Real Options, Agency Conflicts, and Financial Policy

by

David C. MauerEdwin L. Cox School of Business

Southern Methodist UniversityP.O. Box 750333

Dallas, TX 75275-0333(214) 768-4150

dmauer@mail.cox.smu.edu

and

Sudipto SarkarMichael DeGroote School of Business

McMaster University1280 Main Street West

Hamilton, ON L8S 4M4(905) 525-9140

Sudisarkar@cs.com

Current Draft: October, 2001

We thank Peter MacKay, Rex Thompson and seminar participants at the University of Texas atDallas for many helpful comments and suggestions.

Real Options, Agency Conflicts, and Financial Policy

Abstract

We examine the impact of stockholder-bondholder conflicts over the exercisedecision of a firm’s investment option on corporate financing decisions. We findthat an equity-maximizing firm exercises the option too early relative to a value-maximizing strategy, and we show how this problem can be characterized as oneof overinvestment in risky investment projects. Equityholders’ incentive tooverinvest significantly decreases optimal leverage and debt maturity, andincreases the credit spread of risky debt. Numerical simulations establish that forreasonable parameter inputs the agency conflict of overinvestment producesleverage ratios, debt maturities and credit spreads that are jointly consistent withthose observed in practice. Furthermore, consistent with recent empirical work onthe determinants of corporate debt maturity structure, the model predicts that highgrowth firms and firms with high marginal tax rates optimally choose shorter-term debt, while firms with relatively high default costs optimally choose longer-term debt.

Real Options, Agency Conflicts, and Financial Policy

I. Introduction

The traditional balancing theory of optimal capital structure argues that corporate debt

levels are determined by trading off the tax advantage of debt financing against expected

bankruptcy costs. However, many corporate specialists argue that expected bankruptcy costs are

not large enough to explain observed corporate long-term debt levels, which historically have

ranged from 20% to 45% of firm value.1 Nevertheless, recent work by Graham (2000) shows

that firms continue to carry debt levels well below what would maximize the tax benefit of debt,

which suggests that debt financing is costly. Starting with the seminal work of Jensen and

Meckling (1976) and Myers (1977), corporate theorists have held out hope that the agency costs

of debt resulting from conflicts of interest between equityholders and debtholders could be large

enough to explain observed leverage ratios.2 However, recent theoretical work by Leland (1998)

and Parrino and Weisbach (1999) suggests that the agency costs of debt are probably not large

enough to explain observed leverage ratios.

This paper examines the effects of stockholder-bondholder conflicts on the firm’s

investment and financing decisions in a contingent claims model where the firm has an option to

invest in a project. Both the exercise decision of the real option and the financing of the

investment cost are jointly and simultaneously determined to maximize the value of the firm’s

investment option. The optimal amount and maturity of debt financing are determined by a

1 For example, see Miller (1977), Berens and Cuny (1995) and Damodaran (1997).2 Jensen and Meckling (1976) argue that managers acting on behalf of equityholders have an incentive to overinvestin risky and possibly negative net present value projects in order to transfer wealth from bondholders toequityholders. Myers (1977) argues that managers acting on behalf of equityholders also have an incentive tounderinvest in positive net present value projects because equityholders bear the lion’s share of the cost of theinvestment but share the benefits of the investment with debtholders. Both over- and underinvestment incentives aredriven by risky debt and limited liability equity, and the resulting agency costs are composed of the loss of firmvalue resulting from the suboptimal investment decisions, the higher cost of debt financing given that bondholders

2

trade-off between interest tax shields and bankruptcy and agency costs of debt. The agency

problem in the model results from a conflict of interest between debt and equity over the timing

of the exercise of the real option. We show that levered equityholders have a strong incentive to

overinvest in the project as manifested by their decision to exercise the investment option too

early relative to the exercise policy that maximizes total firm value. Directly analogous to the

risk-shifting agency problem of Jensen and Meckling (1976), this occurs because equityholders

can transfer risk to bondholders while preserving upside potential. We measure the agency cost

of this risk-shifting incentive as the loss in total firm value when the investment policy is chosen

to maximize levered equity value rather than total firm value.

We examine the magnitude of this agency cost and assess the economic impact of this

agency conflict on the firm’s optimal leverage ratio, optimal debt maturity level, and credit

spread of risky debt for a base case set of model parameters and for economically reasonable

variations in model parameters. We find that the agency cost of overinvestment is economically

significant and that the conflict produces leverage ratios, debt maturity levels and credit spreads

of risky debt that are consistent with those observed in practice. Specifically, we find that:

1. The firm will reduce leverage and shorten debt maturity to mitigate the agency conflict

resulting from equityholder’s incentive to overinvest in the risky investment project.

2. The agency cost of debt at the optimal leverage and debt maturity is economically

significant, amounting to about 7.4% of levered firm value for our set of base case

parameters. Although the tax-advantage of debt prevents the firm from reducing debt to

an arbitrarily low level, the impact of this agency conflict on financial policy is

significant. At the base case parameters, optimal leverage ratios are 20% lower than what

rationally anticipate these decisions, and the loss of firm flexibility resulting from bond covenants that restrictcorporate financing and investment decisions.

3

they would be without the agency problem and optimal debt maturity levels are reduced

from infinite maturity debt to empirically reasonable finite maturity debt.

3. The model produces credit spreads of risky debt that match levels observed in practice for

companies and industries with similar leverage ratios and debt maturity levels.

4. The model predicts that riskier firms (high asset value volatility and/or bankruptcy costs)

have smaller optimal leverage ratios and longer optimal debt maturity levels. By

contrast, firms in higher marginal tax brackets have larger optimal leverage ratios and

shorter optimal debt maturity levels. Finally, the model predicts that high-growth firms

have significantly shorter optimal maturity levels than do low-growth firms. These

predictions are consistent with the recent empirical findings of Barclay and Smith (1995)

and Stohs and Mauer (1996).

Several other recent papers model shareholder-bondholder conflicts and examine the

effects of these conflicts on investment and financing decisions. Leland (1998) extends the

models of Leland (1994a, 1994b) and Leland and Toft (1996) to explicitly compute agency costs

of debt in a contingent-claims model where the firm may costlessly switch back and forth

between a high and a low asset volatility. Within this framework, Leland examines equityholder

risk-shifting incentives and quantifies the magnitude of the agency cost of asset substitution and

the influence of risk-shifting incentives on the level and maturity of debt.3 Similar to our paper,

Leland finds that lower leverage and shorter debt maturity reduce the agency cost of asset

substitution. However, in sharp contrast with our paper he concludes that agency costs are small

and have a relatively unimportant impact on financial policy. Indeed, his model predicts that the

3 Earlier work by Barnea, Haugen and Senbet (1980), Gavish and Kalay (1983) and Green and Talmor (1986)examines asset substitution in static single-period models.

4

firm will optimally choose a corner solution of infinite maturity debt, despite agency costs

reaching their maximum level at this debt maturity level.

The key difference between the Leland framework and our framework is his assumption

that firm asset value is exogenous and is therefore independent of financial structure. Implicitly,

an increase in asset risk is accomplished by replacing the firm’s current set of assets with a new

set of assets having a larger volatility but exactly the same value. Accordingly, agency costs in

his model only reflect the impact of asset substitution on the value of debt interest tax shields and

expected bankruptcy costs. By contrast, our agency cost measure captures both the Leland

effects and the potentially much more significant loss of pure operating firm value attributable to

suboptimal investment decisions. Of course, it is the loss of firm operating/asset value resulting

from suboptimal investment decisions that forms the core of the agency costs of risky debt

financing.4

Parrino and Weisbach (1999) examine equityholder over- and underinvestment incentives

in a setting where the firm may choose to invest in a project whose stochastic cash flows are

correlated with the stochastic cash flows of the firm’s existing assets, and where the project

investment decision is now or never, i.e., there is no investment flexibility. They conclude that

the costs resulting from suboptimal investment decisions are economically insignificant.

However, they do not examine the impact of these agency conflicts on the optimal debt level and

maturity, and credit spreads of risky debt.

4 In a model virtually identical to that in Leland (1998), Ericsson (2000) assumes that the firm starts with low-riskassets and may costlessly switch to high-risk assets but can never subsequently reverse the decision. Although thisstructure magnifies the agency costs of debt, it maintains the assumption that firm operating/asset value isexogenous.

