Financing and Advising: Optimal Financial

Contracts with Venture Capitalists

CATHERINE CASAMATTA n

ABSTRACT

This paper analyses the joint provision of e¡ort by an entrepreneur and by an

advisor to improve the productivity of an investment project. Without moral

hazard, it is optimal that both exert e¡ort.With moral hazard, if the entrepre-

neur™s e¡ort is more e„cient (less costly) than the advisor™s e¡ort, the latter is

not hired if she does not provide funds. Outside ¢nancing arises endogenously.

This explains why investors like venture capitalists are value enhancing. The

level of outside ¢nancing determines whether common stocks or convertible

bonds should be issued in response to incentives.

THE VENTURE CAPITAL INDUSTRY has grown dramatically over the last decade. In the

United States, venture capital (hereafter VC) investments grew from $3.3 billion

in 1990 to $100 billion in 2000. In Europe, funds invested in VC grew from $6.4

billion in 1998 to more than $10 billion in 1999. The success of VC is largely due

to the active involvement of the venture capitalists. These so-called hands-on in-

vestors carefully select the investment projects they are proposed (Sahlman

(1988, 1990)) and remain deeply involved in those projects after investment is rea-

lized. Their most recognized roles include the extraction of information on the

quality of the projects (Gompers (1995)), the monitoring of the ¢rms (Lerner

(1995), Hellmann and Puri (2002)), and also the provision of managerial advice

to entrepreneurs. This advising role has been extensively documented empiri-

cally by Gorman and Sahlman (1989), Sahlman (1990), Bygrave and Timmons

(1992), Gompers and Lerner (1999), and more recently Hellmann and Puri (2002).

Venture capitalists contribute to the de¢nition of the ¢rm™s strategy and ¢nancial

University of Toulouse, CRG, and CEPR. This paper is a revised version of chapter 3 of my

n

Ph.D. dissertation, University of Toulouse. Bruno Biais has provided invaluable advice at

every stage of the paper: Special thanks to him. I am indebted to an anonymous referee and

especially to Rick Green (the editor) for very useful comments and advice. Many thanks also

for helpful suggestions and discussions to Sudipto Bhattacharya, Alex Gˇmbel, Michel Habib,

Antoine Renucci, Nathalie Rossiensky, Javier Suarez, and Wilfried Zantman, as well as parti-

cipants at the 1999 EEA meeting, the 1999 AFFI international meeting, the 1999 workshop on

corporate ¢nance at the University of Toulouse, the 1999 conference on Entrepreneurship,

Banking and the Public Policy at the University of Helsinky, the 2000 EFMA meeting, and

the 2000 ESSFM at Gerzensee. I also bene¢ted from comments at seminars at SITE (Stock-

holm School of Economics), ESSEC, and HEC Lausanne.

2059

2060 The Journal of Finance

policy, to the professionalization of their internal organization, and to the

recruitment of key employees.

This paper provides a theory for the dual (i.e., ¢nancing and advising) role of

venture capitalists. Entrepreneurs endowed with the creativity and technical

skills needed to develop innovative ideas may lack business expertise and need

managerial advice. I analyze a model where, in the ¢rst best, some e¡ort should

be provided both by an entrepreneur and by an advisor. In line with the view that

entrepreneurial vision is really key to the success of the venture, I assume that

the entrepreneur™s e¡ort is more e„cient (less costly) than the advisor™s. I consid-

er the case where advice can be provided by consultants or by venture capitalists.

Quite plausibly, I assume that the level of e¡ort exerted by the advisor, as well as

by the entrepreneur, to develop the project is not observable. Consequently the

entrepreneur and the advisor face a double moral-hazard problem. To induce

them to provide e¡ort, both the entrepreneur and the advisor must be given prop-

er incentives through the cash-£ow rights they receive over the outcome of the

project. In addition to e¡ort, the project requires ¢nancial investment. This can

be provided by the entrepreneur, the advisor, or pure ¢nanciers.

The ¢rst question raised in the paper is: Why should the entrepreneur ask for

advice from venture capitalists rather than from consultants? What makes VC

advising di¡erent from consultant advising? I show that, even if the entrepreneur

is not wealth constrained and could himself fund all the initial investment, he

chooses to obtain funding from the advisor, thus relying on VC advising rather

than on consultants.1 To understand the intuition of the result, consider the ex-

treme case where the advisor could not provide funds. In this case, although the

project would be more pro¢table with external advice, the entrepreneur chooses

not to hire a consultant. This is because the rent the entrepreneur would need to

leave to the consultant (to motivate her) is too high. If, in contrast with the main-

tained hypothesis, the advisor™s e¡ort was more e„cient than the manager™s,

(pure) consultants could be hired in equilibrium. This suggests that the relative

roles of consultants and venture capitalists depend on how crucial their advice is

to the success of the ventures. More drastic innovations that rely on the entrepre-

neur™s human capital are more likely to rely on VC advising rather than consul-

tant advising.

The model concludes that venture capitalists, through their ¢nancial partici-

pation, can provide advice that could not otherwise be provided by consultants.

The second objective of the paper is to investigate the relative roles of external

¢nancing (venture capital) and internal ¢nancing (entrepreneurial ¢nancial

participation). The result of the analysis is that some amount of external ¢nan-

cing guarantees an optimal provision of e¡ort by the venture capitalist and in-

creases the value of the ¢rm. Projects requiring a small initial investment

compared to their expected cash £ows are optimally ¢nanced by outside capital

only. In that case, outside ¢nancing comes as a compensation for the agency rent

left to the venture capitalist for incentive motive. The ¢nancial participation of

1

Of course, when the entrepreneur is wealth constrained, VC ¢nancing is all the more de-

sirable.

Financing and Advising 2061

the entrepreneur is shown to be valuable for those projects where the initial in-

vestment is large compared to the expected cash £ows. In that case, pure outside

¢nancing would produce too much advising e¡ort and not enough entrepreneur-

ial e¡ort. This e¡ect is corrected by the entrepreneur™s ¢nancial participation.

This implies a positive correlation between the level of entrepreneurial ¢nancial

investment and the pro¢tability of start-up ¢rms, for the less pro¢table start-ups

only.

The last question raised in the paper concerns the implementation of the con-

tract between the entrepreneur and the venture capitalist. The way the ¢nancial

agreement is designed must take into account the two agents™ incentives. It must

also provide them an expected return at least equal to their investment. Conse-

quently, two regimes arise depending on the amount invested by the investor.

When the amount invested by the venture capitalist is low, he receives common

stocks, while the entrepreneur is given preferred equity. When the amount in-

vested by the venture capitalist is high, he is given convertible bonds or preferred

equity. The intuition of this result is that when the investment of one agent is low,

she gets a small share of outcome. In order to motivate her, she must be given

higher-powered incentives. In the ¢rst regime, the investor is given more power-

ful incentives to exert e¡ort because her investment is low. The second regime

corresponds to the symmetric case, where the entrepreneur must be given higher-

powered incentives, since his investment is lower.

These results are consistent with the way venture capitalists structure their

¢nancial contracts. Fenn, Liang, and Prowse (1998) observe that business angels

invest smaller amounts of money than venture capitalists and acquire common

stocks. In contrast, venture capitalists acquire convertible bonds (see also

Kaplan and Str˛mberg (2003)). The two regimes identi¢ed in my theoretical

model can be interpreted respectively as business angel ¢nancing and venture

capitalist ¢nancing. The present analysis can thus be viewed as a ¢rst step to-

wards understanding the di¡erences between business angels and venture capi-

talists. While both types of investors play a signi¢cant role in early stage

¢nancing, the analysis of their di¡erences has not received, to my knowledge,

much attention in the literature so far.

