Growth Opportunities, Knowledge Capital andLeverage: Evidence from US Biotech Firms ∗

Qiao Liu†

First Draft: December, 1999This Draft: November, 2000

Abstract

This paper investigates the interaction among a firm’s knowledge capital, growthopportunities, earning dynamics, and optimal leverage level. Under the corporatetaxation and personal taxation framework, by assuming knowledge capital positivelyaffects the realization of a firm’s growth opportunities, I find a positive relation betweena firm’s optimal debt level and its knowledge capital. Meanwhile, I identify a negativerelation between R&D investment and leverage in the presence of better measures fora firm’s knowledge capital. By using the data collected for US biotech firms, I findthat firms’ debt ratios are indeed positively related to their knowledge capital mea-sures: citation-weighted patent counts or claim-weighted patent counts. Furthermore,by employing an event study approach, I find a firm tends to increase its leverage afterthe enhancement of its knowledge capital.

Keywords: Growth Options, Capital Structure, Corporate and Personal Taxation,Knowledge Capital, Citation-weighted and Claim-weighted Patent Counts.

∗This is a revised version of Chapter 3 of my UCLA dissertation. I am grateful to Hongbin Cai, BradCornell, Michael Darby, David K. Levine, and Shijun Liu for helpful suggestions. Any errors remain my ownresponsibilities.

†Send Correspondence to: Qiao Liu, School of Economics and Finance, University of Hong Kong,Pokfulam, Hong Kong. Phone: (852) 2859-1059, Fax: (852)2548-1152, e–mail qliu@hku.hk

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1 Introduction

Since Modigliani and Miller (1958)’s seminal work, financial economists have made

great progress understanding the determinants of optimal capital structure. Now, people

understand the most important departures from the Modigliani and Miller assumptions

that make capital structure relevant to firm value. Despite advancement made on this

topic, surprisingly small literature has ever studied the dynamics between a firm’s growth

opportunities and its financing structure, an emerging issue due to the birth, formation and

fast growth of a series of high-tech industries in recent twenty years.

High-tech industries are distinguished from others by the three characteristics: inten-

sive R&D investment, crucial roles played by the firm’s knowledge capital, great growth

opportunities.1 There is no doubt that the factors that have been identified as important in

explaining the firm’s capital structure in previous studies still apply to high-tech industries

to some extent. However, the features specific to high-tech firms certainly make the firms’

financing choice display certain pattern, which cannot be fully explained by previous theo-

ries on capital structure. Firms, especially high-tech firms could be defined as a collection

of assets in place and growth opportunities.2 An interesting issue here is how assets in place

(i.e., knowledge based assets) affect the firm’s growth opportunities, which further affect the

firm’s financing structure.

This article aims to study the determinants of a firm’s capital structure under an R&D

intensive and technologically innovative environment, in which knowledge capital and growth

opportunities play crucial roles. Recent evidence suggests that a firm with high knowledge

capital is more likely to make technological innovations and therefore has greater growth

opportunities. Growth opportunities affect the variability and permanence of a firm’s cash

flow stream, which in turn, influence its optimal leverage. My objective is to clarify the1Growth opportunities in high-tech firms are also highly unpredictable given the fact that firms with

more knowledge capital normally pursue high-risk and high-return R&D strategies. The stakes of their R&Dprojects, therefore, are high.

2See Myers (1977), Myers and Majluf (1984), and Zingales (2000) for this insight.

interaction among leverage, knowledge capital, growth opportunities, and earnings.

Several studies have investigated the links between human capital and firm leverage. The

theoretical and empirical evidence, however, is still inconclusive. Williamson (1988) stresses

the link between debt capacity and the liquidation value of assets. He argues that the assets

that are redeployable are good candidates for debt finance because, if they are managed

improperly, the manager will be unable to pay the debt, and then the creditors will take the

assets away from the firm and redemploy them. The degree of redeployability of high-tech

firm’s knowledge capital is normally very low, consequently, firms with more knowledge assets

should be less levered. Shleifer and Vishny (1992) apply a market equilibrium approach to

explore the determinants of liquidation values of assets. In their argument, when a firm in

financial distress needs to sell assets, its industry peers are likely to be experiencing problems

themselves, leading to asset sales at prices below value in best use. This constitutes an ex

ante private costs of leverage. Using this logic, they explain the difference in leverage levels

across industries and over business cycles. Following their argument, we should observe that

industries or firms with high knowledge assets to be less levered given the fact that those

assets normally have low liquidation value.

Hart and Moore (1994) is one of the first articles that theoretically models debt maturity

and the inalienability of human capital. A rich set of implications are derived from their

worked-out model. However, the roles of intangible assets (a concept that is close to knowl-

edge capital in my study) are ambiguous: one of their implications is that shorter term debts

(debt) should be used since intangible assets normally have low liquidation values, therefore

creditors require quicker payment paths. Besides theoretical exploration, extensive empiri-

cal analysis has been undertaken to understand the relation between intangible assets and

capital structure. For example, Titman and Wessels (1988) identified a negative relationship

between R&D expenditures (a proxy for knowledge capital) and firm leverage.

In this article, I combine the technological innovative, R&D intensive nature of high-tech

firms with the tax-driven approach to optimal capital structure. While this study assumes

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away investment and agency problems, it allows a more reasonable cash flow process and

directly relates leverage to various measures of knowledge capital. Most importantly, it

captures the effects of growth opportunities on cash flow stream and optimal leverage. In

my model, I assume that the value–maximizing firm trades off the advantages and costs

of debt financing. This could be conceptualized as the firm minimizing the value of the

competing claims of non-owners. Under the corporate and personal tax framework, 3 the

cash flow to the government either is equal to a fraction of the firm’s cash flow in excess of

interest payments on its debt plus non-debt tax shields,4 or is equal to zero when the cash

flow is insufficient to cover these obligations.5 Thus the government’s claim to a firm’s cash

flow could be treated as a European call option written on the firm’s cash flows with exercise

price equal to the sum of its debt and non-debt tax shields. Similarly, personal tax payments

of debt-holders can be seen as an option with an exercise price equal to the firm’s debt level.

Obviously, the non-owner claims to the firm’s cash flow could be understood as a gov-

ernment option portfolio with a long position in its corporate tax option and short position

in the personal tax option. At the optimal debt level, the firm equates the tax rate weighted

marginal effects of the debt on the two options. The interaction among optimal debt level,

the firm’s growth opportunities, knowledge capital, therefore, depends upon relative magni-

tudes of marginal effects of debt on the two options.

In my model, I explicitly model the interaction among growth opportunities, knowledge

capital, earnings, and leverage. I assume that a firm with high knowledge capital is more

likely to execute its growth potentials, which in turn affects its cash flow stream. Thus,

the firm’s earning process follows a jump-diffusion process with its jump (exercise growth3See Miller (1977), DeAngelo and Masulis (1980), Kale, Noe, and Ramirez (1991), Givoly, Hayn, Ofer,

and Sarig (1996).4I do not incorporate the carryback and carryforward provisions of tax codes into my model. But their

effects on tax will be reflected in the changes of the firm’s tax shield, qualitative results of my paper will beindependent of this assumption.

5However, in my model, I assume that all debt service payments are deductible for the firm and taxablefor the bondholder in order to be consistent with the classical bankruptcy cost–tax shield literature. Inactuality, interest payments determine the probability of tax loss whereas the total debt payment ( principleand interest) is relevant for determining the probability of default. Making above assumptions will notchange the results qualitatively.

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options) probability endogenously determined by its knowledge capital. Clearly, I find a way

of relating a firm’s knowledge capital to its growth opportunities, which is further related to

the cash flow stream and to the two taxation options. Through comparative static analysis,

I identify a positive relation between the firm’s knowledge capital and its leverage level. This

result is in contrast with most previous studies.

