Irreversible Investment Managerial Discretion and Optimal Capital Structure

et

stini

J20

e odefaovect, tdecnag

U-shaped relationship between agency costs of debt and the managerial compensation parameters: themanagers reservation income, salary and ownership share.

2008 Elsevier B.V. All rights reserved.

e nane hasbeen

e real-discuserging

derived a valuation result for corporate bonds and employed thisresult in constructing a proof on capital-structure irrelevance.Brennan and Schwartz (1978) used the real-options approach toreach a result on optimal capital structure and incorporated bank-ruptcy costs and default probability in their derivation of an opti-mal capital structure. It is fair to say that the now well-appliedreal-options analytical platform on agency costs and capital struc-ture can be largely attributed to the work of Mello and Parsosns

growth opportunities (Childs et al., 2005), incomplete markets(Hugonnier and Morellec, 2007) and a handful of further modellingextensions. However, despite the rich variety of models on capitalstructure and agency costs, this debate has yet to fully incorporatea classic agency problem: the ownermanager conict. Most ofthese models have discussed corporate settings in which a creditorsigned a contract with an entrepreneur who was also the soleowner, thus prompting the need to include managerialdiscretion in investment decision making, within the real-optionsframework.

Journal of Banking & Finance 33 (2009) 709718

Contents lists availab

k

w.E-mail address: [email protected] incentives of a manager who makes the nancing and invest-ment decisions and thus by redening agency costs of debt in areal-options context.

The real-options account of the interaction between investmentand nancing decisions is now over thirty-years-old. Drawing onthe then recently developed option pricing theory, Merton (1974)

explored the fundamental issue of optimal debt maturity and withLeland (1998) who incorporated the choice of corporate risk andprovided a most comprehensive account of the agency-theoreticagenda within the real-options framework. This platform has sincebeen enriched with market structure considerations (Lambrecht,2001), nancing constraints (Boyle and Guthrie, 2003), stochasticobjective is to make a contribution to this debate by exploring

interest between shareholders and creditors. In this paper, our debate was further advanced by Leland (1994) who introduced

the exibility of debt renegotiation, Leland and Toft (1996) whoKeywords:Agency conictsIrreversible investmentManagerial compensationCapital structure

1. Introduction

Being the cornerstone of corporatital-structure relevance to rm valuclusive debate which has longoperational exibility insights of thstream of literature has extensivelyand optimal capital structure as em0378-4266/$ - see front matter 2008 Elsevier B.V. Adoi:10.1016/j.jbankn.2008.11.002ce, the question of cap-generated a still incon-

enriched with theoptions paradigm. Thissed investment timingout of the conicts of

(1992) who examined the case of a hypothetical mining invest-ment with operational and nancial exibility and were the rstto measure agency costs of debt. Mauer and Triantis (1994)produced probably the richest operational exibility setting inthe debate on optimal capital structure and suggested that whileoperational exibility signicantly affected the nancing decisions,nancing exibility had little effect on the operational decisionmaking. The real-options account of the optimal capital-structureD92E22G31

reservation income. Yield spreads (optimal leverage ratios) are increasing (decreasing) in the managerssalary and ownership stake, while they are decreasing (increasing) in the managers reservation income.Exploring agency costs of debt as deviations from a value-maximizing investment policy, we document aIrreversible investment, managerial discr

Andreas AndrikopoulosUniversity of the Aegean, Department of Financial and Management Engineering, 31 Fo

a r t i c l e i n f o

Article history:Received 18 June 2008Accepted 6 November 2008Available online 19 November 2008

JEL classication:D81

a b s t r a c t

We explore the signicancment timing, endogenousagers incentive to under(order to work on the projesequent income, should hements decreases with ma

Journal of Ban

journal homepage: wwll rights reserved.ion and optimal capital structure

Str., 82 100 Chios, Greece

f employee compensation and alternative (reservation) income on invest-ult, yield spreads and capital structure. In a real-options setting, a man-r)invest in a project is associated to labor income he has to forego inhe managers salary, his stake on the projects equity capital and his sub-ide to terminate operations. We nd that the optimal level of coupon pay-erial salary and ownership stake while it is increasing in the managers

le at ScienceDirect

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elsevier .com/ locate / jbf

Cadenillas et al. (2004) built on the option-like features of cor-porate securities and explored shareholdermanager conicts aswell as the effect of managerial compensation on capital structure.In this modelling framework, managers were only rewarded withstock and decided on corporate risk and the level of effort theywere to exert, while the choice of leverage and of the level of man-agerial compensation was made by the shareholders. In a corporatesetting where stock ownership is the only compensation of risk

710 A. Andrikopoulos / Journal of Bankingaverse managers which face costly effort, the capital-structurechoice would depend on the managers efciency, momentum aswell as company size. Grenadier and Wang (2005) revisited thequestion of investment timing for an option to invest, in the con-text of ownermanager contracts in an all-equity rm. In theiragency-theoretic contribution to the problem of optimal invest-ment timing, they explored the issue of asymmetric informationand costly effort. Decomposing the option to invest into a man-agers option and an owners option, they found that both underin-vestment and overinvestment can hold in equilibrium. Mauer andSarkar (2005) examined the effect of the conict between share-holders and creditors on capital structure and on investment tim-ing. Based on the tax-deductibility of interest income, they foundthat the shareholders choice of investment and nancing will gen-erate deviations from value maximization and will create agencyconicts and costs. In their model, the shareholders incentive tooverinvest imposes agency costs on yield spreads and the resultingcost of capital determines nancing as well as investmentdecisions.

Making a contribution to the ongoing debate on the interactionbetween investment timing and capital structure, this paper ismotivated by empirical ndings that the ownercreditor agencyconict alone cannot explain the observed variations in deviationsfrom value-maximizing investment (Parrino and Weisbach, 1999)and that managerial compensation is signicant in determiningcapital structure (e.g. Smith and Watts, 1992) as well as corporatevalue (e.g. Coles et al., 2001). We explore over-and-under invest-ment with respect to the managers compensation and interactionswith corporate investors, in the framework of a levered rm.Investment timing, real option value, optimal capital structureand agency costs of debt are estimated for various structures ofmanagers compensation and reservation income. For the purposesof our analysis on investment timing, we employ the investmentnancing setting of Mauer and Sarkar (2005), where corporatedecision makers decide on investment timing and optimal capitalstructure, which is implemented at the moment when the projectstarts. Section 2 lays out our real-options framework, Section 3analyzes some analytical and numerical results and Section 4 con-cludes the paper, indicating directions for future research.

