price of rapid exits in vc

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Annals of Finance (2008) 4:2953DOI 10.1007/s10436-006-0065-8

R E S E A R C H A R T I CL E

The price of rapid exit in venture capital-backed IPOs

Silvia Rossetto

Received: 20 July 2006 / Revised: 18 October 2006 / Published online: 12 December 2006 Springer-Verlag 2006

Abstract This paper proposes an explanation for two empirical puzzles sur-rounding initial public offerings (IPOs). Firstly, it is well documented that IPOunderpricing increases during hot issue periods. Secondly, venture capital(VC) backed IPOs are less underpriced than non-venture capital backed IPOsduring normal periods of activity, but the reverse is true during hot issue peri-ods: VC backed IPOs are more underpriced than non-VC backed ones. This

paper shows that when IPOs are driven by the initial investors desire to exitfrom an existing investment in order to finance a new venture, both the valueof the new venture and the value of the existing firm to be sold in the IPOdrive the investors choice of price and fraction of shares sold in the IPO. Whenthis is the case, the availability of attractive new ventures increases equilibriumunderpricing, which is what we observe during hot issue periods. Moreover, Ishow that underpricing is affected by the severity of the moral hazard problembetween an investor and the firms manager. In the presence of a moral hazardproblem the degree of equilibrium underpricing is more sensitive to changes in

the value of the new venture. This can explain why venture capitalists, who oftenfinance firms with more severe moral hazard problems, underprice IPOs less innormal periods, but underprice more strongly during hot issue periods. Furtherempirical implications relating the fraction of shares sold and the degree ofunderpricing are presented.

Keywords IPO Venture capital Signaling Exit

JEL Classification Numbers C72 D82 G24 G31 G32


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30 S. Rossetto

1 Introduction

The number of initial public offerings (IPOs) increased dramatically duringthe period from 1998 to 2000. At the same time the level of underpricing

also increased.1 These twin occurrences are the distinctive elements of whatis called a hot issue market. During the same period, venture capital (VC)backed IPOs were significantly more underpriced than non-VC backed ones(Ljungqvist and Habib 2001; Franzke 2004). This phenomenon is puzzling sincegenerally VC backed firms are less underpriced than non-VC backed ones(Barry et al. 1990). This paper proposes an explanation for both these phenom-ena based on an asymmetric information problem and a moral hazard one.

The existence of hot issue markets is not new. Ibbotson and Ritter (1995)report examples of IPOs clustering with higher underpricing for the last 40 years

in different countries. The IPO cluster of the early 1980s was due to an excep-tional investment in the natural resource industry: in that period high oil pricescaused an extraordinarily favorable situation in the oil sector, and many natu-ral resources start-up companies were taken public in highly underpriced IPOs(Ritter 1984). In the second half of the 1990s, the diffusion of the use of Internetand new communication services triggered an impressive IPO wave, coupledwith strong underpricing.

At the same time IPOs are usually the most profitable exit route for the ven-ture capitalist (Dai 2005). Although IPOs constitute a small fraction of the total

VC portfolio (between 20% and 35%, according to Cumming and MacIntosh2003), they contribute the highest returns (from 30% to more than 50% of totalreturn according to Gompers and Lerner 1999).

In early studies, VC backed IPOs were found to be less underpriced thannon-VC backed IPOs (Barry et al. 1990; Megginson and Weiss 1991; Lin andSmith 1998). However, more recently it has been noticed that during hot issuemarkets, VC backed IPOs are significantly more underpriced than non-VCbacked IPOs (Francis and Hasan 2001; Franzke 2004; Ljungqvist and Habib2001; Smart and Zutter 2003; Loughran and Ritter 2004; Lee and Wahal 2004)

(Table 1 summarizes the results of these studies). No theoretical model has yetattempted to explain this cyclical regularity in the underpricing of VC backedfirms.