In order to test whether my model correctly captures the interaction among growth

opportunities, knowledge capital and leverage. I used the data collected for US biotech firms

to test the hypotheses derived from the model. The focus on the biotech industry allows study

of the effect of knowledge capital on growth opportunities and optimal capital structure in a

cross-section of different firms within a single industry. This effectively excludes the possible

influences of other non-knowledge, non-industry factors on the firm’s financing decisions.

By applying regressions and event study approach, I find that firms with more knowledge

capital have higher debt-asset ratio; I also find that the firm have incentive to increase its

leverage right after the enhancement of its knowledge capital. Empirical evidence supports

the model well.

Kale, Noe, and Ramirez (1991) also studied optimal leverage decisions under a corporate

and personal taxation framework. However, they focus on the effect of business risk on

leverage. Also, they use the dispersion of earnings as a proxy for business risk, which

implicitly assumes that the earning process is exogenously determined. Raymar (1991)

constructs a model of capital structure when earning process is assumed to be mean-reverting.

His model is one of the first that explicitly model the firm’s earning dynamics. He found

that earning dynamics affect a firm’s optimal capital structure. However, the earning process

addressed in his study is still exogenous. Also, he fails to take into account the effects of

growth opportunities on a firm’s earning dynamics.

The remainder of the paper is organized as follows: in section 2, I lay out the model and

then explore the interaction among knowledge capital, growth opportunities, and optimal

debt level. Section 3 provides empirical evidence of how firm-specific knowledge capital

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affects the level of capital structure. Section 4 studies the changes in firm leverage level as

firm-specific knowledge capital stock changes. Section 5 concludes the paper.

2 The Model

In this section, I lay out the model and then derive the firm’s optimal debt level. Finally,

we use numerical analysis to explore the interaction among knowledge capital, growth op-

portunities, and optimal leverage level.

2.1 the model setup

The first challenge I encounter is how to incorporate a firm’s growth opportunities into the

model. To understand this issue under real options framework, a high-tech firm owns growth

options, which will be exercised whenever the firm makes innovative breakthrough. However,

the exercise dates are unknown. We do not know when these growth opportunities could

be materialized and have real impact on the firm’s cash flows and its financing structure.

To avoid the difficulties of modeling the “put options” with unknown exercise dates, I rely

on the empirical evidence that has been documented by several studies: the firm with more

knowledge capital is more likely to materialize the growth potentials.6 Specifically, I assume

that a firm with more knowledge capital is more likely to materialize the growth opportuni-

ties, therefore, its cash flows follow a jump diffusion process with jump probability related

to its knowledge capital.

Consider a firm in an R&D intensive and technologically innovative environment. Let

X be firm-specific knowledge capital measure,7 and I be the operating cash flow to the firm

before debt, tax and depreciation. I, represents the value of cash flows generated by the

firm’s business activities. It is also assumed that these cash flows are spanned by the cash

flows of marketed securities. Due to the innovative nature implicit in the environment,6See Zucker, Darby, and Brewer (1998), Hall, Jaffe, and Trajtenberg (1999).7Note that X could be a vector, in which each element captures certain type of knowledge capital.

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firm-specific knowledge capital may generate discontinuities in the firm’s operating cash

flows. The “discontinuities” are caused by technological innovations, scientific breakthrough,

or ingenious commercialization of ideas, which successfully materialize the firm’s growth

opportunities. Thus, I assume that the firm’s operating cash flows before tax, debts and

depreciation, I, follows the following jump-diffusion process:

dI(t)I(t)

= (R(t)− λµJ)dt +√

σdz(t) + Jdq, (1)

where σ is the risk (standard deviation) of the continuous component of the firm’s cash flow;

R(t) is the risk-free interest rate; dz(t) is the increment of a standard Wiener process. I also

assume that the following holds:

ln[1 + J ] ∼ N(ln[1 + µJ ]− 12σ2

J , σ2J) (2)

In above model specifications, J(t) is the percentage jump size (conditional on jump

occurring) that is lognormally, identically and independently distributed over time, with

unconditional mean µJ . σJ measures the dispersion of jump size. q(t) is a Poisson jump

counter with intensity, λ. That is, Prob(dq(t) = 1) = λdt and Prob(dq(t) = 0) = 1 − λdt.

We also assume the probability of more than one jump occurring is Prob(dq(t) ≥ 2) = ◦(dt),

where a function f(h) is ◦(h) if limh→0f(h)

h = 0.

In order to capture the effect of growth opportunities which are related to the firm’s

knowledge capital, I further assume that

λ = λ0 + λ1X. (3)

In equation (3) the intensity of jump occurring is related to the stock of the firm’s

knowledge capital. An intuitive interpretation is that the firm’s operating cash flows evolve

continuously in most of the time. But occasionally, a “jump” occurs due to the technological

breakthrough made possible by the firm’s knowledge capital. The frequency or intensity of

the “jump” depends on the firm’s knowledge base. Note that I do not identify the difference

between the jump frequency and jump size. I assume that the jump size is just a random

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draw from certain probability distribution. So knowledge capital only influences cash flow

through the “jump” intensity, λ.

I have followed the standard practice and specify from the outset a stochastic structure

of a firm’s cash flow under a risk-neutral probability measure. By using this assumption, I

am able to value the firm’s future risky payoff as if the economy were risk neutral. The trade

off here is that we have to sacrifice some economic intuitions in the model. For example,

the jump intensity, λ and jump size, µJ , in my model are not the actual jump intensity and

jump size. They are jump intensity and jump size under risk neutral probability measure. In

other words, they are risk adjusted jump intensity and jump size. Therefore, the magnitude

and sign of λ, µJ may be counterintuitive in some situations.

I study the firm’s optimal capital structure choice under the corporate tax and personal

tax framework. I abstract my model from agency problem, adverse selection, and contests

for corporate control. The basic approach used is similar to that in Kale, Noe, and Ramirez

(1991), DeAngelo and Masulis (1980), and Miller (1977).

For simplicity, I assume that the marginal personal tax rate on capital gains is zero and

let τp and τc be the marginal personal tax rate on debt income, and the marginal corporate

tax rate, respectively.8 Let D represent the tax-deductible debt service charge, and Π be the

depreciation charge, or more broadly, non-debt tax shields.

Clearly, corporate tax collected by the government is given by:

Tc = τcE[max{I −D − Π, 0}] (4)

Similarly, personal tax paid by the firm’s debt holders is given by

Tp = τpE[min{I,D}] (5)8Assuming the marginal personal tax rate on capital gains to be zero could simplify our model dramati-

cally. And this is a less outrageous simplification than it looks. First, the tax rate on capital gains normallyis lower. Second, the shareholders need pay no taxes on their gains until realized and only a small fraction ofaccumulated gains are, in fact, realized and taxed in any year. Also, taxes on capital gains can not only bedeferred at the option of the holders, but also be avoided if held until death. Third, I don’t model explicitlytax-timing options equityholders have in a multi-period setting. Thus, assuming personal tax rate on capitalgains to be zero could reduce the errors due to this modeling simplification.

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Since I assume that the marginal tax rate on capital gains is zero, the total tax collected

by the government is therefore the sum of corporate tax and personal tax paid by debt

holders. Let T denote the total tax liability collected by the government. I have:

T = Tc + Tc

= τcE[max{I −D − Π, 0}] + τpE[min{I, D}]

= τcE[max{I −D − Π, 0}] + τpE[I −max{I −D, 0}]

= τcC(D + Π) + τp[I∗ − C(D)]

= τcC(D + Π)− τpC(D) + τpI∗. (6)

where I∗ is the expected value of I under risk-neutral valuation, C(·) is the value of a

European call option. Note that the argument in C(·) represents the exercise price. In the

option of corporate tax collected by government, the exercise price is D+Π. Because, unless

the cash flow is bigger than D + Π, the government will not collect anything. In the option

of personal income tax paid by debt holders, the exercise price is D. When the cash flow is

greater than D, their tax payment is reduced from τpI to τpD, that is, by τp[I −D]. On the

other hand, if the cash flow is less than D, then the government only gets τpI.