2. An investment setting

We explore the case of a rm that has a monopolistic, perpetualright to implement an investment project. The projects cost is I.The decision to invest is made by the rms manager.1 The man-agers compensation consists of an equity stake a on the rm anda xed salary Cp which is collected per unit of time.2 In order for

1 In this approach, implicit is the assumption that the shareholders cannot managethe operations of theproject themselves and this is why the manager is hired. Thisassumption matters in the discussion ofthe managers deviations from equitymaximizing investment in Section 3: the shareholders are worseoff in the sense thatinvestment and nancing choices are not aligned with their objectives but, ontheother hand, running the project on their own is more inefcient (e.g. substantialdecline in operatingprotability).

2 One could argue here that the managers compensation is taxed. Imposing a

personal tax rate wouldnot change our conclusions on investment timing and capitalstructure. Alternatively, one could thinkof Cp as the after-tax managers income fromsalary.the project to start, the manager will have to give up previousemployment that yields income PI. The rms income from projectsoperations is taxed at a tax rate sc. Projects operations generate sto-chastic revenue P and incur a xed cost C per unit of time. The man-agers salary is part of the xed cost, hence we must have C > Cp. Wealso assume that the dynamics of P can be replicated by forming aportfolio of traded assets in a risk neutral, no-arbitrage economyand satisfy the following stochastic differential equation

dP r dPdt rPdz; 1where r is a risk free interest rate, r is the standard deviation of an-nual returns on a portfolio that perfectly replicates the dynamics ofP, d is a convenience yield that can be earned by holding the produc-tion output in inventory, dt is an increment of time and dz is theincrement of a Wieners process. When the option to invest is exer-cised, the capital-structure choice is implemented and the invest-ment project could be partly nanced with a debt contract, inwhich case the amount of debt nancing is K and the shareholderscontribute the rest I K. This nancing arrangement can happen inthe setting of a line-of-credit contract (or a loan commitment), inwhich external funds are committed up to a contractually speci-ed amount to be available in a future point in time for the rmsneeds. The amount of debt nancing K is determined in a contractsigned by the manager and the creditor. If debt nancing is pro-vided, the rm faces a xed coupon payment R per unit of time. Pro-ject abandonment and bankruptcy are decided upon by themanager. Should the rm go bankrupt, the creditor will take overthe rms assets, suffering bankruptcy costs b (0 < b < 1). In theevent of bankruptcy, the manager will nd employment in anotherjob that yields an income of RI that can be considered as a kind ofreservation income.

2.1. Solving for the unlevered asset value

After the project has started, the operational exibility that isavailable to the managers discretion consists of the option to shutdown the project. In this all-equity case, well-known portfolio rep-lication arguments can be used to show that the managers wealthMU(P) satises

0:5r2P2MUPP r dPMUP rMU aP C1 sc Cp 0: 2The general solution of (2) is of the form

MuP a Pd C

r

1 sc Cpr A1P

b1 A2Pb2 for P > PUA ; 3

where A1 and A2 are constants to be determined and PUA is the opti-

mal abandonment level, maximizing the managers wealth. Thesolution to the homogeneous part of the equation yields

b1 12 r d

r2

r dr2

12

2 2rr2

> 1

sand

b2 12 r d

r2

r dr2

12

2 2rr2

s< 0:

Since the abandonment option is decreasing in P, we needA1 = 0.

The equation for the value of managers wealth in the case ofthe unlevered rm is subject to the following boundary conditions.

limP!1

MUP a Pd C

r

1 sc Cpr 4:1

MUPUA RI and 4:2U

& Finance 33 (2009) 709718@M@P

PPUA

0 4:3

MLP a Pd C R

r

1 sc

Cpr a P

LD

d C R

r

!1 sc Cpr RI

!P

PL

!b212

king & Finance 33 (2009) 709718 711Applying (4.1)(4.3), (4.1), we get

MUP a Pd C

r

1 sc

Cpr a P

UA

d C

r

" #1 sc Cpr RI

!P

PUA

!b2; 5

where

PUA db2a Cr 1 sc Cpr RI

a1 sc1 b2:

As for the shareholders, the value of the unlevered rm VU(P) satis-es the following partial differential equation

0:5r2P2VUPP r dPVUP rVU P C1 sc 0 for P > PUA6

subject to the boundary conditions

limP!1

VUP Pd C

r

1 sc 7:1

and

VUPUA 0: 7:2The solution of (6) yields

VUP Pd C

r

1 sc P

UA

d C

r

!P

PUA

!b21 sc 8

the abandonment trigger PUA being known from the solution to themanagerial wealth problem. These differences in the operatingchoices of corporate decision makers and residual claimants seenhere in the case of default and investment triggers create the needfor an effective system of corporate control (Fama and Jensen,1983).

This valuation result will be needed to calculate the asset valueaccruing to the creditor in the event of default.