This paper offers a new explanation both to the hot issue puzzle and to theventure capitalists underpricing strategy. In my model an early stage investor(or the entrepreneur himself) takes the firm public to exit and raise funds fora new opportunity. Pstor and Veronesi (2005) show that hot issue periodsare correlated with the raising of funding for new investment opportunities.Similarly Black and Gilson (1998) found that IPOs are used as a tool to exitfrom a firm and to raise funds. I assume that the early stage investor has pri-vate information on both the value of the present firm and the new investment
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The price of rapid exit in venture capital-backed IPOs 31

Table 1 VC underpricing across time

Lee and Wahal (2004)(19802000) underpricing VC 27% NVC 19%(19801989) underpricing VC 8% NVC 9%

(19901998) underpricing VC 16.17% NVC 16.70%(1999) underpricing VC 89% NVC 42%(2000) underpricing VC 68% NVC 36%Loughran and Ritter (2004)(19801989) underpricing VC 8% NVC 7.1%(19901998) underpricing VC 16.1% NVC 13.8%(19992000) underpricing VC 82.2% NVC 38.5%(20012003) underpricing VC 15% NVC 9.4%

opportunitys profitability. The early stage investors can then choose the stakeand the price of the firm from which he wishes to exit via an IPO (the IPOfirm). Moreover, although the return on the new investment opportunity doesnot directly affect the payoff of outside investors buying into the IPO, it affectsthe pricing strategy of the early stage investor.2

I show that the early stage investors choice of IPO price P and fraction of shares sold has the following properties. In equilibrium there is a one toone mapping between and P which can be described by a decreasing func-tion P(). The investors decision is therefore effectively reduced to choosing

a point on the function P(). The point actually chosen depends on how profit-able the new opportunity is compared to the true value of the IPO firm. Inequilibrium the point chosen on the function P() is a signal of the ratio of thenew opportunitys profits over the true value of the IPO firm. Hence investorsdo not learn the precise value of the IPO firm, or the exact profitability of theoutside opportunity. I show that for a given value of the IPO firm an increasein the profitability of the outside opportunity leads the early stage investor tosell a larger fraction of shares at a lower price. This leads to a decrease in theequilibrium price to value ratio of the IPO firm. Therefore, as new opportuni-

ties become more profitable, equilibrium underpricing increases. This impliesthat, in periods of economic expansions with many new investment opportu-nities, there is more exit and higher underpricing, just as observed during hotissue markets. In contrast, in periods when there are few and less profitableinvestment opportunities, exiting investors retain a larger fraction of sharesand underprice less.3 The idea of waves of quick and costly disinvestment isin line with many empirical studies finding that during hot issue markets firmstaken public are usually younger and less established (see Lowry and Schwert

2 Leone et al. (2003) find that the level of information asymmetry on the intended use of IPOd t ib t i ifi tl t th d t i ti f th l l f d i i th hi h i
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2002; Loughran and Ritter 2004 for US firms and Rydqvist and Hogholm 1995;Giudici and Roosenboom 2004 for European firms).

In the second part of the paper I extend the model to describe VC backedIPOs and to explain how the underpricing strategy of venture capital backed

IPOs differs from non-VC backed IPOs in hot and cold issue markets. Venturecapitalists distinguish themselves from an early stage investor (or an entrepre-neur) because they invest in projects with a stronger entrepreneurial moralhazard problem (Sahlman 1990; Gompers 1995). The contractual solution ofthe moral hazard problem between entrepreneur of the new venture and ven-ture capitalist affects the underpricing and the fraction of shares sold in theIPO of the old venture. As in the basic model, exit through IPO by a venturecapitalist is triggered by the arrival of a new investment opportunity and theIPO is seen as a fund raising stage. This idea is supported among others byJeng

and Wells (2000) which found that IPOs are the strongest driver of venturecapital investing.

The introduction of a moral hazard problem affects the VCs pricing duringthe IPO. A venture capitalist has to give the entrepreneur a share in the firm inorder to induce him to exert effort (Sahlman 1990). Crucially, the more profit-able the new venture is, the lower is the fraction of shares the venture capitalisthas to offer to the entrepreneur. Therefore, the VCs share in the new ventureis an increasing function of the profitability of the new venture.