Note that in equation (6), the total tax liabilities, T, is a function of τp, τc, D, D + Π, R

and the maturity of the firm’s debt τ . Other studies have assumed that R(t) is stochastic,

but this increase in complexity has only a relatively minor quantitative impact on the results.

For convenience, I assume R to be deterministic.

Lemma: If (a) a firm’s cash flow, I, follows the jump-diffusion process given in equation

(1)–(3); (b) the instantnous risk-free interest rate, R, is deterministic; and (c)the measure of

the firm-specific knowledge capital, X, is exogenously given; then the value of the European

call option written on the firm’s cash flows, I, with exercise price D and maturity τ is given

by the following:

C(t, τ) = I(t)Π1(t, τ, I,X)−D(t)e−RtΠ2(t, τ, I,X). (7)

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where the risk-neutral probabilities, Π1 and Π2, are recovered from inverting the respective

characteristic functions:

Π1(t, τ, I, X) =12

+1π

∫ ∞

0Re[

e−iφ ln[D]f1(t, τ, I, X)iφ

]dφ, (8)

and

Π2(t, τ, I, X) =12

+1π

∫ ∞

0Re[

e−iφ ln[D]f2(t, τ, I, X)iφ

]dφ, (9)

in which f1 and f2 are defined as:

f1(t, τ) = exp{[[λ0(1 + µJ)[(1 + µJ)iφeiφ2 (iφ+1)σ2

J − 1]− λ0µJ(iφ + 1)

+Riφ +12σiφ(iφ + 1)]τ + [[λ1(1 + µJ)[(1 + µJ)iφ

eiφ2 (iφ+1)σ2

J − 1]− λ1µJ(iφ + 1)]τX + ln(I)iφ} (10)

and

f2(t, τ) = exp{[R(iφ + 1) + λ0[(1 + µJ)iφeiφ2 (iφ−1)σ2

J − 1− µJ iφ]

+12σiφ(iφ− 1)]τ

+λ1[(1 + µJ)iφeiφ2 (iφ−1)σ2

J − 1− µJ iφ]τX

+ ln(I)iφ−Rτ}. (11)

Proof: See Appendix.

2.2 the optimal capital structure

Under the corporate taxation and personal taxation framework, the competing claims of non-

owners of a firm could be represented as the government’s tax liability defined in equation

(6). As I explained before, the tax liabilities, T, could be seen as a portfolio of options.

In section 2.1, I derive the formula for the European call option given that the firm’s cash

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flows follow a jump-diffusion process with jump intensity endogenously related to the firm’s

knowledge capital, X.

Now, I assume that the firm’s owners take an ex ante efficiency view. In other words,

given investment risks, firm owners choose the optimal debt level to maximize the value of

the claims to themselves. Therefore, the firm’s problem is to choose the best D∗, which

minimizes the total tax liabilities of the firm’s claimholders: τcC(D + Π) − τpC(D) + τpI∗.

The first order condition of this problem is that, at optimal D∗

∂T∂D

|D=D∗= τc∂C(D + Π)

∂D|D=D∗ −τp

∂C(D)∂D

|D=D∗= 0, (12)

when D∗ > 0. When D∗ = 0, the corresponding first order condition is

∂T∂D

|D=0= τc∂C(D + Π)

∂D|D=0 −τp

∂C(D)∂D

|D=0≥ 0, (13)

where I∗ doesn’t appear in equations because it is a constant and is gone when taking

derivative.

As explained in Section 2.1, given risk neutral probability measures, the first order condi-

tions above could be easily represented as the following partial derivatives of the call options

defined above:

∂C(D + Π)∂D

= I∂Π1(t, τ, I,X)

∂D− (D + Π)e−Rτ Π2(t, τ, I, X)

∂D− e−RτΠ2(t, τ, I, X), (14)

where we have∂Π1(D + Π)

∂D=

1π

∫ ∞

0Re(

−e−iφ ln[D+Π]f1(·)D + Π

)dφ (15)

and∂Π2(D + Π)

∂D=

1π

∫ ∞

0Re(

−e−iφ ln[D+Π]f2(·)D + Π

)dφ (16)

This eventually gives us

∂C(D + Π)∂D

= I1π

∫ ∞

0Re(

−e−iφ ln[D+Π]f1(·)D + Π

)dφ

−(D + Π)e−Rτ 1π

∫ ∞

0Re(

−e−iφ ln[D+Π]f2(·)D + Π

)dφ

−e−Rτ [12

+1π

∫ ∞

0Re(

e−iφ ln[D+Π]f2(·)iφ

)dφ]. (17)

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Similarly, we can have

∂C(D)∂D

= I1π

∫ ∞

0Re(

−e−iφ ln[D]f1(·)D

)dφ

−(D)e−Rτ 1π

∫ ∞

0Re(

−e−iφ ln[D]f2(·)D

)dφ

−e−Rτ [12

+1π

∫ ∞

0Re(

e−iφ ln[D]f2(·)iφ

)dφ]. (18)

At D = D∗, the following condition must hold

G(τc, τp, D∗, X) =∂T∂D

|D=D∗= τc∂C(D + Π)

∂D|D=D∗ −τp

∂C(D)∂D

|D=D∗= 0. (19)

The key here is to find D∗ that makes G(τc, τp, X,D∗) = 0. Unfortunately, given that I have

assumed the firm’s operating cash flows follow the jump-diffusion process with the jump

probability endogenously related to firm’s knowledge capital, X, I am not able to address

the above first-order conditions analytically. Nor could I simplify the assumptions in order

to solve the model analytically without changing my research questions. I will check the

existence and properties of optimal debt level, D∗, by using numerical analysis. As I will

explain later, the results I obtain from numerical analysis appear very robust.

2.3 The Numerical Analysis

The endogenous jump component imbedded in the model makes it impossible for me to

analyze the model in an analytical manner. In this subsection, I examine numerically the

properties of the firm’s capital structure under a technologically innovative and R&D in-

tensive environment. Basically, I assign economically reasonable values to the parameters

implicit in the model. Then I try to solve out the optimal debt level taking the parameter

values as given. To explore the properties of the optimal debt level, I examine how the

optimal debt levels change with the changes in parameter values. Note that I am not able

to prove the existence of a unique optimal debt level. However, by trying a rich set of of

parameter values, I find that the results are quite robust.

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For all cases, the firm’s mean operating cash flow is normalized to be 1,000. And for

the base case, the parameter values are chosen as follows: Non-debt tax shields, NTS =

250; marginal corporate tax rate, τc = 0.35; marginal personal income tax rate, τp = 0.28;

risk-free interest rate, R = 0.07; maturity of the firm’s debt, τ = 2.0; standard deviation of

the firm’s cash flow(continuous component), σ = 0.1; jump size, µJ = −0.1; 9 dispersion of

jump size, σ2J = 0.04; λ0 = 0.1; knowledge capital related jump intensity, λ1 = 0.1.

Consider that high-tech firms normally do not issue too much debt. And when they

issue debt, the maturities are normally shorter. In the base model, I choose τ to be 2 years.

Also note that non-debt tax shields here include depreciation deductions, investment tax

credits and so on. Under an R&D intensive environment, large part of R&D expenditures

are non-taxable. Specifically, if a firm has large amount of R&D expenditures, under current

tax codes, its non-debt tax shields will also be relatively large.10 The values of jump–related

parameters are chosen based on previous research (Bates (1991); Darby, Liu and Zucker

(1999)). The jump size and jump intensity are measured under risk-neutral probability

framework. The risk premium related to jump risk has already been implicitly included in the

parameters. Therefore, the size or sign of jump-related parameters might be counterintuitive.