The present model o¡ers a rationale for the use of convertible bonds or outside

equity in the ¢nancing of start-ups to motivate the investor and advisor.2 Other

papers explain the use of convertible claims in VC ¢nancing by focusing on the

incentives convertible claims provide to managers. For example, Green (1984) and

Biais and Casamatta (1999) show that convertible bonds induce managers to ex-

ert e¡ort while precluding ine„cient risk taking. To the extent that the model

derives the optimality of a mix of outside debt and outside equity, it is also related

to the literature on optimal outside equity ¢nancing that includes Chang (1993),

Dewatripont and Tirole (1994), or Fluck (1998, 1999) and that does not speci¢cally

focus on venture capital ¢nance.

2

An original approach is developed in Cestone and White (1998), who ¢nd that outside equi-

ty acts as a commitment device for the venture capitalist not to fund competing ¢rms.

2062 The Journal of Finance

While the current paper focuses on how VC contracts deal with moral hazard

issues, Cornelli and Yosha (1997), Bergemann and Hege (1998), Habib and Johnsen

(2000), and Dessi (2001) analyze how ¢nancial contracts elicit information revela-

tion, and are useful in discriminating across projects and taking e„cient conti-

nuation or liquidation decisions.3

The special focus of the present model on the e„ciency of the joint e¡orts of the

manager and the investor is shared by a couple of recent papers.4 In Repullo and

Suarez (1999), unlike in the present paper, the entrepreneur does not have the

option to implement the project alone. This makes my ¢rst question irrelevant

in their setting. Schmidt (1999) also considers a double moral-hazard setting to

explain the use of convertible bonds in VC ¢nancing. However, investment in his

model is an unobservable variable, while the present model distinguishes be-

tween ¢nancial investment and e¡ort. In contrast to these papers, I endogenize

the level of ¢nancial investment by the venture capitalist, and study under which

conditions consultants are not valuable for the entrepreneur.

The paper is organized as follows. The model and the assumptions are pre-

sented in Section I. The optimal contract is solved in Section II. Here I study

why entrepreneurs are unwilling to hire pure consultants and analyze the opti-

mal provision of e¡ort and level of outside ¢nancing. Section III discusses how to

implement the contracts between the VC and the entrepreneur with ¢nancial

claims such as convertible bonds or stocks. Concluding remarks are made in Sec-

tion IV. All proofs are in the Appendix.

I. The Model

Consider an entrepreneur endowed with an innovative investment project.The

project requires three types of inputs: One contractible initial investment I

(money) and two unobservable (and a fortiori noncontractible) investments de-

noted e and a, where e represents the innovative e¡ort put into the project and a

the management e¡ort to run the project properly. The project is risky and gen-

¬

erates a veri¢able random outcome R. To keep things simple, assume that it can

either succeed or fail. R takes the value Ru in case of success and Rd(oRu) in case

¬

of failure. The probability of success is denoted pu. The probability of failure is

denoted (1 À pu).

The production technology is the following: If I is not invested, pu is equal to 0;

if I is invested, pu ¼ min[e þ a; 1]5 where e and a are continuous variables that take

values between 0 and 1.

3

Admati and P£eiderer (1994) ¢rst studied the problem of acquisition of information in the

context of stage ¢nancing. They argue that assigning a ¢xed claim to the venture capitalist

prevents him from strategic trading and induces optimal continuation decisions.

4

While not focusing on double moral-hazard problems, Renucci (2000) and Cestone (2001)

analyze situations where the intervention of a venture capitalist may also be valuable.

5

The assumption that unobservable e¡ort increases the probability of success of the project

is in line with Holmstr˛m and Tirole (1997). The additive speci¢cation implies that the two

e¡orts are not complementary: Their joint realization is not required to implement the pro-

ject. Instead, each e¡ort contributes separately to improve the pro¢tability of the project.

Financing and Advising 2063

There is also a continuum of risk-neutral advisors and pure ¢nanciers.The dif-

ferent types of agents di¡er in their ability to provide the nonobservable e¡orts e

and a. Speci¢cally, e can only be provided by the entrepreneur while a must be

provided by an outside advisor. Although the entrepreneur is endowed with the

technical skills and creativity required to develop his idea, he lacks management

expertise. Pure ¢nanciers cannot provide a or e.

Both e¡orts are costly. Let cE ( Á ) denote the entrepreneur™s disutility of e¡ort,

and cA( Á ) the advisor™s disutility of e¡ort. Assume

e2

cE °eÞ ¼ b ; °1aÞ

2

and

a2

cA °aÞ ¼ g : °1bÞ

2

Assume that for a given level of e¡ort, the cost is lower for the entrepreneur than

for the advisor: g4b, that is, the e¡ort of the entrepreneur is more e„cient. It

would be equivalent to consider that the two agents have the same cost function,

and that the impact of each e¡ort on pu is weighted by b , and 1 respectively. This

1

g

assumption captures the idea that the entrepreneur™s contribution is more impor-

tant for success than the managerial expertise of the advisor. The consequences

of relaxing this assumption are discussed later.

Agents are not a priori wealth constrained. Any of them can provide the initial

investment I. However, I assume that once the ¢rm is created, agents are pro-

tected by limited liability. The only thing that can be shared is the outcome of

the project.6 All agents are risk neutral.Their opportunity cost of putting money

into the ¢rm is the riskless interest rate r, normalized to zero. Denote AVC the

amount of money provided by the advisor, AF the money provided by the pure

¢nancier, and I À AVC À AF the money provided by the entrepreneur.7 If AVC ¼ 0,

the advisor who exerts e¡ort a will be called a consultant, while if AVC40, she

will be called a venture capitalist.

The social value of the project is

e2 a2

V°e; aÞ ¼ min½e þ a; 1Ru þ max½0; 1 À °e þ aÞRd À b À g À I: °2Þ

2 2

As a benchmark, let us determine the optimal levels of e¡orts when all inputs are

contractible (i.e., when e¡orts are observable). This corresponds to the ¢rst-best

solution that maximizes the social value of the project. It is straightforward to

see that it is optimal to have both the entrepreneur and the advisor exert strictly

positive levels of e¡ort. When both e¡orts are observable, the optimal levels of

6

This assumption is in the line of Innes (1990) and is meant to make the problem interest-

ing under risk neutrality.

7

Note that the amount of money the entrepreneur puts into the ¢rm may be negative if

AVC þ AF4I, in which case he receives a strictly positive transfer when investment is made.

2064 The Journal of Finance

e¡ort are given by the ¢rst-order conditions of the maximization of V:

1

eFB ¼ °Ru À Rd Þ °3Þ

b

and

1

aFB ¼ °Ru À Rd Þ: °4Þ

g

1

þ °Ru À Rd Þo1, so that the constraint min[e þ a;1] 1 is not bind-

1

Assume b g

ing at the ¢rst best. Note that as the e¡ort of the entrepreneur is more e„cient

than the e¡ort of the advisor, the optimal level of e¡ort eFB is larger than aFB.The

¢rst-best value of the project is then given by

11 1

þ °Ru À Rd Þ2 þ Rd À I:

V FB ¼ °5Þ

2b g

Assume that

11 1

þ °Ru À Rd Þ2 þ Rd I

°6Þ

I

2b g

so that, when the ¢rst-best levels of e¡ort are provided, the project is pro¢table.