An increase in the profitability of new ventures increases the venture cap-

italists profits in a convex way: higher profitability itself increases the VCsprofits per share and in addition the VCs ownership augments, multiplying theper share profits. When new investment opportunities are very good, i.e., in hotperiods, a venture capitalist becomes relatively more eager to invest in the newventure and to raise more capital. He is therefore ready to sell more sharesand to accept higher underpricing. This changes the shape of the function P()from which the VC chooses in equilibrium and this affects the way in whichequilibrium underpricing fluctuates in response to changes in the new venturesprofitability. Due to the convex relationship between the new ventures profit-

ability and the VCs profits, the degree of underpricing fluctuates more stronglybetween hot and cold markets compared to firms with no moral hazard prob-lem. I show that the venture capitalist limits his stake in the new venture andthen disinvests less during the IPO and underprices less than an early stageinvestor. The reverse is true during hot issue periods.

The literature on IPOs is very extensive (seeWelch and Ritter 2002; Jenkinsonand Ljungqvist 2001 for reviews). Among the different explanations offered forIPO underpricing and hot issue, Ritter (1984) and Grinblatt and Hwang(1989) suggest underpricing could be driven by risk. However, this hypothesisis rejected empirically by Ritter (1984) himself: underpricing is not higher inperiods of high uncertainty. Benveniste and Spindt (1989) and Loughran andRitter (2002) argue that underpricing compensates the underwriter for the cost
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Benveniste et al. (2002) and Lowry and Schwert (2002) suggest thatinformation spillovers in the learning process associated with an IPO inducefirms from the same sector to go public in the same period. There is, however,no conclusive evidence on sector clustering: while Helwege and Liang (2004)

reject the hypothesis of sector clustering during hot periods, Lewis and Ivanov(2002) find evidence of a positive effect of technological innovation on IPOactivity. Stoughton et al. (2001) investigate IPO decisions when market pricingconveys information on the products quality to consumers. A hot issuemar-ket can then arise when uncertainty about market size is high and consumerpreferences exhibit network externalities.

Milne and Ritzberger (2001) move away from the asymmetric informationframework and show that in a general equilibrium setting underpricing is apossible equilibrium outcome when issuing new shares if the issuing institution

has control over the issuing price.Other papers interpret these anomalies as the result of bounded rationality

in the form of over-optimism among investors and analysts (Rajan and Servaes1997; Ljungqvist et al. 2006). In periods of over optimism, high post-IPO pricesinduce more firms to take advantage of the favorable situation to go public. Iargue instead that hot issue periods may thus not be triggered by optimismon the demand side, the outside investors, but rather by the supply side, that iswhen early stage investors have a strong incentive to exit in order to enter newventures.

There are a number of empirical studies that capture how VC underpricingvaries over time, but no theoretical models offer an explanation.4 Empiricalpapers that find lower IPO underpricing by the VC backed firms interpretedthe phenomenon as a result of the certification role of venture capitalists. Leeand Wahal (2004) hypothesize that VC backed IPOs must be more underpricedthan non-VC backed IPOs because the IPO is an opportunity to affirm VC rep-utation and attract additional funds from investors. The effect should becomestronger during hot issue periods.

The structure of the paper is as follows. Section 2 describes the IPO exit

behavior of a generic (non-VC backed) firm. In Sect. 3, the VC backed IPOmodel is presented. In Sect. 4, I compare the results of the two models andderive empirical implications. The final section summarizes and concludes thepaper. All proofs are in the Appendix.