5

Finally, Mauer and Ott (2000) and Titman and Tsyplakov (2000) examine the impact of

underinvestment incentives on corporate financial policy.5 Mauer and Ott (2000) find that the

costs resulting from equityholders’ incentive to underinvest in growth options significantly

reduce optimal leverage but are not large enough to prevent the firm from optimally choosing

infinite maturity debt. Titman and Tsyplakov (2000) construct a model allowing for continuous

financing and investment choices and study equityholders’ incentive to underinvest in

production, i.e., choose a rate of investment lower than that which maximizes total firm value.

Similar to Mauer and Ott, they find that the agency cost of underinvestment decreases as

leverage and debt maturity are reduced. However, firm value is maximized under a corner

solution of short maturity debt, as opposed to a corner solution of infinite maturity debt.6

The fundamental difference between the model in this paper and the models in Mauer and

Ott (2000) and Titman and Tsyplakov (2000) is that we focus on overinvestment incentives as

opposed to underinvestment incentives. Although both types of shareholder-bondholder

conflicts arise in practice, equityholder incentives to underinvest generally only occur in

situations where the firm already has debt outstanding (debt overhang) and the probability of

failing to meet promised debt payments is high. By contrast, levered equityholders always have

an incentive to overinvest, assuming that debt is not risk-free. Importantly, our results establish

5 The models in these papers have their origins in the work of Brennan and Schwartz (1984), Mello and Parsons(1992), and Mauer and Triantis (1994). Brennan and Schwartz (1984) examine the influence of financial policy oninvestment policy in a setting where bond covenants restrict investment decisions. Mello and Parsons (1992)examine how debt financing influences the operating decisions of a mining firm. Finally, Mauer and Triantis (1994)examine interactions between dynamic financing and investment decisions in a setting where debt covenantsconstrain the firm’s choice of operating policies to maximize total firm value, i.e., where there are no residualagency costs.6 Specifically, when debt policy is static (i.e., cannot be adjusted over time) infinite maturity debt is optimal; andwhen debt policy is dynamic firm value is U-shaped in debt maturity and reaches a maximum at short-term debt.Since Titman and Tsyplakov’s numerical solutions only allow for a shortest debt maturity of 5 years, it is not clearwhat the true optimal debt maturity level is in their model.

6

that the overinvestment incentive can by itself drive interior optimal debt levels and finite debt

maturities that are consistent with those observed in practice.

The remainder of the paper is organized as follows. Section II describes the basic model

and specifies the decisions to be made by the firm. Section III illustrates the overinvestment

incentive and shows that maximizing equity value (rather than total firm value) results in earlier

investment, or equivalently a preference for riskier investments. We examine the effects of

overinvestment on agency costs, leverage ratios, and credit spreads of risky debt. Section IV

extends the basic model to include finite maturity debt and examines how the incentive to

overinvest influences the joint determination of optimal leverage and debt maturity. Section V

concludes.

II. The Model

A. Basic Assumptions

Consider a firm whose only asset is an option to invest in a production facility by paying

a fixed investment amount of I. As discussed below, the firm can finance the cost of the

investment by issuing bonds. Once the firm exercises the option, the facility produces a single

commodity that is infinitely divisible and is produced at the rate of one unit per year. The cost of

producing one unit of the commodity is C, which is constant through time. As the commodity is

produced, it is simultaneously sold in a perfectly competitive market at a price P per unit. The

evolution of the commodity price through time follows geometric Brownian motion:

PdzPdtdP σ+α= , (1)

7

where the drift (α) and volatility (σ) are constants and dz is the increment of a standard Wiener

process. The convenience yield of the commodity is assumed to be a constant proportion, δ, of

the commodity price.

The facility’s operating profits are taxed instantaneously at a constant rate τ.7 For

simplicity, we do not model economic depreciation of the production facility. Furthermore, we

assume a symmetric tax system with full loss-offset provisions. The latter assumption is only an

approximation of the current U.S. tax system that allows for a partial offset of operating losses

through carryback and carryforward provisions.

After the investment option is exercised and the facility begins operating, the firm has the

option to abandon operations at any time. For simplicity, we assume that the salvage value of

the production facility net of closing costs is zero.

Finally, we assume that there exists a riskless security that yields a constant instantaneous

rate of return of r per year. We further assume that the commodity price is spanned by traded

securities such as a futures contract. Then it is well known that a continuously rebalanced self-

financing portfolio can be constructed that replicates the value of the firm’s investment option

and post exercise operating value, and allows for the determination of the optimal exercise and

abandonment policies.

B. Pure Operating Value of the Production Facility

First consider the value of the firm after the investment option is exercised for the special

case where the cost of exercising the option is entirely financed with equity. We examine this

case only to identify the pure operating value of the production facility (i.e., post-exercise

8

unlevered firm value), and to endogenously determine the commodity price at which the firm

will abandon the production facility. Standard risk-neutral valuation arguments require that

unlevered firm value, )P(VU , must satisfy the following differential equation:

21 0)1)(CP(rVPV)r(VP UU

PUPP

22 =τ−−+−δ−+σ , APP > , (2)

where AP is the price at which the unlevered firm abandons the production facility. The general

solution of (2) is

21 PAPA)1(rCP)P(V 21

U ββ ++τ−

−δ

= , APP > , (3)

where 1A and 2A are constant to be determined and

1r2r21r

21

2

2

221 >σ

+

σ

δ−−+

σ

δ−−=β ,

0r2r21r

21

2

2

222 <σ

+

σ

δ−−−

σ

δ−−=β .

The unlevered firm value in (3) must satisfy three boundary conditions:

)1(rCP)P(Vlim U

Pτ−

−δ

=∞→

, (4a)

0)P(V AU = , (4b)

7 Although we do not model personal taxes, it would be straightforward to include constant personal tax rates onequity and debt income.

9

0P

V

APP

U=

∂∂

=

. (4c)

Condition (4a) requires that the abandonment option is worthless if the commodity price gets

large, and is satisfied only if 0A1 = . Conditions (4b) and (4c) require, respectively, that the

firm has zero net salvage value if the production facility is abandoned and that the abandonment

trigger price is optimally chosen. Substituting (3) into (4a)-(4c) gives the unlevered firm value

as

−δ

−−δ

τ−=β2

A

AUPP

rCP

rCP)1()P(V , (5)

where the endogenous abandonment trigger price is given by

rC

1P

2

2A

δβ−β−

= .

C. Levered Firm and Security Values

Consider next the case where the cost of exercising the investment option is at least

partially financed with debt. Prior to the exercise of the investment option, we assume that the

firm finalizes an agreement with the bondholders under which bondholders will pay the firm K

when the firm makes the investment in the production facility (exercises the option), in return for

a continuous coupon payment of R per unit time thereafter. We initially assume that the debt has

infinite maturity barring default, but we will later relax this assumption. Furthermore, we

assume that the timing of the investment decision is entirely at the discretion of the equityholders

and cannot be contracted in advance by bondholders. Finally, we assume that bondholders have

10

rational expectations and fully anticipate that equityholders may choose an exercise strategy that

harms the value of their fixed coupon claim against the firm’s production facility. As such,

bondholders will require that their future commitment of K to finance the exercise of the

investment option be fair relative to the agreed coupon and the investment exercise strategy to be

adopted by the equityholders.

Taking the coupon R and financing K as given for now, our objective here is to compute

the market value of the equity, debt and levered firm after the investment option is exercised and

the production facility is operating. The differential equation describing the market value of

levered equity is the same as that in (2), except that the cash flow accruing to equityholders is

now )1)(RCP( τ−−− per unit time. The analogous general solution for the value of levered

equity is

21 PBPB)1(r

RCP)P(E 21ββ ++τ−

+

−δ

= , BPP > , (6)

where 1B and 2B are constants to be determined, 1β and 2β are given immediately below

equation (3), and BP is the endogenously determined commodity price at which equityholders

choose to default on the firm’s debt.

The general solution in (6) must satisfy the following boundary conditions:

)1(r

RCP)P(ElimP

τ−

+

−δ

=∞→

, (7a)

0)P(E B = , (7b)

0PE

BPP=

∂∂

=. (7c)

11

Condition (7a) requires that 1B equals zero, ensuring that the option to default on debt payments

is worthless if the commodity price gets large. Conditions (7b) and (7c) require, respectively,

that equity value is zero in default and that the default trigger is optimally chosen to maximize

the market value of equity.8 Substituting (6) into conditions (7a)-(7c) gives the market value of

equity as

+

−δ

−+

−δ

τ−=β2

B

BPP

rRCP

rRCP)1()P(E , (8)

where the endogenous bankruptcy trigger is given by

r)RC(

1P

2

2B

+δβ−β−

= .

