DBJ Discussion Paper Series, No.1101

Risk Management in Corporate Financial Policy

Worawat Margsiri(Fordham University)
andAntonio S. Mello(University of Wisconsin-Madison)

July

2011

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings,
conclusions or recommendations expressed in these papers are those of the authors and do
not reflect the views of the Institute.

Risk Management in Corporate Financial Policy
Worawat Margsiri

Antonio S. Mello

Fordham University

University of Wisconsin-Madison
January 30, 2011

Abstract
This work shows how risk management interacts with the …rm’s …nancial structure, its investment
and dividend policies. Financially constrained …rms simultaneously determine their optimal capital
structure and how to fund investments by deciding the level of cash retained and the level of risk.
A …rm’s cash ‡ow rate and leverage a¤ect its risk taking. Firms with low interest coverage takegreater risks if they have investment opportunities. The pro…le of the investment matters to a …rm’s
risk strategy: Large, lumpy investments induce more aggressive behavior than small, incremental
investments. Although it is common for …rms with investment opportunities to have lower leverage
ratios, it is possible that a …rm with investments decide to have high levels of debt, as long as leverageadds more to the probability of investing than to the probability of defaulting. When investors do
not observe the …rm’s cash ‡ow rate and whether the …rm has growth options, risk and dividend
choices reveal information about the value of the …rm. Both debt and equity …nancing relax …nancial
constraints and accelerate investment, but …rms do not freely choose to fund with more debt or equity.
Debt …nancing can lead to overhang after investment, and equity …nancing incurs high issuance costs.
When the …rm decides to fund investment with additional equity, it always follows a low risk strategy,
because a riskier strategy to accelerate investment becomes unnecessary.
JEL Classi…cation: G31, G32, G33, G35
Keywords: Risk Management, Investment, Financial Policy
Corresponding address: Wisconsin Business School, University of Wisconsin, 975 University Avenue, Madison, WI 537061323. Tel: (608) 263-3423, Fax: (608) 265-4195, Email: amello@bus.wisc.edu.

1

Risk Management in Corporate Financial Policy

Abstract
This work shows how risk management interacts with the …rm’s …nancial structure, its investment anddividend policies. Financially constrained …rms simultaneously determine their optimal capital structureand how to fund investments by deciding the level of cash retained and the level of risk. A …rm’s cash
‡ow rate and leverage a¤ect its risk taking. Firms with low interest coverage take greater risks if they
have investment opportunities. The pro…le of the investment matters to a …rm’s risk strategy: Large,
lumpy investments induce more aggressive behavior than small, incremental investments. Although it iscommon for …rms with investment opportunities to have lower leverage ratios, it is possible that a …rm
with investments decide to have high levels of debt, as long as leverage adds more to the probability ofinvesting than to the probability of defaulting. When investors do not observe the …rm’s cash ‡ow rate andwhether the …rm has growth options, risk and dividend choices reveal information about the value of the…rm. Both debt and equity …nancing relax …nancial constraints and accelerate investment, but …rms do
not freely choose to fund with more debt or equity. Debt …nancing can lead to overhang after investment,
and equity …nancing incurs high issuance costs. When the …rm decides to fund investment with additional
equity, it always follows a low risk strategy, because a riskier strategy to accelerate investment becomes
unnecessary.

21

Introduction

Risk management is one of the most important activities in corporate …nance. Yet, despite the growing
attention it has received in the last …fteen years, risk management is still at an embryonic stage. This ispartly due to the fact that risk, being everywhere, interacts with the various …nancial policies of the …rm
in ways that are not easy to decipher. There have been important advances explaining …rms’motivations
to control risks. In most cases, the reasons highlight either capital market imperfections [see, for example,
Smith and Stulz (1985), and Froot et al (1993)]; incomplete information [Ross (1997)] or managerial
agency problems [Tufano (1998)]. Usually, these reasons relate …nancial risk management to a particularpolicy of the …rm, such as investment policy, capital structure policy or cash management, and thenevaluate how each policy improves on the value of the …rm. The reality is that all these policies work
together. Financial policy is not really separable from investment policy. And since cash sourced inside
the …rm is cheaper than cash sourced outside, liquidity management is related both to …nancial policy
and to dividend policy. A better understanding of the role of risk management requires that the …rm’s
capital structure as well as its investment and dividend policies must be considered in conjunction withrisk management.
To analyze how risk management interacts with the various policies of the …rm, we use a dynamic
model of a …rm that generates cash from existing assets and which has growth opportunities. Cash ‡ows
follow a random walk with a drift, so the …rm hedges cash ‡ow shocks that persist over time. This allows
us to measure the e¤ects of risk management on the value of the …rm and its claims, and not just on thenext instant’s cash ‡ows. The dynamic model allows us to incorporate revisions in some control variables.
For example, investment gives the …rm the opportunity to revise its capital structure.
The …rm is …nanced with equity and debt. In the basic model, after an initial contribution, equityholders
are assumed to have no additional money to invest in the …rm. The cash ‡ows that originate from operating
the assets are used to make payments to the claimholders. With no possibility of resorting to current
equityholders’deep pockets, it is possible that the …rm may run out of cash. When that happens, the …rm
falls into …nancial distress, and is assumed to be liquidated. Liquidation imposes costs to equityholders
and debtholders, since both lose everything. Costly bankruptcy creates incentives to retain cash in the…rm.
Risk management lets equityholders change the risk pro…le of the …rm’s cash ‡ows. Changing the riskof the cash ‡ows alters the expected costs of bankruptcy. Yet it also changes the timing of investing, sinceinvestment is funded in part with accumulated cash balances.
We …nd that risk management varies with the circumstances: At times the …rm follows a low-risk

3strategy; at other times it is deliberately more aggressive. Risk management depends critically on anumber of factors, particularly the …rm’s rate of operating cash ‡ows, the amount of cash balances available,
leverage, dividends, the costs of …nancial distress and the type of investment.
Firms with low interest coverage ratios, resulting from either high leverage or a low growth rate of
cash ‡ows, are …rms with low levels of cash accruing to equityholders. The marginal bene…t of a low risk
strategy is therefore small, and equityholders might seek more risk. For such equityholders, the trade o¤between accelerating investment and the loss from liquidation of a …rm that generates low cash ‡ow favors
the adoption of a riskier strategy.
On the other hand, equityholders of …rms with a high cash ‡ow generation ability have strong incentives
to reduce the probability of liquidation, so they tend to follow a low risk strategy. A higher rate of cash
‡ow generation also makes it easier to fund investments, a valuable option that should not be risked byan aggressive strategy, especially when leverage is not too high.
Cash balances (inside equity) relate to risk management in a straightforward way: Lower cash balances
make …rms act conservatively in order to reduce the likelihood of bankruptcy, a policy that becomes
relatively more important than the exercise of a distant (for lack of funds) option to invest. At higher
levels of cash balances, the option to invest becomes more feasible, and taking risks can help speed up theinvestment.

This behavior di¤ers from the behavior of …rms that are …nancially unconstrained. In an

unconstrained …rm, equityholders of a levered …rm take on more risk when the value of the assets-in-place
falls low enough and the value of the abandonment option increases.
Firms with investment opportunities do not necessarily have low leverage ratios. Leverage helps tofund investment. The incentive to borrow to add to cash balances needed for investing might outweighthe cost of having more debt. What is not obvious is that a …rm with an opportunity to invest right away
if it issues more debt will necessarily do so. At times, the amount of debt needed to invest sooner is just
too much, and speeding up investment to attain greater operating cash ‡ows, can later on put the …rm
in greater danger from the higher debt obligations. Clearly, achieving larger size by levering up does notnecessarily translate into higher valuation.
The pro…le of an investment matters greatly to the risk management policy of the …rm. Consider two
opposite cases: on one hand, a discrete irreversible investment opportunity that requires signi…cant up-front
costs, similar to a real option; on the other hand, small investments that are made continuously. These
are simpli…cations, but their di¤erent characteristics can help us draw interesting conclusions. When theinvestment is like a real option, adopting a high risk strategy can be optimal for a …nancially constrained…rm. The lumpiness of the investment creates the incentive to take risks when these can improve thechance that the …rm can get enough cash to make the investment. On the other hand, if the investment4

occurs continuously in small increments, adopting a high risk strategy can hurt the …rm’s cash balances,in which case a risk management policy adds little value. Hence, cash ‡ow volatility hurts …rm value
when investment is small and occurs with some regularity. For a …rm with no investment opportunities,
there is only downside in following a risky strategy, unless the …rm is highly leverered and is …nanciallyunconstrained, in which case equityholders will try to bet their way out of bankruptcy.
Risk management appears to be relatively insensitive to the pro…tability of an investment. This may
seem unusual. The explanation lies in the fact that a more pro…table investment creates two e¤ects that
impact the incentives to change risk in opposite ways: On the one hand, more risk increases the probabilityof investing when investment is lumpy. On the other, more risk increases the likelihood of bankruptcy. In
most circumstances, one e¤ect does not seem to dominate the other.
Many papers have found that …rms’…nancing relies mainly on internal equity and debt. This choice
is captured in our basic model, which is extended to allow also outside equity issuance at the time of theinvestment. Additional equity mitigates the …rm’s …nancial constraint and speeds up investment. Unlike
debt, equity increases cash balances but not the risk of default. But equity is expensive to issue, so …rms
issue additional equity only when the reduction in the expected cost of default is greater than the issuingcosts. Whether the …rm issues debt or equity to fund investment matters to its risk policy. More equity…nancing is re‡ected in a more conservative risk strategy before the investment, similar to the behavior ofa …rm that …nances investment with debt but has a low debt to cash ‡ow coverage ratio.
Once the investment takes place, there is no incentive for the …rm to adopt a risky strategy. In
essence, relaxing the …nancial constraints by allowing the …rm to issue equity at low issuance costs tofund investment makes the …rm behave more conservatively. A high risk strategy adds little to help fundinvestment that low cost equity issuance does not provide.
Next, we modify the model to incorporate asymmetries in information between fully informed insiders(existing equityholders) and imperfectly informed stock market investors. Outside investors cannot observe
the quality of the assets in place, measured by the cash ‡ow growth rate, and whether the …rm has growth
opportunities; instead they form expectations about the …rm based on publicly available information. The
actions of insiders managing the …rm provide important signals that help investors revise their valuationof the …rm. Investors observe the cash balances, but understand that these are volatile, and therefore havetrouble …guring out the …rm’s true cash ‡ow rate. Finally, investors can see when the …rm starts paying
dividends, and whether the …rm behaves more conservatively or more aggressively.
In such a setting, investors observe changes in the …rm’s cash balances over time. Suppose cash balances
gradually increase. If at some level of cash balances investors see the …rm announcing a dividend payout,
they conclude that the …rm must not have growth opportunities in the foreseeable future. If, instead,5

investors notice that the …rm switches from a low risk strategy to a more aggressive one, they conclude
that the higher risk following an increase in cash balances cannot be the result of some harmful desire togamble on bankruptcy, but instead an attempt to accelerate investment. A …rm that keeps accumulating
cash ‡ows beyond that level and neither switches risk nor announces dividends must be a …rm that has
an investment opportunity but may have the true cash ‡ow rate di¤erent from what they had expected.
Our results show how risk management and dividend policy can reveal important information that helps
investors …gure out the type of the …rm and its fundamental value. When cash balances are low, …nanciallyconstrained …rms do not pay dividends and follow low risk strategies. As cash balances increase, …rms
with investment opportunities switch to a high risk strategy, while still refraining from making dividend
payments, in order to conserve cash for future investments. Switching to a higher risk strategy increases thelikelihood of investing with internal cash balances. Firms start to pay dividends only after the investment
is made, but only insofar as the cash remaining in the …rm after the investment is high enough: Oncethe investment is implemented, the value of the assets in place increases, and therefore the opportunity
cost of going bankrupt also increases. Firms with no investment opportunities will continue to use a low
risk strategy and do not pay dividends unless cash balances are high enough to avoid bankruptcy. An
important implication is that a risk management policy provides information to outside investors about
the value of the investment opportunities a …rm has, and correspondingly a¤ects their valuation of the…rm.
In a recent paper closely related to ours, Bolton et al (2009) also explore the interactions amongcorporate investment, …nancing and risk management. There are, however, important distinctions between
our work and theirs. First, in their model …rms continuously adjust investment, and thus have no real
options. Given that data show that investment is lumpy, we believe that discrete and signi…cant investmentout‡ows are important. We show that the characteristics of the …rm’s investment matter to the risk
strategy. In Bolton et al. hedging a¤ects the value of the …rm through the costs of margin requirements.
When these costs are low, presumably …rms could eliminate all systematic risk. In our model, wheninvestment implies …xed adjustment costs, a risk taking strategy can be optimal even in a frictionlessworld.
Second, in our model …rms decide on what risk to take by evaluating the impact of the choice on thevalue of the …rm and its claims, whereas in Bolton et al (2009) the i.i.d nature of the shocks allows themto analyze how risk management a¤ects the next instant’s cash ‡ows. Obviously, managing the risk ofnext instant liquidity and managing the risk of the …rm’s value are two very di¤erent objectives.
We begin with a basic model of a …nancially constrained …rm, …nanced both with debt and equity.
After the initial investment, equityholders are assumed to have no more funds to inject if the …rm has a6negative cash ‡ow. If the …rm exhausts its cash reserves, it goes bankrupt and is liquidated, and both
equityholders and bondholders lose everything. This creates incentives to carry cash balances in the …rm.
The …rm has the opportunity to make an investment that requires the payment of a lump sum amount andthe investment is irreversible. Once the investment is made, the …rm can issue additional debt and revise
its optimal capital structure. Besides deciding on the optimal capital structure and investment, the …rm
must also choose its dividend policy as well as how much risk it bears. Risk management is executed byadjusting the volatility of the …rm’s cash ‡ows produced by current operations. The assumptions of themodel are outlined in Section 2. Section 3 computes the values of the equity and the debt, both the initialdebt after the investment is made and the additional debt issued when the investment takes place. Section
4 determines the values of the …rm’s claims before investment and the initial cash balances. Section 5
examines a …rm with no investment opportunities and contrasts it with the …rm in the previous sections.
Section 6 provides a numerical example to illustrate the interactions among the various policies of the …rmand how they relate to risk management.