This ¢rst-best solution can be implemented in a number of ways. E¡orts e and a

must be provided by the entrepreneur and by the advisor, respectively, but the

identity of the agent providing the ¢nancial investment I is irrelevant. Thus, the

Modigliani and Miller theorem holds in the ¢rst best. Financial structure is in-

determinate and real decisions do not depend on ¢nancial decisions. Participa-

tion is ensured as capital suppliers receive an expected income equal to the

opportunity cost of their investment.This is always feasible since, by assumption,

the NPVof the project is positive in the ¢rst best.

When there is no moral-hazard problem, it is always optimal for the entrepre-

neur to ask for the services of an advisor.Whether the advisor is a consultant or a

venture capitalist is irrelevant: The same social value can be attained when a

¢nancier, an advisor, or the entrepreneur himself provides the ¢nancial invest-

ment I.We will see later that this contrasts sharply with the conclusions derived

under moral hazard.

II. Optimal Contract with Moral Hazard

The timing of the game is as follows. First, the contract is signed and I is in-

vested. Second, agents choose their level of e¡ort. Third, the outcome of the pro-

ject is realized. The two agents choose their e¡ort level to maximize their

expected utility, given the contract and given their rational expectation of the

equilibrium level of e¡ort of the other.This is a simultaneous move game. Assum-

ing simultaneous moves is natural, since e¡ort levels are not observable. As all

agents are risk neutral, their expected utility is perfectly identi¢ed by their net

expected payo¡s. Those payo¡s depend on the ¢nancial contract they agree on,

Financing and Advising 2065

which speci¢es the ¢nancial contribution of each party and the share of the rev-

enue allocated to each party in each state of nature.

Denote ay (resp. ay ) the share of the revenue accruing to the entrepreneur

A

E

(resp. the advisor) in state yA{u, d}. If a pure ¢nancier is included in the contract,

she receives a share: 1 À (ay þ aA) in state y.

y

E

Contrary to the ¢rst-best case, the way the cash £ow is shared determines how

much e¡ort will be provided. The level of e¡ort chosen by the entrepreneur is gi-

ven by his incentive compatibility condition, denoted (IC)E:

^2

e

aÞau Ru aÞÞad Rd

e 2 arg max°^ þ þ °1 À °^ þ À b À °I À °AVC þ AF ÞÞ; °7Þ

e e

E E

2

^

e

which means that he chooses the level of e¡ort that maximizes his expected prof-

it, given the contract established, his rational expectation of the e¡ort level of the

other agent, and given his cost of e¡ort.

Equivalently, the incentive compatibility condition of the advisor, denoted

(IC)VC , is given by:

a2

^

aÞau Ru aÞÞad Rd

a 2 arg max°e þ þ °1 À °e þ À g À AVC : °8Þ

^A ^A

2

a

^

Assume bRu o1 (A.1). Assumption (A.1) simply ensures that we get an interior so-

1

lution when one agent is given maximal incentives. In the remainder of the ana-

lysis, (A.1) will be assumed to hold. The following lemma states what levels of

e¡ort are chosen by the entrepreneur and by the advisor as a function of the para-

meters of the contract.

LEMMA 1: The levels of e¡ort e and a are given by the ¢rst order conditions of the incen-

tive compatibility constraints (IC)E and (IC)VC :

1

e ¼ °au Ru À ad Rd Þ °9Þ

bE E

and

1

a ¼ °au Ru À ad Rd Þ: °10Þ

gA A

For each agent, the level of e¡ort increases in the di¡erence between his pro¢t

in state u and his pro¢t in state d. Indeed, e (resp. a) is increasing in au (resp. au ),

E A

and decreasing in aE (resp. ad ). Increasing the share of the ¢nal outcome given to

d

A

one agent in case of success reduces the share left to the other agent and corre-

spondingly his incentives. The optimal contract will re£ect this trade-o¡.

The ¢nancial contract is chosen to maximize the expected utility of the entre-

preneur. The underlying assumption is that the entrepreneur has a unique, inno-

vative idea, and can ask for business advice and money from a large number of

agents.The participation constraints of the advisor and of the ¢nancier, ensuring

that they recoup their investment in expectations, must be included in the

entrepreneur™s program. The participation constraint of the advisor, denoted

2066 The Journal of Finance

(PC)VC , is

a2

aÞau Ru aÞÞad Rd

°e þ þ °1 À °e þ À g ! AVC : °11Þ

A A

2

The participation constraint of the ¢nancier, denoted (PC)F , is

°e þ aÞ°1 À °au þ au ÞÞRu þ °1 À °e þ aÞÞ°1 À °ad þ ad ÞÞRd ! AF : °12Þ

E A E A

Hence the program to be maximized is

e2

aÞau Ru aÞÞad Rd

°e þ þ °1 À °e þ À b À °I À °AVC þ AF ÞÞ;

max E E

2

ay ;ay ;AVC ;AF

EA

s:t: °PCÞVC ;

°13Þ

°PCÞF ;

°ICÞVC ;

°ICÞE ;

°au ; ad ; au ; ad Þ ! 0 °14Þ

EEAA

au þ au °15Þ

1

E A

ad þ ad °16Þ

1;

E A

where yA{u, d} and the last three conditions are feasibility constraints ensuring

limited liability holds for all agents.

A. Provision of E¡orts and External Financing when the Advisor Is a Consultant

The previous section established that without moral-hazard problems, the en-

trepreneur was indi¡erent to whether he hires a consultant or contracts with a

venture capitalist. Under moral hazard, however, the entrepreneur never chooses

to hire a pure consultant, as stated in the next proposition.

PROPOSITION 1: If AVC ¼ 0, the entrepreneur maximizes his expected utility by not hiring

a consultant. The entrepreneur exerts his ¢rst-best level of e¡ort eFB if the amount of

outside ¢nancing is not too large (AF Rd).

The intuition of Proposition 1 is the following.To induce the consultant to exert

e¡ort, the entrepreneur needs to give her a strictly positive share of the ¢nal in-

come in case of success. This a¡ects the entrepreneur™s own pro¢t in three ways.

The ¢rst one is a direct revenue e¡ect: The entrepreneur™s share of income is low-

er. The second one is an incentive e¡ect: Having a lower share of income, the ef-

fort provided by the entrepreneur decreases and is not fully o¡set by the e¡ort

exerted by the consultant, because the consultant™s e¡ort is less e„cient. Overall,

the probability of success decreases. The third e¡ect is a reduction in the

Financing and Advising 2067

entrepreneur™s cost of e¡ort, since his e¡ort is lower. The ¢rst two e¡ects a¡ect

negatively the entrepreneur™s pro¢t while the third e¡ect is positive. However the

cost e¡ect is not high enough to compensate the ¢rst two, and the entrepreneur

maximizes his pro¢t by not hiring a consultant. This is, however, only a second-

best optimum: Because the cost of e¡ort is convex, it would be technologically

e„cient to split the provision of e¡ort between the two agents, but this is subop-

timal because of incentive considerations. Starting from the case presented in

Proposition 1 where the entrepreneur does not hire an advisor, a small amount

of business advice would increase the value of the project. The entrepreneur is

not able to recoup the cost of this enhancement in social value, however.The rent

he would have to surrender to the consultant would be too large compared to the

increase in value the consultant™s advice would induce.