For example, in above model, I assume the jump size, µJ to be -0.1. This is consistent with

the risk neutral assumption. But it doesn’t mean that the firm has a downward jump in its

operating cash flows. The only correct way to understand it is that the firm has experienced

a discontinuity in its operating cash flows (the firm has exercised a growth option which

increases its operating incomes) and this discontinuity is caused by knowledge capital.

To illustrate the relationship between optimal debt level and knowledge capital measures,

I graph the total expected tax liabilities based on equation (6) for three firms that are

identical in every aspect except for their knowledge capital contents.11 The firm with “high”9The jump size here is not the actual jump size, but the risk-adjusted jump size.

10Hall and Wosinska (1999) present extensive evidence on R&D tax credit. According to their calculation,the R&D tax credit can run as high as 10% of the firm’s taxable income. I believe the percentage should beeven higher for high-tech firms that rely heavily on R&D expenditures.

11Note that when I calculate the total tax liabilities based on equation (6), for the purpose of simplicity,I do not include τpI∗. This would not have any qualitative effects.

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knowledge capital, H, has X = 5; the firm with “medium” knowledge capital, M, has X = 1;

and the firm with “low” knowledge capital, L, has X = 0. The functions Ti(D), i = H, M, L

for the firms attain a unique interior minimum at D∗i : D∗

L = 533.97, D∗M = 571.39, D∗

H =

765.98. Clearly, the firm with higher knowledge capital has a higher debt level. Figure 1

graphs the firms’ tax liability against different debt levels for the three firms.

To further explore the relation between knowledge capital and optimal debt level, I

calculate a firm’s optimal debt levels under different knowledge capital levels. As shown in

table 1, when knowledge capital measure (X) increases, the optimal debt level also increases.

There is a positive relation between theist two variables. Figure 2 graphs this relation.

As shown in table 1 and figure 2, the firm’s optimal debt level increases with its knowledge

capital. This is in contrast with the evidence from previous studies. Titman and Wessels

(1988) and Rajan and Zingales(1995) examine the relationship between a firm’s debt ratio

and its intangible assets. One of their findings is that there is a negative relation between the

two variables in most cases. Jensen and Meckling (1976) have attributed this to the growth

opportunities available to firm with high R&D expenditures (a proxy for intangible asset).

They argue that a firm with high growth opportunities should be cautions with the use of

debt because of bankruptcy costs of debt financing. Titman (1984) explains the negative

relation between a firm’s R&D expenditures and leverage by relating the firm’s leverage

to the uniqueness of its product and whether there are specialized services required in its

production process. Based on his argument, the more intangible assets the firm has, the less

likely the firm will turn to debt financing.

If I believe firm-specific R&D expenditures is a good measure for the firm’s knowledge

capital, I would be surprised to see the results from my model is not consistent with previous

studies. However, R&D is a very poor measure of a firm’s knowledge capital: it only captures

the inputs a firm makes in order to augment its knowledge capital, it does not capture quality

of knowledge capital or the output of the firm’s research activities.12 Therefore, the empirical12In contrast, variables such as the number of patents, the number of patent claims, or the number of

patent cites a firm receives during certain period, are more appropriate measures of a firm’s knowledge

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results based on R&D expenditures may be misleading.

My argument focuses on the interaction among growth opportunities, knowledge capital,

and earnings. The exercise of growth options changes the dynamics of a firm’s cash flows,

which in turn affects the firm’s financing decisions. Knowledge capital, in my model, deter-

mines whether and how often the firm is able to materialize its growth opportunities. In

other words, I study the interaction between the firm’s leverage and its knowledge by exam-

ining how knowledge capital affect the firm’s earning dynamics. Raymar(1991) investigates

how earnings affect capital structure. However, earnings are assumed to be mean-reverting

in his model. Clearly, he does not consider how knowledge capital and growth opportunities

affect the earning dynamics.

The key point of my model is that I add a jump component into the firm’s earning

dynamics and relate its jump intensity to the firm’s knowledge capital. Ex ante, a firm’s

equityholders do not know whether knowledge capital will bring along additional cash flows

to the firm. They do not know when a jump would occur (growth options being exercised).

But they know that a firm with more knowledge capital is more likely to execute the growth

options and would execute them more often. Clearly, knowledge capital act like some type

of “collateral” in my model. From this perspective, I would say that the knowledge capital,

even though they are intangibles, could be “collateralized”.

Under the agency theory framework, Chang (1987) finds that leverage increases with the

fraction of unobservable cash flows. This looks similar to my conclusion. But my model

relates the dynamics of cash flows to the growth options and firm-specific knowledge capital.

Besides, my model takes a tax-driven approach, which is totally different from the agency

problem approach adopted in Chang (1987).

To reconcile the roles played by R&D expenditure in a firm’s financing decision, I de-

compose its effects on optimal debt level into two parts: one aims to capture the firm’s

knowledge capital; the other captures the firm’s non-debt tax shields. The second effect

capital.

14

could be very significant under current tax codes. Take the biotechnology firms as example,

biotech firms’ debt levels normally are smaller than their R&D expenditures by one mag-

nitude order. Therefore, tax credits enjoyed by R&D investment could be very significant

in explaining biotech a firm’s leverage. Given that the firm’s knowledge capital could be

better proxied by other measures such as patent variables, I believe the main effect of R&D

investment on capital structure lies in its tax credits. If this hypothesis is true, we would

observe a negative relation between R&D investment and firm leverage while the relation

between firm leverage and knowledge capital remains positive.

In the following example, I increase the firm’s non debt tax shields, NTS , from 250 to

300(supposedly, it is caused by the increase in R&D expenditures). Numerical results show

that as non debt tax credits increase, the firm’s optimal debt level goes down correspondingly.

Panel A of figure 3 presents evidence on how non-debt tax credits affect the firm’s optimal

debt level. Clearly, we observe a negative relation. This result is consistent with previous

studies conditional on that we are able to find better measures for the firm’s knowledge

capital that totally dominate R&D investment’s role as a proxy for knowledge capital.

Numerical analysis enables me to further explore implications of the model. I first increase

λ1 from 0.1 to 0.2. λ1 measures the impact of firm-specific knowledge capital on the likelihood

and frequency of firm exercising growth options. As shown in Panel B of figure 3, the higher

quality of the firm’s knowledge capital (measured by higher λ1), the more likely that growth

opportunities will be materialized. Therefore, the optimal debt level tends to be higher.

When I change the magnitude of σ2J , I identify the same trend (as shown in Panel C

of figure 3). σ2J measures the variability of the jump size. Under Black-Scholes framework,

higher σ2J increases the value of growth options, which further increases the firm’s optimal

debt level. However, Panel C shows that the effect of σ2J on optimal debt level is not that

significant.

In the last experiment, I examine how the changes in σ (standard deviation of the firm’s

operation income excluding jump components, or standard deviation of the firm’s business

15

risks caused by assets in place). As shown in Panel D of figure 3, increase in σ leads to a

decrease in the firm’s optimal debt level. In other words, if I exclude growth opportunities

and only focus on how assets in place affect the firm’s financing decision, I would argue that

higher business risk (measured by σ) leads to lower optimal debt level. But this relation may

not hold anymore once I take into account knowledge capital and growth opportunities. In

that case, business risks are not only determined by σ, but also dependent on the variability

jump components which captures the interaction between knowledge capital and growth

opportunities.

Based on above numerical analysis, we develop the following hypotheses:

Hypothesis 1.: Firms with a high knowledge capital will increase their leverage more than

firms with a low knowledge capital.