Section 7 looks at investments with di¤erent characteristics.

Section 8 considers asymmetry of information between insiders and outside investors, and evaluates theinformation content of risk management, as well as dividend decisions. Section 9 relaxes the constraint on
additional equity issuance. Section 10 highlights the main conclusion.

2

Assumptions of the Model

Consider a …rm managed by equityholders who maximize the value of their claim. At time t = 0; equityholders contribute an amount X0 to the …rm. The …rm also sells debt with a perpetual coupon c to0

increase its initial capital from X0 to X0 . After t = 0; equityholders are assumed to be unable to makeadditional capital contributions, and outside …nancing is possible only with debt, and occurs when the…rm takes on a new investment.

This is meant to replicate …rms re…nancing decisions that appear to

be largely associated with important events, such as investments. This also captures the notion that it isusually more di¢ cult for a …rm to borrow when it has a low cash balance and is close to liquidation thanwhen it has a high cash balance and is making investments.
The …rm generates cash ‡ows from its operations at a rate of. The …rm’s cash balances, X; evolve

according to a Brownian motion with a drift:dX = (

c(1)d)dt + dZ,

where c is the coupon payment to debtholders, d is the dividend payment to equityholders,instantaneous volatility rate of the cash ‡ows, and Z
payments equal c(1), whereis theN (0; t). Since debt is tax deductible, net coupon

is the corporate tax rate.
7(1)

There is a constant instantaneous riskless interest rate of . For simplicity, it is assumed that the cash
balances held in the …rm earn no interest; otherwise the …rm would receive an additional cash ‡ow equal
to Xrdt from investing its cash balances, where r is the instantaneous interest rate earned on X.
It is assumed that when cash balances become zero (X = 0), the …rm is declared insolvent and isliquidated. Although there may be some value left in the …rm, equityholders are assumed not to havepockets deep enough to rescue the …rm. Liquidation at zero cash balances also assumes that strategic
default is not feasible. Any changes in these assumptions would change the event of bankruptcy.
Equityholders decide the …rm’s capital structure as well as when to invest and when to pay dividends.
They also determine the risk level of the …rm’s operations. At all times they can costlessly change the riskof the cash ‡ows by choosing the volatility rate , where

may take any values between

L (low risk) andH (high risk).

The …rm has one irreversible project that will increase the instantaneous cash ‡ows by a factor of(i.e.,

increases to>1). To make the investment, the …rm must spend a lump-sum equal to I > 0. At thetime of the investment, equityholders have the opportunity to alter the …rm’s capital structure and issue
additional perpetual debt to partly …nance the investment. Denote c1 as the coupon of the original debt
and c2 as that of the new debt, then the new debt will increase the total coupon payments from c1 to
c1 + c2. Newly issued debt is assumed to have the same seniority as outstanding debt. Later we generalize
the model to allow for additional equity …nance and analyze a di¤erent type of investment. Instead ofa one-time …xed investment opportunity, we will look at many small investments.

Although corporate

investments appear to be lumpy, we wish to understand how the characteristics of the investment impact
risk management and payout policies.
In the setting just described, the objective of the equityholders is to maximize the value of the equity bychoosing the …rm’s …nancial policy (the initial capital structure and the re…nancing upon making the newinvestment), the dividend policy, the timing of the investment in the new project and the risk management.

3

Values of the Equity and Debt after Investment

After the investment is made, both the remaining cash balances and the …rm’s cash ‡ows change, and sodo the value functions describing the …rm’s securities. Therefore, we solve the model backward, starting…rst with the value functions right after the investment, and then proceed to determine the value functions
before the investment. We denote E A , D1A and D2A as the value functions after the investment for theequity, the initial debt, and the additional debt, respectively. Later we will consider that additional outside
equity is also available.
83.1

Value of the Equity After Investment

After the investment is made, the company has both the initial and the new debt, so the total coupon
payments are c1 + c2. At that time, equityholders maximize E A , the value of the equity after investment,by choosing the dividend payout and the risk level. E A , d, andE A = maxfd + (;d(c1 + c2)(1)

have to satisfy the following expression:
A
d)EX
+

1
2

2

A
EXX
g

(2)

A
The …rst-order condition with respect to the dividend d is EX= 1: This means that the dividend

policy switches between paying no dividends to paying maximum dividends. The …rst-order condition
with respect to the level of riskA
is EXX= 0, which implies that the risk policy switches between highand low risk levels.
De…ne the dividend threshold Xd as the point at which the …rm switches between paying no dividends
to paying dividends. Then the following proposition summarizes the dividend and risk policies after the…rm makes the investment:
Proposition 1 After the investment, the …rm pays no dividend if X

Xd , and pays as dividends all the

cash left after paying coupons on the debt if X > Xd . At all times the …rm chooses a low risk strategy,

L.

Proof. See Milne and Robertson (1996).
From proposition 1, in the region 0 < X < Xd , Equation (2) can be re-written as follows:
EA = ((c1 + c2)(1

A
))EX
+

1
2

2 A
L EXX

(3)

There are three boundary and smoothness conditions that de…ne the equity value function and the
optimal dividend policy:
Condition 1: E A jX=0 = 0. This is the boundary condition at liquidation; it says that when cash
balances are zero (X = 0), the …rm is liquidated and the equityholders receive nothing. Whatever thevalue of the equity at that point, it is lost. Therefore equityholders bear a direct deadweight cost if they
let X go to zero.
A
Condition 2: EX
jX=Xd = 1: This is the continuity condition, stating that at the dividend threshold(X = Xd ), the marginal value of cash kept in the …rm or the …rst derivative of the equity value function withA
respect to X, EX, equals the marginal value of cash paid out, 1: For a one time lump-sum dividend payment,

this condition would be su¢ cient to guarantee the optimality of Xd [see Dixit and Pindyck (1994)]. Dumas(1991), however, points out that for continuous dividend payments, the order of di¤erentiation increases

9

by one, so Condition 2 holds for any Xd . This implies that an additional condition is required to guarantee
the optimality of Xd :A
Condition 3: EXX
jX=Xd = 0: This is the optimality condition for Xd ; At the dividend thresholdA(X = Xd ), the second derivative of the equity value function with respect to X, EXX, must be equal tozero. For more details, see Dumas (1991) and Dixit (1993).
The solution to the value of the equity takes the general form:AA

E A (X) = A1 em1 X + A2 em2 X ;
where
mA
1 =

(

mA
2 =

(

(c1 + c2)(1

)) +

and
(c1 + c2)(1

))

p

(

p

(

(4)

(c1 + c2)(1))2 + 22L

(c1 + c2)(1))2 + 2

2
L

2
L

2
L

;

(5)

:

(6)

The coe¢ cients A1 and A2 are obtained from Conditions 1 and 2, or explicitly:
A

A

em1 X
E (X) = A mA X
m1 e 1 d

em2 X
;
mA
2 Xd
mA
2e

A

and Xd is obtained from Condition 3:

mA

Xd =
For X

(7)

1
)
2 log( mA
2

mA
1

mA
2

:

(8)

Xd , the cash balances are more than enough to pay out dividends, and the …rm pays all theexcess cash above Xd to equityholders as dividends, keeping only Xd in the …rm. The equity value has theformA

E A (X) = X

Xd +em1 XdAA
m1 em1 Xd

A

em2 Xd
:
mA
2 Xd
mA
2e

(9)

Delaying dividend payments by choosing a high threshold for cash balances, Xd ; allows the …rm toaccumulate more cash and reduce the risk of liquidation (X = 0), but it also reduces the value of thedividend payments to the equityholders. Therefore, the optimal dividend condition requires that at Xd ,the marginal bene…t of retaining one extra dollar of cash in the …rm equals the marginal costs of payingthat dollar out as a dividend.
Jensen and Meckling (1976) show that equityholders of levered …rms have an incentive to increaserisk after debt has been issued. The call feature of the equity in a levered …rm increases in value withvolatility. When equityholders bear some of the costs of …nancial distress, however, they tend to favor
low risk strategies. For example, Purnanandam (2008) has shown that if a …rm faces potential losses tocompetitors when its value declines, equityholders have incentives to reduce …rm risk even if the …rm is10partly …nanced with debt. In our model, bankruptcy destroys the cash ‡ows to equity from continuation,
as well as the equityholders’exit option. The assumption that equityholders are cash constrained makes
them choose a low risk strategy for the …rm. Following Shleifer and Vishny (1995) we assume that …rms
…nd it di¢ cult to attract additional outside equity after investors observe a history of poor performance.

3.2

Value of Initial Debt after Investment

After the investment, for cash balances X
D1A = c1 + (Xd , the value of the original debt D1A satis…es:(c1 + c2)(1

))D1A
X +

1
2

2
A
L D1XX :(10)

The general solution to Equation (10) has the formAA

D1A (X) = B1A em1 X + B2A em2 X +

c1

;

(11)

where the term c1 represents the present value of the coupon payments if the …rm is never liquidated, andAA

the term B1A em1 X + B2A em2 X represents the expected value lost due to liquidation. The coupon c1 is set
when the debt is issued at t = 0, and debtholders receive c1 payments continuously unless cash balances
become zero. Formally, a boundary condition applies to D1A at X = 0:
Condition 4: D1A jX=0 = 0: This condition speci…es that when cash balances are zero, the …rm isliquidated, and the debt value becomes zero. Consequently, debtholders also bear deadweight costs ofbankruptcy.
Because the …rm will not keep cash balances above Xd , the value of the debt becomes constant for
X > Xd : Therefore, the next condition applies to D1A at X = Xd :Condition 5: D1A
X jX=Xd = 0: This is the smooth-pasting condition at Xd . It means that the change

in the debt is zero once X reaches Xd . Note that because Xd does not maximize D1A (X), there is no
optimality condition associated with D1A , suggesting there are agency costs of debt …nancing.
Conditions 4 and 5 give B1A and B2A . Explicitly:A

D1 (X) =

c1

A

1

A

em1 Xd em2 X mA
1A
em1 Xd mA
1AA

em2 Xd em1 X mA
2A
em2 Xd mA
2

!

(12)

It is easy to verify that D1A (X) is increasing in Xd , which means that debtholders prefer that equityholders keep more cash in the …rm.

11

3.3

Value of Additional Debt after Investment

After investment, the value of additional debt issued to fund the investment, D2A satis…es
D2A = c2 + ((c1 + c2)(1

)

A
d)DX
+

1
2

2
A
L DXX :

(13)

Similar to D1A , Equation (13) has the general solution:AA

D2A (X) = C1A em1 X + C2A em2 X +

c2

;

(14)

with two boundary and smooth-pasting conditions:
Condition 6: D2A jX=0 = 0: When the cash balances are zero, the value of the additional debt is also
zero. Original debt and additional debt have equal priority.
Condition 7: D2A
X jX=Xd = 0: This is the smooth-pasting condition at Xd , meaning that the change inthe value of the new debt is zero when the …rm starts paying cash as dividends, at Xd .
C1A and C2A can be solved using Conditions 6 and 7. Explicitly,A

D2 (X) =

4

A

c2

A

em1 Xd em2 X mA
1A
em1 Xd mA
1

1

A

A

em2 Xd em1 X mA
2A
em2 Xd mA
2

!