The main result of Proposition 1 comes from the combination of two condi-

tions. First, the consultant is less e„cient, and second, he does not invest money

into the project. If one of these assumptions is relaxed, it becomes optimal to hire

an advisor. Consider the case where the entrepreneur™s e¡ort is less e„cient. He

would then ¢nd it optimal to hire a consultant. In the venture capital setting,

however, the entrepreneur™s speci¢c expertise is key to the success of the venture.

This prevents him from hiring a consultant. In the following section, we will see

that one way to overcome this ine„ciency is to ask the advisor to participate ¢-

nancially in the project, in the spirit of venture capital ¢nancing and advising.

Intuitively, asking the advisor to contribute ¢nancially compensates the entre-

preneur for granting the advisor a share of the proceeds and reduces the cost of

getting business advice. This suggests that the relative roles of consultants and

venture capitalists depend on how crucial their advice is to the success of the

ventures. Pure consultants can be hired if their e¡ort is more e„cient than that

of entrepreneurs. More drastic innovations that presumably rely on the entrepre-

neur™s human capital are more likely to need VC advising.

The last part of Proposition 1 simply states when the ¢rst-best level of entrepre-

neurial e¡ort is achieved. If AVC is lower than Rd, the revenue promised to the

¢nancier is a constant, and the entrepreneur captures any increase in value in-

duced by his e¡ort. This gives rise to strong incentives to exert e¡ort. This is re-

miniscent of the classical Harris and Raviv (1979) result. However, due to limited

liability, if outside ¢nancing is higher than Rd, the ¢rst-best level of e¡ort is in-

feasible because the di¡erence between the revenue of the entrepreneur in the

good and bad states is not large enough.

B. Provision of E¡orts and External Financing when All Agents Can Invest

Let us now turn to the case where all agents can invest money into the ¢rm,

that is, when AVC and AF can both be positive. When AVC and AF are chosen to

maximize the entrepreneur™s expected payo¡, the two participation constraints

PCVC and PCF are obviously binding.8 The program boils down to maximizing

8

If they were not, increasing the ¢nancial participation of the advisor and of the ¢nancier

would make the entrepreneur better o¡ without a¡ecting incentives.

2068 The Journal of Finance

the NPV of the project subject to the incentive compatibility conditions and the

feasibility conditions described at the beginning of this section. From this sec-

tion on, I restrict the analysis to the case where the revenue of the pure ¢nancier

does not decrease with the project™s income. As argued by Innes (1990), this as-

sumption deters secret infusion of cash into the ¢rm™s accounts by insiders.9 The

nondecreasing condition thus generates more robust contracts.10 To re£ect this

assumption, the condition

°1 À °au þ au ÞÞRu ! °1 À °ad þ ad ÞÞRd ; °17Þ

E A E A

is added to the program. The next proposition establishes that venture capital

¢nancing is desirable.

PROPOSITION 2:When all agents can invest, it is optimal to ask for venture capital ¢nan-

n

cing: AVC40. The level of e¡ort exerted by theVC a n is strictly positive.

Proposition 2 states that the entrepreneur is willing to hire an advisor who

also invests a strictly positive amount of money into the project. Combined with

Proposition 1, it implies that ¢nancing and advising must go hand in hand. The

¢nancial participation of theVC compensates the entrepreneur for conceding part

of the project™s income to motivate her. Optimally chosen, theVC™s ¢nancial invest-

ment exactly o¡sets the agency rent he is given to be induced to work. The entre-

preneur™s objective turns out to be aligned with NPV maximization, which

requires a positive e¡ort a. The entrepreneur strictly prefers to have a ¢nancial

partner investing in the project, even though he is wealthy enough to implement

the project alone. A real ¢nancial partnership with the advisor arises endogenously.

This result provides a rationale for the commonly observed behavior of VC in-

vestors, or business angels. A distinctive feature is their personal involvement

along with their ¢nancial investment to develop the projects they back. For in-

stance, Gorman and Sahlman (1989) report that venture capitalists spend a great

deal of time in the ¢rms they invest in, providing advice and experience. Hell-

mann and Puri (2002) also document this ˜˜soft side™™ of venture capital. Less

unanimity is found concerning the advising role of business angels. Although it

is sometimes argued that they are less deeply involved in the projects they ¢nance

(see for instance Ehrlich et al. (1994)), many authors do ¢nd an important advis-

ing role in angels™ ¢nancing.11 Prowse (1998, p. 790) reports from interviews with

business angels that ˜˜ ctive angels almost always provide more than money. An-

A

gels will often help companies arrange additional ¢nancing, hire top manage-

9

Such a situation may occur if the monetary outcome is perfectly veri¢able but not the ori-

gin of this outcome.

10

This is at the expense of e„ciency since those contracts provide less powerful incentives

to exert e¡ort. For the sake of completeness, I present in the Appendix the results when this

condition does not hold. The main insights of this section concerning the role of venture ca-

pital ¢nancing are qualitatively unchanged.

11

Other evidence is found in Freear, Sohl, and Wetzel (1994) or Mason and Harrison (2000).

See also Berger and Udell (1998) and Lerner (1998) for a discussion on the di¡erent character-

istics of angel investors.

Financing and Advising 2069

ment, and recruit knowledgeable board members. Angels also help solve major

operational problemsy and develop the company™s long-term strategy.™™

One of the insights of the model is that the level of e¡ort provided by the advi-

sor depends on the level of her ¢nancial contribution to the project. It is thus nat-

ural to investigate to what extent the ¢nancial participation of the entrepreneur

is also desirable.

PROPOSITION 3: There exists a threshold I n such that the ¢nancial participation of the

entrepreneur increases the NPVof the project if the initial investment I is large (I4I n),

while it is neutral if I is small (I I n).

COROLLARY 1: When I4I n, the entrepreneur™s e¡ort e n decreases with the amount of

outside ¢nancing, while theVC™s e¡ort a n increases with outside ¢nancing.

Proposition 3 states that the ¢nancial participation of the entrepreneur can

enhance the value of the project if the initial investment needed is large. The in-

tuition is that there is a maximal amount of outside ¢nancing (I n) that can be

raised while maintaining incentives for both agents to exert e¡ort. As stated in

Corollary 1, each extra dollar of outside ¢nancing above I n a¡ects negatively the

entrepreneur™s e¡ort and reduces the project™s value. The reason is the following.

Increasing outside ¢nancing raises the share of the ¢nal income left to outside

investors. This, in turn, destroys the entrepreneur™s incentives to work. If the en-

trepreneur is wealthy enough, investing his own resources into the project re-

duces the amount of outside capital to be raised and preserves the

entrepreneur™s own incentives. The project™s value consequently increases. If the

level of investment is below I n, it can be entirely ¢nanced by outside capital, for

outside ¢nancing o¡sets the expected income left to the venture capitalist for

incentive reasons. In that case, the NPV is maximal without the entrepreneur™s

¢nancial participation.

The assumption of the model that no agent is wealth constrained is clearly an

important one. The above result states that the entrepreneur™s participation is

e„cient for some values of the parameters. It is likely though that some entrepre-

neurs have no cash to invest in their ¢rm. I turn to the case where this assumption

is relaxed. Suppose that the entrepreneur has no personal wealth. Proposition 3

shows that for those projects requiring a low initial outlay, the entrepreneur™s

wealth constraint has no bite. It can, however, be detrimental to the project™s va-

lue if the initial investment required is large. Proposition 4 sheds light on the

impact of the entrepreneur™s wealth constraint.