2.2. Calculating managerial wealth in a levered rm

In the case of a levered rm, the value of managers wealthML(P) satises

0:5r2P2MLPP r dPMLP rML aP C R1 sc Cp 0:9

The general solution of (9) is of the form

MLP a Pd C R

r

1 sc Cpr A3P

b1 A4Pb2 for P > PLD;

10where A3 and A4 are constants to be determined and P

LD is the opti-

mal default trigger, as seen from the managers point of view.Since the abandonment option is decreasing in P, we need

A3 = 0. The equation for the value of managerial wealth in the caseof the unlevered rm is subject to the following boundaryconditions.

limP!1

MLP a Pd C R

r

1 sc Cpr 11:1

MLPLD RI and 11:2@ML

@P

0 11:3

A. Andrikopoulos / Journal of BanPPLD

If we apply (11.1), (11.2) and (11.3) to (10) we getD

and

PLD db2 a CRr 1 sc Cpr RI

a1 sc1 b2:

As for the shareholder, the value of equity EL(P) satises the follow-ing partial differential equation

0:5r2P2ELPP r dPELP rEL P C R1 sc 0 13subject to the boundary conditions

limP!1

ELP a Pd C R

r

1 sc Cpr and 14:1

ELPLD 0: 14:2The solution yields

ELP Pd C R

r

1 sc P

LD

d C R

r

!P

PLD

!b21 sc:

15PLD being known from the solution to the managerial wealthproblem.

Following e.g. Leland (1994), the value of debt D(P) after theexercise of the investment option, is given by

DP Rr A5Pb1 A6Pb2 16

and constants A5 and A6 are determined by the boundary conditions

limP!1

DP Rrand 17:1

DPLD 1 bVUPLD: 17:2Implicit in (17.2) is the assumption that, if the rm goes bankruptand the creditor becomes the sole owner, the creditor will hire amanager to run the then unlevered rm and the manager will ofsimilar type as the one we have discussed so far. This can be a legit-imate assumption since it is more efcient for the new owners tocontinue operating the project with managers that have morerm-specic knowledge and value (Douglas, 2001). Substitutingfor (17.1) and (17.2) in (16) yields

DP Rr 1 bVUPLD

Rr

P

PLD

!b2: 18

Summing debt and equity and rearranging the components of thevalue of the levered rm yields

VLP VUP scRr

1 P

PLD

!b20@1A bVUPLD PPLD

!b2: 19

(19) demonstrates that the value of levered rm is equal to thesum of the value of unlevered rm and the tax benets of debtminus the value of bankruptcy costs.3

3 The effect of the tax advantages of debt and of the bankruptcy costs on the choiceof capital structurehas recently been conrmed in a survey on the decision-making

criteria of European CFOs (Brounen et al., 2006) as well as in empirical work oninternational evidence on the capital structure choice (de Jong et al., 2008; Wu andYue, 2009).

(26). We dene agency costs of debt as

king2.3. Pricing the option to invest

The manager has the right to choose the time of project imple-mentation. Upon exercise of this real option, the manager will startreceiving salary Cp, he will pay a fraction a of the equitys contribu-tion to investment cost (since he is rewarded with this portion ofthe rms equity) but he will also have to part with his previous in-come PI, which could be taken to be the present value of a perpet-ual stream of salary payments that come from competingprofessional engagements, even within the same rm.

Let PM be the exercise trigger for the investment option and Kthe amount of debt nancing. The value of the managers exibilityM before the option is exercised satises

12r2P2MPP r drPMP rM 0; P < PM: 20

The solution of (20) is of the form

MP A7Pb1 A8Pb2 ; P < PM; 21

where constants A7 and A8 are determined with the boundaryconditions

MPM MLPM aI K PI 22:1and

@M@P

PPM

@ML

@P

PPM

22:2

can be used to numerically solve for PM.Upon exercise, the creditors will be willing to supply capital

only equal to the equilibrium value of debt under an investmentpolicy that maximizes the managers wealth. Therefore, at exercise,we will have K = D(PM). Yield spreads are dened as the differencebetween the effective rate that is charged on corporate debt RDP andthe risk free rate of interest r. We introduce yield spreads in ouranalysis of managerial compensation and capital structure basedon the theoretical prediction of John and John (1993) that yieldspreads are expected to be increasing in managerial ownership,since managerial ownership affects the outcome of agency con-icts and may lead to deviations from value and equitymaximization.

Let FM be the value of the option to invest as a rms asset, if theinvestment policy aims at maximizing managerial wealth. FM canbe calculated if we measure the value of M with Cp, RI, PI equalto zero and a equal to 1, maintaining however, PM as an investmenttrigger. If we set Cp, RI, PI equal to zero and a equal to 1 and furtheruse this parameter set to estimate an investment trigger we cannd an equity-maximizing investment trigger PE.

In the same vein, we can calculate the value of the option to in-vest under a policy that aims at maximizing the value of all in-volved stakeholders: debt, equity and managerial wealth. Totalvalue is given by

TVLTVL D 1 aEL ML: 23

Since the managers wealth ML includes a portion a of equityownership, we have to subtract aEL, in order to avoid a double cal-culation of this part of equity value. Accordingly, total investmentcost includes not only I, but also PI, which is the income that themanager foregoes in order to get involved in the project.

In this rst-best case the option to invest satises

1 2 2 F

712 A. Andrikopoulos / Journal of Ban2r P FPP r drPFP rF 0; P < P : 24

PF being a rst-best, value-maximizing investment trigger.ACM FPF FMPMFPF : 28

As a benchmark, we can calculate agency costs of debt in thecase of an equity-maximizing investment, abandonment andnancing policy. Agency costs of debt due to equity maximizationare thus dened as

ACE FPF FEPEFPF ; 29

where FE is the value of the option to invest in the setting of an equi-ty-maximizing investment policy.

Numerical results in the following discussion on investmenttiming can help discuss investment timing and capital structureas outcomes of the decision makers employment conditions: highsalary, low salary and large ownership stake.

3. Numerical results

In this section we discuss the effect of the managers reservationincome, salary and ownership stake on investment timing, optimalcapital structure, yield spreads and agency costs of debt. Numericalresults on the effect of the other parameters interest rate, bank-ruptcy costs, volatility, etc. can be found in previous work on realoptions and capital structure (e.g. Leland, 1998; Mauer and Ott,2000). Without any loss of generality, we will assume that RI PI,that is the income themanagerwill have to forego, should he decideto implement the project, is the same as his reservation income.

Throughout the numerical analysis of this section we employthe same reference set of parameters: P = $1, R = $0.8, C = $0.75,RI = $1, Cp = $0.04, I = $3, r = 0.05, d = 0.02, a = 0.03, b = 0.35,sc = 0.2, r = 0.3.