:

(15)

Values of Equity and Debt before Investment

De…ne E B and DB as the values of the equity and the debt before the investment, respectively. Cash0balances, an instant before the investment, are denoted by Xi , and an instant after the investment by Xi .
0

Xi depends on the cost of the investment, I , and also on the amount raised from issuing new debt, D2A ,0which in turn depends on Xi :0

Xi = Xi0

I + D2A (Xi ):00This equation allows us to write Xi in terms of Xi : Xi = Xi + I(16)
0

D2A (Xi ), which shows that the0

investment threshold is determined by: 1) the cash balances after the investment Xi ; and 2) the amount0of additional debt the …rm issues to …nance the investment, itself a function of Xi and c2. Thus, the0investment policy is jointly determined by Xi and c2. In other words, how much cash balances the …rm
optimally plans to have after investing and how much debt the …rm issues to …nance the investment
determine when the …rm invests.
The value of the equity an instant before investing and an instant after investing must be equal, leading
to the value-matching condition:
Condition 8: E B jX=Xi = E A jX=X 0 :i12Because investment is lumpy, the smooth-pasting condition is su¢ cient to guarantee the optimalityof the investment policy, and because the investment policy is set by Xi0 and c2, there are two related
optimality conditions:
B
Condition 9: EX
jX=Xi (1A
D2A
X jX=X 0 ) = EX jX=X 0 : This is the smooth-pasting condition that guarii

antees the optimality of Xi : To understand this condition, …rst consider the case of no new debt to fundB
A
investment. Then EX
jX=Xi = EX
jX=X 0 . This condition requires that the marginal value of cash in thei…rm, before and after investment, is the same. When the …rm has low cash balances (X is low), themarginal value of cash in the …rm is high; as cash balances increase, the marginal value of cash in the…rm declines; when the …rm accumulates enough cash so that the marginal value of cash before and afterinvestment is the same, the …rm invests.
Next, consider that the …rm issues an amount of new debt equal to D2A to fund the investment. By
increasing cash at the investment threshold, the …rm in e¤ect reduces the marginal value of cash before
investment, hence the term (1D2A
X ). This is true even if there are issuance costs. How much additional

debt the …rm will issue is determined by the next condition:B
jX=Xi D2A
Condition 10: EX
c2 jX=X 0 =iAEc2
jX=X 0 : This condition sets the optimal coupon c2, or theioptimal amount of additional debt. The left-hand side of the expression represents the marginal bene…ts
from issuing additional debt: The increase in the coupon c2 increases the cash balances by D2A
c2 . TheB
higher cash balances then a¤ect marginal bene…t of the new debt through the term EX. Hence, the productof the two terms represents the total marginal bene…t of the new debt.
The marginal costs of issuing new debt are seen on the right-hand side of Condition 10. Debt requires
higher coupon payments in the future, which reduces the value of equity after investment by E1A
c2 .
Condition 11: E B jX=0 = 0: This is the boundary condition at liquidation; it means that when the …rmruns out of cash, the value of equity is zero.

4.1

Value of Equity Before Investment

Before investment, E B , d, andmust satisfy the expression:

E B = maxfd + (
d;

c1(1

)

B
d)EX
+

1
2

2

B
EXX
g

The following proposition establishes the optimal dividend policy before investing I:
Proposition 2 It is not optimal to pay dividends before investing.

13

(17)

Proof. See Appendix 1
The intuition behind Proposition 2 is straightforward: If the …rm chooses to pay maximum dividend, it
will not have enough cash balance to invest. If the investment project is pro…table (the net present value
is strictly positive), it is optimal to conserve cash and increase the probability of investing; hence, it is not
optimal to pay dividends before investment.
The next proposition establishes the optimal risk strategy before investing I:
Proposition 3 There is a unique risk switching point Xs at which the …rm chooses
choosesL

if X

Xs , andH if X > Xs :Proof. See Appendix 2
From Proposition 2 and 3 when 0 < X < Xs , the …rm chooses
EB = (

c1(1

B
d)EX
+

)

De…ne E BL as the equity value function when

L , and Equation (17) becomes:

1
2

2 B
L EXX :

L is chosen.

(18)

Then the general solution to Equation(18) has the form
BL

m1
E BL (X) = AL
1e

where
mBL
=
1

(

mBL
=
2

(

c1(1

)) +

and
c1(1

When Xs < X < Xi , the …rm chooses
EB = (

))

X

p

(

p

(

BL

m2
+ AL
2e

X

;

(19)

c1(1

))2 + 22L

c1(1))2 + 2

2
L

2
L

2
L

;

(20)

:

(21)

H , and Equation (17) becomes:

c1(1

B
d)EX
+

)

De…ne E BH as the equity value function when

1
2

2
B
H EXX :

(22)

is chosen. Then for Xs < X

HXi , the generalsolution to the previous expression has the form
BH

m1
E BH (X) = AH
1 e

where
mBH
=
1

(

mBH
=
2

(

c1(1

)) +

and
c1(1

))

X

p

(

p

(

14

BH

m2
+ AH
2 e

X

;

(23)

c1(1

))2 + 22H

c1(1))2 + 2

2
H

2
H

2
H

;

(24)

:

(25)

The boundary, smooth-pasting and optimality conditions are respectively:
Condition 12: E BL jX=Xs = E BH jX=Xs : This value-matching condition guarantees the continuity ofthe value function at the risk switching point.
BL
BH
Condition 13: EX
jX=Xs = EX
jX=Xs : This smooth-pasting condition ensures the continuity of the…rst derivative. It means that the marginal value of following a high risk strategy is equal to the marginalvalue of following a low risk one. Because the control is instantaneous, this condition is not su¢ cient toguarantee the optimality of Xs . We need a higher derivative for such optimality [see Dumas (1991) for
details].
BL
BH
Condition 14: EXX
jX=Xs = EXX
jX=Xs : This condition guarantees the optimality of Xs . It meansthat the change in the marginal value of the high risk strategy should equal the change in the marginalvalue of the low risk strategy.
Also, note that when X is approaching zero, equityholders choose low risk,

L , so the value function

at liquidation is E BL . Therefore, Condition 11 becomes E BL jX=0 = 0:
L
H
H
The coe¢ cients AL
1 , A2 , A1 and A2 are obtained from Conditions 8 and 11-13. They can be solved

analytically and are given in Appendix 3.
0The optimal investment threshold Xi (as determined by Xi and c2) is obtained from Conditions 9 and
10, but it is not possible to solve the problem analytically, and we must resort to a numerical solution.
Finally, the optimal risk policy Xs is obtained by Condition 14, and is given by
mBL

Xs =

2 log( m1BL )
2

mBL
1

mBL
2

:

(26)

It is interesting that, from Equation (26), for a given coupon c1, the risk switching threshold Xs is
independent of the multiplierof the cash ‡ows after the investment I is made. At …rst, this result may

seem counter-intuitive: The higheris, the more pro…table the investment, so the …rm should be moreconservative and increase Xs . To understand this, consider the marginal bene…ts and costs of changing
risk (through changing Xs ). An increase inheightens the incentives not only to reduce the probabilityof liquidation (by increasing Xs ) but also to increase the probability of investing (by lowering Xs ). The
two e¤ects seem to o¤set each other, and leave Xs unchanged.1
This is a bit more complicated, however, because although v does not directly a¤ect Xs , it does soindirectly through c1, as the next proposition states:
1 Another way to see this result is to recognize that E BL (X) can be written as E BL (X) = E A (X 0 )F (X), and E BH (X) =i
0
E A (Xi )G(X), where E A (Xi0 ) is a function of , and F (X) and G(X) are independent of : Condition 14 can then be written0
as E A (Xi ) [FXX (Xs ) GXX (Xs )] = 0, which implies that a change in a¤ects equally FXX (Xs ), and GXX (Xs ).

15

Proposition 4 Everything else constant, for a low
For a high, there is a unique c1, Xs is a monotonically decreasing function in c1.

0, such that Xs is monotonically increasing with c1 for c1 < c1, andmonotonically decreasing with c1 for c1

c1.

Proof. See Appendix 4.
Proposition 5 states that the e¤ect of leverage on risk management di¤ers, depending on whether …rms
have a high or a low cash ‡ow generating ability relative to their debt obligations (interest rate coverage
ratio). First, for …rms with a low coverage ratio - high leverage (high c1) or low current cash ‡ows (low) - there is a small chance that there will be enough cash balance to make the investment, so as leverageincreases, these …rms tend to seek higher risks in order to increase the likelihood of investing. An increasein leverage only makes these …rms more aggressive. (Higher c1 leads to lower Xs :)Next, consider …rms with high cash ‡ow generating ability (high ). These …rms have strong incentives
to reduce the probability of being liquidated, so when the level of debt is not too high (low c1), an increasein leverage will make equityholders more conservative (Higher c1 leads to higher Xs ).

4.2

Value of Initial Debt Before Investment

Sincechanges at Xs , the value function of the initial debt also changes. De…ne DBL as the debt valuefunction for 0 < X < Xs . DBL (X) satis…es the equation:
D1BL = c1 + ((c1 + c2)(1))D1BL
X +

BL

BL

1
2

2
BL
L D1XX ;(27)

with the general solution:
D1A (X) = B1BL em1

X+ B2BL em2

X

+

c1

;

(28)

De…ne D1BH (X) as the debt value function for Xs < X < Xi . D1BH satis…es the equation:
DBH = c1 + ((c1 + c2)(1))D1BH
X +

1
2

2
BH
H D1XX ;(29)

with the general solution:
BH

D1A (X) = B1BH em1

X

BH+ B2BH em2

X

+

c1

;

(30)

and the boundary and smoothness conditions:
Condition 15: D1BL jX=0 = 0: This condition means that at liquidation the value of the debt is zero.
Condition 16: D1BL jX=Xs = D1BH jX=Xs . This condition guarantees the continuity of the valuefunction at Xs :16

BH
Condition 17: D1BL
X jX=Xs = D1X jX=Xs : This condition at Xs ensures the continuity of the …rst

derivative. Notice that since Xs is chosen to maximize the value of the equity ex post, there is no
optimality condition for the initial debt.
Condition 18: D1BH jX=Xi = D1A jX=X 0 : This is the value-matching condition at Xi . Again, Xi isichosen to maximize the value of equity ex post, so there is no optimality condition.
These four conditions determine the coe¢ cients B1BL , B2BL , B1BH , and B2BH analytically. (see Appendix
5).

4.3

Initial Cash Balances

At t = 0, the …rm decides how much cash balances it must have. Equityholders are cash constrained andonly contribute with X0 . The rest comes from issuing debt. De…ne X0 as the cash balances just before0

the initial debt is issued, and X0 as the cash balances after the initial debt is issued. Because the amountof cash raised from the issuance of the initial debt D1B depends on the level of cash balances after debt
0

is issued X0 , we write00

X0 = X0 + D1B (X0 ):(31)

The level of cash balances before debt is issued, X0 ; is given exogenously, so how much debt the …rm
0

initially issues determines the cash balances it will have, X0 . In other words, there is only one degree of00freedom in Equation (31), and the choice of the coupon payments c1 determines D1B (X0 ) and X0 , for agiven cash ‡ow generating process de…ned in Equation (1). Formally, at t = 0, the equityholders choose00c1 to maximize equity value, subject to the constraint that X0 satis…es Equation (31), and that Xi ; Xs0and c2 maximize equity value, given that the initial debt and cash balances X0 are already decided. Thatis, the equityholders
0max E B (X0 );

(32)

c1

subject to:1) Condition 3: The optimality condition that determines the dividend threshold, Xd :02) Condition 9: The smooth-pasting condition that determines the investment threshold, Xi .
3) Condition 10: The smooth-pasting condition that determines the optimal amount of new debt at
the moment of investing, c2.
4) Condition 14: The optimality condition that determines the risk switching point, Xs
05) Equation (31): The constraint that determines the initial cash balance X0 :

17

0

Xi

0

6) The bounds of the choice variable: 0

Xi ; Xs ; Xd ; c1; c2 < 1. This restriction implies that the

choice variables must be …nite and non-negative.
Because the value function is continuous, the optimal c1 always exists, but we cannot rule out caseswith corner-solutions. The lowest coupon the …rm can choose is zero, and the maximum must be …nite.
The solution to the equityholders’maximization problem can only be obtained numerically.