PROPOSITION 4: The maximal amount of outside ¢nancing (Imax) that the entrepreneur

can raise under moral hazard is strictly lower than the maximal level of investment,

such that the project is pro¢table in the ¢rst best (I ).

Proposition 4 re£ects the ¢nancial constraints faced by the entrepreneur be-

cause of moral-hazard problems. If the project requires an initial investment lar-

ger than Imax but lower than I , it is, by assumption, potentially pro¢table.

2070 The Journal of Finance

However, if the entrepreneur has no personal wealth to invest, he is rationed on

the capital market and cannot implement his project. If the level of outside

¢nancing that must be raised is above Imax, too large a share of pro¢ts must be

left to the investors so that they recoup their investment. This, in turn, destroys

the entrepreneur™s incentives to exert e¡ort and leads to a negative NPV project:

Capital suppliers cannot recover the opportunity cost of their investment and

refuse to invest.

The ¢rst part of Proposition 3 along with Proposition 4 illustrates the impact of

agency costs on the ¢rm™s investment policy as well as the role of net worth or cash

£ows in mitigating these costs, as documented by Fazzari, Hubbard, and Peterson

(1988), Gilchrist and Himmelberg (1995), or Lamont (1997). Raising external capi-

tal is expensive. It dilutes the entrepreneur™s stake in the ¢rm and discourages

e¡ort. This lowers the ¢rm™s value and reduces investment. However, Proposition

2 as well as the last part of Proposition 3 unveils another aspect of the role of ex-

ternal ¢nance. In the speci¢c venture capital setting, raising external capital is

value enhancing, since it guarantees the involvement of the venture capitalist.

Contrary to the traditional agency view of corporate ¢nance,12 projects ¢nanced

by external capital can be more pro¢table than pure internally ¢nanced projects.

The above results delineate two types of situations. In the ¢rst one, projects

should be entirely ¢nanced by external venture capital. This ensures that a su„-

cient level of e¡ort a is exerted by the venture capitalist. This case arises when

the initial investment is lower than I n. Note that I n increases with (Ru À Rd)2.

When I is small compared to (Ru À Rd)2, projects exhibit high expected pro¢tabil-

ity. In the opposite case, projects with lower expected pro¢tability bene¢t from

the ¢nancial contribution of the entrepreneur. For those projects, the relation

between the level of investment of the entrepreneur and the pro¢tability of the

project is expected to be positive.

This model explains why the joint provision of advice and money is so often

observed in the case of start-ups. Although business expertise is not the exclusive

property of VCs, it may sometimes be the only way for an entrepreneur to obtain

e„cient advice. The next section investigates which ¢nancial claims purchased

by venture capitalists optimally cope with the double-sided moral-hazard pro-

blem studied here.

III. Optimal Financial Contracts between Venture Capitalists and

Entrepreneurs

The previous section established the optimality of the venture capitalist™s ¢-

nancial participation in the entrepreneur™s project. This section aims at de¢ning

which ¢nancial claims will be optimally held by venture capitalists in response

to their ¢nancial investment. The objective is to determine which ¢nancial

claims will provide powerful incentives for both the venture capitalist and the

entrepreneur. I restrict the analysis to the case where the only outside investor

12

Surveys of this numerous literature include Harris and Raviv (1991) or Allen and Winton

(1995).

Financing and Advising 2071

is the VC. Such a restriction is harmless from an e„ciency point of view. The

presence of a pure ¢nancier along with the VC in the contract with the entrepre-

neur is irrelevant to the levels of e¡ort exerted.13 The following proposition states

which ¢nancial claims are optimally issued, depending on the level of outside

¢nancing.

n

PROPOSITION 5: There exists a threshold AVC , strictly lower than I n, such that

n

When AVC AVC , the optimal contract can be implemented by giving com-

mon stocks to the VC and preferred stocks to the entrepreneur.

n

When AVC4AVC , the optimal contract can be implemented by giving preferred

stocks or convertible bonds to theVC and common stocks to the entrepreneur.

Recall that I n is the maximal amount of outside ¢nancing that can be raised

while inducing optimal e¡orts for both agents. Proposition 5 states that within

the optimal range of outside ¢nancing, incentive problems can be solved using

di¡erent instruments. Two regimes arise. When the amount of outside ¢nancing

is small, the VC™s expected income is small, too. She must then be given higher-

powered incentives to be induced to work. In that case, the entrepreneur is given

preferred stocks that grant him a higher dividend than common stocks if the bad

state of nature is realized. If the good state of nature is realized, the income is

high enough so that common and preferred stocks give the same return. As a con-

sequence, the VC who owns only common stocks is proportionally better remun-

erated in state Ru than in state Rd, which gives her more powerful incentives to

exert e¡ort. When the amount of outside ¢nancing is large, the VC must be

pledged a large share of pro¢ts in order to recoup her investment. As there is

little left for the entrepreneur, he is less prone to make an e¡ort, and needs a

higher-powered incentive scheme.When theVC is given convertible bonds or pre-

ferred stocks, she captures most of the income in state Rd. The common stocks

held by the entrepreneur are only valuable in the good state of nature.The entre-

preneur intensi¢es his e¡ort to increase the probability of state Ru occurring.

The speci¢c venture capital setting studied here provides a rationale for the

use of convertible and equity-like claims as the optimal source of outside ¢nance.

These results contribute to the literature on the optimal capital structure of

¢rms.The main insight is that outside equity, or equity-like claims, provide prop-

er incentives to active investors such as venture capitalists. This is consistent

with the empirical observation that convertible claims (bonds or preferred

stocks) are extensively used in VC ¢nancing, as evidenced by Sahlman (1988,

1990) or Kaplan and Str˛mberg (2000).

These two regimes are also related to the ¢ndings of Fenn, Liang, and Prowse

(1998).They compare empirically the ¢nancial claims used by business angels and

venture capitalists. In their sample of 107 U.S. ¢rms of high-tech sectors (medical

13

This is true when the ¢nancial contract of the pure ¢nancier cannot decrease with the

¢nal outcome of the project. Otherwise it could improve incentives as mentioned in footnote

10.

2072 The Journal of Finance

equipment and software industry), they ¢nd that business-angel-backed ¢rms ob-

tain an average funding of U.S. $1.5 million, while venture-capital-backed ¢rms

obtain an average funding of U.S. $12 million. In addition, three-quarters of the

business angels™deals involve the acquisition of common stock, while three-quar-

ters of the venture capitalists™deals involve the acquisition of convertible claims.

Quite consistently, Proposition 5 states that when theVC™s ¢nancial participation

is small, she purchases common stocks, while she obtains convertible bonds or

preferred stocks when her ¢nancial contribution is large.