3.1. Investment timing and capital structure: The effect of managerialcompensation

We explore the effect of the parameters which are related to themanagers compensation (reservation income, salary and owner-ship share) on investment timing and capital structure. It is the ex-tent of deviation from value-maximizing investment which affectsthe size of the yield spread imposed by the creditor and it is thiscost of debt that affects the managers choice over coupon sizeand capital structure.

3.1.1. Managerial compensation and the interaction betweeninvestment and nancing decisions: Managers reservation incomewhere constants A9 and A10 are calculated with the boundaryconditions

FPF TVLPF I PI 26and

@F@P

PPF

@VL

@P

PPF

27

TV given in (23). (27) can be used to numerically solve for theinvestment trigger PF, in the value-maximizing setting of (25) andThe solution of (24) is of the form

FP A9Pb1 A10Pb2 ; P < PF ; 25

& Finance 33 (2009) 709718The managers reservation income affects the managers invest-ment and nancing decisions and therefore affects the value of thereal option to invest and the magnitude of the yield spread on

0.85

Option value to the manager vs coupon payment for varying reservation income

0.6 0.7 0.8 0.9 1 1.1 1.2 1.30.5

1

1.5

2

Reservation income

Inve

stm

e FB

EB

Fig. 1b. Sensitivity of investment trigger to the managers reservation income. Theinvestment trigger is chosen so as to maximize the value of the managers option toinvest (MB). The dashed line is the rst-best investment trigger (FB) whichmaximizes value for all parties (shareholder, creditor and manager) and the dottedline is the investment trigger in an operating policy which maximizes equity value(EB). Output price (P) is $1, coupon payment (R) is $0.8, operating cost (C) is $0.75,managers salary (Cp) is $0.04, project cost (I) is 3$, risk free rate of interest (r) is0.05, dividend yield (d) is 0.02, managers ownership share (a) is 0.03, bankruptcycosts (b) are 0.35, tax rate for corporate income (sc) is 0.2 and standard deviation ofannual returns (r) is 0.3.

120

130

140

150

160

spre

ad

Yield spread vs Reservation income

A. Andrikopoulos / Journal of Banking & Finance 33 (2009) 709718 713corporate debt. Our numerical solutions can be synopsized in thefollowing result:

Result 1: The managers reservation income has a positive effecton the level of the investment trigger and it has a negative effect onthe value of the managers real option to invest as well as on thelevel of the yield spread.

The value of the managers option to invest and the subsequentvalue of managerial wealth after the real option has been exercisedare decreasing in the managers reservation income (Fig. 1a); high-er levels of reservation income essentially delay investment andprecipitate default thus reducing the prospective value of income

0 0.5 1 1.5 2 2.5 30.5

0.55

0.6

0.65

0.7

0.75

0.8

Coupon

Opt

ion

valu

e to

the

man

ager

RI=1

RI=1.1RI=1.2

Fig. 1a. Sensitivity of option value to coupon payments, for varying levels of themanagers reservation income. Output price (P) is $1, operating cost (C) is $0.75,managers salary (Cp) is $0.04, project cost (I) is $3, risk free rate of interest (r) is0.05, dividend yield (d) is 0.02, managers ownership share (a) is 0.03, bankruptcycosts are 0.35 (b), tax rate for corporate income (sc) is 0.2, and standard deviation ofannual returns (r) is 0.3.out of project implementation.4

The effect of the reservation income on the managers option toinvest stems from the impact of reservation income on investmenttiming and the capital-structure choice. If the reservation income isvery low, the manager will be very eager to start the project in or-der to earn the salary and benet from the tax shield of debt, thusending up to overinvest, compared to both the rst-best (FB) andthe equity-maximizing (EB) investment policies (Fig. 1b). On theother end, if the managers reservation income is high, he willnot start the project until protability is high enough to compen-sate him for the sacrice of the reservation income, thus resultingin an exercise policy of underinvestment. For intermediate levels ofreservation income RI ranging from $0.8 to $0.92 the managerwill have an incentive to overinvest with respect to the FB policyand underinvest with respect to the EB policy.

Deviations from value-maximizing investment -project startand termination- have their impact on the yield spreads. The man-agers reservation income has a decreasing effect on yield spreads(Fig. 1c); High levels of reservation income weaken the managersequity-driven incentive to overinvest and this effect outweighs themanagers motive for early default. These conditions make thecreditors decrease yield spreads and hence the cost of debt. Loweryield spreads -associated with higher reservation income- will in-

4 Differentiating the default trigger can show that the effect of managerialcompensation on the level ofthe default trigger is similar in spirit to the effects oninvestment timing; high salary makes projectrelatedemployment more attractive anddelays default, whereas high reservation income makesalternative employmentopportunities more attractive and thus precipitates default.2.5

3

3.5

nt tr

igge

r MB

Investment trigger vs Reservation incomecrease the level of the optimal coupon payment as well as the opti-mal leverage ratio5, since debt is cheaper and also because increasedtax shields are required to induce the manager to give up his reser-vation income and start the project. As far as I know, there has beenno previous research to associate the managers income from alter-native employment opportunities with the capital-structure ques-tion in a dynamic setting of irreversible investment.

0.8 0.9 1 1.1 1.2 1.370

80

90

100

110

Reservation income

Yiel

d

Fig. 1c. Sensitivity of the yield spread to the managers reservation income. Yieldspread is dened as the difference between the effective rate on corporate debt andthe risk free rate (r). The effective rate is calculated as the ratio of coupon R to debtvalue D(P). The spread is measured in basis points. Output price (P) is $1, couponpayment (R) is $0.8, operating cost (C) is $0.75, managers salary (Cp) is $0.04,project cost (I) is $3, risk free rate of interest (r) is 0.05, dividend yield (d) is 0.02,managers ownership share (a) is 0.03, bankruptcy costs (b) are 0.35, tax rate forcorporate income (sc) is 0.2 and the standard deviation of annual returns (r) is 0.3.