Hypothesis 2.: In presence of other variables that better measure firms’ knowledge capital,

the effect of R&D investment on leverage mainly lies in the tax credits it enjoys. From this

perspective, there should be a negative relation between R&D expenditures and firm leverage.

Hypothesis 3.: When defining a firm as the collection of assets in place and growth oppor-

tunities, its business risks could be decomposed into two parts. Since the two have different

impacts on leverage, the relation between business risk and leverage is ambiguous. Failing to

capture the taxonomy of business risks may generate misleading results.

In the following two sections, I will use the data collected for US biotech firms to test

above hypotheses.

3 The Analysis of Capital Structure Level

In this section, I analyze firms’ relative leverage as a function of knowledge variables. If my

model is correct, I should observe significant cross-sectional associations between leverage

and variables that indicate firms’ knowledge capital. In my test, I focus on biotech firms for

the following reasons: 1. biotech firms rely on growth opportunities; 2. knowledge capital

16

play irreplaceable role in biotech firms; 3. Focusing on biotech industry provides a relative

clean environment for me to test the hypotheses.

3.1 Sample Selection

My analysis starts from 156 biotech firms that had gone public before 1992.13 Among the

156 firms, I am able to find 129 companies that have records in the COMPUSTAT database.

I exclude the firm-year observations that correspond to a firm’s first two appearances in the

COMPUSTAT database.

My sample selection criteria limit my analysis to biotech firms only. While this approach

enables me to economize on the time and cost for data collection, the conclusions of my

analysis do not necessarily apply to other industries, especially non-high-tech industries.

Even though I believe my model is very general, its implications have to be accepted with

reservation before they are fully supported by empirical evidence.

3.2 Variables for The Analysis of Leverage Level

In this subsection, I define the variables used in the empirical analysis.

3.2.1. Measure of Leverage

In this study, I measure the leverage level at the end of each fiscal year. Three different

methods are used:

Leverage1 =total debt (book value)

total assets (book value), (20)

Leverage2 =total debt (book value)

total debt (book value) + common equity(market value), (21)

and

Leverage3 =total liabilities

total assets. (22)

13The firms I study here is a subset of the biotech companies collected by Lynne Zucker and MichaelDarby for their on-going project on “Intellectual Human Capital, Technology Transfer, and the Organizationof Leading-Edge Industries: The Case of Biotechnology”. The initial database contains 751 biotech firms.In this study, I focus only on public firms due to the limitation of accessibility to accounting and otherfirm-specific information.

17

Leverage1 measures the firm’s leverage based on book values. Leverage2 is based on

market values. Leverage3 is the broadest definition of leverage. It can be viewed as a proxy

for what is left for shareholders in case of liquidation. However, it does not provide a good

indication of whether the firm is at risk of default in the near future. Also, since total

liabilities also includes such items like accounts payable, which may be used for transaction

purposes rather than for financing, it may overstate the amount of leverage. In my analyses,

I mainly rely on leverage1 and leverage2.

3.2.2.Measure of Knowledge Capital

The literature has been pretty settled on using patent data to measure a firm’s knowl-

edge capital. Compared to R&D investment, patent data capture the output of a firm’s

research projects. Therefore, it precisely measures a firm’s knowledge base. Given that the

distribution of private patent values is extremely skewed, the quality of patent counts as

meaningful measure of knowledge capital is severely undermined. In this study, I use the

number of future cites a patent receives and the number of a patent’s claims to control the

quality of a patent. I go to the US Patent and Trademark Office web page to search for

patent information for biotech firms. For each firm, I record how many patents were applied

in each year, how many claims each of them has (clm), and how many subsequent citations a

patent receives since it is approved (cit). Define Cit(t,s) = number of cites received at time

s to the patents applied for at time t; then Cit(t) =∑T

s=t Cit(t, s)= total number of cites

for the patents applied for at time t. Similarly, we define Clm(t) = total number of claims

for the patents applied for at time t. Note that in our paper, T = 1997.

Assume a single depreciation rate for the value of a patent,δ. If I denote the firm’s

knowledge capital at time t as K(t), we have

K(t) = (1− δ)K(t− 1) + Cit(t) (23)

Equation (23) is used to calculate a firm’s knowledge capital at time t. If we use claims

instead of citations, we have K1(t), whose definition is exactly the same as equation (23)ex-

cept that claim counts are used. Here, I assume δ to be 0.2 in this study. The empirical

18

results are not sensitive to the value of δ.

3.2.3. Other Control Variables

Previous empirical studies have identified a number of factors that are related to a firm’s

optimal financing decision. I need to control these variables in the empirical analysis.

A. Tangibility of Assets

Most theories on capital structure argue that the characteristics of assets affects a firm’s

leverage. E.g., if the tangibility of assets is higher, it is easier for the firm to liquidate the

assets and recover their value. Therefore, a firm is more likely to use debt financing. In this

study, I use two variables to measure a firm’s asset tangibility: the ratio of intangible assets

to total assets (INT/TA); and the ratio of inventory plus gross plant and equipment to total

assets (IGP/TA). We should observe INT/TA has negative relation with capital structure

and IGP/TA has a positive sign.

B. Size

A number of authors have suggested that leverage are also related to firm size.14 The

argument is as follows: large firm is relatively more diversified and less prone to bankruptcy.

Therefore, large firm should be highly leveraged. In the empirical study, I use the natural

logarithm of net sales, LSIZE, as the measure for firm size.

C. Uniqueness

Titman (1984) presents a model in which a firm’s liquidation decision is causally linked

to its bankruptcy status. As a result, the costs that a firm can potentially impose on its

customers, suppliers, and workers by liquidating are relevant to its capital structure decisions.

Customers, workers, and suppliers of the firm that produces unique or specialized products

probably suffer relatively higher costs when liquidating. Therefore, uniqueness is expected

to be negatively related to debt ratios. I use selling, general and administrative expenses

over total assets (SGA/TA) as the proxy for a firm’s uniqueness.

D. Profitability14Warner,(1977); Ang, Chua, and McConnell (1982); Smith (1977).

19

Myers (1977) suggests that firms prefer raising capital, first from retained earnings, second

from debt and third from issuing new equity. This may be due to the costs of issuing

equity or due to asymmetric information discussed by Myers and Majluf (1984). In either

case, we should expect that the amount of earning available to be retained is an important

determinant of a firm’s capital structure. The more profitable a firm is, the less leveraged

the firm will be. I use the ratio of operating income over sales (OI/S) as an indicator of

profitability.

R&D investment is a key variable in my model. It captures a firm’s non-debt tax shields,

growth opportunities, and knowledge capital. However, as I explained before, in presence of

better measures for knowledge capital and growth opportunities, R&D investment mainly

works as a measure for a firm’s non-debt tax shields. I use the natural log of R&D expendi-

tures (LRND) as the measure for R&D. I expect it to be negatively related to leverage.

Table 2 presents the definitions and the descriptive statistics for the variables defined

above. One interesting observation is that the average leverage ratio is just 0.063 when

market values are used for calculation. Clearly, most biotech firms in my sample are lightly

levered. It, however, is not a concern in this study since I am mainly interested in the

cross-sectional difference in leverage within a single industry.

3.3 Results of Regressions

My sample includes 129 public biotech firms. I drop the firm-year observations that include

missing values. This leaves me with 107 firms and 437 observations. Table 3 presents the

OLS regression results. In regressions (1)-(3), I use the book value of leverage (leverage1) as

the dependent variable. In regression (3), specifically, I adopt average leverage of a firm as

the dependant variable. In regressions (4) and (5), the market value of leverage (leverage2)

is used as dependant variable.

Considering the heterogeneity in firm size, I scale K(t) and K1(t) by total assets to capture

a firm’s knowledge capital(K/TA, K1/TA). This practice is consistent with Hall (1999).