It is important to stress that the optimal ¢nancial claims in each investment

regime are not unique. In the model, convertible bonds do just as well as preferred

stocks, and both can be used indi¡erently. This indeterminacy is itself an impor-

tant feature of real venture capital contracts. As noted by Kaplan and Str˛mberg

(2003) ˜˜WhileVCs use convertible securities most frequently, they also implement

the same allocation of rights using combinations of multiple classes of common

stock and straight preferred stock.™™

What matters is how the cash-£ow rights allocated to each party (entrepreneur

and venture capitalist) vary with the ¢rm™s performance.14 On this issue, Kaplan

and Str˛mberg (2003) ¢nd that VCs™ cash-£ow rights tend to decrease with the

¢rm™s performance, while the founder™s cash-£ow rights tend to increase with per-

formance. This is consistent with the second regime described in Proposition 5

where theVC™s investment is high, and where she is given convertible bonds, while

the entrepreneur is given common stocks. In this case, the VC™s cash-£ow rights

decrease with the ¢rm™s performance, while the entrepreneur™s rights increase

with performance.

IV. Conclusion

This paper analyzes a double-moral hazard problem whereby two agents must

exert e¡ort to improve the pro¢tability of a venture. Because of incentive consid-

erations, the most e„cient agent prefers not to hire the less e„cient one if the

latter does not invest money into the project. In the venture capital setting, this

implies that entrepreneurs do not want to rely on consultant advising when their

own expertise is key to the success of the venture. To enhance the pro¢tability of

their project, entrepreneurs must ask advisors to invest ¢nancially into the pro-

ject, in the spirit of venture capital ¢nancing and advising. This determines an

optimal amount of outside ¢nancing. Traditional corporate ¢nance theory em-

phasizes the agency costs associated with external ¢nancing, while this model

highlights the reduction in agency costs owing to external ¢nancing. The ¢nan-

cial claims purchased by venture capitalists also respond to incentive considera-

tions. Common stocks provide high-powered incentives to venture capitalists. In

contrast, convertible bonds are given to the venture capitalists when strong

incentives must be provided to entrepreneurs.

14

Thus the present analysis determines the optimal allocation of shares between managers

and investors according to performance. See Fluck (1999) for an analysis of the dynamics of

the allocation of shares between managers and investors.

Financing and Advising 2073

The analysis of the model yields the following empirical predictions.

First, there should be a relationship between the level of the venture capital-

ist™s ¢nancial participation and the type of ¢nancial claim that is issued by

the ¢rm. Common stocks should be associated with small ¢nancial invest-

ment, while convertible bonds should be associated with large ¢nancial in-

vestment. This is consistent with the empirical ¢ndings of Fenn, Liang, and

Prowse (1998) and Kaplan and Str˛mberg (2003).

Second, the model predicts that in very innovative lines of business venture

capital-backed ¢rms should be more pro¢table than non-VC-backed ¢rms:

For those projects, onlyVCs can provide business advice to improve the ¢rm™s

pro¢tability.This suggests that a variable indicating the presence of venture

capital should be included in the regression explaining the pro¢tability of

very innovative ¢rms.

Third, consultant services should be more frequent in those start-ups where

the entrepreneur™s competencies are not unique or crucial. Less innovative

¢rms should rely more on consultant advising. To test this hypothesis, one

could identify the product market strategies of di¡erent start-ups, in the spirit

of the analysis of Hellmann and Puri (2000), and compare the frequency of use

of consultant services between groups of di¡erent innovativeness.

Fourth, there should be a positive correlation between the level of entrepre-

neurial ¢nancial investment (expressed as a percentage of total investment)

and the pro¢tability of start-up ¢rms. This e¡ect should be stronger among

groups of less pro¢table start-ups. In gathering ¢rm-speci¢c data on ¢nancing

patterns of start-ups, one could add the level of entrepreneurial investment in

the explanatory variables of the ¢rms™ pro¢tability.

Appendix

Proof of Lemma 1: The levels of e¡ort chosen by the entrepreneur and the investor,

given by the FOCs of ICE and ICVC , are:

1uu dd

e ¼ max 0; min½1; °aE R À aE R Þ °A1Þ

b

and

1uu

a ¼ max 0; min½1; °aA R À ad Rd Þ : °A2Þ

A

g

Under assumption (A.1), bRu o1, which implies:

1

81 u u

< b°aE R À ad Rd Þo1

E

and °A3Þ

: 1°au Ru À ad Rd Þo1

gA A

2074 The Journal of Finance

We next show that when e ¼ 0, the entrepreneur never chooses au and aE such

d

E

that:

1uu

°aE R À ad Rd Þo0: °A4Þ

E

b

When e ¼ 0, a must be strictly positive (otherwise the project cannot be imple-

mented); hence it is given by

1

a ¼ °au Ru À ad Rd Þ: °A5Þ

gA A

The constraints (PC)VC and (PC)F are binding. If they were not, increasing AF

and AVC would increase the entrepreneur™s expected income without a¡ecting

the advisor™s incentives. Replacing a, AF, and AVC by their value, the program de-

¢ned in Section II becomes

max °Ru À Rd Þ1°au Ru À ad Rd Þ À 2g°au Ru À ad Rd Þ2 þ Rd À I

1

°A6Þ

gA A A A

au ;ad

AA

s:t: ad Rd À au Ru ! 0; °A7Þ

E E

au Ru þ au Ru Ru ; °A8Þ

E A

ad Rd þ ad Rd Rd °A9Þ

E A

Suppose equation (A7) is binding. Solving the program gives

au Ru À ad Rd ¼ Ru À Rd : °A10Þ

A A

Given that e ¼ 0, e¡ort a is equal to 1°Ru À Rd Þ, which corresponds to its ¢rst-best

g

value.

Suppose now that equation (A7) is not binding, that is aE Rd À aE Ru ¼ e, e40. It

d u

is easy to see that the solution described in equation (A10) can still be attained.

This is because when aE Rd4au Ru, the share of outcome given to the ¢nancier

d

E

can adjust to induce the ¢rst-best level of e¡ort a.15 The value of the objective

function is then

1u

½R À Rd 2 þ Rd À I: °A11Þ

2g

u d

Hence, when e ¼ 0, it is e„cient for the entrepreneur to choose aE and aE such

that equation (A7) is binding. With no loss of generality, equation (A1) can

15

Note that this would not be true anymore if there was no pure ¢nancier. In that case,

setting aE Rd ¼ aE Ru when e ¼ 0 would be the only way to induce the ¢rst best level of e¡ort

d u

a. Equation (A7) would then have to be binding.

Financing and Advising 2075

be replaced by

1

e ¼ °au Ru À ad Rd Þ; °A12Þ

bE E

which states the ¢rst part of Lemma 1.

Equivalently, let us show that when a ¼ 0, the entrepreneur never chooses au

A

d

and aA such that

1uu

°aA R À ad Rd Þo0: °A13Þ

A

g

By the same reasoning as before, when a ¼ 0, the program solved by the entrepre-

neur is

max°Ru À Rd Þb°au Ru À ad Rd Þ À 2b þ °au Ru À ad Rd Þ2 þ Rd À I

1 1

°A14Þ

E E E E

au ;ad

EE

ad Rd À au Ru ! 0; °A15Þ

s:t: A A

au Ru þ au Ru Ru ; °A16Þ

E A

ad Rd þ ad Rd Rd °A17Þ

E A

Because of the presence of the pure ¢nancier, the same solution can be attained

whether equation (A15) is binding or not and is characterized by

au Ru À ad Rd ¼ Ru À Rd : °A18Þ

E E

Given that a ¼ 0, e¡ort e is set at its ¢rst-best value, that is, e ¼ b°Ru À Rd Þ. The

1

value of the objective function is then

1u

½R À Rd 2 þ Rd À I: °A19Þ

2b

As a consequence, with no loss of generality, equation (A2) can be replaced by

1

a ¼ °au Ru À ad Rd Þ: °A20Þ

gA A

Proof of Proposition 1: The ¢rst step of the proof is to show that Lemma 1 still

holds when one imposes AVC ¼ 0 in the general program.The main di¡erence with

the case where AVC can be optimally chosen is that (PC)VC may not be binding.