5

Value of Equity with No Investment

Equityholders may forgo the investment opportunity altogether if the value created by investing is nothigh enough to justify the cost of investing. In this case, the instantaneous cash ‡ow rate is , as long as
the …rm keeps operating. De…ne E N and DN to be the value functions for the equity and the debt of a…rm with no investment opportunities, respectively. Denote cN as the coupon payment to creditors, and
XdN as the dividend threshold for such a …rm. E N can be viewed as a special case of E A in which= 1,

I = 0; c1 = cN and c2 = 0 i.e., for X < XdN :N

E N (X) =

em1 X
N

and
DN (X) =

N

cN

1

N

m 1 XdmN
1 eNNem 2 X
N ;
mN
2 Xd
mN
2 e

N

N

em1 Xd em2 X mN
1NN
em1 Xd mN
1

N

(33)

N

em2 Xd em1 X mN
2NN
em2 Xd mN
2

!

;

(34)

BL
N
BL
where mN
1 = m1 , and m2 = m2 , and
mN

XdN

If X

=

1
)
2 log( mN
2

mN
1= Xs :

mN
2
(35)

XdN ,
E N (X) = X

andDN (X) =

cN

N

1

N

XdN + E N (XdN );NN

em1 Xd em2 Xd mN
1NN
em1 Xd mN
1

N

(36)
N

N

N

em2 Xd em1 Xd mN
2NN
em2 Xd mN
2

!

:

(37)

At t = 0 the …rm chooses X0N , the level of initial cash balances it plans to have after the debt DN isissued. The change in cash balances is:
X0N = X0 + DN (X0N ):

18

(38)

So at t = 0, the equityholders solve the problem:
max E N (X0N );
cN

(39)

subject to:1) Equation (35): This is the equation that sets the dividend threshold, XdN :2) Equation (36): This is the constraint that determines the initial cash balance, X0N :3) The bounds of the choice variables: 0

XdN ; cN < 1, which must have …nite and non-negativevalues.
It is worth noting that XdN = Xs is no coincidence. That is, the dividend threshold of a …rm with noinvestment opportunities is the same as the risk switching point of an otherwise identical …rm but withinvestment opportunities. A proof of this is provided in Appendix 2.
Firms keep cash balances up to the point where the probability of default is su¢ ciently low. Recall
that cash balances held have an instantaneous opportunity cost of , for they do not earn any interest.
In this regard, …rms with and without investment opportunities have the same threshold. Yet, once…rms accumulate enough cash balances, the actions of the two types of …rms start to diverge: Firms
with investment opportunities continue to accumulate cash, but since they already have enough cash to
avoid bankruptcy, they can adopt a riskier strategy to speed up investment. Firms without investment
opportunities, on the other hand, have no reason to accumulate more cash, and therefore decide to pay
out all excess cash as dividend.
It is often argued that …rms with investment opportunities should have lower leverage than …rms
without investment opportunities, or that cN > c1: There are two reasons for this: First, servicing thedebt reduces the cash ‡ows and gives rise to underinvestment. Second, debt increases the probabilityof bankruptcy and can destroy the value of investment opportunities. These reasons are clearly seen in
our model. Notice that from Equation (19), c1 reduces the net cash ‡ows and hence slows down theaccumulation of cash in the …rm. Also, from Equations (20) and (21), c1 a¤ects the terms m1 and m2 ,and increases the probability of default.
In our setting, however, it is possible that the …rm with investment opportunities operates with higher
leverage than the …rm with no investment opportunities, cN < c1 , because cash balances partly fundedwith debt increase the probability of investing. To verify this, di¤erentiate Equations (19) and (23) with
BH
BL
respect to X: EX; EX> 0; which implies that an increase in X increases the probability of investing andthus increases the value of the equity both in high and low-risk strategies. Although initial debt reduces
future cash ‡ows and increases the probability of default, it does help to increase initial cash balances.

19In equilibrium, the …rm trades o¤ this cost against the bene…t of having initial debt. If the value of theinvestment opportunity is su¢ ciently high, it may be optimal for …rms with investment opportunities tohave higher leverage ratios than those without such opportunities.

6

Numerical Example

Both the extent of the problem and the path dependency of cash balances make it impossible to derive
analytical solutions. We thus resort to numerical methods. There are eight input parameters to themodel:;

L;H;; I; ;and X0 : The parameter values used in the numerical example are based on

ten-year historical annual data of active, non-…nancial U.S. …rms from the Compustat dataset, for theperiod 1997

2006. Years 2007

09 are not used to avoid the e¤ects of the 2008 …nancial crisis. Any …rms

with fewer than ten-years of observations, or with total asset values lower than $100 million are excluded.
The …nal dataset consists of 1; 489 …rms.
First, we …nd an estimate of: We compute the average cash ‡ow rate for each …rm in the sample.

Cash ‡ow rate is de…ned as the change in earnings before interest, tax, depreciation and amortization(EBITDA) minus the change in net working capital, and minus the change in net …xed assets, divided by
the average total assets of the …rm. The reason why we include the change in net working capital andthe change in …xed assets in the calculation is because even without a large new investment, …rms have toreinvest cash in existing operations to replace depreciated assets and to …nance any necessary changes tothese assets. The average cash ‡ow rate for all …rms is 0:075 per year, with a standard deviation of 0:078:
So

is set as 0:075.
Next, we …nd estimates for

L and

H.

We compute the standard deviation of the cash ‡ow rate

for each …rm, and then …nd the average standard deviation for all the …rms in the sample. The average
standard deviation of the cash ‡ow rate is 0:15, with a standard deviation of 0:13. We assume that theobserved standard deviation is the low volatility of the cash ‡ow, i.e.,
the ability to increase the standard deviation of the cash ‡ow to

L = 0:15, and that the …rm has

H = 0:20.

This 33 percent change inthe standard deviation of a cash ‡ow rate is not unreasonable. For example, this can be achieved if a …rmchanges its hedging by 33 percent of the output.
We then estimate the scaling factor

by calculating the …ve-year average of the cash ‡ow rate between

1996 and 2001 and between 2002 and 2006. During 1996
is 0:0635, and during 2002
set the scaling factor as

2001; the estimated average of cash ‡ow rates

2006 it increases to 0:087: The increase is approximately 37 percent, so we= 1:37:

To …nd an estimate for I, we calculate the …ve-year average of the …xed assets and working capital,
20divided by the total assets for the period 1997 2001, and repeat the calculation for the period 2002 2006.
During 1997
0:89

2001 it is 0:65, and during 2002

2006 it increases to 0:89. We then assume that I =0:65 = 0:24:

Next, the discount rate chosen for the …rm is equal to 10 percent. The average three-month Treasurybill rate during 1997

2006 is about 3 percent. If we assume a market risk premium of 5 percent, thenthe representative …rm has a beta of 1:4:
The initial cash that equityholders invest in the …rm X0 is not observable. We choose 0:08, since thisnumber gives a leverage ratio of 0:35, the average leverage ratio of all …rms in the sample.
Finally, the corporate tax rate is assumed to be 35 percent, the statutory tax rate.
Table 1 summarizes the parameters values chosen for the example. The output of the model is shownin Table 2.
At t = 0, the equityholders put X0 = 0:08 in the …rm, and the …rm optimally borrows D1BL = 0:2404by issuing perpetual debt with c1 = 0:0390. As a result, the …rm has an initial cash balance equal
to X00 = X0 + D1BL = 0:08 + 0:2404 = 0:3204. This is lower than the optimal risk switching point,
Xs = 0:3696; so the …rm chooses a low risk strategy, i.e.,

L = 0:15. The …rm will switch back and forth

between the high and low risk strategies whenever the cash balance crosses Xs . At t = 0, the equity valueof the …rm E BL is 0:4531, and the debt value D1BL is 0:2404, making the total market value of the …rm
equal to 0:6935. The leverage ratio is 35 percent.
When cash balances reach Xi = 0:4221, the …rm invests I = 0:24. At this point the value of the equity
E A is 0:5564, and the value of original debt D1A is 0:2470. The investment costs the …rm 0:24, but will
increase the cash ‡ow rate by 37 percent. The …rm optimally …nances the investment with additional debt
0of D2A = 0:1961, and coupon c2 = 0:0309. Cash balances after investment are Xi = Xi
0:4221

I + D2A =0:24 + 0:1961 = 0:3782: Because cash balances after investment are lower than the dividend

threshold level Xd = 0:3951, the …rm waits and does not pay any dividend until cash balances reach Xd .
Next, compare this …rm with a second …rm with the same parameters but no investment (growth)
opportunity. Table 3 shows that this second …rm has equity value equal to E N = 0:4190, which is lessthan the value of the equity of the …rst …rm which has an investment opportunity. It issues initial debt
0with coupon cN = 0:0370, and market value DN = 0:2048, making the initial cash balance X0 = X0 +DN = 0:08 + 0:2048 = 0:2848. The leverage ratio is 0:3284. The …rm always follows a low risk strategy,i.e.,

L = 0:15. It accumulates cash balances up to the dividend threshold of Xd = 0:3744; after which it

starts to pay dividends.
The example shows that a …rm with investment opportunities does not necessarily have less leverage.
21

Such a …rm wants to have high cash balances to be as close as possible to the investment threshold. In theexample, the incentive to borrow to maintain high cash balances and invest outweighs the costs of having
more debt.
Also, note that even though the …rm with the investment opportunity has a choice to invest right away
by issuing enough debt to …nance the investment, it …nds that this is not optimal, because the amount it
would have to borrow would be just too much and create a debt overhang problem. As Table 4 shows, if
the …rm invests at t = 0, it has to issue debt D1A = 0:4188 with a coupon c1 = 0:0711. The cash balance
0

after paying the cost of the investment X0 is 0:08 + 0:4188

0:24 = 0:2588, and the dividend threshold

Xd = 0:3928. The equity value E A = 0:4271, less than in the base case previously illustrated. This showsthat the ‡exibility to time the investment as well as the ability to manage risk add value to the …rm (inthe example just shown 5:74 percent).
In sum, …nancial policy, investment and risk management interact di¤erently for …rms with di¤erent
characteristics.

6.1

0E¤ect of Changes in X0 on X0 , Xs , Xi , c1 and c2

How does the initial cash invested by the equityholders, X0 , change the …nancial, risk and investment
policies of the …rm? If equityholders are severely cash constrained, they can only put a relatively small
amount X0 in the …rm. Usually, the …rm will operate with a high leverage ratio, but the debt reduces
future cash ‡ows and potentially creates an overhang problem. Figure 1 shows how the base case resultschange as the cash invested in the …rm by the equityholders at t = 0 varies.
0

As X0 becomes larger, the initial cash X0 becomes larger, as seen in Panel 1, and the …rm does notneed to borrow as much, as seen in Panel 4; c1 declines as X0 increases. Also, lower initial debt levels
induce the …rm to take on less risk, as indicated by the higher switching point, Xs in Panel 2. This happens
because for a given level of cash ‡ow the relation between c1 and Xs is negative. For …rms with higher
operating cash ‡ow rates, , this might not be the case.
Also, lower initial debt allows the …rm to issue more debt later on to …nance the investment, as seen by
the rising c2 in Panel 4. Both lower initial debt and higher additional debt allow the …rm to invest more
quickly and reduce the underinvestment problem as indicated by the lower Xi in Panel 3.

6.2

0E¤ect of Changes in v on X0 , Xs , Xi , c1 and c2

How do the results change as the investment cash ‡ow multiplier, ; changes? Panel 1 of Figure 2 showsthat asincreases, the …rm wants to have larger cash balances in order to invest sooner. So, initial cash
22

0

0

balances X0 increase with : As a result of the higher X0 , the …rm is able to lower the investment threshold
Xi , as seen by the declining Xi in Panel 3.
In Panel 4, an increase inleads to increases in c1 and c2. The higheris, the more able the …rm is

to …nance it through the issuance of additional debt, and the higher is the incentive to borrow more at theinitial date and start with higher cash balances. This result assumes that I does not change, so it should
be interpreted as a result relating to the pro…tability of making the investment.
The relation between

and Xs is shown in Panel 2. The more valuable the investment opportunity,

the lower the risk switching point, Xs , which means that the …rm engages in a high risk strategy sooner
and for a longer period of time. This is because asincreases, c1 increases (see Panel 4), and an increasein c1 leads to a reduction in Xs : Recall from Proposition 4 that a negative relation between c1 and Xs
holds if

6.3

is not high.

E¤ect of Changes in c1 on Xs

The solid line in Figure 3 shows the relation between initial leverage c1 and risk policy, Xs , for a …rm withlow cash ‡ow rate,= 0:075. An increase in the coupon c1 reduces the cash ‡ows to equityholders. As aresult, equityholders have less incentive to keep the …rm operating under a low risk strategy, hence a lower
Xs .
Figure 3 (dashed line) also shows that the relation between leverage, c1; and risk management, Xs ; isnot monotonic in the case of …rms with high cash ‡ow generation. In this case, equityholders have strong
incentives to keep …rms solvent. Therefore, if leverage increases, equityholders try to make the …rms safer
by pursuing a low risk strategy (increase Xs ), provided that c1 is not too high. If leverage is very high,however, cash ‡ows after coupon payments are low and a debt overhang problem may result. Keeping a
low risk strategy is not optimal and equityholders will follow a high risk strategy more often (reduce Xs ).