Note that AB PP ≥ as 0R ≥ .

Since debt has no stated maturity, the general solution for debt value is

21 PCPCrR)P(D 21

ββ ++= , BPP > , (9)

where the constants 1C and 2C are determined by the conditions that

rR)P(Dlim

P=

∞→, (10a)

)P(V)b1()P(D BU

B −= . (10b)

8 Condition (7b) ensures that absolute priority is respected in bankruptcy.

12

Condition (10a) requires that 1C equals zero; as the probability of default goes to zero the

market value of debt equals the value of a perpetuity paying R per unit time. Condition (10b)

requires that in bankruptcy bondholders receive the unlevered value of the firm (equation (5)

evaluated at BPP = ) minus bankruptcy costs amounting to the fraction b ( 1b0 ≤≤ ) of

unlevered firm value.9 Substituting (9) into conditions (10a) and (10b) gives the value of risky

debt as

2

BB

U

PP

rR)P(V)b1(

rR)P(D

β

−−+= . (11)

The total value of the levered firm is the sum of equations (8) and (11), which can be

written as

22

BB

U

B

ULPP)P(bV

PP1

rR)P(V)P(V

ββ

−

−

τ+= . (12)

The value of the levered firm is equal to the value of the unlevered firm plus the expected tax

shield of debt minus expected bankruptcy costs.

D. Investment Decision

Currently, the firm possesses an option to invest in the production facility and a contract

with bondholders whereby they will provide K dollars to help finance the investment in return

for a coupon payment of R. Since the investment option is the firm’s only asset, the current

value of the firm equals the value of the investment option. Our objective here is to determine

the value of the option and the optimal exercise policy for the option.

9 Note that 0)P(V B

U > since AB PP > for R > 0.

13

Denoting F(P) as the value of the option (the firm’s current value), it is straightforward to

show that F(P) must satisfy the following differential equation:

21 0rFPF)r(FP PPP

22 =−δ−+σ , IPP < , (13)

where IP is the endogenously determined commodity price at which the firm exercises the

option. The general solution of (13) is

21 PP)P(F 21ββ Ω+Ω= , IPP < , (14)

where 1Ω and 2Ω are constants to be determined and 1β (> 1) and 2β (< 0) are given

immediately below equation (3).

The investment option must satisfy three boundary conditions. First, the option must be

worthless if the commodity price is absorbed at zero. This stipulation requires that 2Ω equals

zero in equation (14). Additionally, since the equityholders control the investment exercise

decision, they will choose the exercise policy that maximizes the market value of equity. Since

equityholders’ exercise decision does not maximize total firm value (i.e., the sum of debt and

equity value) we call this the “second-best” case, and denote the investment exercise trigger as

SIP . The remaining two boundary conditions that allow for the determination of 1Ω in (14) and

SIP are

)KI()P(E)P(F SI

SI −−= , (15a)

SI

SI PPPP P

EPF

== ∂∂

=∂∂ . (15b)

14

Condition (15a) is a continuity (or value matching) condition requiring that the value of the

option equals the value of the equity net of equityholders’ contribution to the financing of the

production facility (I – K) when P reaches SIP . Condition (15b) is a smooth-pasting (or high

contact) condition requiring that the investment exercise trigger be chosen to maximize the

market value of equity.

Setting 02 =Ω in (14) and substituting the resulting equation into condition (15a) gives

the (second-best) value of the investment option (firm) as

[ ]1

SI

SI

S

PP)KI()P(E)P(F

β

−−= . (16)

The appropriate value of K is easy to determine. Rational bondholders will not agree to a

contract giving the firm K dollars when equityholders choose to invest, unless K is a fair price

for the debt. Realizing that after the contract is finalized they cannot force equityholders to

choose a firm-value-maximizing exercise policy, they will value the debt (and thereby determine

the amount of K) under the assumption that the ex-post exercise policy will maximize equity

value rather than total firm value. As such, the incentive-compatible K must equal the debt value

at the second-best (or equity-value-maximizing) investment trigger:

2

B

SI

BUS

I PP

rR)P(V)b1(

rR)P(DK

β

−−+=≡ . (17)

15

Substituting this value for K into (16) and noting that )P(V)P(D)P(E SI

LSI

SI =+ (the value of the

levered firm in equation (12) evaluated at SIPP = ) gives the second-best value of the investment

option as

[ ]1

SI

SI

LS

PPI)P(V)P(F

β

−= . (18)

The second-best investment trigger price, SIP , can be determined from condition (15b).

Substituting equations (8) and (14) into (15b) gives the implicit equation:

0PP

rRCP1

1KI

rRCP11

2

B

SIB

1

2SI

1=

+

−δ

−

ββ

+τ−

−−

+−

δ

β

−β

, (19)

where K is given in (17). The nonlinear algebraic equation in (19) can be numerically solved for

SIP .

For comparison, we compute the value of the investment option (firm) and exercise

policy under a “first-best” scenario where equityholders are contractually obligated to pursue a

firm-value-maximizing investment policy. Denoting FIP as the first-best investment trigger

price, the value matching and smooth-pasting boundary conditions are

I)P(V)P(F FI

LFI −= , (20a)

FI

FI PP

L

PP PV

PF

== ∂∂

=∂∂ . (20b)

16

Setting 02 =Ω in (14) and substituting the resulting equation into conditions (20a) and (20b)

gives the (first-best) investment option value as

[ ]1

FI

FI

LF

PPI)P(V)P(F

β

−= , (21)

and the implicit equation for the first-best trigger price as

2

B

FIB

1

2FI

1 PP

rCPb

r)1(R1

1I

r)1(R

rCP11

β

−δ

+τ−

τ

−

ββ

+τ−

−τ−

τ+−

δ

β

−

0PPP)b1(1

2

A

FI

2

A

1

2 =

δβ−

−

ββ

+β

. (22)

As before, equation (22) can be numerically solved for FIP .

III. Analysis of the Model

A. Base-Case

Since we are interested in examining the magnitude of the agency costs of debt, we focus

our attention on numerical solutions of the model. We adopt the following base-case parameter

values. The cost of exercising the investment option (I) to build the production facility and begin

operating is $5. Once the facility is built, the annual rate of production is one unit per year, the

cost of production (C) is $0.75 per unit, and the corporate tax rate (τ) is 30%. We assume that

the current price of the commodity (P) is $1.00, which in conjunction with the cost of production

indicates that the firm would enjoy positive after-tax operating profits if it decided to

immediately exercise the option to build the production facility. The annualized risk-free rate of

17

interest (r) is 5%, and the annualized convenience yield (δ) and volatility (σ) of the commodity

price are 2% and 25%, respectively. Finally, we assume initially that the debt has a fixed

promised coupon payment (R) of $0.85 and that bankruptcy costs (b) are 50% of the value of

unlevered assets in bankruptcy, i.e., when P = BP .10

For these base-case parameters, the firm-value-maximizing (or first-best) investment

policy is to exercise the investment option when P rises to 55.1$PFI = . By comparison, if the

firm were unlevered (i.e., R = 0), it would wait until the commodity price reached 94.1$PUI = .11

The levered firm exercises the investment option earlier to accelerate earning the interest tax

shield of debt financing. However, if the levered firm forsakes firm value maximization and

instead chooses the exercise policy to maximize the market value of equity, the firm will exercise

the investment option when P rises to 21.1$PSI = . Thus, if the firm maximizes equity value

rather than total firm value it will make the investment much earlier.

To gain some perspective on the magnitude of the difference between SIP and F

IP , we

can compute the expected first passage time between the two trigger prices. Assuming a 10%

annual expected rate of appreciation (α) in the output price, the expected amount of time it

would take for the commodity price to reach $1.55 starting at $1.21 is

[ ] 6.3)25.0)(50.0(10.0)21.1ln()55.1ln(

)50.0()Pln()Pln(t~E 22

SI

FI =

−

−=

σ−α

−= years.

