

AtildeS[B w

1(y) ]h(y | e) dy w (e) (7)


1(y)









e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES






















































e

F5

e

AtildeSAtildeSF

5


w cent cent (e )

H3(w0 1 F) (9)







e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES





















































e

w05

e

AtildeSAtildeS

w01

e

U r

dU r

dw0









V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES






















































V 5 HAtildeS


`

AtildeSy w

1 (y) h(y | e ) dy (11)





































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES

















































































H AtildeS


























Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES


































































Ew 5H `


1 H (AtildeS | e ) (12)








CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES




















































CF1(e ) 5H `


1 H (AtildeS | e ) (13)




























6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES


































































6 Conclusion







Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES


















































Appendix









w 1 (y) 5 c (y F V r) 1 (1 c ) (U r B) (A-1)








w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES



















































w0

(y w0 F)h3(y) dy

1 Hw0

0Fh3(y) B (A-2)



U (e) 5 HAtildeS


`

AtildeS[B 1 w

1 (y)]h(y | e) dy w (e)

5 U r 1 H`



U cent (e ) 5 c H`












VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES


















































VF

5V

AtildeSAtildeSF

5V


5 0 (A-5)

and

Vw0

5V

AtildeSS

w0

VU r

dU r

dw01

Ve

e

w0

5V



AtildeSD (y)dy



Vw0

5 0

(A-6)

whereV


AtildeSh(y | e )dy


AtildeSD (y)dy

acute


w cent cent (e )

(A-7)



0 5 0 u


dVd Atildes

F 5 w0 5 0

5 H`

AringyD (y)dy


gt 0 (A-8)







Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES





















































Vw0 F 5 w0 5 0

5 H`

AringyD (y)dy






dV

dAtildeS 5V

AtildeS 1Vw

dw





AtildeSc

5H `

AtildeS h2(y)dy

2V AtildeS2 (A-11)



Er 5 V r (A-12)



E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES


















































E1 5 V r 1(1 c ) H `





Dr 5 HF

0yh3(y)dy 1 F[1 H3(F)] 5 F 1 H

F

0(y F)h3(y )dy (A-14)


D1 5 F (A-15)



REFERENCES
















































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