2 The hot issue market model

2.1 The time structure

Consider a risk neutral early stage investor who holds a stake in a firm whosevalue is V [L, ) where L is the minimum possible firm value. I assume that
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1 2

IPO

Investor sells on the market

Investor knows V and

Outside investors do not

Signaling through D and

Investor sells remaining shares

V is publicly known

Fig. 1 Time structure of the hot issue market model

there is no agency problem between the early stage investor and the entre-preneur (this case is dealt with in the next section). At t = 1 the early stageinvestor has the opportunity to invest in a new venture whose expected return

is [L, ), where L is the lowest possible expected return. The early stageinvestor has limited capital or limited capacity in managing companies,5 and,therefore, needs to exit from the existing firm in order to invest in the new ven-ture.6 Hence, at date t = 1 the early stage investor decides to take the existingfirm public in order to reinvest the IPO proceeds in the new venture. He makesa take it or leave it offer to outside investors, who are also risk neutral andact in a perfectly competitive market: he fixes the firms price at Pand offers tosell a fraction of it. Outside investors observing the price and the fraction ofshares tendered decide if they are willing to buy the shares or not.

At date 2, the value of the firm which is now publicly traded becomes knownto all investors and the final fraction can be sold at the true value without anyfurther discount. The time structure of the model is sketched in Fig. 1.

2.2 IPO of the early stage investor

At time 1 the early stage investor sells through an IPO all or part of his stakein order to be able to invest in the new opportunity. The amount of capitalavailable for investment in the new venture is determined by the IPO proceeds,

P. The early stage investor chooses and P so as to maximize his expectedwealth W, which is given by the sum of the expected returns from investing theIPO proceeds at time 1 in the new venture, P, and the return from sellingthe remaining stake, (1 ) V, at time 2. Assuming a zero interest rate, theobjective function for the early stage investor is:7

max ,P

W = max,P

P+ (1 ) V. (1)

5 The financial constraint, here exogenous, may apply even to a financial institution subject to

agency conflicts with its own investors.6 The positive relation between IPOs and availability of equity financing is also supported by the

i i l fi di f Ch t l (1993) d L (2003)
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I derive the optimal pricing schedule of the early stage investor when thereis asymmetric information both on the value of the firm taken public and on theprofitability of the new investment opportunity. Although the profitability of anew opportunity does not directly influence the outside investors pay-offs, it

determines the early stage investors pay-off from exiting the existing venture,which is useful information when determining the IPO price. It is worthwhileto notice that the early stage investor maximizes not only over the price and thefraction of shares, but indirectly also over the optimal level of capital to investin the new investment opportunity.

Investors observe the price and the fraction of shares sold in the IPO. Theythen decide if they are willing to buy shares or not. The problem faced by theearly stage investor is a double asymmetric information one and can be solvedas proposed by Quinzii and Rochet (1985) and Grinblatt and Hwang (1989).

Proposition 1 When the new investment opportunity and the firm value are un-

known to outside investors, there exists a unique Pareto dominant partially sep-

arating equilibrium. WhenV

L

L(2)

the early stage investor sets

P =L

V, (3)

=

L

L

V

LL1

. (4)

When VL 1
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L

V

1

b

pL

L

pL

p p

V

L

P

Fig. 2 Price and shares sold during IPO by the early stage investor (L = 1, L = 1.05)

is infeasible, the early stage investor settles with the corner solution of sellingeverything ( = 1) and the price then equals the lowest possible firm value(P= L).

The implicit relationship between Pand given by (3) and (4) can be writ-ten as

P= L

L1L . (5)

A higher fraction of shares sold therefore comes in equilibrium at a lower

price Pand total proceeds are given by 1

L . In his choice ofPand the early

stage investor faces a trade off. On the one hand he would like to raise theprice Pso as to have more funds to invest in the new opportunity. At the sametime doing so forces him to sell a smaller fraction of shares, which reduces hisproceeds. Crucially, the trade-off changes with V, because the effective value ofthe proceeds raised depends on how good the new opportunity is, and the costof issuing more shares depends on how underpriced the firm is at the IPO stage.This allows different types of early stage investors (defined by their ratio V) tochoose different values ofP and so as to signal V. Otherwise identical highvalue firms (low

V) sell at higher prices (but are more strongly underpriced)

and sell fewer shares than low value firms (high

V) (see Fig. 2).In principle, the early stage investor could deviate from the proposed equi-librium in two different ways. Firstly, he could choose a point P and that isconsistent with equilibrium, i.e, that lies on (5) but that does not correspondto his true type, i.e., (3) and (4) are violated. Secondly, he could deviate to apoint outside the function (5) in which case the deviation is observed by outsideinvestors.