10 Although bankruptcy costs of 50% may appear high, we show later that lower bankruptcy costs actually inducelarger agency costs. Recent empirical estimates of total bankruptcy costs range from 10-20% of firm value inAndrade and Kaplan (1998) to 50% of firm value in Franks and Torous (1994).11 The price at which an unlevered firm would exercise the investment option, U

IP , can be found as

18

Clearly, there is a significant difference between the timing of the first- and second-best

investment decisions.

The incentive of equityholders to exercise the investment option too early relative to the

firm-value maximizing policy is easy to explain. Similar to the first-best policy, equityholders

following a second-best policy have a strong desire to exercise the option quickly to speed up the

realization of interest tax shields earned on debt financing. However, unlike the first-best policy,

equityholders are not concerned about the welfare of bondholders, and are therefore not

concerned about the increased risk of bankruptcy resulting from their earlier exercise decision.

With limited liability, equityholders can shift the greater default risk of an early exercise decision

to the bondholders, and can capture the resulting loss in bond value while simultaneously

enjoying earlier receipt of debt interest tax shields.12 As we will see shortly, however, rational

bondholders will require compensation for this added risk and it will be in equityholders’ interest

to mitigate the conflict over the timing of the investment exercise decision.

It is natural to characterize this agency problem as one of overinvestment rather than

investing too early. Since equityholders choose to exercise the investment option at a lower

commodity price, the probability that investment takes place by any given future date increases.

As such, the expected amount of investment by that date is greater. In this sense, equityholders

overinvest relative to the firm-value-maximizing investment policy.

[ ]

−==

β1

UI

UI

UUUI

PPI)P(V)P(FmaxargP

12 For the base-case parameters, the endogenous bankruptcy trigger price is 36.0$PB = . (By comparison, anunlevered firm will abandon the production facility when the commodity price falls to 17.0$PA = .) Clearly, thefirm can directly influence the probability of default by its choice of when to exercise the investment option.

19

Another way to characterize the difference between the first- and second-best exercise

policies, which is directly analogous to the Jensen and Meckling (1976) risk-shifting or asset

substitution problem, is that equityholders have an incentive to choose riskier investment

projects. Figure 1 graphs first- and second-best investment trigger prices as a function of the

volatility of the output price, σ. Observe that both FIP and S

IP increase as volatility increases

and that SI

FI PP ≥ with the gap between the two prices growing as volatility increases.13 Now,

imagine a series of investment projects that differ only in their risk (σ), which is sequenced from

low to high risk as displayed on the x-axis in Figure 1. At the current base-case commodity price

of $1.00, first-best firm-value-maximizing policy makers will immediately choose all projects

with risk levels less than or equal to 11%, while second-best equity-value-maximizers will

immediately choose all projects with risk levels less than or equal to about 17.5%. Analogously,

if the current commodity price were $1.50, first-best policy makers would immediately choose

all projects up to a risk level of 24%, while second-best policy makers would immediately

choose all projects up to a risk level of a little more than 33%. Thus, at any given output price

level, a firm that maximizes the market value of equity will have a preference for higher risk

projects than does a firm that maximizes total firm value.

We compute the agency cost of overinvestment as the difference between the current firm

(option) values under first-and second-best policies. As a proportion of the second-best firm

value, the agency cost for the base-case parameters is equal to

13 The incentive to wait longer as volatility increases is a standard result in the real options literature (see, e.g., Dixitand Pindyck (1994)), deriving from the fact that the value of waiting to invest in an irreversible investment increaseswith volatility. However, the gap between the first- and second-best trigger prices also widens as volatilityincreases. The reason is that default risk increases with volatility and therefore the first-best policy will attempt tooffset this higher default risk by waiting for an even higher commodity price before exercising the investmentoption. Of course, equityholders have no such concern, and therefore the gap between the first- and second-besttrigger prices widens as volatility increases. Finally, note that as volatility tends toward zero the first- and second-

20

0148.014.24

14.2450.24)P(F

)P(F)P(FAC S

SF=

−=

−= ,

or 1.48% of (second-best) firm value.14 Alternatively, the agency cost of overinvestment can be

expressed as the difference between the credit spread of risky debt (in basis points) under

second- and first-best investment policies:

35.3688.8223.119r)P(D

Rr)P(D

RAC FI

SI

CS =−=

−−

−= basis points,

where )P(D/R SI and )P(D/R F

I are the interest costs or yields of debt when the firm exercises

the investment option (and issues the debt) under the second- and first-best investment policies,

respectively. Because the firm cannot credibly commit to adopting a firm-value-maximizing

exercise strategy, the cost of debt financing will be higher by about 36 basis points.

B. Optimal Leverage

Although the agency cost component of the credit spread (36 basis points) seems

economically significant, the loss in firm value (1.48%) appears small. However, the important

question is not whether agency costs are economically significant holding leverage constant, but

whether this agency conflict significantly influences optimal leverage choice. Furthermore, an

equally important question is whether the agency problem of overinvestment can produce

best trigger prices converge at a price below $1.0. With zero or low uncertainty debt is riskless and equityholdershave no incentive to deviate from the first-best exercise policy.14 Note that AC is independent of the commodity price (P = $1.00 for the base-case), as can be seen when )P(FS

and )P(FF in equations (18) and (21), respectively, are substituted into the expression for AC.

21

optimal leverage ratios and credit spreads of risky debt that are consistent with those observed in

practice.

Table 1 displays first- and second-best firm characteristics and agency costs of debt for

coupon payments (R) ranging from $0 to $3.00, holding all other parameters constant at their

base-case values. Observe that second-best firm value is maximized at a coupon payment of

$0.85, which corresponds to an optimal leverage ratio of 38%. In comparison, the first-best firm

value is maximized at a coupon payment of $2.64, which corresponds to an optimal leverage

ratio of 61%.15 Figure 2 displays first- and second-best firm values as a function of the leverage

ratio.

In the model, optimal leverage is driven by the trade-off between debt tax shields and

bankruptcy and agency costs of debt. However, the difference between the first- and second-best

optimal leverage ratios is by definition driven only by the agency conflict. Observe in Table 1

that as the firm increases leverage and the incentive to overinvest increases, the agency cost

component of the credit spread increases.16 This higher cost of debt financing for an equity-

value-maximizing firm quickly offsets the interest tax shield advantage of debt financing, and the

resulting second-best optimal leverage ratio is significantly smaller than the first-best optimal

leverage ratio. For the base case parameters, the agency cost induced reduction in the optimal

leverage ratio is over 20%. Clearly, this is an economically significant reduction in leverage.

15 The first- and second-best leverage ratios are computed as )P(V/)P(DL F

ILF

IF = and )P(V/)P(DL SI

LSIS = ,

respectively. Note that the leverage ratios are computed using debt and levered firm values evaluated at theinvestment trigger prices, since the firm does not issue debt until the investment option is exercised.16 Also note that S

IP is monotonically decreasing in R, with the firm eventually entering immediately, i.e.,

0.1$)0(PPSI =< . By comparison, F

IP first decreases and then increases in R. For low levels of R, an increase in Rencourages both firm types to enter sooner to take advantage of the larger interest tax shields. However, as Rincreases and the probability of costly bankruptcy becomes significant, the first-best firm s incentive to wait for ahigher output price to moderate bankruptcy risk dominates the incentive to enter sooner to capture interest taxshields, and F

IP will start to increase.

22

The second-best optimal leverage ratio of 38% and corresponding credit spread of risky

debt of 119 basis points are in line with empirical averages.17 In particular, Damodaran (1997)

shows that average leverage ratios have historically ranged from 20% to 45% of firm value.

Furthermore, Collin-Dufresne, Goldstein and Martin (2001) show that credit spreads on long-

term bonds of industrial companies with leverage ratios between 35% and 45% have averaged

124 basis points (with a standard deviation of 64 basis points) over the period from 1988 to 1997.

Thus, for reasonable parameter inputs, our model produces empirically consistent leverage ratios

and credit spreads of risky debt.

Finally, observe that at the optimal leverage the agency cost of overinvestment appears to

be highly economically significant. From Table 1, the loss in firm value when the firm chooses

to maximize equity value instead of total firm value is 8% ((26.07 − 24.14)/24.14). This

represents the potential gain in firm value if the firm could credibly commit to not overinvest in

the investment option. Alternatively, the 8% figure represents the upper bound on the

monitoring and alignment costs a firm would be willing to bear to prevent overinvestment.