5 We dene the optimal leverage ratio as the prevailing leverage ratio when thecoupon payment is at its optimal level.

In the case of our numerical example (Fig. 1b), the optimal sizeof the coupon ranges from $1.02 for the RI = $1 case to $1.29 for theRI = $1.2 case. However, due to the fact that optimal coupon pay-ment increases with the reservation income, the decline in optionvalue starts at lower coupon levels in the case of low reservationincomes and this is the reason that after the optimal coupon pay-ment has been reached and before option exercise option valuefor low reservation income can briey be less than option valuefor options with higher reservation income. For our parameterset, option should be immediately exercised for coupon values onthe right of the kink in the coupon-option graph. After the optionto invest has been exercised, we are essentially addressing an issueof the effect of coupon payments on managers wealth when he isin charge of an ongoing project and the negative association be-tween reservation income and the value of the managerial optionstill holds for the reasons discussed above.

In the setting of our numerical example, we observe that, as weexpected, optimal leverage is increasing in the managers reserva-tion income; optimal leverage ratio is 0.43 for R = $1 and it in-creases to 0.52 for R = $1.2. It is the lower yield spreads for highlevels of reservation income that make increased leverage moreattractive in the case of higher reservation income.

option at a lower level of P (Fig. 2b). For low salary levels, themanager does not want to give up his reservation income andget involved in the project, thus leading to phenomena of underin-vestment with respect to both FB and EB policies.

Associated with the managers motive to overinvest, the effectof the managers salary on the yield spreads is positive. An in-creased salary will strengthen the managers incentive to overin-vest so as to start getting paid and will also make him want to(suboptimally) keep the project alive for as long as possible, so asto maintain the xed income ow. This overinvestment motiveleads to high spreads in the cases of high salaries (Fig. 2c). Highercosts of debt for higher levels of salary mean that, as the managerssalary increases, the optimal coupon size and the optimal leverageratio decrease; optimal coupon size is $1.29 and optimal leverageis 0.52 for a salary of $0.03, while optimal coupon size is $0.75and optimal leverage is 0.27 for a salary of $0.05).

Our result on the effect of managers salary on investment tim-ing and capital structure extends the discussion in Mauer and Sar-kar (2005) on the determinants of investment and nancingdecisions in a real-options framework.

3.1.3. Managerial compensation and the interaction betweeninvestment and nancing decisions: Managers ownership stake

Managerial ownership has often been employed as a contrac-tual mechanism in the direction of aligning the objectives of themanagers with the ones of the owners. The following result sum-

714 A. Andrikopoulos / Journal of Banking & Finance 33 (2009) 7097183.1.2. Managerial compensation and the interaction betweeninvestment and nancing decisions: Managers salary

Having examined the impact of the managers reservation in-come on investment timing and the capital-structure choice, weproceed to explore the effect of the managers compensation con-tract that consists of salary and a share of equity ownership. Ournumerical examination of the effect of the managers salary onthe interaction between investment and nancing decisions hasyielded the following result.

Result 2: The managers salary has a negative effect on the levelof the investment trigger and it has a positive effect on the value ofthe managers real option to invest as well as on the level of theyield spread.

High levels of salary naturally make the managers option worthmore and also increase managerial wealth in the case of managingan ongoing levered company after the project has started (Fig. 2a).Furthermore, the higher the managers salary, the stronger themanagers motive to start the project and hence to exercise the real

0 0. 5 1 1. 5 2 2. 5 30. 5

0. 55

0. 6

0. 65

0. 7

0. 75

0. 8

0. 85

0. 9

Coupon

Opt

ion

valu

e to

the

man

ager

Cp =0 .0 5

Cp =0 .0 4

Cp =0 .0 3

Option value to the manager vs coupon payment for varying manager's salary

Fig. 2a. Sensitivity of option value to coupon payments, for varying managerssalary. Output price (P) is $1, operating cost (C) is $0.75, managers reservationincome (RI) is $1, project cost (I) is $3, risk free rate of interest (r) is 0.05, dividend

yield (d) is 0.02, managers ownership share (a) is 0.03, bankruptcy costs are 0.35(b), tax rate for corporate income (sc) is 0.2 and standard deviation of annual returns(r) is 0.3.marizes the ndings of our analysis on effect of managerial owner-ship on the managers choice over investment timing and capitalstructure.

Result 3: The managers ownership share has a negative effecton the level of the investment trigger and it has a positive effecton the value of the managers real option to invest as well as onthe level of the yield spread.

The effect of the managers ownership share on the value of hisoption to start a project is, of course, positive (Fig. 3a). The higherthe compensation involved in running the project, the more valu-able will the option be and the more valuable his wealth will be

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.060.5

1

1.5

2

2.5

3

3.5

Manager's salary

Inve

stm

ent t

rigge

r

MB

FB

EB

Investment trigger vs Manager's salary

Fig. 2b. Sensitivity of investment trigger to the managers salary. The investmenttrigger is chosen so as to maximize the value of the managers option to invest (MB).The dashed line is the rst-best investment trigger (FB) which maximizes value forall parties (shareholder, creditor and manager) and the dotted line is the investmenttrigger in an operating policy which maximizes equity value (EB). Output price (P) is$1, coupon payment (R) is $0.8, operating cost (C) is $0.75, managers reservationincome (RI) is $1, project cost (I) is 3$, risk free rate of interest (r) is 0.05, dividend

yield (d) is 0.02, managers ownership share (a) is 0.03, bankruptcy costs (b) are0.35, tax rate for corporate income (sc) is 0.2 and standard deviation of annualreturns (r) is 0.3.

deviations from equity-maximizing and also from value-maximiz-ing investment is in line with the intuition of John and John (1993)that managerial ownership affects the agency costs of both equityand debt. It is interesting that, for high levels of a, additional own-ership does not offer improved alignment with equity-maximizinginvestment policies. This is a result of the fact that for high levels ofmanagerial ownership, the sensitivity of the investment trigger tothe managers salary and reservation income weakens and thedeviations from equity-maximization cannot be further restrainedby granting the managers an additional stake of corporate owner-ship. The weak sensitivity of the investment trigger with respect tomanagerial ownership agrees with empirical evidence in Singh andDavidson (2003) that increased managerial ownership cannoteliminate managerial motives to exercise discretion and deviatefrom equity maximization.