20

Other explanatory variables include: IGP/TA, and INT/TA, which capture the tangibility

of a firm’s assets; SGA/TA, which captures the uniqueness; LRND, which captures the

intensity of a firms’ R&D investment; LSIZE, which captures firm size; and finally, OI/S,

which captures the profitability.

The regression results are consistent with the implications derived from the model. All

variables except INT/TA have the expected signs. The knowledge capital, K/TA (citation

counts) and K1/TA (claim counts), are significantly positive in all regressions. It confirms

empirically the positive correlation between knowledge capital and leverage. Table 3 also

shows that a firm’s R&D expenditures, LRND, is significantly negative in all regressions. It

is consistent with hypothesis 2 developed from the model. Note that R&D plays multiple

roles in this study. It, on one hand, captures a firm’s non-debt tax shields; on the other

hand, it captures a firm’s growth opportunity. In presence of better measures for growth

opportunities and knowledge capital, this effect has been dominated.

In the regressions, uniqueness variable, SGA/TA, is significantly negative. It confirms

the findings in Titman (1984): the more unique a firm’s assets are, the less leveraged the

firm will be. Size variable, LSIZE, is significantly positive, which implies that large firms

are more likely to use debt financing. This is also consistent with previous studies. Without

surprise, the sign of IGP/TA is positive. This demonstrates that a firm’s asset tangibility

positively relates to its leverage level. Surprisingly, INT/TA has positive sign and it is

significant in some regressions. It may be due to the overlapping roles played by intangible

with other variables meant to measure knowledge capital or non-debt tax shields. OI/S, the

variable that captures a firm’s profitability, is negative in all regressions. However, it is not

significant. Consider the fact that most biotech firms in my sample are start-ups and do not

have much operating income, it is not surprising this variable is not significant.

As shown in Table 2, the average leverage for biotech firms is pretty low. I observe

that about 20% firms do not have any debt in at least one time period. Given that, people

may argue that OLS regressions may misspecify the relationship between firm leverage and

21

explanatory variables. To address this concern, I apply TOBIT models. Table 4 presents

the results of TOBIT regressions. Clearly, the story does not change and the significance of

knowledge capital variables gets even stronger.

Based on empirical evidence, it is safe to argue that high-tech firm’s knowledge stock

indeed is a very important determinant of the firm’s leverage. The empirical results also

provide evidence on the roles played by R&D investment in the presence of better knowledge

capital measures (Hypothesis 2). In this article, I do not endeavor to test hypothesis 3

since I do not have reliable measures for a firm’s business risks. The variance of firm’s

operating incomes could be decomposed into two parts: one relates to the assets in place;

the other relates to its growth opportunities. However, it is hard to tell which is which in

empirical experiments. Evidence from previous studies on capital structure, however, helps

us understand this issue. E.g., Jaffe and Westerfield (1987) find a positive relation between

business risks and optimal debt level; Castanias (1983) finds a negative relations between

these two; Kale, Noe, and Ramirez (1991) identify a U-shape relation. Clearly, the evidence

is inclusive. I believe failing to distinguish the two parts of risks that contribute to a firm’s

overall business risks may be responsible for the ambiguous relation between business risks

and leverage.

4 The Analysis of Changes in Capital Structure

The key implication from my model is that once a firm’s knowledge capital has been en-

hanced, it will increase its leverage. In this section, I design a test to see whether firm

leverage changes significantly after the occurring of events that represent the enhancement

of a firm’s knowledge capital. Section 4.1 discusses the research methodology. Section 4.2.

presents the results of event study.

22

4.1 The Study Design

It is well known that high-tech firms are built upon technological innovations. Technological

innovations dramatically enhance a firm’s knowledge base. This, in turn, changes a firm’s

earning dynamics. Once a firm makes technological breakthrough, it normally will appear in

the press. Thus, high-tech firm’s technology related news announcements provide us with a

unique opportunity to study how a firm’s optimal financing decisions change as its knowledge

base improves.

I search each of the 129 public biotech firms in the Lexis/Nexis database for the entire

1983-1992 period.15 I am able to identify five different types of innovation news: (1) FDA

approval; (2) patent grant; (3) scientific breakthroughs discovered by scientists affiliated

to the firm;(4) strategic alliances or research joint ventures formed by the firm with other

firms; (5) other technology related news that cannot be classified into any of the other four

categories.

I identify 717 news announcements made by 118 firms during 1983-1992. I drop the

announcements made in the fourth quarter of 1987 to control the effects of market crash.

Some announcements are dropped since they occurred in the year the firm first appeared in

COMPUSTAT database. My strategy is based on the following logic: if a firm made some

announcements in year t, the firm’s knowledge capital was increased correspondingly in that

year. In other words, the firm has successfully materialized its growth opportunities. Based

on my model, the firm’s leverage will increase. Therefore, by comparing the firm leverages

in year t-1 and year t+1, I am able to know whether the firm’s leverage level has increased

due to the enhancement of its knowledge capital.15I choose this period to make the results comparable to the results obtained from regression analysis.

23

4.2 Results of The Event Study

The event period in this study is in terms of year. I only count it once if a firm makes

multiple announcements in one given year. Thus I collect 306 event year.16 For the 306

event year, I calculate a firm’s leverage in year t-1 and in year t+1,and then compare them.

I use both t-test and Wilcoxon signed-rank test to test the hypothesis that the leverage in

year t-1 is the same as the one in year t+1.

As Table 5 shows, if I choose leverage3 (total liabilities/total debt) as the measure for

leverage, both t-test and Wilcoxon sign-rank test reject the hypothesis. It implies that the

firm’s leverage significantly increases in year t+1. When I choose leverage1 (total debt/total

asset), the t-statistic is 2.3419, which rejects the hypothesis that the leverage level in year t-1

is the same as its level in year t+1 at 1.62% confidence level. The evidence from Wilcoxon

signed-rank test is weaker, where p value is just about 0.3064. When I choose leverage2 (total

debt/(total debt+market value)), the t-statistics is (p = 0.0355). Again, the result of t-test

reject the hypothesis. The result from Wilcoxon sign-rank test is the basically the same.

Here, the Wilcoxon signed-rank statistic = 1.979 (p=0.0478), which rejects the hypothesis

at 5% confidence level.

The evidence from time series study weakly confirms the main implication derived from

the model: a firm with high knowledge capital will have high leverage. However, in the event

study, I did not control other factors that may have caused the changes in firm leverage.

Given the fact that bio-tech firms are technology-oriented, I believe the result is reliable.

5 Conclusion

This paper studies high-tech firms’ optimal capital structure under an R&D intensive and

technologically innovative world. I investigate the interaction among firm leverage, growth

opportunities, knowledge capital, and earning dynamics. By assuming a firm’s earnings fol-16On average, a biotech firm makes two technology-related announcements in one given year.

24

low a jump-diffusion process with jump intensity endogenously related to a firm’s knowledge

capital, I find the links between growth opportunities and knowledge capital. This enable me

to further explore how they work together to determine a firm’s optimal capital structure.

Due to the complexity brought along by the jump component, I am not able to solve the

model analytically. However, numerical analyses yield several very interesting results:

• For reasonable parameter values, there is a positive relationship between a firm’s knowl-

edge capital and its optimal leverage. Firms with high knowledge base are expected

to be highly levered, ceteris paribus. Note that knowledge capital in this article has

very subtle meaning: it is different from R&D expenditures, or intangible assets per

se. It is able to capture the technological innovation nature people have witnessed over

the past two decades in high-tech industries. I believe the number of patent citations,

number of firm’s linkage to or affiliation with ”star” scientists, etc., are good proxies

for knowledge capital.

• As shown in previous studies, there exists a negative relationship between a firm’s

leverage and its R&D expenditures. Note that my argument is based on the tax

credits enjoyed by a firm’s R&D expenditures .