We now describe why the first type of deviation is not profitable. Considerthe early stage investor of a low value firm and compare it to a high value firmwith an identical new opportunity. Intuitively, the early stage investor of thelow value firm chooses in equilibrium to sell a relatively large fraction of sharesat a relatively low price, which gives him relatively high proceeds to reinvest
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tunity cost of investing less in the new venture is smaller for a high value firm,because the fraction of shares retained in the first period can be sold at a higherprice later on. Hence, only the early stage investor of a high value firm is willingto sell fewer shares in exchange for a higher price and it does not pay a low

value firm to mimic this behavior. Moreover, the marginal effect of the signalis greater the higher is the firm value: a further reduction of shares sold and theresulting lower returns is marginally more expensive (i.e., the second derivativeis positive).

Similarly, when the early stage investor has a highly profitable new opportu-nity, he has no incentive to mimic the low profitability investment opportunityeven though this would allow him to set a higher price. Doing so would reducethe fraction of shares he can sell and lower the proceeds. This is more costlywhen the new opportunity is better. An early stage investor with a highly profit-

able opportunity is therefore willing to incur high underpricing: the loss frominvesting less in the new investment would be higher than the gain from settinga higher price. Conversely, when the new investment opportunity is not veryprofitable, the early stage investor does not gain much from the high proceedsof the IPO: the loss from leaving money on the table is too high and the gainfrom investing the proceeds is too low to compensate for it.

Consider now the second type of deviation. If the early stage investor wereto deviate from equilibrium and attempted to sell shares at a higher price thanthat implied by (5), this would violate relation (4) and investors would simply

not buy any shares. Setting instead a price lower than that given by relation (4),the early stage investor would be giving up proceeds and then get less profitsfrom the new investment opportunity. He can therefore do better selling thesame amount of shares at a higher price and such a deviation would not beprofitable. Hence, deviating from (5) is never profitable.

The outcome is a partially separating equilibrium where the shares sold sig-nal the ratio between firm value and investment profitability. An early stageinvestor who takes public a very valuable firm would retain many shares andset a high price. However, when in addition he has a very valuable new invest-

ment opportunity, he would also like to have high proceeds. He then prefers toset a lower price and sell more shares such that the proceeds are higher. Outsideinvestors observing the amount of shares tendered know that the price is equalor below the true value of the firm taken public, although they cannot quantifythe eventual underpricing.9 They are then willing to buy the shares.

Empirically our results mean that higher value firms are sold with a lower freefloat than low value firms. Practitioners confirm these results: CFOs interpretthe amount of shares sold during an IPO as a negative signal on the quality ofthe firm taken public (Brau and Fawcett 2006). Empirical studies do not agreeon the relation between shares retained and firm value. Brennan (1990) and

9
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Smith (1986) find a negative relation between shares retained and firm valuewhile Garfinkel (1989), Jegadeesh et al. (1993) and Michaely and Shaw (1994)find a positive one. This however does not contradict my model. The fraction ofshares is not determined only by the firm value, but also by the outside option

of the early stage investor. To the best of my knowledge empirical studies havenot controlled for this second determinant.

Underpricing is measured as the first day return relative to the issue price(in our notation DVD ). Therefore we should witness that the higher is the valueof the new investment opportunity the higher is the first day return (underpric-ing) and the higher is the fraction of shares sold in the IPO. This allows us tounderstand the time variation of IPO underpricing. Good investment prospectstrigger a hot issue market: early stage investors take existing firms public,sell more shares at a low price, and invest the proceeds in the new ventures.