C. Comparative Statics

Table 2 illustrates the effects of varying model parameters on the agency cost of

overinvestment, allowing for the endogenous choice of optimal leverage. The first row reports

the base case results where the agency cost of overinvestment is 8% and the first- and second-

17 Note that the second-best model statistics are the relevant ones to compare with empirically observed data, sincepresumably real world leverage ratios and credit spreads of risky debt reflect the consequences of agencyconflicts between debt and equity holders.

23

best leverage ratios are 61% and 38%, respectively. Subsequent pairs of rows illustrate the

effects of parameter variation around base case values.18

An increase in output price volatility (σ) results in a decrease in agency costs and a

significant decrease in optimal leverage. Specifically, when volatility increases from 20% to

30%, agency costs decrease from 8.33% to 7.63% and the (second-best) optimal leverage ratio

decreases from 45% to 33%. As volatility increases, the value of waiting to invest increases and

both first- and second-best policy makers wait for a higher output price before exercising the

investment option. This leads to an increase in current firm (option) value, a lessened incentive

to overinvest, and a decrease in agency costs. Observe that the higher current firm value

encourages both first- and second-best policy makers to increase the promised coupon payment

of debt. Nevertheless, the increase in debt service is modest despite the increase in firm value,

and both first- and second-best leverage ratios decrease.

A decrease in the convenience yield (δ) of the commodity price results in a sharp increase

in firm value, enhanced debt capacity (as reflected in an increase in the optimal coupon

payment), and a corresponding increase in the agency cost of overinvestment. The net result is

that the (second-best) optimal leverage ratio decreases, but only by a small amount. Holding the

risk-adjusted discount rate constant, a decrease in the convenience yield implies a larger rate of

output price appreciation (α) and therefore a larger current firm (option) value.19 By

conventional interpretation (see, e.g., Leland and Toft (1996)), firms with smaller δ’s are viewed

18 Note that in each row the second-best credit spread is always lower than the first-best credit spread because theoptimal second-best leverage is always lower than the first-best leverage. Since leverage is not held constant acrossfirst- and second-best cases, it would be inappropriate to infer that the agency cost component of the credit spread isnegative.19 Given the assumption that the commodity price is spanned by traded assets, the risk-adjusted discount rate forcommodity price risk, pr , must satisfy the relation δ+α=ηρσ+= rr p , where η is the price of risk and ρ is the

24

as high growth firms that are predicted to have a greater propensity for agency conflicts and

therefore lower leverage ratios. Given this perspective, our model predicts that high growth

firms do indeed have larger agency costs, but the resulting reduction in the optimal leverage ratio

is small.

Surprisingly, an increase in bankruptcy costs (b) from 25% to 75% results in a decrease

in agency costs (from 10.61% to 6.21%). As seen in the table, an increase in bankruptcy costs

has virtually no effect on an equity-value maximizer’s choice of an optimal coupon payment.

Nevertheless, the resulting reduction in debt value and corresponding increase in the interest cost

of debt encourages the firm to wait for a higher output price before exercising the investment

option. At the higher price, the disparity between the first- and second-best investment trigger

prices narrows and the agency cost of overinvestment decreases. As expected, however, the

optimal first- and second-best leverage ratios sharply decrease as bankruptcy costs increase.

An increase in the tax rate (τ) from 25% to 35% results in a large increase in agency costs

(from 5.27% to 11.38%), and a modest increase in the (second-best) optimal leverage ratio (from

36% to 40%). An increase in the tax rate has two effects: first, after-tax operating cash flows

decrease; and second, interest tax shields increase. The net result is that the disparity between

the first- and second-best exercise policies widens, firm value decreases, and agency costs

increase. Note that the optimal second-best coupon payment actually decreases as the tax rate

increases, because the decrease in the unlevered component of firm value and the corresponding

incentive to exercise the investment option even earlier reduces the firm’s debt capacity.

A decrease in the risk-free rate of interest (r) results in a decrease in firm value, a sharp

drop in optimal leverage, and a corresponding reduction in agency costs. Although one might

instantaneous correlation of the spanning asset (or dynamic portfolio of spanning assets) with the systematic pricing

25

expect borrowing costs to fall as the risk-free rate decreases, the credit spread of risky debt

sharply increases. The underlying driver of these effects is that the risk-adjusted (or risk-neutral)

drift rate of the commodity price decreases as r decreases.20 This in turn decreases the value of

the investment option, reduces optimal leverage and encourages both first- and second-best

policy makers to delay exercise of the investment option. As a result, the disparity between first-

and second-best exercise policies narrows and agency costs decrease.

Finally, an increase in the cost of exercising the investment option (I) decreases the value

of the option and encourages both first- and second-best policy makers to delay exercise of the

option. At the higher investment trigger prices, the agency cost of debt is lower.

IV. Finite Debt Maturity

A. Modeling Issues

The preceding analysis illustrates that the agency problem of overinvestment has a

significant impact on optimal leverage and credit spreads of risky debt when the debt that the

firm can issue has infinite maturity. Important remaining questions are whether this agency

conflict influences debt maturity choice, and whether it can drive interior optimal leverage and

debt maturity.

We adopt the finite debt maturity framework originally developed by Leland (1994b) and

subsequently used by Leland (1998), Mauer and Ott (2000), Ericsson (2000) and Titman and

Tsyplakov (2000). We assume that the debt has no stated maturity, but the firm continuously

retires a constant fraction m of its outstanding debt principal and replaces it with new debt

factor. Thus, if pr is held constant, a decrease in δ must be accompanied by an increase in α.

26

having the same coupon rate, principal amount, and priority in bankruptcy as the debt retired.

Denote the total debt principal amount as Q and the coupon rate of debt as ρ. Since all debt has

infinite original maturity and since the principal amount of debt retired is simultaneously

replaced with a like amount, the periodic debt service requirements are a fixed coupon payment

ρQ and a fixed (sinking fund) payment amounting to the fraction m of currently outstanding debt

principal Q. In this setting, the average maturity of debt equals T = 1/m. As the rollover rate m

increases, average debt maturity decreases; if m = 0, debt has infinite maturity (except when

default occurs) as in our basic model setup.

Consider the periodic after-tax cash flows to equity, debt and the firm (i.e., the sum of

equity and debt after-tax cash flows) after the investment option is exercised and the production

facility is operating. We have that

( )[ ] ( )[ ] Q)1)(CP(Q)P(DmQQ)P(Dm)1)(QCP( τρ+τ−−=−−ρ+−+τ−ρ−− , (23)

where the first term in square brackets is the after-tax cash flow to equityholders and the second

term in square brackets is the after-tax cash flow to debtholders. Note that the firm continuously

retires debt at face value in the amount mQ and replaces the debt with a new debt issue in the

amount mD(P). Since the market value of newly-issued debt D(P) depends on the current output

price P, the refunding cost to equityholders ( ))P(DQm − can be either positive ( Q)P(D < ) or

negative ( Q)P(D > ). Importantly, note that the magnitude of this refunding cost depends on

debt maturity; as m increases and average debt maturity decreases, refunding costs increase when

the output price is low and the market value of newly-issued debt is also low. Accordingly,

20 From footnote 19 we know that the risk-adjusted drift rate of the commodity price is δ−=ηρσ−α r . Holding αand δ constant, a reduction in r decreases the risk-adjusted drift rate (increases ηρσ ) and thereby reduces the currentvalue of the firm (investment option).

27

unless there are offsetting benefits from choosing shorter-term debt, the firm will optimally

choose infinite maturity debt (i.e., m = 0).21 Finally, note that total firm after-tax cash flows (the

right-hand-side of (23)) are independent of m, and therefore levered firm value does not directly

depend on m.

Within this framework, it is straightforward to show that the market value of debt is22

)m(

BB

U2

PPQ

mrm)P(V)b1(Q

mrm)P(D

θ

++ρ

−−+++ρ

= , (24)

where

0)mr(2r21r

21)m( 2

2

222 <σ

++

σ

δ−−−

σ

δ−−=θ ,

and the total market value of the firm is given by

22

BB

U

B

ULPP)P(bV

PP1

rQ)P(V)P(V

ββ

−

−

τρ+= . (25)

The market value of equity is simply )P(D)P(V)P(E L −= . The output price at which

equityholders choose to default on the debt, BP , can be determined from the smooth-pasting

condition 0PPPE B ==∂∂ . Applying this condition gives

21 Note that the interest tax shield benefit of debt is independent of m.22 Equation (24) is the solution to the differential equation:

21 0Q)m(D)mr(PD)r(DP PPP

22 =+ρ++−δ−+σ , BPP > ,

subject to the conditions that Qmrm)P(Dlim

P ++ρ

=∞→

and )P(V)b1()P(D BU

B −= .