Fig. 3c shows that the higher the managers stake on equityownership, the higher the yield spread will be. This is becausethe higher the managers equity stake, the stronger the tendencyof the manager to abide by an equity-maximizing policy callingfor overinvestment and late default in order to rip off the taxshields of debt. Therefore, in the case of increased managerial own-ership, the increased risk of debt contracts can lead to an increasedyield spread. This result is in accordance with the theoretical pre-diction of John and John (1993) as well as the empirical evidence ofStrock Bagnani et al. (1994) and Dadyvenko and Strebulaev (2007)that yield spreads should be increasing in the ownership compo-nent of managerial compensation.

0.02 0.025 0.03 0.035 0.04 0.045 0.0570

80

90

100

110

120

130

140

150

160

Manager's salary

Yiel

d sp

read

Yiled spread vs Manager's Salary

Fig. 2c. Sensitivity of the yield spread to the managers salary. Yield spread isdened as the difference between the effective rate on corporate debt and the riskfree rate (r). The effective rate is calculated as the ratio of coupon R to debt valueD(P). The spread is measured in basis points. Output price (P) is $1, coupon payment(R) is $0.8, operating cost (C) is $0.75, managers reservation income (RI) is $1,project cost (I) is $3, risk free rate of interest (r) is 0.05, dividend yield (d) is 0.02,managers ownership share (a) is 0.03, bankruptcy costs (b) are 0.35, tax rate for

A. Andrikopoulos / Journal of Banking & Finance 33 (2009) 709718 715after the exercise of the investment option (on the right of thekink).

The level of the investment exercise trigger is decreasing in thelevel of the managers ownership share; for low levels of manage-rial ownership share, the manager is less eager to leave his previ-ous (reservation) income in order to start the project and gain asmall portion of corporate prots and tax shields and thereforehe tends to underinvest, compared to both the rst-best invest-ment trigger and the equity-maximizing investment policy. Forsufciently high levels of ownership share, he is more willing topart with his reservation income and benet from the tax shields

corporate income (sc) is 0.2 and the standard deviation of annual returns (r) is 0.3.of debt and this is why he will end up overinvesting (Fig. 3b).Our nding that managerial ownership can be associated with

0 0.5 1 1.5 2 2.5 3

0.8

1

1.2

1.4

1.6

1.8

2

Coupon

Opt

ion

valu

e to

the

man

ager

a=0.7

a=0.5

a=0.3

Option value to the manager vs coupon payment for varying ownership shares

Fig. 3a. Sensitivity of option value to coupon payments, for varying managersownership share. Output price (P) is $1, operating cost (C) is $0.75, managers salary(Cp) is $0.04, managers reservation income (RI) is $1, project cost (I) is $3, risk freerate of interest (r) is 0.05, dividend yield (d) is 0.02, bankruptcy costs are 0.35 (b),tax rate for corporate income (sc) is 0.2 and standard deviation of annual returns (r)is 0.3.The positive effect of managerial ownership on yield spreadsand hence on the cost of debt means that higher levels of manage-rial ownership will be associated with lower levels of optimal cou-pon payment and also with lower optimal leverage ratios; as themanagers ownership stake increases, the size of the optimal cou-pon decreases from $1.02 for a = 0.03 to $0.87 for a = 0.07. For thisparameter range, the optimal leverage ratio falls from 0.43 to 0.27because the equity-driven incentive to overinvest leads to in-creased yield spreads and therefore to a lower optimal coupon

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.4

1.6

1.8

2

2.2

2.4

2.6

Manager's ownership share

Inve

stm

ent t

rigge

r

MB

FB

EB

Investment trigger vs Manager's ownership share

Fig. 3b. Sensitivity of investment trigger to the managers ownership share. Theinvestment trigger is chosen so as to maximize the value of the managers option toinvest (MB). The dashed line is the rst-best investment trigger (FB) whichmaximizes value for all parties (shareholder, creditor and manager) and the dottedline is the investment trigger in an operating policy which maximizes equity value(EB). Output price (P) is $1, coupon payment (R) is $0.8, operating cost (C) is $0.75,managers reservation income (RI) is $1, managers salary (Cp) is $0.04, project cost

(I) is 3$, risk free rate of interest (r) is 0.05, dividend yield (d) is 0.02, bankruptcycosts (b) are 0.35, tax rate for corporate income (sc) is 0.2 and standard deviation ofannual returns (r) is 0.3.

tion income in the case of default. As salary increases, these agency

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Reservation income

Agen

cy c

osts

of d

ebt AC M

AC E

Agency costs of debt vs Reservation income

Fig. 4a. Sensitivity of agency costs of debt to the managers reservation income.Agency costs of debt (ACM) are dened as the percentage difference between optionvalue under a nancinginvestment policy that maximizes managerial wealth andone that maximizes value for all parties (shareholder, creditor and the manager).The ACE line plots agency costs of debt in an equity-maximizing investmentnancing policy. Output price (P) is $1, coupon payment (R) is $0.8, operating cost(C) is $0.75, managers salary (Cp) is $0.05, project cost (I) is $3, risk free rate ofinterest is (r) 0.05, dividend yield (d) is 0.02, managers ownership share (a) is 0.03,bankruptcy costs (b) are 0.35, tax rate for corporate income (sc) is 0.2 and standarddeviation of annual returns (r) is 0.3.

king & Finance 33 (2009) 709718and leverage ratio. This result is in accordance with ndings in Jen-sen et al. (1992) that higher insider ownership is associated withlower levels of debt.