As firms are taken public, the most profitable opportunities are exploited, andthe underpricing tends to decrease over time. When the new firms are maturefor exit, i.e., once the opportunity wave passed, fewer firms will be takenpublic and fewer shares will be sold in the IPO and firms will be less under-priced. Empirical studies confirm this idea of quick and costly exits. Not only hotissues are found to be correlated to growth opportunities (Choe et al. 1993 andPstor and Veronesi (2005)), but also during hot issue periods the firms takenpublic are usually younger and less established (see Lowry and Schwert 2002Loughran and Ritter 2004 for US firms; Rydqvist and Hogholm 1995; Giudici

and Roosenboom 2004 for European firms).

3 The venture capitalist

In this Section I present a model of VC backed IPOs. The comparison of thismodel with the one of the early stage investor will offer an explanation forwhy VC backed IPOs show different underpricing across time compared to thenon-VC backed ones (see next Section).

Gompers (1995, p. 1461) finds that [v]enture capitalists concentrate invest-ments in early stage companies and high technology industries where informa-tional asymmetries are highest. Such investments are characterized by the lackof tangible assets and by their low or non-existent current cash flows. Agencyproblems are likely to be particularly severe under those circumstances. AsAdmati and Pfleiderer (1994) and Kaplan and Stromberg (2003) pointed out,the superior capability in information gathering and monitoring of the venturecapitalist helps them to mitigate the agency problems. The exploitation of thiscomparative advantage induces the venture capitalist to invest in firms wheremoral hazard problems are more severe.

I distinguish a venture capitalist from an early stage investor by consideringa simple model of moral hazard between venture capitalist and entrepreneur.
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players: the venture capitalist, the entrepreneurs of the existing and of the newfirm, the outside investors.

At date 0, the venture capitalist invests in venture i. Its gross return, i, isstochastic. In particular i 0, depends probabilistically on the amountof effort e [0, e] exerted by the entrepreneur where e is the highest possibleeffort. Define with i (e) the expected profitability of the new venture i giventhe effort e. Define L as the lowest expected profitability of any entrepre-neur who exerts maximum effort, e. The expected marginal productivity of theentrepreneurs effort is i (e). We assume that e (L + 1)L. This conditionguarantees both the new venture has a positive NPV and that the resultingsignalling schedule is monotonic and it will be explained in details below. Theeffort exerted is unobservable and is costly for the entrepreneur. The cost is setfor simplicity equal to e.

The degree of moral hazard depends on the productivity of entrepreneurialeffort, which may reflect either the quality of the entrepreneur or of his idea.Entrepreneurial productivity is a function of effort exerted and is defined as thechange in profitability of the firm as a function of the effort exerted. I define byf (i | e) the probability distribution for the i- venture to generate return giventhe entrepreneurs effort, e. Both the venture capitalist and the entrepreneurare risk neutral and have limited liability.

I assume that the venture capitalist has all the bargaining power, but hasto give enough incentives to the entrepreneur to exert effort. Assume that

the monotone likelihood ratio property (MLRP) is satisfied and therefore

i

f(i|e)

ef(i|e)

> 0 (Salani 1999). I also assume that the marginal increase in

profitability due to an increase in effort is higher than the marginal cost for therelevant values of effort: i (e) > i/e. This condition implies the optimal effortis a corner solution where optimally the maximum effort is exerted.10

In order to mitigate the moral hazard problem, the venture capitalist hasto leave a fraction of the shares to the entrepreneur as a compensation forthe effort exerted. I define by i L, 1 the endogenous profit share of theventure capitalist.

The value V depends on the realization ofi. At the stage when the firmis taken public, we assume that i is common knowledge. Therefore L is alsocommon knowledge. However, the exact realization i is not known to outsideinvestors. This firm value can be observed by both the venture capitalist andthe entrepreneur, but not by outside investors. At the same time the venturecapitalist has a new investment opportunity. Given his limits in managementcapacity he wants to exit and take the firm public to invest the proceeds in thenew venture.11

The characteristics of the contract between the venture capitalist and theentrepreneur of the new venture are not known to outside investors: outside
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40 S. Rossetto

0 1 2

VC signs contract with Entrepreneur IPO VCsells 1-

Moral Hazard problem

on the effort exerted by Entrepreneur

VC knows V and (e)

Outside investors do not

Signaling through D and

Fig. 3 Time structure of the venture capital model

investors know only that the venture capitalist finances the new venture throughequity, but they do not know the size of the investment, K, the share participa-tion of the venture capitalist, i, and the quality of the entrepreneur.