7

Pro…le of the Investment and Risk Management

So far we have dealt with investment that is lumpy. It costs the …rm a non-trivial amount, I, to invest,
and the …rm must have the …nancial capacity to pay for the cost of the investment all at once. Althoughmany corporate investments have the characteristics of real options, this is an obvious simpli…cation.
When investment is irreversible with a contingent, lump-sum up-front cost, we have shown that it canbe optimal for a …nancially constrained …rm to adopt a high risk strategy: When the option to invest isout of the money - the cash balances X are lower than the cash balance threshold to invest, Xi - and the23

…rm is su¢ ciently far from the bankruptcy threshold (X is far from 0), volatility works in favor of the…rm. After the option is exercised, if the …rm does not have any other investments left, it gains nothingfrom following a high risk strategy, and reverts to a low risk strategy. Our model predicts that …nanciallyconstrained …rms with investment opportunities that require large …xed adjustment costs may intentionallychoose higher risk strategies.
This result contrasts with the results on risk management in other studies. Leland (1998) and Bolton
et al. (2009) …nd that, unless there are large costs associated with risk reducing, …rms with investment
opportunities tend to follow low risk strategies. Hence the question: Do di¤erent investment pro…les a¤ect
corporate risk management di¤erently?
To analyze this question, we consider a …rm that is similar in every way to the …rm in our base model,
but makes continuous investments, instead of a large investment. For this …rm, investment costs i are paideach instant and increase the instantaneous operating cash ‡ow by a factor of ; so the new cash ‡ow rate
becomes. Ifi, the …rm should invest continuously because investment increases cash ‡ows

and the value of equity.
De…ne E i as the equity value function of such …rm. Then E i , , and d satisfy the equation:
E i = maxfd + (
;d

c(1

)

d

i
i)EX
+

1
2

2

i
EXX
g

(40)

i
= 1, which implies
Similar to the results in Section 3, the …rst-order condition with respect to d is EXthat the …rm maintains all cash in the …rm as long as the marginal bene…t of holding cash is greaterthan one, and pays out all cash when the marginal bene…t of holding cash equals one, and the …rst-ordercondition with respect toiis EXX= 0, implying that the …rm choosesi
L if EXX < 0, and choosesLotherwise.
The equity value function before the …rm pays dividends is E i =2 log(
mi1

mi
1)
mi
2
mi2

i
em1 X
i
mi
i
m1 e 1 Xd

i

em2 X
i i
mi2 em2 Xd, where Xdi =ii, and mi1 > 0, and mi2 < 0: It, then, can be veri…ed that EXX< 0, and EX> 1 for X 2 [0; Xdi ).

ii
The …rm pays dividends for cash balances above Xdi ; therefore, for X 2 [Xdi ; 1), EXX= 0: So EXX
isalways non-positive, suggesting that the …rm chooses

L at all times.

i
In other words, when the cash balance is low and EXX< 0, the …rm chooses a low risk strategy, andisince the …rm pays out all residual cash ‡ows as dividends when EX= 1, cash balances will never get toithe level at which EXX0; hence the …rm will never switch to a high risk strategy.

The continuous investment i can be thought of as small incremental investments that the …rm makes
on a regular basis, such as R&D and small upgrading expenditures. Under this type of investment policy,
cash ‡ow volatility hurts …rm value, since it increases the probability that the …rm will not have the cash to24

pay for the cost of investing i. Minton and Schrand (1999) empirically …nd that for this type of investment,
volatility reduces …rm value. The former CFO of Merck, Judy Lewent, in an interview [Nichols(1994)] also
indicates that cash ‡ow stability helped Merck sustain a steady ‡ow of investments needed for its pipelineof drugs.

8

Asymmetrical Information: What Changes in Risk Management and Dividend Reveal to Investors

Cash ‡ows from existing assets and potential growth opportunities are the most important variables invaluing a company. Firms’choices regarding risk and dividend policies reveal something to outside investors
about the …rm’s cash ‡ow generating ability and its growth options.
We assume that investors observe the …rm’s current cash balances and dividends, as well as whether a…rm changes its risk strategy. With this information, outside investors form expectations about the …rm’s
cash ‡ow rate from existing assets, , and the investment opportunities.
For simplicity, the …rm may have one of two possible cash ‡ow rates,

1 or

2 ; where

1 <2 : The …rm

may or may not have investment opportunities. Thus, there are four possible types of …rms, depending on
the cash ‡ow rates and the investment opportunities:
Type-1 …rm has a low cash ‡ow rate ( 1 ) and no investment opportunity. Type-2 …rm has a low
cash ‡ow rate ( 1 ) and a pro…table investment opportunity. Type-3 …rm has a high cash ‡ow rate ( 2 )and no investment opportunity. Type-4 …rm has a high cash ‡ow rate ( 2 ) and a pro…table investment
opportunity. The equity values of the four types are denoted by E 1 ; E 2 ; E 3 and E 4 , respectively.
From our analysis so far we are able to conclude that:
If the …rm is of type-1, it will use a low risk strategy at all times, and will pay dividends at Xd 1 : If
the …rm is of type-2, it will use a low risk strategy if X < Xs 1 ; otherwise, it will use high a risk strategy
before it invests. If the …rm is of type-3, it will use a low risk strategy at all times and will pay dividends
at Xd 2 . Finally, if the …rm is of type-4, it will use a low risk strategy if X < Xs 2 ; otherwise it will use ahigh risk strategy before it invests.
It is obvious that a type-1 …rm has the lowest equity value of all, and that a type-4 …rm has the highest
equity value of all, or E 1 = min[E 1 ; E 2 ; E 3 ; E 4 ] and E 4 = max[E 1 ; E 2 ; E 3 ; E 4 ]: However, the value of a
type-2 …rm may be higher or lower than that of a type-3 …rm, depending on the relative values of
the investment opportunity.

25

and

Investors’expectations of the value of the equity are a function of the unobserved cash ‡ow rate andthe investment opportunities, given the observed actions of the …rm and the current cash balances. The
expectation can be expressed as EjX;Y , where X are the observed cash balances, and Y is a variable thattakes on three possible values: 1 if the …rm pays dividends, 2 if the …rm changes its risk strategy, and 0 if
the …rm neither pays dividends nor switches risk.
From Equation (35), we know that the risk switching point of the …rm with investment opportunities
is the same as the dividend threshold of the …rm without investments. As there are two possible cash ‡ow
rates, there are two levels of cash balances at which investors expect the …rm either to pay dividends or
to change risk. De…ne the …rst expected level as X 1 = Xd 1 = Xs 1 , and the second expected level as
X 2 = Xd 2 = Xs 2 . Figure 4 shows that X 1 can be higher or lower than X 2 , depending on the values
of

1 and

2 : When

1 and

2 are low, X

1< X 2 , and when they are high X 1 > X 2 : So, we consider

two cases:

8.1

Case 1: X 1 < X 2

Before X reaches X 1 , outside investors observe no action (Y = 0) and every type of …rm uses

L , sothey learn nothing about the …rm’s type. The expected equity value is an equally weighted average of thevalues of the various possible …rm types:
EjX<X 1 ;Y =0 =E1 + E2 + E3 + E4
:
4

(41)

Once the cash balances reach X 1 , if investors observe that the …rm pays dividends (Y = 1), they
conclude that the …rm has no investment opportunity in sight and must be a type-1 …rm. Therefore,
EjX=X 1 ;Y =1 = E 1 :(42)

Note that in this event, there would be a drop in the market value of the …rm’s equity, since E 1 <EjX<X 1 ;Y =0 :If at X 1 , outside investors observe a change in the …rm’s risk strategy fromLto

H , (Y= 2),

they might speculate that the …rm is taking greater risks presumably to boost its future investment
opportunities. Hence they conclude that the …rm is of type-2. The equity value is:
EjX=X 1 ;Y =2 = E 2 :This can result in a rise or fall in the equity value, depending on the relative values of E 2 and E 3 :

26

(43)

However, if the …rm does nothing (Y = 0), it signals to outside investors that it is generating high cash
‡ow rates ( 2 ), and must be either type-3 or type-4, resulting in an expected equity value of:
EjX=X 1 ;Y =0 =1 3 1 4
E + E ;
2
2

(44)

leading to an upward revision in the value of the equity.
At the next level of cash balances, X 2 , a type-3 …rm will pay dividends and a type-4 …rm will takegreater risks. Outside investors will revise their expectations of the value of the equity to E 3 for the type-3…rm and to E 4 for the type-4 …rm:
EjX=X 2 ;Y =1 = E 3 ;(45)

EjX=X 2 ;Y =2 = E 4 :

(46)

and

The value of the equity either drops to E 3 or increases to E 4 . We can use a numerical example to illustrate
the value revisions by outside investors.
First assume that the …rm has no initial debt and …nances investment solely from internal cash balances.
The set of parameter values are:and

L = 0:20.

1 = 0:07,

2 = 0:08,= 1:5, I = 0:30,= :35,= 0:1,

L = 0:15

Suppose that the true type of the …rm is 4 ( 2 = 0:08), but investors do not know that.

Panels 1 and 2 in Figure 5 plot the cash balances and outside investors’expectations of the equity values
over time, measured in months. If the …rm is seen as having

1 = 0:07, then X

1= Xd 1 = Xs 1 = 0:4320;

which is reached in month 26; as seen in Panel 1. If, on the other hand, the …rm is seen as having
then X2

2 = 0:08,= Xd = Xs = 0:4359, which is reached in month 31.
22

A type-4 …rm will take on high risk only after its cash balance reaches 0:4359. So, in month 26 when
the cash balance is 0:4232; it does nothing. The fact that the …rm does not switch from
dividends reveals to outside investors that the …rm has a high cash ‡ow rate,

L to

H or pay

2 , and therefore must beeither type-3 or type-4. The market value of the equity will therefore increase on this date (month 26), as
seen in Panel 2.
When cash balances increase to 0:4359 in month 31, the …rm switches to a high risk strategy, andinvestors then conclude that it is a type-4 …rm. The market value of the equity will increase again at thispoint. In this example, one can expect to see two upward jumps in …rm value, as shown in Panel 2.

8.2

Case 2: X 1 > X 2

When the cash balances reach X 2 = Xs 2 = Xd 2 , a …rm with2 (type-3 or type-4) either pays dividends

or changes risk policies (see Panels 3 and 4 in Figure 5). A …rm with27

1 (type-1 or type-2) will wait until

its cash balances reach X 1 = Xs 1 = Xd 1 .
When the …rm’s cash balance reaches X 2 , if investors observe a dividend (Y = 1), they will conclude
that the …rm has

2 and no investment opportunity; therefore, it is a type-3 …rm. At this point, the equity

value becomes
EjX=X 2 ;Y =1 = E 3 :(47)

Depending on the relative values of E 2 and E 3 , the equity value may go up or down at this point.
If the …rm switches risk (Y = 2), it reveals that it has

2 and an investment opportunity, therefore it

is a type-4 …rm. The equity value increases to
EjX=X 2 ;Y =2 = E 4 :(48)

If, however, investors observe no actions (Y = 0), they’ll conclude that the …rm has

1 and must beeither type-1 or type-2. The expected equity value declines to
EjX=X 2 ;Y =0 =1 1 1 2
E + E :
2
2

(49)

At X 1 the …rm’s true type is revealed. A dividend payment (Y = 1) signals that the …rm has no
investment opportunity and is of type-1. Risk switching (Y = 2) signals that the …rm has an investment
opportunity and is of type-2. The corresponding equity values for type-1 and type-2 are
EjX=X 1 ;Y =1 = E 1 ;(50)

EjX=X 1 ;Y =2 = E 2 :

(51)

and

At X 1 , the equity value will decline if it is type-1 and increase if it is type-2.
A numerical example illustrates the equity value revisions by outside investors. Suppose that theunobservable true type of the …rm is type-1. Here1 = 0:13 and

2 = 0:14; and the rest of the parameters

are as in Case 1. Panels 3 and 4 of Figure 5 plot the cash balances and the equity values against timemeasured in months. Investors know that a …rm with

2 = 0:14 will pay dividends or will switch risk

at X a2 = Xda2 = Xsa2 = 0:4296, which is reached in month 12 (in Panel 3). A …rm with

1 = 0:13 has

X a2 = Xda2 = Xsa2 = 0:4354; a value that is reached in month 18. A type-1 …rm pays dividends only whencash balances reach 0:4354, and the …rm does nothing in month 12 when cash balances are 0:4296. At
this point, the market value of the equity falls because investors realize that the …rm must have