28

0P

)m(Qmrm)P(V)b1(

PZ1

B

2B

U

B

2 =θ

++ρ

−−−β

+δτ− , (26)

where

−δ

τ−−τρ

−−=rCP)1(

rQ)P(V)b1(Z B

BU .

Equation (26) can be numerically solved for BP . Observe that BP is a function of m.

Specifically, holding leverage constant it is straightforward to show that BP increases as m

increases (average maturity decreases); and therefore both expected refunding costs and

bankruptcy costs increase as debt maturity decreases.

Finally, consider the value of the firm’s investment option (i.e., current firm value) and

the optimal investment trigger price. For the first-best case where the firm chooses the trigger

price to maximize total firm value, the investment option value, )P(FF , and equation

determining the investment trigger price, FIP , are identical to those for the case of infinite

maturity debt in equations (21) and (22), respectively. However, note that now the coupon

payment, R, is specified as ρQ, and the bankruptcy trigger price, BP , is given by the solution to

equation (26). Analogously, for the second-best case the investment option value, )P(FS , is

identical to that in equation (18). However, the equity-value-maximizing investment trigger

price, SIP , is the solution to the equation:

2

B

SI

1

2

1

SI

PP1Z)KI(Q

mrm

rrC11P)1(

β

ββ

−+−−

++ρ

−τρ

+

−

β

−δ

τ−

29

0PPQ

mrm)P(V)b1(1)m(

)m(

B

SI

BU

1

22

=

++ρ

−−

−

βθ

+θ

, (27)

where Z is given immediately below (26), and where the fair price of debt, K, is given by

)m(

B

SI

BUS

I

2

PPQ

mrm)P(V)b1(Q

mrm)P(DK

θ

++ρ

−−+++ρ

=≡ . (28)

B. Optimal Debt Maturity

Table 3 shows first- and second-best firm value characteristics and the agency cost of

overinvestment for debt maturities (T) ranging from 1 year (m = 1) to infinite maturity debt (m =

0). For each maturity level, the reported results are at the optimal leverage. Optimal leverage is

computed by choosing the face value of debt, Q, which maximizes the current firm (option)

value, F. Thus, for each maturity level we report first- and second-best optimal face values, FQ

and SQ , and the corresponding leverage ratios, FL and SL . The parameter values are the same

base case values used earlier, with the addition of the coupon rate of debt, ρ, which is set equal to

6%.23

As can be seen in Table 3, the firm-value-maximizing strategy is to choose infinite

maturity debt, since first-best firm (option) value is maximized when debt has infinite maturity.

For this choice, the first-best firm characteristics are identical to those in the base case of Table

2, where all debt is assumed to have infinite maturity. In particular, the optimal face value of

debt, 44.07, gives a promised coupon payment of 2.64 ((0.06)(44.07)) and an optimal leverage

ratio of 61%. By contrast, the equity-value-maximizing strategy is to choose an optimal debt

30

maturity of 20 years, since second-best firm (option) value is maximized at this maturity level.

The resulting optimal leverage ratio is 41%, which is slightly larger than the 38% leverage ratio

that the second-best firm would have optimally chosen if it were forced to issue infinite maturity

debt (see Table 2). Figure 3 displays first- and second-best firm values as a function of debt

maturity.24

Observe in the table that the agency cost of overinvestment decreases as debt maturity is

shortened. Indeed, the firm could drive agency costs to zero by choosing one- or two-year

maturity debt. There are two reasons why agency costs decrease as debt maturity decreases.

First, as debt maturity decreases, both first- and second-best policy makers optimally choose

lower debt levels and wait for higher output prices before exercising the investment option. As a

result, the default risk of debt is considerably less and equityholders’ incentive to overinvest is

minimized. Analogously, the second reason is that short maturity debt is continually rolled over

and replaced with new debt that is priced to reflect any deviations from a value-maximizing

investment strategy. This frequent repricing of debt therefore discourages overinvestment.

Nevertheless, a short maturity strategy is not optimal, since the debt capacity of the firm

and the corresponding interest tax shields of debt financing are substantially smaller at shorter

debt maturities. As discussed above, the reason is that as the firm shortens debt maturity (m

increases), equityholders potentially face much larger debt refunding costs when the output price

is low. To offset these higher expected refunding costs the firm prudently chooses much lower

debt levels. Because expected refunding costs increase as debt maturity decreases and because

debt capacity and interest tax shields are lower, the firm-value-maximizing strategy is to

23 Note that our coupon rate input choice is irrelevant (beyond aesthetic appeal), since the dollar coupon payment,ρQ, is determined by the choice of Q.

31

optimally choose infinite maturity debt. However, an equity-maximizing firm that faces agency

costs of overinvestment cannot ignore the much larger agency costs of long-term debt. As a

result, the second-best solution is to choose finite maturity debt that balances the benefit of a

reduction of agency costs against the smaller debt capacity and larger expected refunding costs

of shorter-term debt.25

C. Comparative Statics

Table 4 displays optimal leverage and maturity results for the base case and for variation

of base case parameter values. As can be seen in the table, the (first-best) firm-value-

maximizing strategy always chooses infinite maturity debt. By contrast, the (second-best)

equity-value-maximizing firm virtually always chooses finite maturity debt. It should be clear

that the only reason an equity-value-maximizing firm chooses finite maturity debt is to mitigate

the agency cost of overinvestment. Interestingly, despite the fact that agency costs decrease as

debt maturity decreases, the equilibrium level of agency costs at the optimal leverage and debt

maturity for the base case parameters is 7.43%. The following discussion of the numerical

comparative static results focuses on the optimal debt maturity and leverage ratio choices of an

equity-value-maximizing firm.

An increase in output price volatility (σ) from 20% to 30% results in a significant

decrease in optimal leverage (from 48% to 34%) and a significant increase in optimal debt

24 Observe in Figure 3 that the second-best (equity-maximizing) firm value is relatively flat for debt maturities above15 years. Thus, although 20-year debt maximizes firm value, as a practical matter any debt maturity less than 20years but greater than or equal to 15 years is “close” to being optimal.25 Note in Table 3 that the debt capacity of an equity-value-maximizing firm is actually maximized at 10 year debtrather than 20 year debt. In particular, although second-best firm value is maximized for 20 year debt, the optimalface value of debt reaches a maximum for 10 year debt. However, note that the leverage ratio reaches it highestlevel of 41% for 20 year debt.

32

maturity (from 15 years to 34 years). Thus, the model predicts that debt levels should be

negatively related to asset risk and debt maturity should be positively related to asset risk.

Consistent with the empirical results of Barclay and Smith (1995), our model predicts

that high growth firms (firms with low payout rates δ) use significantly shorter maturity debt.

Specifically, a 1% decrease in δ from 2.5% to 1.5% reduces optimal debt maturity from 42 years

to 12 years. However, the results indicate that high growth firms attempt to moderate the agency

cost of overinvestment only by reducing debt maturity; the optimal leverage ratio is actually a

little higher at the shorter debt maturity.

The table also illustrates that firms that face larger default costs (b) lengthen debt

maturity and reduce optimal leverage.26 Specifically, a firm having relatively low bankruptcy

costs (b = 25%) optimally chooses 7-year debt and a leverage ratio of 47%, while a firm with

high bankruptcy costs (b = 75%) optimally chooses 51-year debt and a leverage ratio of 37%.

By contrast, the table illustrates that firms in higher tax brackets (τ) optimally choose shorter-

term debt and higher leverage ratios. Thus, as the corporate tax rate is increased from 25% to

35% optimal debt maturity decreases from 26 years to 17 years and the optimal leverage ratio

increases from 37% to 44%. Both the default risk and tax status predictions of the model are

consistent with the empirical results of Stohs and Mauer (1996), who find that debt maturity is

significantly positively related to a firm’s credit risk and significantly negatively related to a

firm’s effective tax rate.