3.2. The effect of managerial compensation on agency costs of debt

Agency costs of debt were dened in (28) as the percentage dif-ference of option value under an investment policy that maximizestotal value (i.e. equity, debt, managerial wealth) and option valueunder an investment policy that aims at maximizing managerial

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5120

125

130

135

140

145

150

155

Manager's ownership share

Yiel

d sp

read

Yield spread vs Manager's ownership share

Fig. 3c. Sensitivity of the yield spread to the managers ownership share. Yieldspread is dened as the difference between the effective rate on corporate debt andthe risk free rate (r). The effective rate is calculated as the ratio of coupon R to debtvalue D(P). The spread is measured in basis points. Output price (P) is $1, couponpayment (R) is $0.8, operating cost (C) is $0.75, managers reservation income (RI) is$1, managers salary (Cp) is $0.04, project cost (I) is $3, risk free rate of interest (r) is0.05, dividend yield (d) is 0.02, bankruptcy costs (b) are 0.35, tax rate for corporateincome (sc) is 0.2 and the standard deviation of annual returns (r) is 0.3.

716 A. Andrikopoulos / Journal of Banwealth. Our numerical solutions on the effect of managerial com-pensation on agency costs have produced the following nding.

Result 4: There is an U-shaped relationship between agencycosts of debt and the managerial compensation parameters: themanagers reservation income, salary and ownership share.

We see in Fig. 4a that there exists an U-shaped pattern with re-spect to the effect of the managers reservation income to theagency costs of debt. For very low values of reservation incomethere is a strong incentive to overinvest and this leads to deviationsfrom value maximization. As the reservation income increases,overinvestment incentives weaken and agency costs of debt de-crease. However, beyond a point, high values of reservation incomedecrease the attractiveness of project-related compensation to themanager and thus he tends to underinvest and underinvestmentleads to increased agency costs of debt. The ACE line in Fig. 4ashows agency costs of debt under an equity-maximizing setting,as dened in (28). We see that the agency costs of debt are lowerunder the equity-maximizing investment and nancing policies,in cases reservation income is too low (worse managerial overin-vestment) or too high (worse managerial underinvestment). Forintermediate values of reservation income, we see that the agencycosts of debt under an equity-maximizing policy are higher thanunder a policy that maximizes managerial wealth. This means thatthe creation of an agency conict generates an outcome that is clo-ser to the rst-best value maximization under the managers thanunder the shareholders wealth maximization. This result can beconsidered as an extension of the intuition of Brander and Poitevin(1992) and John and John (1993), in the direction of dynamicinvestment choice.We now proceed to discuss the effect of managers salary on theagency costs of debt (Fig. 4b). We see that there exists a U-shapedrelationship between managerial salary and the agency costs ofdebt. For very low salary levels the manager will tend to underin-vest because he will not have sufcient motivation to part withthe reservation income and default too early because the lowerthe managers salary the greater the attractiveness of the reserva-0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.0550

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Manager's salary

Agen

cy c

osts

of d

ebt

ACE

ACM

Agency costs of debt vs manager's salary

Fig. 4b. Sensitivity of agency costs of debt to the managers salary. Agency costs ofdebt (ACM) are dened as the percentage difference between option value under anancinginvestment policy that maximizes managerial wealth and one thatmaximizes value for all parties (shareholder, creditor and the manager). The ACEline plots agency costs of debt in an equity-maximizing investmentnancingpolicy. Output price (P) is $1, coupon payment (R) is $0.8, operating cost (C) is $0.75,managers reservation income (RI) is $1, project cost (I) is $3, risk free rate ofinterest is (r) 0.05, dividend yield (d) is 0.02, managers ownership share (a) is 0.03,bankruptcy costs (b) are 0.35, tax rate for corporate income (sc) is 0.2 and standarddeviation of annual returns (r) is 0.3.

effects weaken and the managers policy approaches value-maxi-mization choices. Beyond a certain point of salary increase how-ever, the manager will have an incentive to invest too early so asto earn the high salary and will also have the incentive to defaulttoo late so as not to give up the substantial salary income. Thesemanagerial incentives cause the agency costs of debt to increasein the case of high salary compensations. Between these two ex-treme cases, agency costs of debt in an equity-maximizing regimeare higher, compared to agency costs of debt under a policy thatmaximizes managerial wealth.

Agency costs of debt have a U-shaped relationship with themanagers ownership stake. For low levels of managerial owner-ship, the manager will underinvest since compensation from theproject may be less attractive compared to the reservation income.This underinvestment motive weakens as the managers owner-ship stake increases, shortening the deviations from a value-max-imizing investment policy. However, beyond a point, increasedownership renders the project increasingly attractive, leading tooverinvestment and an increase in deviations from value-maximiz-ing policies. We observe in Fig. 4c that agency costs of debt under apolicy that maximizes managerial wealth (ACM) are lower thanagency costs of debt in a setting of equity maximization (ACE). Thisis because the overinvestment incentives of the shareholders arepartly offset by the effects of the managers reservation income.This effect of managerial ownership on the agency costs of debtis more prevalent when managerial ownership is at low levels.

pected wealth. Assuming a reference level of managerial wealth(real option value) of $1.2 as a working example, Fig. 4d demon-strates the family of contracts yielding the same level of expectedwealth for the manager. As expected, there is a tradeoff betweensalary and stock ownership along the compensation contracts thatyield the same expected wealth of $1.2 to the manager. If the man-ager is rewarded with higher levels of stock ownership, there hasto be a decrease in the salary in order to keep the managers wealthat the same level. Furthermore, we see in Fig. 4d that increased lev-els of the managers reservation income warrant increased com-pensation in the employment contract of the project for the samelevel of expected managerial wealth. As we saw in Fig. 1a, higherlevels of reservation income decrease expected managerial wealthfrom the project (i.e. the managers real option). Therefore, as thereservation income increases, we must also increase managerialcompensation in order to achieve the same level of expected man-agerial wealth. Observing the wide range of contracts that corre-sponds to a given level of managerial wealth, welfareconsiderations raise the question of an optimal contract; one thatmakes it incentive compatible for the manager to implement theinvestment policy that maximizes total value. If we solve numeri-cally for the optimal contract, we nd that a contract that grantsthe manager with a salary of $0.041 and an ownership stake of0.044, is consistent with both the benchmark level of $1.2 of ex-pected managerial wealth and also value maximization as it in-duces rst-best investment timing.