Suppose ¢rst that e ¼ 0. E¡ort a is given by equation (A20) and (PC )F is bind-

ing. The program solved by the entrepreneur is written

max 1½Ru À Rd À °au Ru À ad Rd Þ þ °au Ru À ad Rd Þ þ Rd À I À ad Rd °A21Þ

A A A A A

g

au ;ad

AA

s:t: ad Rd À au Ru ! 0 °A22Þ

E E

2076 The Journal of Finance

À ad R d Þ 2 þ ad R d ! 0

1uu

2g°aA R °A23Þ

A A

au Ru þ au Ru Ru ; °A24Þ

E A

ad Rd þ ad Rd Rd °A25Þ

E A

d

The optimal solution is to set aA ¼ 0 and au Ru ¼ 1°Ru À Rd Þ. For the reasons

A 2

mentioned in the proof of Lemma 1, this solution is feasible whether equation

(A22) is binding or not.

Suppose next that a ¼ 0. E¡ort e is given by equation (A12) and (PC)F is bind-

ing. (PC)VC is written

1uu

°aE R À ad Rd Þ°au Ru À ad Rd Þ þ ad Rd ! 0: °A26Þ

E A A A

b

If au Ru ¼ aA Rd, the optimal solution of the program is given by equation (A18).

d

A

E¡ort e is set at its ¢rst-best level, given that a ¼ 0.

If au Ruoad Rd (for instance, au Ru ¼ ad Rd À e, e40) it is not possible anymore to

A A A A

induce the ¢rst-best level of e¡ort e. Indeed, at the optimum, we have

au Ru À ad Rd ¼ Ru À Rd þ e; °A27Þ

E E

which induces too large a level of e¡ort e compared to the ¢rst best. The value of

the objective function is strictly lower than in the case where aA Ru ¼ aA Rd.

u d

Hence, Lemma 1 still holds when there is no ¢nancial participation by the

advisor.

The second step of the proof consists of solving the general program after re-

placing (IC)VC and (IC)E using the expressions in Lemma 1. Note that (PC)F is

still binding and can also be replaced. After manipulations, the program to solve

is the following:

max½b°au Ru Àad Rd Þ þ 1°au Ru À ad Rd Þ½Ru À Rd À °au Ru À ad Rd Þ

1

E E gA A A A

ay ;ay

°A28Þ

EA

ad Rd Þ2

uu d

ad R d

1

À 2b°aE R À þR ÀI À

E A

1uu

À ad Rd Þ þ b°au Ru À ad Rd Þ°au Ru À ad Rd Þ þ ad Rd ! 0

1

2g°aA R °A29Þ

s:t: A E E A A A

au Ru þ au Ru Ru ; °A30Þ

E A

ad Rd þ ad Rd Rd ; °A31Þ

E A

where yA{u, d}. Note that equation (A29) representing (PC)VC cannot be binding

if e40 and a40.The constraint (PC)VC can only be binding if a ¼ 0 and au ¼ ad ¼ 0,

A A

¼ 0, which corresponds to the case where the entrepreneur does not hire a con-

Financing and Advising 2077

sultant.To establish Proposition 1, it will be demonstrated that the entrepreneur

is strictly better o¡ if (PC)VC is binding.

Setting ad ¼ 0 is optimal since it lowers the expected outcome of the advisor,

A

and increases the entrepreneur™s pro¢t without a¡ecting the latter™s incentives to

exert e¡ort. De¢ne X ¼ au Ru À aE Rd and Y ¼ aA Ru. Equation (A29) states

d u

E

121

Y þ XY ! 0: °A32Þ

2g b

As X40, it is automatically satis¢ed when Y ! 0, which implies that it is redon-

dant compared to the feasibility constraint. The program solved by the entrepre-

neur is:

12 1 1

X þ Y °Ru À Rd À Y Þ

max À X þ

2b b g

X;Y

s:t: Y ! 0

The objective function is concave if 2b4g and convex otherwise.The Lagrangian

of the program is

12 1 1

X þ Y °Ru À Rd À Y Þ þ lY :

L¼À X þ °A33Þ

2b b g

The solutions must verify

@L

¼ 0 , À X þ °Ru À Rd À Y Þ ¼ 0 °A34Þ

@X

1 1

@L

¼ 0 , À X þ °Ru À Rd À 2Y Þ ¼ 0 °A35Þ

b g

@Y

l ! 0; Y ! 0; lY ¼ 0

If l ¼ 0, equations (A34) and (A35) implyY ¼ [(g À b)/(g À 2b)](Ru À Rd). Note, how-

ever, that this solution is not feasible if 2b4g (since Y must be positive). In that

case, we must have Y ¼ 0 and X ¼ Ru À Rd. If 2bog, Y ¼ [(g À b)/(g À 2b)](Ru À Rd)

is feasible, but recall that in that case, the objective function is convex, which

means that Y de¢ned above is a minimum. The maximum is then also de¢ned by

Y ¼ 0 and X ¼ Ru À Rd.To conclude, it is optimal for the entrepreneur to setY ¼ 0,

that is, not to hire a consultant. The optimal level of e¡ort of the entrepreneur is

then e ¼ b°Ru À Rd Þ ¼ eFB . Note that if e ¼ eFB, the expected income of the pure

1

¢nancier is at most equal to Rd, which means that this solution holds forAF Rd.

In case the entrepreneur needs to borrow more than Rd (say, if he is wealth con-

strained), it can be shown (using the same methodology) that the result of the

2078 The Journal of Finance

proposition goes through: The entrepreneur never hires a consultant. However,

because outside ¢nancing is too large, he is induced to exert a level of e¡ort

strictly lower than the ¢rst best. More formal proof is available upon request. &

Optimal Contract when the Revenue of the Pure Financier Is Not Constrained to Be

Nondecreasing

Using Lemma 1, the program of the entrepreneur becomes:

À ad Rd Þ2 þ 1°au Ru À ad Rd Þ°au Ru À ad Rd Þ þ ad Rd

uu

1

2b°aE R

max E gA A E E E

ay ;ay ;AVC ;AF

EA

À °I À °AVC þ AF ÞÞ °A36Þ

s:t: 2g°au Ru À ad Rd Þ2 þ b°au Ru À ad Rd Þ°au Ru À ad Rd Þ þ ad ÞRd ! AVC °A37Þ

1 1

A A A A E E A

1uu

ad R d Þ 1uu

ad R d Þ °Ru À Rd À °au Ru À ad Rd Þ

b°aE R À þ g °aA R À

E A E E

À °au Ru À ad Rd ÞÞ þ Rd À °ad Rd þ ad Rd Þ ! AF °A38Þ

A A A E

°au ; ad ; au ; ad Þ ! 0 °A39Þ

EEAA

1 À °au þ au Þ ! 0 °A40Þ

E A

1 À °ad þ ad Þ ! 0 °A41Þ

E A

where yA{u, d}. The participation constraints are binding. If they were not, in-

creasing AF and AVC would increase the entrepreneur™s expected income with-

out a¡ecting the advisor™s incentives. Replace then AF and AVC in the objective

function. The program is written

max À2g°au Ru À ad Rd Þ2 þ °Ru À Rd Þ½b°au Ru À ad Rd Þ þ 1°au Ru À ad Rd Þ

1 1

A A E E gA A

ay ;ay ;