• My numerical analysis shows that the effects of business risks on firm leverage is am-

biguous. Carefully designed study should distinguish the contributions of assets in

place and potential growth opportunities to a firm’s overall business risks. Using the

variance or standard deviation of a firm’s cash flows as the measure for business risk

without disentangling the risks related to assets in place and growth opportunities may

lead to false conclusion.

The results from the empirical study confirm the model implications. I find that firm

leverage to be positively related to its knowledge capital measures. Also, I find that R&D

expenditures have a negative influence on a firm’s leverage level in the presence of other

better measures for knowledge capital.

25

Last, I use event study approach to investigate how changes in a firm’s knowledge capital

affect a firm’s capital structure. I find that firms normally increase their leverage subsequent

to the increase in their knowledge capital.

In this study, I have assumed that a firm’s knowledge capital is exogenously given when

the firm optimizes it capital structure. A more realistic scenario is that the two decisions

are made simultaneously. Endogenizing a firm’s knowledge capital into the firm’s optimal

financing is on our future research agenda. Also, in this study, I have not explicitly model

the effects of business risks on the firm’s leverage. Future studies should try to disentangle

the risks related to a firm’s assets in place and the risks related to its growth opportunities.

To the best of my knowledge, this is the first study that systematically explores the in-

teraction among high-tech firm’s knowledge capital, growth opportunities, earning dynamics

and leverage. This study contributes to the literature on capital structure. It also pro-

vides an angle to understand the relation between a firm’s assets in place and its growth

opportunities, a challenging issue in current corporate finance research.

26

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Appendix: Proof to the Lemma in the text

The valuation partial differential equation (PDE) in main text can be rewritten as:

0 = (R− λµJ −12σ)

∂C∂L

+12σ

∂2C∂L2 −

∂C∂τ

−RC

+λIE[C(t, τ, L + ln(1 + J), X)− C(t, τ, L, X)] (A. 1)

where we have applied the transformation L(t) = ln I(t). Inserting the following conjectured

solution

C(t, τ) = I(t)Π1(t, τ, I, X)−De−RτΠ2(t, τ, I,X) (A. 2)

into (A.1) produces the PDEs for the risk-neutralized probabilities, Πj, for j = 1, 2:

0 = (R− λµJ −12σ)

∂Π1

∂L+

12σ

∂2Π1

∂L2 − ∂Π1

∂τ− λµJΠ1

+λIE[(1 + ln(1 + J))Π1(t, τ, L + ln(1 + J), X)− Π1(t, τ, L, X)] (A. 3)

and

0 = (R− λµJ −12σ)

∂Π2

∂L+

12σ

∂2Π2

∂L2 − ∂Π2

∂τ

+λIE[Π2(t, τ, L + ln(1 + J), X)− Π2(t, τ, L, X)] (A. 4)

Equations (A.3) and (A.4) are the Fokker-Planck forward equations for probability functions.

This implies that Π1 and Π2 must indeed be valid probability functions, with values bounded

between 0 and 1. These PDEs are separately solved subject to the terminal conditions

Πj(t + τ, 0, L, X) = 1L(t+τ)≥ln[D], (A. 5)

where j = 1, 2. The corresponding characteristic functions for π1 and π2 will also satisfy

similar PDFs:

0 = (R− λµJ −12σ)

∂f1

∂L+

12σ

∂2f1

∂L2 −∂f1

∂τ− λµJf1

+λIE[(1 + ln(1 + J))f1(t, L + ln(1 + J), X, τ)− f1(t, L, X, τ)] (A. 6)

30

and

0 = (R− λµJ −12σ)

∂f2

∂L+

12σ

∂2f2

∂L2 −∂f2

∂τ

+λIE[f2(t, L + ln(1 + J), X, τ)− f2(t, L,X, τ)] (A. 7)

subject to the terminal conditions

fj(t + τ, 0, X; φ) = eiφL(t+τ). (A. 8)

for j = 1, and2. Conjecture that the solutions to the PDEs (A.6) and (A.7) are respectively

given by

f1(t, τ) = exp{u(τ) + y∗(τ)X(t) + iφ ln[I(t)]} (A. 9)

and

f2(t, τ) = exp{z(τ) + yx(τ)X(t) + iφ ln[I(t)]−Rτ} (A. 10)

with u(0) = y∗(0) = 0 and z(0) = yx(0) = 0. By the separation of variable technique, we

can solve the PDEs as follows:

f1(t, τ) = exp{[[λ0(1 + µJ)[(1 + µJ)iφeiφ2 (iφ+1)σ2

J − 1]− λ0µJ(iφ + 1)

+Riφ +12σiφ(iφ + 1)]τ + [[λ1(1 + µJ)[(1 + µJ)iφ

eiφ2 (iφ+1)σ2

J − 1]− λ1µJ(iφ + 1)]τX + ln(I)iφ} (A. 11)

and

f2(t, τ) = exp{[R(iφ + 1) + λ0[(1 + µJ)iφeiφ2 (iφ−1)σ2

J − 1− µJ iφ]

+12σiφ(iφ− 1)]τ

+λ1[(1 + µJ)iφeiφ2 (iφ−1)σ2

J − 1− µJ iφ]τX

+ ln(I)iφ−Rτ} (A. 12)

Q.E.D.

31

Table 1 The Relationship between Knowledge Capital (X) and Optimal Debt Level

In this table, I use numerical analysis to solve out the optimal debt level, D* that minimize a firm’s total taxliabilities as defined in equation (6) in the text. The same D* also makes the first order condition defined inequation (20) hold. In the numerical analysis, I assume the following parameter values: non-debt taxshields, NTS = 250; mean operating income, I* = 1000; marginal corporate tax rate, τC = 0.35; marginalpersonal income tax rate, τP = 0.28; risk-free interest rate, R = 0.07;debt maturity, τ = 2; σ = 0.1; jump size,µJ = -0.1; dispersion of jump size, σJ

2 = 0.04; λ0 = 0.1; knowledge capital related jump intensity, λ1 = 0.1.

Knowledgecapital, X

0 0.2 0.4 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Optimal debtlevel, D*

534.0 541.5 555.5 563.0 571.4 578.8 588.2 595.7 605.1 614.4

Knowledgecapital, X

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

Optimal debtlevel, D*

623.8 631.3 642.5 651.9 661.2 670.6 681.8 691.1 702.4 713.6

Table 2 Variables for The Analysis of Leverage Levels

Definitions and descriptive statistics for variables used in the analysis of capital structure levels are includein this table. The sample includes 437 observations for 107 biotech firms during 1983-1992 period.Accounting information was obtained from COMPUSTAT database, with balance sheet items defined as ofthe end of each fiscal year. Patent data were hand collected by searching US Patent and Trademark Officewebsite. I drop the firm-year observations that contain missing values.

Dependent Variables Definition Mean Std. Dev.

Leverage1(book value) Total debts/total assets 0.129 0.230

Leverage2(market value) Total debts/(total debts +market value) 0.063 0.113

Leverage3 Total liabilities/total assets 0.299 0.340

Knowledge Stockvariables

Definition Mean Std. Dev.

Knowledge stock (K/TA) Citation weighted patent counts/ totalassets

0.425 1.238

Knowledge stock(K1/TA)

Claim weighted patent counts /total assets 2.029 5.045

Other control variables Definition Mean Std. Dev.Firm size(LSIZE )

Natural logarithm of net sales 1.678 1.527

R&D intensity(LRND)

Natural logarithm of R&D expenditures 1.465 1.575

Tangibility of assets(IGP/TA)

(Inventory+gross plant)/total assets 0.436 0.333

intangibility of assets(INT/TA)

Intangible assets/total assets 0.034 0.112

Profitability(OI/S)

Operating income/net sales -2.471 15.177

Uniqueness(SGA/TA)

Selling, general, and administrativeexpenditures/Total assets

0.136 0.289

Table 3 Regression Coefficient Estimates: Determinants of Capital Structure levels

The table presents the results of OLS regressions. The sample consists of 437 firm year observations for107 biotech firms during 1983-1992. The absolute values of t-statistics appear in parentheses below eachcoefficient estimate. We use both the book value and market value of leverage as the dependent variables.For regression [3], we use each firm’s average leverage level as the dependent variables.