As in the early stage investors case, when taking a firm public the venturecapitalist makes an offer to outside investors setting a price,P,andtheamountofshares distributed, . Investors face a double asymmetric information problem:both the existing firm value and the profitability of the new venture are privateinformation. However, contrary to the early stage investors case, both the valueof the firm and the profitability of the new venture are determined by the termsof the contract between the venture capitalist and the respective entrepreneur.Specifically these terms are the capital invested, K, and profit share, .

At date 2, after the IPO, the firm value is revealed to all players and theventure capitalist sells the remaining shares, 1 , on the market. At this point,the cycle repeats itself: the selling of the stake of the new firm at period 1 and 2,the venture capitalists investment in a new venture, etc. The new time structureis sketched in Fig. 3.

3.1 The contract between venture capitalist and the entrepreneur

Before solving for the optimal pricing strategy of the venture capitalist whendoing the IPO, I first derive the contract between the venture capitalist and theentrepreneur. The interaction between IPO and VC-entrepreneur contract isnot trivial. The amount of capital that the venture capitalist invests in the newinvestment opportunity depends on the outcome of the IPO. The amount ofcapital that is invested in a firm in turn influences the contract with the entre-preneur and therefore the profitability of the new firm. At the same time theprofitability affects the pricing and thus the capital raised during the IPO.

The venture capitalist can induce the entrepreneur to exert effort offeringshares, i.e., diminishing his own equity stake,

i. The higher is the stake of the

entrepreneur, the greater is his incentive to exert effort and therefore increasethe firms expected profits.12
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Proposition 2 The optimal equity stake of the venture capitalist is

i = 1 e

i (e) K(6)

The entrepreneurs optimal stake, 1 i, depends on his marginal produc-tivity. The higher is the entrepreneurs quality, the lower the fraction of sharesthat the venture capitalist has to concede to the entrepreneur to induce him toexert maximum effort.

This result captures an important feature of the VC industry: the better is thefirms quality, the higher is the venture capitalists stake. In practice the venturecapitalist tends to finance new ventures through convertible debt or convertiblepreferred stock. When the firm turns out to be more successful the venture cap-

italist exercises the options and increases his cash flow rights (Sahlman 1990;Gompers 1999; Baker and Gompers 1999; Kaplan and Stromberg 2003).The contract between the venture capitalist and the entrepreneur is not influ-

enced by how the venture capitalist will exit from the firm, i.e., the pricing atthe IPO stage [see Eq. (6)]. Intuitively, the outcome of the IPO does not affectthe moral hazard problem between the venture capitalist and the entrepreneurand hence the objective at the contract stage remains the same, to maximizefirm value: the higher the firm value in the first period, the more valuable thesubsequent IPO and the higher the venture capitalists profits. Due to this prop-erty, the recursive element of the model vanishes and the analysis boils down tothe static problem of how moral hazard in the subsequent venture affects IPOstructure.

On the other hand, the outcome of the IPO, namely the level of pricing andthe amount of shares sold, influences the expected profits of the venture cap-italist. The IPO determines the amount of capital invested in the firm, K, andhence the profitability of the venture.

Finally, we can derive the lower bound of the participation of the venturecapitalist, L. This occurs when the expected profitability of the new ventureis at the minimum, = L, and the venture capitalist invests the maximum

possible proceeds (K = L). This implies:

L =LL e

LL. (7)

3.2 Venture capitalistentrepreneur contracting and the IPO

Having solved for the contract between venture capitalist and entrepreneur, Iconsider now the optimal combination of price and shares retained for a venturecapitalist when taking a firm public. The steps are similar to the ones in Sect. 2.However, the venture capitalist has to take into account how the proceeds of
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42 S. Rossetto

particular outside investors do not know the marginal productivity of the entre-preneur of the new venture, and cannot observe the stake that the venturecapitalist will have in the new venture.