EA

1 uu

°aE R À ad Rd Þ2 þ Rd À I

À °A42Þ

E

2b

s:t: ay ! 0; ay ! 0; 1 À °au þ au Þ ! 0; 1 À °ad þ ad Þ ! 0 °A43Þ

A E A E A E

where yA{u,d}. Consider ¢rst not taking into account the feasibility constraints,

and de¢ne X ¼ aE Ru À aE Rd and Y ¼ aA Ru À aA Rd. The objective function is con-

u d u d

cave since the Hessian is negative semide¢nitive. First-order conditions of the

maximization of the objective function give

X ¼ Y ¼ Ru À Rd :

It is straightforward to see that if feasible, this solution corresponds to the ¢rst-

best levels of e¡ort being exerted. Replacing X andY by their value, and using the

Financing and Advising 2079

u u

fact that aE þ aA 1, it follows that this solution is feasible if and only if

2°Ru À Rd Þ þ ad Rd þ ad Rd Ru : °A44Þ

E A

d d

Since the smallest possible value for aE and aA is 0, it follows that ¢rst-best

levels of e¡ort can be implemented if and only if Ru 2Rd.

If Ru42Rd, one must write down the Lagrangian L of the program, including

all the feasibility constraints described above:

1uu d1 1uu

dd u uu dd dd

L ¼ À °aA R À aA R Þ þ °R À R Þ °aE R À aE R Þ þ °aA R À aA R Þ

2g b g

1 uu

°aE R À ad Rd Þ2 þ l1 au Ru þ l2 ad Rd þ l3 au Ru þ l4 ad Rd

À E E E A A

2b

þl5 °Ru À °au Ru þ au Ru ÞÞ þ l6 °Rd À °ad Rd þ ad Rd ÞÞ °A45Þ

E A E A

Straight application of the theorem of Kuhn-Tucker and tedious algebra give the

following solution:

8d

> a n R d ¼ ad n R d ¼ 0

>E

<u A

gRd þb°Ru ÀRd Þ

u

°A46Þ

aR¼ ;

n

>E gþb

> u n u bRd þg°Ru ÀRd Þ

:a R ¼ :

A gþb

To conclude, note that a n40 in both cases. Also, (PCVC) binding implies that

AVC40 under the optimal contract: The results of Proposition 2 still hold.

n n

The maximal amount of outside ¢nancing is given by AVC þ AF. Replacing the

parameters of the contract by their optimal value gives the following:

1

°Ru À Rd Þ2 ;

if Ru 2Rd ; AVC þ AF Rd À

n n

°A47Þ

2g

°Ru À 2Rd Þ½3gbRu þ 2gRd °g À 2bÞ

if Ru 42Rd ; AVC þ AF

n n

2b°g þ bÞ2

Rd

d

þR 1À °A48Þ

:

2g

If the entrepreneur has to raise an amount of outside capital larger than the va-

lues de¢ned above, the previously de¢ned optimal contract cannot hold anymore

and the value of the project decreases, which corresponds to the results of Propo-

sition 3. The main di¡erences with the case where the revenue of the ¢nancier is

nondecreasing are that (1) e¡orts are higher and (2) the ¢nancier needs to invest

n

a strictly positive amount of capital (AF40) while her contribution is neutral

when her revenue is nondecreasing. &

2080 The Journal of Finance

Proof of Proposition 2: The program to be solved is the same as in the previous

section, except that equation (17) must be added to the program.

Note that the limited liability constraint represented in equation (A40) be-

comes redundant, as it is automatically satis¢ed when equation (17) holds. The

new Lagrangian is the following:

1 uu d1 1uu

d d2 u uu dd dd

L ¼ À °aA R À aA R Þ þ °R À R Þ °aE R À aE R Þ þ °aA R À aA R Þ

2g b g

1

À °au Ru À ad Rd Þ2 þ l1 au Ru þ l2 ad Rd þ l3 au Ru þ l4 ad Rd

2b E E E E A A

þ l5 °Ru À Rd À °au Ru À ad Rd Þ À °au Ru À ad Rd ÞÞ þ l6 °Rd À °ad Rd þ ad Rd ÞÞ

E E A A E A

°A49Þ

Again, straight application of the theorem of Kuhn-Tucker gives

u d g

aEn Ru À aEn Rd ¼ gþb°Ru À Rd Þ;

°A50Þ

u d b

aAn Ru aAn Rd u d

À ¼ gþb°R À R Þ:

Replace au , au , aE and ad in (PCF) and (PCVC) to obtain

d

EA A

A F ¼ R d À ad R d À ad R d

n

°A51Þ

E A

°Ru À Rd Þ2 b2 þ 2g2

þ ad R d

n

¼ °A52Þ

AVC A

2 2g

°g þ bÞ

Note that the solutions presented in equation (A50) imply that a n40 and that

n

the minimum value of AVC is strictly positive, which concludes the proof of Pro-

position 2. &

Proof of Proposition 3: De¢ne

°Ru À Rd Þ2 b2 þ 2g2

þ Rd ;

In °A53Þ

2 2g

°g þ bÞ

and use equations (A51) and (A52) to state that under the optimal contract

n n

AF þAVC I n.

If I I n, the project can entirely be ¢nanced by outside capital and the entre-

preneur™s participation is useless. In that case, the value of the project is

°g2 þ b2 þ bgÞ u

°R À Rd Þ2 þ Rd À I:

V¼ °A54Þ

n

2gb°g þ bÞ

Financing and Advising 2081

If I4I n, either the entrepreneur is able to invest I À I n and the second-best out-

come is feasible, that is, the value of the project isV n de¢ned above, or one must

solve the general program adding the constraint

AVC þ AF 4I n : °A55Þ

d

Replace AF and AVC by their value in (PCVC) and (PCF), set aE ¼ 0 (which is

obviously optimal when equation (A55) holds) and use the fact that constraint

(17) is binding to get

11 1

Y 2 þ °Ru À Rd ÞY þ Rd ;

þ AF ¼ À À °A56Þ

AVC

b 2g b

whereYstands for aARu À ad Rd. The determinant D is

u

A

°Ru À Rd Þ2 2g À b

À 2°°AVC þ AF Þ À Rd Þ

D¼ °A57Þ

:

b2 gb

The solution is readily computed and gives

p¬¬¬¬

g°Ru À Rd Þ À gb D

Y¼ °A58Þ

:

2g À b

u

Replacing Y by its value, and using equation (17) to ¢nd the expression of ae

gives, for AVC þ AF4I n

d

aEn ¼ 0;

p¬¬

¬

°gÀbÞ°Ru ÀRd Þþgb D

au n Ru °A59Þ

¼ ;

E 2gÀb

p¬¬

¬

g°Ru ÀRd ÞÀgb D

au n Ru À ad n Rd ¼ :

A A 2gÀb

Check that the value of the project is then strictly lower than V n de¢ned in

equation (A54). When the entrepreneur is forced to raise an amount of outside

capital strictly larger than I n, the value of the project decreases. Put di¡erently,

if I4I n, the entrepreneur™s ¢nancial participation increases the value of the

project.