Finally, a decrease in the risk-free rate (r) or in the cost of exercising the investment

option (I) results in a decrease in optimal debt maturity and a decrease in the optimal leverage

ratio. As discussed earlier, a decrease in the risk-free rate reduces the risk-adjusted drift rate of

33

the commodity price, which in turn reduces firm value and debt capacity. As illustrated in Table

4, the firm’s response is to significantly shorten debt maturity while simultaneously reducing

leverage.

V. Conclusions

Since the early work of Jensen and Meckling (1976) and Myers (1977), financial theorists

have studied the interplay between conflicts of interest between debt and equity holders over real

investment decisions and corporate financing decisions. Although we have learned a great deal

about the qualitative impact of these agency conflicts on financing decisions, it has only been in

recent years that work in this area has turned to the important questions of how big are agency

costs and do they significantly influence financing decisions. However, the messages from this

work are mixed. Some authors find that agency costs are small and have little influence on

financing decisions, while others find that agency costs are significant but not large enough to

produce empirically consistent estimates of corporate leverage and debt maturity levels.

In this paper we develop a model of a firm that has an option to invest in a production

facility where the price of the commodity produced follows an exogenous stochastic process.

The cost of exercising the option and building the production facility is financed with debt and

equity. The optimal amount and maturity of debt are driven by the tax-deductibility of interest

payments, bankruptcy costs that result from an endogenous bankruptcy decision, endogenous

debt refunding costs, and agency costs resulting from a conflict between debt and equity holders

over the timing of the investment decision. We assume that bondholders commit to financing a

portion of the cost of the investment before the option is exercised, and that it is prohibitively

26 In a model that focuses on the liquidity risk of short-term debt, Diamond (1991) also predicts that higher creditrisk firms will employ longer-term debt.

34

costly to write and enforce a contract whereby an equity-maximizing firm adopts an exercise

policy that maximizes total firm value. Having rational expectations, bondholders fully

anticipate that the firm will choose an exercise strategy that maximizes equity value. We show

that this equity-maximizing strategy results in the firm exercising the investment option too early

relative to a firm-value-maximizing strategy. We further show how this early exercise decision

can be characterized as an incentive to overinvest in risky projects.

We find that this agency problem of overinvestment significantly reduces firm value and

increases credit spreads of risky debt. Importantly, we show that the agency conflict of

overinvestment significantly reduces the optimal leverage ratio (by 20% for base case parameter

values) and can simultaneously induce finite interior optimal debt maturities. The resulting

leverage ratios, debt maturity levels, and credit spreads of risky debt are consistent with those

observed in practice. We further establish that although agency costs decrease as debt maturity

decreases, and can be driven to zero for very short-term debt, the firm optimally bears significant

agency costs at the optimal leverage and debt maturity levels. Finally, consistent with recent

empirical work on the determinants of corporate debt maturity structure, the model predicts that

high growth firms and firms with high marginal tax rates optimally choose shorter-term debt,

while firms with relatively high default costs optimally choose longer-term debt.

The model has a number of limitations. First, the real decisions portrayed in the model

are limited to a single investment exercise decision and an abandonment decision on the

underlying unlevered value of the production facility. Although a more complicated set of real

decisions could certainly be accommodated in the model, it is not clear whether the additional

complexity would alter our basic results. Second, the model assumes a static capital structure

where the firm issues debt only once and cannot subsequently alter the debt level through time.

35

Allowing for a dynamic capital structure may significantly increase the agency costs of

overinvestment in our model. Indeed, recent work by Titman and Tsyplakov (2000) illustrates

that agency costs of underinvestment are significantly larger when capital structure is dynamic

than when it is static.27 Finally, it would be interesting to examine deviations from absolute

priority in bankruptcy and to incorporate multiple debt issues in the model. The former might

alter equityholders’ incentive to overinvest and the latter would allow for an analysis of debt

priority and maturity structures.

27 Furthermore, in a model without agency conflicts, Goldstein, Ju and Leland (2001) illustrate that a firm’s debtlevel choice is significantly smaller when the firm has the flexibility to increase the debt level in the future.

36

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Table 1 The Effect of Coupon (R) on the Agency Cost of Debt When Debt has Infinite Maturity____________________________________________________________________________________________________________

Investment Agency Bankruptcy Credit Spread AgencyCoupon Exercise Policy Firm Value Cost (%) Leverage Ratio Trigger (Basis Points) Cost (BP)_______ ______________ ____________ ________ _____________ __________ _______________ ________

R FIP S

IP FF SF AC FL SL BP FCS SCS CSAC____________________________________________________________________________________________________________

0.00 1.94 1.94 22.46 22.46 NA NA NA NA NA NA NA0.20 1.81 1.77 22.95 22.95 0.01 0.07 0.07 0.21 35.26 36.18 0.920.40 1.69 1.60 23.45 23.44 0.06 0.14 0.15 0.26 48.12 52.03 3.900.60 1.61 1.43 23.94 23.87 0.30 0.22 0.24 0.30 62.90 74.54 11.640.85 1.55 1.21 24.50 24.14 1.48 0.30 0.38 0.36 82.88 119.23 36.351.00 1.53 1.09 24.80 23.96 3.49 0.35 0.48 0.39 94.97 162.29 67.331.50 1.56 Immediate 25.54 23.50 8.69 0.47 0.67 0.50 131.60 285.81 154.202.00 1.67 Immediate 25.93 22.33 16.08 0.55 0.79 0.61 160.14 427.43 267.292.50 1.82 Immediate 26.06 19.87 31.17 0.60 0.88 0.72 181.58 642.47 460.902.64 1.87 Immediate 26.07 18.94 37.66 0.61 0.90 0.75 186.58 723.90 537.323.00 1.99 Immediate 26.04 16.04 62.35 0.63 0.95 0.83 197.87 1004.41 806.54

____________________________________________________________________________________________________________Notes. The base case parameter values are as follows: the initial output price, P, is $1.0 per unit; production costs, C, are $0.75 perunit; the cost of exercising the investment option, I, is $5.0; the volatility of the output price, σ, is 25% per year; the convenience yieldof the output price, δ, is 2% per year; the risk-free rate, r, is 5% per year; the corporate tax rate, τ, is 30%; and bankruptcy costs, b, are50% of the value of unlevered assets at the time of bankruptcy.

Table 2 The Agency Cost of Debt at the Optimal Leverage When Debt has Infinite Maturity____________________________________________________________________________________________________________________

Optimal Coupon Investment Agency Optimal Bankruptcy Credit SpreadPayment Exercise Policy Firm Value Cost (%) Leverage Ratio Trigger (Basis Points)

_______________ _______________ _______________ ________ _______________ ______________ _______________

FR SR FIP S

IP FF SF AC FL SL FBP S

BP FCS SCS____________________________________________________________________________________________________________________

Base Case 2.64 0.85 1.87 1.21 26.07 24.14 7.97 0.61 0.38 0.75 0.36 186.58 119.23____________________________________________________________________________________________________________________

20.0=σ 2.23 0.82 1.64 1.09 25.59 23.62 8.33 0.65 0.45 0.77 0.41 127.10 80.7630.0=σ 3.15 0.89 2.12 1.35 26.73 24.83 7.63 0.58 0.33 0.74 0.31 254.10 160.93

015.0=δ 3.56 0.99 1.85 1.09 39.24 36.13 8.61 0.62 0.37 0.74 0.30 162.87 92.54025.0=δ 2.10 0.75 1.89 1.31 18.36 17.07 7.53 0.60 0.39 0.77 0.40 213.17 146.81

25.0b = 3.14 0.85 1.85 1.18 26.79 24.22 10.61 0.69 0.40 0.86 0.36 206.61 114.8975.0b = 2.30 0.84 1.88 1.25 25.56 24.07 6.21 0.54 0.29 0.68 0.35 173.90 122.06

25.0=τ 2.39 0.87 1.85 1.28 26.97 25.62 5.27 0.56 0.36 0.70 0.36 164.88 110.5035.0=τ 2.87 0.82 1.89 1.16 25.21 22.64 11.38 0.65 0.40 0.80 0.35 207.76 126.33

03.0r = 1.76 0.55 1.94 1.38 21.66 20.23 7.05 0.56 0.32 0.69 0.36 235.91 174.2207.0r = 3.76 1.19 1.85 1.01 29.21 26.79 9.03 0.65 0.44 0.83 0.36 159.46 87.15

4I = 2.46 0.76 1.75 1.14 26.53 24.55 8.06 0.61 0.37 0.71 0.34 190.33 121.536I = 2.83 0.93 1.99 1.29 25.64 23.76 7.88 0.61 0.39 0.79 0.37 183.62 116.50

____________________________________________________________________________________________________________________Notes. The base case parameter values are as follows: the initial output price, P, is $1.0 per unit; production costs, C, are $0.75 per unit; the costof exercising the investment option, I, is $5.0; the volatility of the output price, σ, is 25% per year; the convenience yield of the output price, δ, is2% per year; the risk-free rate, r, is 5% per year; the corporate tax rate, τ, is 30%; and bankruptcy costs, b, are 50% of the value of unleveredassets at the time of bankruptcy.