A. Andrikopoulos / Journal of Banking & Finance 33 (2009) 709718 717When the managers stake on equity capital is large, we have seen,in Section 3.1, that the marginal effect of managerial ownership onthe decisions to invest and default is rather small. As a result ofthis, when managerial ownership is large, the agency costs of debtwill not be substantially affected by the extent of managerialownership.

Deviations from value maximization are a result of the debt andemployment contracts. Given that the employment contract deter-mines managerial wealth taking into account both salary and stockownership for a given reservation income there is a plethora ofcontracts that will provide the manager with the same level of ex-

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.005

0.01

0.015

Manager's ownership share

Agen

cy c

osts

of d

ebt

ACE

ACM

Agency costs of debt Manager's ownership share

Fig. 4c. Sensitivity of agency costs of debt to the managers ownership share.Agency costs of debt (ACM) are dened as the percentage difference between optionvalue under a nancinginvestment policy that maximizes managerial wealth andone that maximizes value for all parties (shareholder, creditor and the manager).The ACE line plots agency costs of debt in an equity-maximizing investmentnancing policy. Output price (P) is $1, coupon payment (R) is $0.8, operating cost(C) is $0.75, managers salary (Cp) is $0.05, managers reservation income (RI) is $1,

project cost (I) is $3, risk free rate of interest is (r) 0.05, dividend yield (d) is 0.02,bankruptcy costs (b) are 0.35, tax rate for corporate income (sc) is 0.2 and standarddeviation of annual returns (r) is 0.3.All these contracts that yield the same level of managerialwealth correspond to varying operating policies and hence to vary-ing levels of yield spread. Fig. 4e shows how the dependence of themanagers salary on the ownership stake in the setting of the $1.2benchmark level of managerial wealth affects the level of theinvestment trigger. The investment trigger increases along thisfamily of employment contracts. As we increase managerial own-ership, the investment trigger is affected by two contrasting ef-fects. Increased stock ownership induces overinvestment butdecreased salary depicted in Fig. 4d provides a motive forunderinvestment and the latter effect prevails, leading to the

0.03 0.035 0.04 0.045 0.05 0.0550

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Manager's ownership share

Man

ager

's s

alar

y

RI=1 RI=1.1

Employment contracts that yield the same level of managerial wealth

Fig. 4d. Family of contracts that yield the same expected wealth to the manager, forvarying levels of reservation income (RI). For each value of the stock-ownershipparameter a in the horizontal axis, we nd the respective level of the managerssalary that yields an expected level of managerial wealth equal to $1.2. Output price(P) is $1, coupon payment (R) is $0.8, operating cost (C) is $0.75, project cost (I) is $3,

risk free rate of interest is (r) 0.05, dividend yield (d) is 0.02, bankruptcy costs (b) are0.35, tax rate for corporate income (sc) is 0.2 and standard deviation of annualreturns (r) is 0.3.

Investment trigger vs Managerial compensation (for a given level of managerial wealth)

718 A. Andrikopoulos / Journal of Banking & Finance 33 (2009) 7097184. Concluding comments

Introducing ownermanager conicts to the agency-theoreticupward sloping line of Fig. 4e. It is the investment timing of Fig. 4eand the respective default policies that affect rm value and the le-vel of the yield spread.

0.030.035

0.040.045

0.050.055

00.02

0.040.06

0.080

0.5

1

1.5

2

2.5

3

3.5

Manager'sownership shareManager's salary

Inve

stm

ent t

rigge

r

Fig. 4e. Sensitivity of investment trigger to the parameters of the employmentcontract which are compatible with a given level of expected managerial wealth.We rst nd the employment contracts a and Cp that yield expected managerialwealth equal to $1.2 and then we calculate the resulting investment timing policyfor this family of contracts. Output price (P) is $1, coupon payment (R) is $0.8,operating cost (C) is $0.75, managers reservation income (RI) is $1, project cost (I) is$3, risk free rate of interest is (r) 0.05, dividend yield (d) is 0.02, bankruptcy costs (b)are 0.35, tax rate for corporate income (sc) is 0.2 and standard deviation of annualreturns (r) is 0.3.analysis of the option to invest, we investigated the effect of man-agerial compensation and reservation income on investment tim-ing and nancing decisions. We found that the investmentexercise trigger is negatively associated to the managers salaryand ownership share while it is positively associated to his reser-vation income. The manager will choose a coupon payment thatwill maximize his wealth and this optimal coupon level is increas-ing in the managers reservation income and decreasing with themanagers salary and ownership share. As for the agency costs ofdebt, we documented a U-shaped relationship between the man-agers reservation income and agency costs of debt. A similarU-shaped pattern was found for the case of managers salary andthe managers ownership share. Causally related to the compara-tive statics of the yield spreads, optimal leverage ratios aredecreasing in the managers salary and ownership share but theyare increasing in his reservation income.

Future work in this area should address the issue of trading fric-tions and information asymmetries in the market for nancial andhuman capital and their impact on the managerial decision onwhen to start and how to nance a project. Moreover, the optionto invest could be decomposed into the component owned bythe manager and the one owned by the equity holder. Finally, amore realistic contractual setting of managerial compensationwould call for the inclusion of employee-stock options. The deci-sion makers risk attitude and effort aversion (Palmon et al.,2008) and the non-transferability of these option contracts wouldorient the capital-structure discussion to an analysis of irreversibleinvestment in incomplete capital markets.

Acknowledgment

I thank an anonymous reviewer for many helpful suggestions.

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Irreversible investment, managerial discretion and optimal capital structureIntroductionAn investment settingSolving for the unlevered asset valueCalculating managerial wealth in a levered firmPricing the option to invest

Numerical resultsInvestment timing and capital structure: the The effect of managerial compensationManagerial compensation and the interaction between investment and financing decisions: Managers reservation incomeManagerial compensation and the interaction between investment and financing decisions: Managers salaryManagerial compensation and the interaction between investment and financing decisions: Managers ownership stake

The effect of managerial compensation on agency costs of debt

Concluding commentsAcknowledgmentReferences