1 : Theequity value drops again later, in month 18, when cash balances are 0:4354; and the …rm decides to pay
dividends. At this point, investors know that the …rm is indeed a type-1 …rm. Panel 4 shows that the
expected equity value drops twice in months 12 and 18.
28

9When Firms Issue Equity to Finance Investment

In this section, we extend the base model and allow the …rm to …nance investment by issuing additional
equity. This allows the …rm to invest sooner. Although, equity …nancing reduces the share of the pro…tsof the existing equityholders, if additional equity is sold at market price, the reduction in pro…ts is o¤set
by the increase in the cash received from new equity. If equity issuance were costless, the …rm should…nance investment with equity. In reality, equity has signi…cant …xed issuance costs,2 so the …rm compares
whether the reduction in the default probability is worth the …xed costs.
For …rms that have high cash balances and are far away from the default threshold, the bene…ts ofequity …nancing will not be very high. Therefore, it does not take a high equity issuance costs for these…rms to forego outside equity …nancing altogether.
To analyze the e¤ect of equity …nancing formally, we assume that the …rm already has cash balances
X0 , and existing debt D1B with coupon c1 in place. At the time of the investment, the …rm can sell more
equity and debt to fund the investment. The fraction of the equity sold to outside equityholders is denotedby f . The costs of equity issuance are …xed and denoted by k > 0.
Next, de…ne E1A and E2A as the values, after the investment, of the existing equity and the new equity,
respectively. Also, de…ne E1B as the value before the investment of the existing equity. After investment,
the value of the existing equity is reduced by the fraction sold to the new equityholders. Thus, the valueof the existing equity after investment is
E1A = (1f )E A ;(52)

and the value of the new equity after investment is
E2A = f E A ;(53)

where E A is the total equity value and is equal to E1A + E2A :0

The cash balances after investment, Xi , now depend also on the costs k, and on the amount of new
0equity raised E2A ; which is a function of Xi , so the change in cash balances at the time of investment isgiven by:0

Xi = Xi

00

I + D2A (Xi ) + E2A (Xi )

k:

(54)

Because the dividend received by the existing equityholders is proportional to the fraction of the equity
2 Equity also has dilution costs fromthe underpricing of new shares. Although we do not consider such costs in themodel, they can be incorporated by assuming that the share of the future pro…ts generated by the investment is allocateddisproportionally to the new equityholders, who pay less than the value of these pro…ts.

29

they own, the boundary, smooth-pasting and optimality conditions after investment remain the same. At
the investment threshold, however, the following additional condition must hold:A
Condition 19: E1B
X jX=Xi E2f jX=X 0 =i

E1A
f jX=X 0 : This is a smooth-pasting condition that musti

apply at the time of investing in order to make f optimal. Again, this condition equates the marginal
bene…ts and the marginal costs of changing f . The left-hand side of the condition is the marginal bene…t of
issuing additional equity. On the left-hand side, the term E2A
f is the change in cash from selling additional
equity that results from changing f , and the term E1B
X is the change in the value of the existing equity
due to a change in the cash balance. The product of the two terms represents the total marginal bene…tfrom changing f .
The term on the right-hand side

E1A
f represents the marginal cost of equity issuance, i.e., the reductionin the value of the existing equity due to an increase in f:
From Equations (52) and (53), E1A
f =A
E A , E2A
f = Ef , respectively, implying that the reduction in

pro…ts is completely o¤set by the increase in additional cash from new equity. So Condition 19 simpli…es
to
E1B
X jX=Xi = 1:(55)This equation states that the …rm should issue additional equity to fund the investment up to a point
where the bene…t of one more dollar net of issuance costs raised from additional equity equals one. Before
investment, however, the marginal bene…t of one dollar in the …rm is always greater than one, i.e., E1B
X > 1.
This implies that if k is not too high the …rm should issue additional equity so that it can invest in theAproject immediately, i.e., the …rm chooses Xi = X0 at t = 0, and E1B
X jX=X0 = E1X jX=X 0 = 1:iA

The additional debt D2 with the coupon payment c2 is pinned down by:
A
A
Condition 20: E1A
X jX=X 0 (D2c2 jX=X 0 + E2c2 jX=X 0 ) =
i

i

i

E1A
c2 jX=X 0 : The left-hand side represents theimarginal bene…ts of increasing c2 at the investment threshold. By increasing c2 the …rm increases the cash
holding by D2A
c2 . However, c2 reduces the net cash ‡ow after debt service, and hence reduces the cashAA
received from the new equity issued by E2A
c2 , so the total increase in the cash balance is Dc2 + E2c2 . One
A
dollar increase in the cash balance a¤ects the value of the equity by EX. Hence the product of the twoterms represents the marginal bene…ts of increasing c2:
The marginal costs of increasing c2 can be seen on the right-hand side of Condition 20. The increasein the coupon payment reduces cash ‡ows and reduces the value of the existing equity after investment by
E1A
c2 :
0

A
Because at X = Xi , E1A
X = 1, and from Equation (52) and (53), E1c2 = (130AAf )Ec2, and E2A
c2 = f Ec2 ,then Condition 20 simpli…es to
D2A
c2 jX=X 0 =AEc2
jX=X 0 :

i

i

(56)

This means that the increase the marginal value of additional debt must be equal to the decrease in themarginal value of equity. This condition determines the optimal c2. Because the …rm invests immediately,
it follows the risk strategy described in Proposition 1, i.e., it chooses

L at all times. Proposition 5 formallysummarizes this result.
Proposition 5 If k is su¢ ciently low, the …rm invests in the project immediately. To …nance the investment, the …rm issues additional debt D2A and additional equity E2A . The optimal c is determined by
the condition D2A
c2 jX=X 0 =iAEc2
jX=X 0 , the point where the increase in the marginal value of additionalidebt equals the decrease in the marginal value of new equity. The optimal fraction of equity sold to outsideA
investors, f , is determined by the condition EX
jX=X 0 = 1, the point where the increase in the marginalivalue of additional cash raised by issuing equity is equal to 1. Also, the …rm chooses a low risk strategy,
L , at all times.

If k is su¢ ciently high, the …rm does not issue additional equity to …nance the investment at all. It
will invest when cash balances reach an investment threshold, and then follow the strategies as described in
Sections 4 and 5.
Proof. See Appendix 6.
If the level of debt is …xed, then the …rm chooses to use either only inside equity (cash balances
accumulated in the …rm) or outside equity (cash raised from selling additional equity to new investors),
depending on which one is cheaper. Inside equity allows existing equityholders to keep all the bene…ts of
the investment to themselves and avoid paying …xed issuance costs, although it takes time to accumulate
enough cash in the …rm. Outside equity, on the other hand, allows the …rm to invest sooner, but it
requires paying issuance costs. In equilibrium, the …rm chooses the alternative with the lowest cost to
existing equityholders.
Next, consider the optimal amount of extra debt. Whether the …rm uses inside or outside equity, there
are bene…ts of using some debt to …nance the investment, so the …rm will issue debt so that the marginal
bene…ts of additional debt …nancing equal its marginal costs.
A numerical example illustrates this point. We use the same parameters as in the base case. Also,
assume that the …rm already has outstanding debt with coupon c1 = 0:0390, and cash balances equal to0

X0 = 0:3204:
If the cost of issuing equity, k; is zero, as Proposition 5 suggests, the …rm will invest in the projectright away. The output of the model is shown in Table 5. At t = 0; the …rm issues additional equity with31

f = 0:2168 and additional debt with c2 = 0:0298. The market values of additional equity and debt are
E2A = 0:1259 and D2A = 0:1909, respectively. After paying investment costs, I = 0:24, the remaining
0

cash balance after investment is Xi = 0:3204 + 0:1259 + 0:1909

0:24 = 0:3972: This is the level of cash

balances at which the …rm starts to pay dividends Xd : Since the …rm has no other investment opportunity
in sight, it decides to follow a low risk strategy. With this strategy, the equity value is E1A = 0:4549. Notethat this value is only slightly higher than that of the base case, where it was assumed that the …rm could
not issue outside equity to fund the investment and used internal cash and debt …nancing, (E BL = 0:4531).
The value of the existing equity is reduced as k increases as shown in Figure 6, and when k = 0:0018,
the value of the existing equity of a …rm that …nances investment with additional equity is equal to thevalue of a …rm that does not have this option. Note that it takes only k = 0:0018; or just 0:40 percent of
the value of the existing equity for the …rm to reject issuing outside equity to fund the investment. The
reason it takes only a small issuance cost k to reject issuing outside equity lies in the fact that the …rm
does not face an immediate threat of liquidation, so the bene…ts of equity …nancing are not high. With
costs of issuance higher than k = 0:0018, it is preferable to use internal cash and debt to fund investment.

10

Conclusion

In this paper, we have explored how risk management interacts with the capital structure, investment
and cash management policies of a …nancially constrained …rm. We show that risk management canincrease …rm value by reducing the prospects of bankruptcy and relaxing the …nancial constraints thatdelay investments. Also, we show that risk management is closely related to the dividend policy. Whencash balances are low, …nancially constrained …rms can decide not to pay out dividends; they also follow
low risk strategies, but will switch to high risk strategies when cash balances become high enough.
The relation between leverage and risk management is not obvious. It depends on the level of cash
balances, the rate of cash ‡ow from existing assets and the value of the investment. Firms with high cash
‡ow generating ability act more conservatively, but relatively low leverage and the proximity of investment
can make them more aggressive.
We have shown that the pro…le of the investment matters to the risk strategy: Large, lumpy investments
induce more aggressive behavior than small, incremental investments. Risk management appears to beinsensitive to the pro…tability of the investment after the investment is made, but not before the investment
occurs: the higher the pro…tability of the investment, the greater the incentive to follow a more aggressive
strategy.
When outside investors cannot observe the …rm’s cash ‡ow rate from existing assets and also do not32know whether the …rm has growth opportunities, risk management and dividend policy provide important
information about the …rm.
Finally, we …nd that debt or equity …nancing mitigate …nancial constraints and accelerate investment,
but …rms do not freely choose to add debt or equity. Too much debt that speed investments can lead to
debt overhang after investment, and equity issuance is costly. When the …rm decides to fund investment
with additional equity, it always follows a conservative risk strategy as a riskier strategy to accelerate
investment becomes unnecessary.

33

Appendix
Appendix 1
Without loss of generality, …x c1 and . Before investment, for the …rm with investment opportunities, theB…rst-order condition of Equation (17) with respect to d is EX= 1, implying that the …rm should keep all
BB
cash inside the …rm when EX> 1 and pay maximum dividends when EX
B
the …rm with valuable investment opportunities, EX> 1.

1. It is shown below that for

Therefore, it should not pay dividends before

investing.
The equity value of the …rm with no investment opportunities, E N (X), is given by Equation (33), andthe dividend threshold, XdN , by Equation (35).
At X = XdN ,
N
EX

=

(
1:

=

c1(1

))

EN
(A-1)

For derivations and proofs, see Milne and Robertson (1996).
Next, consider the equity value of the …rm with investment opportunities, E B . Now, for a …xed

andd = 0, Equation (17) becomes Equation (18). Before the dividend payments, the solution to the ODENN

in Equation (18) has the form: E B (X) = Z1 em1 X + Z2 em2 X , and because when the …rm defaults at
X = 0, E B (0) = 0, then Z1 =N

Z2 , and E B = Z1 (em1 X

N

em2 X ), where Z1 is a constant determined by

Condition 8.
BB> 0: This implies= 0, and for all X; EXXX
With this form, it can be veri…ed that at X = XdN , EXX

that E B attains a unique minimum at XdN , and at this point, Equation (18) can be rearranged to yield
B
EX
=

(

c1(1

))

EB :

(A-2)

Next, if the net present values of the investment opportunities are strictly positive, the equity value ofthe …rm with investment opportunities should be greater than that of the …rm without such opportunities,i.e., E B > E N , then at X = XdN ,
B
EX

>

(

=

N
EX

=

1:

c1(1

))

EN

(A-3)

B
B
Since at X = XdN , EX
attains a unique minimum value which is greater than 1, EX> 1 for all X.