Leverage (book value) leverage (market value)

[1] leverage1 [2] leverage1 [3] average levelof leverag1

[4] leverage2 [5] leverage2

Constant 0.0498*

(2.090)0.0452(1.902)

0.0558(1.2190)

0.0229(1.963)

0.0238*

(2.030)

Uniqueness(SGA/TA)

-0.1223**

(2.849)-0.1122**

(2.692)-0.1751*

(2.282)-0.0379(1.806)

-0.0289(1.403)

Size(LSIZE)

0.0205**

(2.540)0.0222**

(2.758)0.0249(1.715)

0.0213**

(5.379)0.0209**

(5.261)

R&D intensity(LRND)

-0.0212**

(2.497)-0.0200**

(2.370)-0.0292(1.847)

-0.0146**

(3.519)-0.0146**

(3.494)

Tangibility(IGP/TA)

0.1619**

(5.081)0.1443**

(4.476)0.1598**

(2.362)0.0535**

(3.435)0.0526**

(3.298)

Intangibility(INT/TA)

0.2679(1.823)

0.2805(1.923)

0.3154(1.067)

0.1036(1.442)

0.1079(1.495)

Profitability(OI/S)

-0.1385E-03(0.197)

-0.2053E-03(0.294)

-0.3883E-03(0.227)

-0.2679E-03(0.779)

-0.2660E-03(0.769)

Citation weighted kno-wledge stock(K/TA)

0.0288**

(3.194)0.0387**

(2.415)0.0111**

(2.516)

Claim weighted know-ledge stock (K1/TA)

0.0089**

(4.047)0.0016(1.469)

Observations 437 437 107 437 437

R-squared 0.1278 0.1398 0.2055 0.1322 0.1238

F-statistics 8.98 9.96 3.66 9.34 8.66

P-value 0.000 0.000 0.001 0.000 0.000

* Significant at 5% confidence level** Significant at 1% confidence level

Table 4 Regression Coefficient Estimates: Determinants of Capital Structure levels (TOBIT models)

TOBIT regression coefficients are presented in this table. The sample consists of 437 firm yearobservations for 107 biotech firms in the 1983-1992 time period. The absolute values of t-statistics appearin parentheses below each coefficient estimate. We use both the book value and market value of leverage asthe dependent variables. Leverage (book value) Leverage (market value)

[1] leverage1 [2] leverage1 [3] leverage2 [4] leverage2Constant -0.0507

(1.631)-0.0529(1.709)

-0.0266(1.752)

0.0249(1.623)

Uniqueness(SGA/TA)

-0.1883**

(3.193)-0.1629**

(2.893)-0.0653**

(2.295)-0.0496(1.802)

Size(LSIZE)

-0.0348**

(3.411)0.0356**

(3.503)0.0288**

(5.769)0.0281**

(5.577)

R&D intensity(LRND)

-0.0226*

(2.131)-0.0212*

(2.015)-0.0154**

(2.964)-0.053**

(2.924)

Tangibility(IGP/TA)

0.2212**

(5.527)0.2031**

(5.014)0.0805**

(4.106)0.0799**

(3.982)

Intangibility(INT/TA)

0.4112**

(2.215)0.4219*

(2.29)0.1673(1.848)

0.1713(1.886)

Profitability(OI/S)

-0.3079E-03(0.342)

-0.3583E-03(0.399)

-0.3706E-03(0.846)

-0.2660E-03(0.769)

Citation weighted kno-wledge stock (K/TA)

0.0365**

(3.283)0.0147**

(2.705)

Claim weighted know-ledge stock (K1/TA)

0.0095**

(3.506)0.0018(1.338)

Observations 437 437 437 437

Log likelihood -109.29 -108.62 121.95 119.21

* Significant at 5% confidence level** Significant at 1% confidence level

Table 5Empirical analysis of changes in leverage due to the enhancement of knowledge capital: Paired t-testand Wilcoxon signed-rank test

For 129 public biotech firms, I search Lexis/Nexis database for firms’ innovation news announcements. Idefine the event period in terms of year. I then compare a firm’s leverage level one year precedingthe event and one year following the event. 306 pairs are collected. I use three different measures to capturethe firm’s leverage level.

Panel A: leverage1 (total debts/total assets)

Variables observations mean Std. Err. Std. Dev.

leverage in year t-1 306 0.1167 0.0103 0.1765leverage in year t+1 306 0.1547 0.0169 0.2972difference 306 0.0379 0.0162 0.2835

t-test for the null hypothesis that the leverage levels are the same for year t-1 and year t+1:t-statistic = 2.3419; p-value = 0.0198.Wilcoxon signed-rank test for the null hypothesis that the medians of the leverages are the same for year t-1and year t+1: P-value = 0.3064.

Panel B: leverage2 (total debts/(total debts+common equity(market value))

Variables observations mean Std. Err. Std. Dev.

leverage in year t-1 306 0.0552 0.0063 0.1102leverage in year t+1 306 0.0697 0.0072 0.1271difference 306 0.0145 0.0068 0.1201

t-test for the null hypothesis that the leverage levels are the same for year t-1 and year t+1:t-statistic = 2.112; p-value = 0.0355.Wilcoxon signed-rank test for the null hypothesis that the medians of the leverages are the same for year t-1and year t+1: P-value = 0.0478.

Panel C: leverage3 (total liabilities/total assets)

Variables observations mean Std. Err. Std. Dev.

leverage in year t-1 306 0.2508 0.0143 0.2454leverage in year t+1 306 0.3123 0.0225 0.3949difference 306 0.0615 0.0226 0.3951

t-test for the null hypothesis that the leverage levels are the same for year t-1 and year t+1:t-statistic = 2.7248; p-value = 0.0068.Wilcoxon signed-rank test for the null hypothesis that the medians of the leverages are the same for year t-1and year t+1: P-value = 0.0012.

Figure 1 Total Tax Liability Under Different Knowledge Capital Regime

-30

-25

-20

-15

-10

-5

0

100

200

300

400

500

550

600

700

765.9

885

095

0

Debt Level

To

tal T

ax L

iab

ility

X = 0

X =1

X = 5

Figure 2 Knowledge Capital vs Firm Leverage

0

100

200

300

400

500

600

700

800

900

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8

Knowledge capital

op

tim

al d

ebt

leve

l

Figure 3 Robustness Analysis

Panel A: Changing Non-debt Tax Shields

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5

Knowledge Capital Measure

Op

tim

al D

ebt

Lev

el

nts=250 nts=300

Panel B: Changing Knowledge Related Jump Coefficient

0

100

200

300

400

500

600

700

800

900

1000

1 2 3 4 5

Knowledge Capital Measure

Op

timal

Deb

t Lev

el

knowledge related jump coefficient = 0.1knowledge related jump coefficient = 0.2

Panel C: Changing the Dispersion of Jump Size

0

100

200

300

400

500

600

700

800

900

1 2 3 4 5

Knowledge Capital Measure

Op

timal

Deb

t Lev

el

dispersion of jump size = 0.04dispersion of jump size=0.1

Panel D: Changing the Standard Deviation of Assets in Place

0

100

200

300

400

500

600

700

800

900

1 2 3 4 5

knowledge capital measure

op

timal

deb

t lev

el

Std. Of Assets in Place = 0.1Std. Of Asset in Place = 0.2