Table 3 The Effect of Debt Maturity on the Agency Cost of Debt at the Optimal Leverage________________________________________________________________________________________________________________________

DebtMaturity Optimal Investment Agency Optimal Bankruptcy Credit Spread(Years) Face Value Exercise Policy Firm Value Cost (%) Leverage Ratio Trigger (Basis Points)

________ _______________ _______________ _______________ ________ _______________ _______________ _______________

T FQ SQ FIP S

IP FF SF AC FL SL FBP S

BP FCS SCS________________________________________________________________________________________________________________________

1 10.66 10.66 1.97 1.96 23.21 23.21 0.00 0.18 0.18 0.58 0.58 94.60 94.60

2 13.88 13.86 1.96 1.94 23.47 23.47 0.00 0.23 0.24 0.62 0.61 92.01 92.13

3 16.32 16.14 1.95 1.89 23.67 23.66 0.02 0.27 0.28 0.64 0.63 92.19 92.83

4 18.31 17.72 1.94 1.83 23.83 23.81 0.07 0.30 0.31 0.65 0.64 93.97 95.60

5 19.99 18.71 1.94 1.77 23.97 23.93 0.16 0.33 0.34 0.66 0.63 96.56 99.35

10 25.76 19.07 1.92 1.53 24.45 24.20 1.06 0.41 0.40 0.69 0.56 111.54 114.73

15 29.24 18.05 1.91 1.42 24.75 24.26 2.04 0.45 0.41 0.71 0.50 123.80 120.70

20 31.59 17.29 1.91 1.36 24.95 24.26 2.84 0.48 0.41 0.72 0.47 132.99 122.92

25 33.30 16.76 1.90 1.33 25.10 24.25 3.47 0.50 0.40 0.72 0.45 139.96 123.77

30 34.59 16.38 1.90 1.31 25.22 24.24 3.97 0.52 0.40 0.73 0.44 145.38 124.07

∞ 44.07 14.14 1.87 1.21 26.07 24.14 7.97 0.61 0.38 0.75 0.36 186.58 119.23________________________________________________________________________________________________________________________Notes. The base case parameter values are as follows: the initial output price, P, is $1.0 per unit; production costs, C, are $0.75 per unit; the cost ofexercising the investment option, I, is $5.0; the volatility of the output price, σ, is 25% per year; the convenience yield of the output price, δ, is 2%per year; the risk-free rate, r, is 5% per year; the corporate tax rate, τ, is 30%; the coupon rate of debt (ρ) is 6% per year; and bankruptcy costs, b, are50% of the value of unlevered assets at the time of bankruptcy.

Table 4 The Agency Cost of Debt at the Optimal Leverage and Debt Maturity____________________________________________________________________________________________________________________

Optimal Optimal Debt Investment Agency Optimal Bankruptcy Credit SpreadFace Value Maturity (Years) Exercise Policy Firm Value Cost (%) Leverage Ratio Trigger (Basis Points)

_________ ____________ ____________ _________ _______ ___________ _________ _____________

FQ SQ FT ST FIP S

IP FF SF AC FL SL FBP S

BP FCS SCS____________________________________________________________________________________________________________________

Base Case 44.07 17.29 ∞ 20 1.87 1.36 26.07 24.26 7.43 0.61 0.41 0.75 0.47 186.73 122.92____________________________________________________________________________________________________________________

20.0=σ 37.16 18.21 ∞ 15 1.64 1.25 25.59 23.90 7.06 0.65 0.48 0.77 0.56 127.10 106.7530.0=σ 52.54 16.43 ∞ 34 2.12 1.45 26.73 24.87 7.48 0.58 0.34 0.74 0.38 254.10 149.16

015.0=δ 59.39 24.30 ∞ 12 1.85 1.33 39.24 36.53 7.42 0.62 0.42 0.74 0.49 162.87 111.82025.0=δ 35.04 13.47 ∞ 42 1.89 1.38 18.36 17.10 7.38 0.60 0.40 0.77 0.46 213.17 142.13

25.0b = 52.26 21.43 ∞ 7 1.85 1.45 26.79 24.58 9.03 0.69 0.47 0.86 0.61 206.61 115.2875.0b = 38.25 15.34 ∞ 51 1.88 1.32 25.56 24.10 6.05 0.54 0.37 0.68 0.40 173.90 125.66

25.0=τ 39.86 16.92 ∞ 26 1.85 1.39 26.97 25.69 4.96 0.56 0.37 0.70 0.45 164.88 114.8935.0=τ 47.79 17.34 ∞ 17 1.89 1.33 25.21 22.81 10.52 0.65 0.44 0.80 0.49 207.76 130.46

03.0r = 29.30 13.01 ∞ 19 1.94 1.53 21.66 20.48 5.78 0.56 0.35 0.69 0.48 235.91 241.1207.0r = 62.64 19.87 ∞ ∞ 1.85 1.09 29.21 26.79 9.03 0.65 0.44 0.83 0.36 159.46 87.16

4I = 40.99 15.73 ∞ 19 1.75 1.27 26.53 24.69 7.49 0.61 0.40 0.71 0.45 190.33 124.356I = 47.14 18.70 ∞ 22 1.99 1.43 25.64 23.88 7.37 0.61 0.41 0.79 0.49 183.62 121.82

____________________________________________________________________________________________________________________Notes. The base case parameter values are as follows: the initial output price, P, is $1.0 per unit; production costs, C, are $0.75 per unit; the cost of exercising the investmentoption, I, is $5.0; the coupon rate of debt (ρ) is 6% per year; the volatility of the output price, σ, is 25% per year; the convenience yield of the output price, δ, is 2% per year;the risk-free rate, r, is 5% per year; the corporate tax rate, τ, is 30%; the coupon rate of debt (ρ) is 6% per year; and bankruptcy costs, b, are 50% of the value of unleveredassets at the time of bankruptcy.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85

Volatility (Sigma) of Output Price

Inve

stm

ent T

rigg

er P

rice

First-Best Second-Best

Figure 1. First- and second-best investment trigger prices as a function of volatility. Thefirst-best investment trigger is the output price at which the investment option is exercised for avalue-maximizing strategy and the second-best investment trigger is the output price at which theinvestment option is exercised for an equity-maximizing strategy. Debt is assumed to haveinfinite maturity. Base case parameters: I = $5, r = 5%, δ = 2%, C = $0.75, R = $0.85, τ = 30%,and b = 0.50.

22

22.5

23

23.5

24

24.5

25

25.5

26

26.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Leverage Ratio

Firm

Val

ue

First-Best Second-Best

Figure 2. First- and second-best firm values as a function of the leverage ratio. The first-best firm value assumes a value-maximizing investment option exercise strategy and the second-best firm value assumes an equity-maximizing investment option exercise strategy. Debt isassumed to have infinite maturity. Base case parameters: P = $1.0, I = $5, r = 5%, δ = 2%, σ =25%, C = $0.75, τ = 30%, and b = 0.50.

23

23.25

23.5

23.75

24

24.25

24.5

24.75

25

25.25

25.5

25.75

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Debt Maturity in Years

Firm

Val

ue

First-Best Second-Best

Figure 3. First- and second-best firm values as a function of debt maturity. The first-bestfirm value assumes a value-maximizing investment option exercise strategy and the second-bestfirm value assumes an equity-maximizing investment option exercise strategy. The firm valuesreflect optimal leverage at each debt maturity level. Base case parameters: P = $1.0, $I = 5, r =5%, δ = 2%, σ = 25%, C = $0.75, ρ = 6%, τ = 30%, and b = 0.50.