Therefore, before investment, it is not optimal for the …rm to pay dividends.
34

Appendix 2
Before investment, for the …rm with investment opportunities, the …rst-order condition of Equation (17)B
is EXX= 0, implying that the …rm should decrease

with respect toand increaseBto the maximum when EXX

B
to the minimum when EXX
<0

0:

B
B
From, Appendix 1, it is argued that EXX= 0 at X = XdN . Since for all X, EXXX
> 0, XdN is theB
BB
unique minimum for EX. From the properties of a minimum, EXX< 0; for X < XdN , and EXX

X

XdN . From Equation (35), Xs = XdN ; therefore, the …rm chooses

X

Xs :

L when X < Xs and0, forH

when

Appendix 3
De…ne
2

and

BH

em1

Xi

6
BH
6
6
em1 Xs
6
L=6
BH
6 mBH
e m 1 Xs
4 1
0

BH

Xi

0

BH

Xs

em1

em2
em2

BH

m2
mBH
2 e

BL

BL

em2

Xs

1
2

AH
1

3

7
6
6 H 7
6 A2 77
A=6
6 L 7;
6 A1 7
5
4
AL
2
2

6
6
6
M =6
6
6
4

0

E A (Xi )
0
0
0

3

7
7
7
7;
BL
BL m2 Xs 7
7
m2 e
5
1
BH

Xs

m1
mBL
2 e

Xs

0

and

0

Xs

(A-4)

(A-5)

3

7
7
7
7:
7
7
5

(A-6)

H
L
L
The coe¢ cients AH
1 , A2 , A1 and A2 can be written in terms of matrix A as

A=L

1

M:

(A-7)

Appendix 4First, di¤erentiating Xs with respect to c1 yields
@Xs
=
@c1
2

(1
2 +(
L

35

)
c1(1

))

H;

(A-8)

where H = (
@Xs
@c1

c1(1

2 2L . Because 2

)) Xs

(1

)
c1(1

2 +(
L

s
> 0, @X@c1 = 0, i¤ H = 0, and the sign of))is the same of that of H:

Ifs
is su¢ ciently small, H < 0, and @X@c1 < 0, and Xs is monotonically decreasing in c1:

If

is su¢ ciently large, there exists c1 = c1 such that at c1, H = 0: To see this, …rst, let c1 = 1

H=

2 2L < 0. Next, let c1 = 0, H = Xs

continuity of H, if

2 2L : It can be veri…ed that as,! +1, lim H ! +1. Byis su¢ ciently large, at c1 = 0, H > 0:

Because H is a continuous function, there exists c1 2 (0; 1), such that H = 0:

Next, we show that H is strictly decreasing in c1, so c1 is unique. Di¤erentiating H with respect to c1
yields@H=@c1
Therefore, if

2 2L (1
2

2 +(
L

)
c1(1

))

2 (

Xs + (c1(1))) < 0:(A-9)

is su¢ ciently high, Xs is monotonically decreasing in c1 for c1 2 [0; c1), and monotoni-cally increasing in c1 for c1 2 (c1; 1):

Appendix 5
De…ne

and

2

B1H

3

6
7
6 H 7
6 B2 77
B=6
6 L 7;
6 B1 7
4
5
B2L

2

6
6
6
N =6
6
6
4

0

c1

D1A (Xi )(A-10)

3

7
7
7
7:
7
7
5

0
0
c1

(A-11)

The coe¢ cients B1H , B2H , B1L , and B2L can be written in terms of matrix B as
B=L

1

where L is de…ne in Equation (A-4).

36

N;(A-12)

Appendix 6
First, note that k is a …xed cost that does not create any bene…ts, so clearly E1B is strictly decreasing ink:ANow, assume that k = 0: If the …rm issues equity, Condition 19 must hold: E1B
X jX=Xi E2f jX=X 0 =i

BE1A
f jX=X 0 . From Equations (52) and (53), E1f =A
E2A
f = Ef . Plugging these results into ConditioniB
20 yields E1B
X jX=Xi = 1. This implies that the …rm should issue equity as long as E1X > 1, and stop

issuing equity when E1BX

1: From Proposition 2 it is always the case that before investment, E1B
X > 1.

This means that the …rm should keep issuing equity until E1B
X = 1, and make the investment immediately,0Ai.e., Xi = X0 , and E1B
X jX=X0 = E1X jX=X 0 . The optimal f is pinned down by the conditioni

E1A
X jX=X 0 = 1:

(A-13)iA
The optimal coupon c2 of the additional debt is pinned down by Condition 20: E1A
X jX=X 0 (D2c2 jX=X 0 +i

E2A
c2 jX=X 0 ) =
i

(1

i

0

A
A
E1A
c2 jX=X 0 : Because at X = Xi , E1X = 1, and from Equation (52) and (53), E1c2 =iAAf )Ec2, and E2A
c2 = f Ec2 , then Condition 20 simpli…es to

AEc2
jX=X 0 :D2A
c2 jX=X 0 =iBecause the …rm invests immediately, it choosesi(A-14)

L at all times.

Next, consider the case in which k > 0: If the …rm does not issue additional equity to …nance investment,
its equity value is E B . The …rm will issue additional equity only if so doing increases the value of theexisting equity E1A above E B . Because E1A is strictly decreasing in k, if k ! 1, E1A ! 0: So there is a

cut-o¤ point, k, such that at k, E1A = E B , and if k is lower than k, the …rm will issue additional equity to…nance investment; otherwise, it will not issue additional equity at all, i.e., it chooses f = 0, and follows
the strategies described in Sections 3 and 4.

37

References
Bolton, P., H. Chen, and N. Wang, 2009, “A Uni…ed Theory of Tobin’s q, Corporate Investment,
Financing, and Risk Management,” Working Paper.
Dixit, A. K., 1993, Art of Smooth Pasting, Fundamentals of Pure and Applied Economics, Routledge,
Abingdon, Oxon.
Dixit, A. K., and R. S. Pindyck, 1994, Investment Under Uncertainty, Princeton University Press,
Princeton, N.J.
Dumas, B., 1991, “Super Contact and Related Optimality Conditions,”Journal of Economics Dynamics and Control, 4, 675-685.
Froot, K., D. Scharfstein, and J. Stein, 1993, “Risk Management, Coordinating Corporate Investment, and Financing Policies,” Journal of Finance, 48, 1629–1658.
Jensen, M.,C., and W. H. Meckling, 1976 “Theory of the Firm: Managerial Behavior, Agency Costs
and Ownership Structure,” Journal of Financial Economics, 3, 305-360.
Leland, H., 1998, “Agency Costs, Risk Management, and Capital Structure,” Journal of Finance, 53,
1213 - 1243.
Nichols, N., 1994, “Scienti…c Management at Merck: An Interview with CFO Judy Lewent”, Harvard
Business Review, January-February, 89-105.
Purnanandam, A., 2008, “Financial Distress and Corporate Risk Management: Theory & Evidence,”
Journal of Financial Economics, 87, 706-739.
Milne, A., and D. Robertson, 1996, "Firm Behaviour under the Threat of Liquidation", Journal of
Economic Dynamics and Control, 20, 1427-1449.
Minton, B., A., and C. Schrand, 1999, “The Impact of Cash Flow Volatility on Discretionary Investment and the Costs of Debt and Equity Financing,” Journal of Financial Economics, 54, 423-460.
Ross, S., A., 1997, “Hedging Long Run Commitments: Exercise in Incomplete Market Pricing,” Economic Note, 26, 99-132.
Shleifer, A., and R. Vishny, 1995, "The Limits to Arbitrage", Journal of Finance, 52, 35-55.
Smith, C. W., and R. Stulz, 1985, “The Determinants of Firms’ Hedging Policies,” Journal of Financial and Quantitative Analysis, 20, 391–406.
Tufano, P., 1998, “Agency Costs of Corporate Risk Management,” Financial Management, 27, 67-77.
38

Table1 : Input Parameters
Parameter Description
X0
Cash investment by the equity holderαCash flow rate
νScaling factor to cash flows after investment
τ
Tax rateρDiscount rateI
Lump-sum fixed investment costs
σL
Low cash flow volatility
σHHigh cash flow volatility
Table 2: Outputs: Base Case
Variable
Description
BL
E
Equity value
BL
D1
Initial debt value
A
E
Equity value at investment thresholdA
D1
Initial debt value at investment thresholdA
D2
Additional debt value at investment thresholdc1
Coupon payments of the initial debt
c2
Coupon payments of the additional debt
X'0
Initial cash balance
Xs
Risk switching point

Value
0.080
0.075
1.370
0.350
0.100
0.240
0.150
0.200

Value
0.45310.2404
0.55640.24700.19610.03900.03090.32040.3696Xi

Investment threshold

0.4221

X'i

Cash balances after investment

0.3782

Xd

Dividend threshold

0.3951

Table 3: Outputs: No Investment Opportunity
Variable
Description
N
E
Equity value
DN
Initial debt valuecN
Coupon payments of the initial debt
X'0
Initial cash balance
Xd
Dividend threshold

Value
0.41900 20480.20480.03700.2848

Table 4: Outputs: Immediate Investment
Variable
Description
A
E
Equity value
A
D1
Initial debt valuec1
Coupon payments of the initial debt
X'0
Initial cash balance
Xd
Dividend threshold

Value
0.42710.41880.07110.2588

Table 5: Outputs: Equity Financing
Variable
Description
A
E1
Equity value
A
D1
Initial debt valueA
E2
Additional equity valueA
D2
Additional debt valuec1
Coupon payments of the initial debt
c2
Coupon payments of the additional debt
fFraction of equity sold to the public
X'0
Initial cash balance
X'i
Cash balances after investment

Value
0.45490.24990.12590.19090.03900.02980.21680.32040.3972

Xd

0.3972

Dividend threshold

0.37440.3928Figure 1: Effect of Changes in X0 on X'0, Xs, Xi, c1, and c2

Panel 1: Effect of Changes in Xo on X'oPanel 2: Effect of Changes in Xo on Xs

0.330
0.325

Xs

X'0

0.320
0.315
0.310
0.305
0.05

0.06

0.07

0.08

0.09

0.378
0.376
0.374
0.372
0.370
0.368
0.366
0.364
0.362
0.360
0.358
0.356

0.1

0.05

0.06

0.07

Xo

0.09

0.1

0.09

0.1

Panel 4: Effect of Changes in Xo on
c1 (Solid Line) and c2 (Dashed Line)

Panel 3: Effect of Changes in Xo on Xi
0.445

0.044

0.440

0.042

0.435
0 435

0.040
0 040

0.430

0.038
c1, c2

Xi

0.08
Xo

0.425
0.420

0.036
0.034

0.415

0.032

0.410

0.030

0.405

0.028
0.05

0.06

0.07

0.08
Xo

0.09

0.1

0.05

0.06

0.07

0.08
Xo

X0 represents the initial cash invested by the equityholders. X’0 represents the cash in the firm from both the equityholders and original debtholders.
Xs is the optimal risk switching threshold point. Xi is the optimal investment threshold point. c1 and c2 are the coupon amounts of the original debt andthe new debt issued to fund the investment, respectively. Parameter values are: X0=0.080, α=0.075, I=0.24, ν=1.37, τ=35%, ρ=0.1, σL= 15%, σH=20%.

Figure 2: Effect of Changes in ν on X'o, Xs, Xi, c1, and c2
Panel 1: Effect of Changes in ν on X'oPanel 2: Effect of Changes in ν on Xs

0.322
0.322
0.321
0.320

Xs

X'0

0.321
0.320
0.319
0.319
0.318
1.35

1.36

1.37

1.38

0.37020.37010.37000.36990.36980.36970.3696
0.36950.36940.36930.3692

1.39

1.35

1.36

ν

1.38

1.39

ν

Panel 4: Effect of Changes in ν on
c1 (Solid Line) and c2 (Dashed Line)

Panel 3: The Effect of Changes in ν on Xi
0.460

0.040

0.450

0.038

0.440

0.036

c1, c2

0.430
Xi

1.37

0.420

0.034
0.032

0.410

0.030

0.400

0.028

0.390
1.35

1.36

1.37
ν

1.38

1.39

1.35

1.36

1.37

1.38

1.39

ν

ν is the factor by which the firm’s instantaneous cash flows increase upon making the investment. X0 represents the initial cash invested by
the equityholders. X’0 represents the cash in the firm from both the equityholders and original debtholders. Xs is the optimal risk switching
threshold point. Xi is the optimal investment threshold point. c1 and c2 are the coupon amounts of the original debt and the new debt issued
to fund the investment, respectively. Parameter values are: X0=0.080, α=0.075, I=0.24, ν=1.37, τ=35%, ρ=0.1, σL= 15%, σH=20%.

Figure 3: Effect of Changes in c1 on Xs
α=0.075 (Solid Line) and α=0.15 (Dashed Line)
0.5
0.45
0.4
0.35
0.3

Xs

0.25
0.2
0.15
0.1
0

0.03

0.06

0.09

0.12

0.15

c1

c1 is the coupon amount on the initial debt. Xs is the optimal risk switching threshold point.
Parameter values are: X0=0.080, α=0.075, I=0.24, ν=1.37, τ=35%, ρ=0.1, σL= 15%, σH=20%.

Figure 4: Xs

α1and Xsα2

versus α1 and α2

0.50
0.45
0.40
0.35

Xa1, Xa20.30

α1=0.130.25

α2=0.140.20
0.15

α1=0.7α2=0.8

0.10
0.05
0.00
0

0.02

0.04

0.06

0.08

α

0.1

0.12

0.14

0.16

0.18

Xα1 and Xα2 are expected levels of risk and dividend switching threshold points, which dependon the values of the cash flow rates, α1 and α2. Parameter values are: X0=0.080, I=0.24, ν=1.37,
τ=35%, ρ=0.1, σL= 15%, σH=20%.

0.2

Figure 5: Cash Balance (X) and Expected Equity Value (Ē)When Investors Cannot Observe α and Investment Opportunity

Panel 1: Cash Balance
True α= 0.08

0.65
0.6

Panel 2: Expected Equity Value (Ē)
True α=0.08

1.1

month 31

1.05

month 31

1

0.55

0.95

month 26

month 26

0.9
Ē

x

0.5
0.45

0.85
0.8

0.4

0.75

0.35

0.7

0.3

0.65
0

10

20

30

40

50

60

0

10

20

Months

30

40

50

60

50

60

MonthsParameter values in panels 1 and 2 are α1 =0.07, α2=0.08, I=0.30, ν=1.5, τ=35%, ρ=0.1, σL= 15%, σH=20% .

Panel 4: Expected Equity Value (Ē)
True α=0.13

Panel 3: Cash Balance
True α=0.13
1

1.9

0.9

1.8

0.8

month 12

1.7

month 18
Ē

x

0.7
0.6

1.5

0.4

1.4

0

10

20

30
Months40

50

60month 18

1.6

0.5

0.3

month 12

1.3
0

10

20

30
MonthsParameter values in panels 3 and 4 are α1 =0.13, α2=0.14, I=0.30, ν=1.5, τ=35%, ρ=0.1, σL= 15%, σH=20% .

40Figure 6: Equity Issuing Costs (k) versus Equity Value (E1B)

0.45500.4545E1B

0.45400.45350.45300.452500.00050.001

0.00150.002

0.00250.003

0.00350.004

kk are the new equity issuing costs. E1B is the value of the existing equity before theinvestment. Parameter values are: X0=0.080, α=0.075, I=0.24, ν=1.37, τ=35%,
ρ=0.1, σL= 15%, σH=20%.

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Miyakawa, Daisuke, "A Dynamic Equilibrium Model for Relationship-Lending," March 2009.
花崎正晴・松下佳菜子「ストック・オプションと企業パフォーマンス−日本企業を対象としたインセ
ンティブ効果の実証分析−」2008 年 9 月
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James, Jason, and Paul A. Kattuman, "Income Inequality over Boom, Slump and Recovery: Japan 1963-2005"
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Otaki, Masayuki, "Involuntary Unemployment Emerging from Dynamic General-Equilibrium Analysis,"
February 2007.
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December 2006.
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Hanazaki, Masaharu and Liu Qun, "Corporate Governance and Investment in East Asia−An Empirical
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Analysis of Asian Crisis-," June 2005.
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Sung Wook, JOH and Ming Ming CHIU, "From Cherry Picking to Bottom Feeding: A source of bankproblems in Japan," April 2005.
Kasahara, Tetsuya, "Excess bankruptcy and excess refinancing in multiple-source financing," December 2004.
慶田昌之「日本の景気循環と景気予測：Markov Switching Dynamic Factor Modelを中心としたサーベイと若干の推計」2004年7月．
Hillas, John, "The Economics of The Structure of The Japanese Firm: A Survey," June 2004.
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松本和幸・吉川洋「高齢化と消費需要」2002年3月．
Hanazaki, Masaharu and Akiyoshi Horiuchi, "The Ups and Downs of the Financial System in Postwar Japan―Evidence from the Manufacturing Sector−,"December 2001.
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Okubo, Masakatsu, "Econometric Evaluation of the Lack of Risk Sharing and Imperfect Financial Integration,"
March 2001.
Sakurai, Kojiro, "How Does Trade Affect the Labor Market? Evidence from Japanese Manufacturing,"
March 2001.
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Hanazaki, Masaharu and Akiyoshi Horiuchi, "Efficiency of the Japanese Financial System in the Postwar
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Matsumoto, Kazuyuki, "A comparison of Japanese and U.S. price indexes and a new approach to theirmeasurement," June 2000.
Dekle, Robert, "Exchange Rates and Corporate Exposure: Evidence from Japanese," April 2000.
松本和幸「サービス価格の推計手法について」2000年3月.
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斉藤孝「戦間期日本における農工間賃金格差」1998年7月.
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Sakashita, Noboru, "An Analytical Model of the Tiebout Process: Numerical Simulations," December 1997.
中里透「地域間所得移転と経済成長−開発政策の政治経済分析−」1997年11月.
Sena, Koichi, "A Comparative Study of Japan and the US Regarding Taxation Policy on Non-Profit
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浅子和美・國則守生・井上徹・村瀬英彰「設備投資と土地投資：1977-1994」1997年3月.
高橋正博「アジアにおける地域の国際ネットワーク化試論−ネットワークの論理的考察とその応用としてのアジア重層ネットワーク構想−」1996年8月.
鈴木和志・小川一夫「土地価格の変動と設備投資−日本の製造業に関するパネルデータによる分析−」
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Hilpert, Hanns Günther, "The Market, the State and the Dragon: A Contribution to the Debate on Economic
Growth in the Asia-Pacific Region," March 1995.
森谷英樹「大都市私鉄の運賃改定とその過程の研究−1985〜1995年−」1995年10月.
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森谷英樹「大都市私鉄の運賃改定とその過程の研究−1966〜1995年−」1995年2月.
Kuo, Wen-jeng, "Japan at the Crossroads: Perspectives of a Foreign Economist," September 1994.
Callon, Scott, "Different Paths: The Rise of Taiwan and Singapore in the Global Personal Computer Industry,"
August 1994.
Callon, Scott, "Unleashing Japan’s Venture Business Sector: Problems and Policies for Reform," August 1994.
Suzuki, Kazuyuki and Kazuo Ogawa, "The Structure of Adjustment Costs and Investment Behavior under
Uncertainty in Heavy Industry: Evidence from Japanese Panel Data," July 1994.
森谷英樹「大都市私鉄の運賃改定とその過程の研究−1945〜1965年−」1994年4月.
Selover, David D., "Interdependence Between the United States and Japan: A Vector Autoregression
Approach," January 1993.
杉原弘恭「日本のコモンズ「入会」」1994年3月.
Suzuki, Kazuyuki, "Production Technology and Productivity Growth in the Japanese Electrical Machinery
Industry," November 1993.
茂木愛一郎「世界のコモンズ−スリランカと英国の事例を踏まえて−」1994年3月.
Matsumura, Toshihiro, "Endogenous Timing in Switch of Technology with Marshallian Externalities," March
1994.
Selover, David D., "The Japanese Saving Rate: Another Literature Review," January 1994.
Selover, David D., "The Japanese Household Saving Function: A Time Series Econometric Analysis, " January
1994.
Yamane, Linus, "A Stylized Macroeconomic Comparison of the U.S. and Japan," June 1993.
Yamane, Linus, "The Effect of Unions on Employment in Japan and the United States, " June 1993.
Yamane, Linus, "Differences in Economic Fluctuations in Japan and the United States: A New Keynesian
Perspective," June 1993.

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9306
9305
9304
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9302
9301
9214
9213
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9211
9210
9209
9208
9207
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9205
9204
9203
9202
9201
9108
9107
9106
9105
9104
9103
9102
9101
9008
9007
9006
9005
9004
9003
9002
9001
8905
8904

Suzuki, Kazuyuki and Kazuo Ogawa, "The Structure of Adjustment Costs and Investment Behavior under
Uncertainty in Heavy Industry: Evidence from Japanese Panel Data," June 1993.
茂木愛一郎「東欧における金融政策について」1993年6月.
宮川努「『貸し渋り』と審査機能−非製造業中小企業の設備投資を中心として−」1993年5月.
Matsumura, Toshihiro, "A Bargaining Approach to Borrowing Diversification: A Study of the Japanese Main
Bank System," May 1993.
根津智治「わが国の金融史と企業の資金調達（メモ）」1993年3月.
森谷英樹「大都市私鉄の投資と公的助成−地方鉄道補助法とその評価−」1993年1月.
Miyagawa, Tsutomu, and Jyoji Tokui, "An Open Economy Approach to the Growth of Tertiary Industries inJapan," January 1993.
竹田陽介「景気循環における中央銀行の政策スタンス」1992年11月.
宮川努・玄田有史・出島敬久「就職動向の時系列分析」1992年10月.
Sharkey, John, "The Political and Economic Impact of Japanese Cotton Piece-Good Competition in India,
1918-1933," October 1992.
竹田陽介「設備投資と株式市場」1992年9月.
Rebick, Marcus E., "Rewards in the Afterlife: The Importance of Late Career Job Placements as Incentives in
the Japanese Firm," July 1992.
Matsumura, Toshihiro, "Piece Regulations and Strategic Investment," June 1992.
千明誠・竹田陽介「80年代における完全雇用経常収支の動向」1992年6月.
吉田健一郎「親会社業績と関係会社の配当−関係会社株式の評価基準に関連して−」1992年6月.
森谷英樹「鉄道運賃・収支と設備投資−運賃改定と設備投資の実証分析（その1）−」1992年5月.
根津智治「アメリカの金融制度改革における銀行隔離論」1992年4月.
Matsumura, Toshihiro, "Market for Lemons and Forward Induction," March 1992.
宇沢弘文「農業自由化と近代経済学」1992年2月.
宮川努「設備投資分析の新展開−誤差修正モデルによる設備投資関数の検証−」1992年2月.
Matsumura, Toshihiro, "Dividends as a Coordination Device," January 1992.
浅子和美・堀内行蔵・茂木愛一郎「大都市の財政問題−ニューヨークと東京−」1991年11月.
Werner, Richard A., "Japanese Capital Outflows and the Role of Land Asset Appreciation," September 1991.
小川善弘「最適都市の構造−都市間の均衡と社会的共通資本−」1991年7月.
Tokui, Jyoji, and Tsutomu Miyagawa, "Price competitiveness and the Investment Behavior in Japanese
Manufacturing Industries," May 1991.
Genda, Yuji, "Does the Performance Bond Work in the Japanese Labor Market?," May 1991.
竹村弘「東京が豊かで地方が貧しいか」1991年5月.
森谷英樹「大都市圏私鉄の設備投資について」1991年5月.
根津智治「日米主要企業の資本構成」1991年5月.
浅子和美・國則守生・井上徹・村瀬英彰「設備投資と資金調達−連立方程式モデルによる推計−」
1990年9月.
Uzawa, Hirohumi, "Theory of Imputations and Global Warming," November 1990.
照山博司・村瀬英彰「日本の銀行貸出市場の不均衡計量分析−サーベイ・データによる局面分離を用
いて−」1990年8月.
Tokui, Jyoji, and Tsutomu Miyagawa, "The Real Effective Exchange Rate and the Investment Behavior inJapanese Manufacturing Industries," August 1990.
堀内行蔵「日本の製造業のパフォーマンス」1990年8月.
徳井丞次・宮川努「わが国製造業の国際競争力と設備投資」1990年8月.
根津智治「貯蓄・投資と金利機能」1990年4月.
冨田博一「わが国企業のＭ＆Ａ」1990年2月.
浅子和美・國則守生・井上徹・村瀬英彰「土地評価とトービンのｑ／Multiple qの計測」1989年9月.
根津智治「セキュリタライゼーションと公的部門の金融活動」1989年5月.
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8902
8901
8805
8804
8803
8802
8801

堀内昭義「証券化−金融システムの構造変化についての分析−」1989年5月.
桜井宏二郎「金融構造と実体経済」1989年5月.
堀内行蔵「レーガノミックスの乗数分析」1989年3月.
岡田羊祐「技術移転論の動向−プロダクトサイクル論を中心として−」1988年12月.
Suzuki, Kazuyuki, and Jyoji Tokui, "Misalignment of the Yen-Dollar Exchange Rate and the International
Competitiveness of the Manufacturing Industries in Japan and the United States," November 1988.
Murase, Hideaki, "Monetary Policy Games in a Stochastic Environment: Does Discretionary Monetary Policy
Cause Stagflation?," November 1988.
國則守生「経済的償却率の推計−我が国建設機械の例−」1988年10月.
石黒隆司・堀内行蔵「先進国の現状と問題点：1980年代−変化と不均衡の時代−」1988年9月.

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