In the presence of entrepreneurial moral hazard the IPO outcome changes

for two reasons. First, the return of the new investment opportunity is now afunction of the venture capitalists stake [derived from Eq. (6)]. The venturecapitalists maximization problem becomes

max ,P

W = max,P

ei+1

1 i+1

KP+ (1 ) V. (8)

Second, the capital invested by the venture capitalist in the new firm, i+1K, isgiven by the capital raised during the IPO, K = P.

Proposition 3 When

L L such that:

dVC dESI for (13)

dVC > dESI for > (14)

When the profitability of the new venture is low, the venture capitalist un-derprices less than an early stage investor. When the profitability of the newventure, , exceeds the threshold , the venture capitalist underprices morethan the early stage investor. When increases further, the venture capitalist

chooses the maximum amount of underpricing,VL

L selling all his shares [con-dition (10) is violated]. The early stage investor reaches the case where he sellsall his shares for the minimum price for higher levels of , i.e., condition (2) isviolated only when is very high and when condition (10) is already violated.

The intuition for this result lies in the convex relation between the profitabil-ity of the new venture and the profits that the venture capitalist derives fromthem. An increase in the profitability of the new investment opportunity hasa linear effect on the profits of the early stage investor, while for the venturecapitalist this effect is more than proportional: an increase in the new ventures

profitability not only increases the VC profits in a direct way, but also softensthe moral hazard and increases his profit share.When the new investment opportunity is less profitable, the venture capi-

talist has to give a large fraction of shares to the entrepreneur to induce himto exert effort. For this reason he is not willing to sell the existing firm morecheaply than the early stage investor with an investment opportunity with sim-ilar profitability.

As the new venture becomes more profitable, the venture capitalist becomesmore eager to invest at an increasing rate. His willingness to underprice the

IPO increases more quickly than that of the early stage investor as his profitsincrease more quickly. Hence he wants to invest more in the new venture andsell more shares of the existing firm than the correspondent early stage investor.He sells more shares at a cheaper price than the early stage investor.

This result can explain the empirical evidence on the underpricing of VCbacked IPOs (Lee and Wahal 2004). On the one hand, Barry et al. (1990),Megginson and Weiss (1991) and Lin and Smith (1998) find that VC backedIPOs are less underpriced than non-VC backed IPOs during normal IPO peri-ods. The opposite happens during hot issue periods studied inFrancis and Hasan(2001), Smart and Zutter (2003), Franzke (2004).

The papers which find less underpricing for VC backed firms, refer to periodsof relatively stable markets or very long periods where the hot issue markets
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of 8%). Lin and Smith (1998) consider a long time series (19791990) withoutdistinguishing the hot market periods and find that VC underpricing is 12%while the early stage investor one is 17%.

The studies that find higher VC underpricing, instead focus on hot issue

market periods and find more underpricing for VC backed firms. For exampleLjungqvist and Habib (2001) for the US and Franzke (2004) for Germany findthat during the hot issue market at the end of the nineties VC backed firms weremore underpriced than non-VC backed firms. Similarly Lee and Wahal (2004)and Loughran and Ritter (2004) find that the underpricing of VC backed IPOsis higher or lower depending on the period considered.

According to the model presented here, these empirical results can be ex-plained by different economic conditions. When the economy is expanding duefor example to technological innovation, and there are many new profitable

investment opportunities, investors want to exit quickly from the existing firmsand do so by taking them public. The opposite occurs when there are fewerand less profitable investment opportunities. Investors, and venture capitalistsin particular, are not very eager to disinvest from existing firms and IPO activityis lower.

4.2 Shares retained in VC and non-VC backed IPOs

I have analyzed so far how the profitability of the new investment opportunityaffects the IPO and in particular the underpricing. The next step is to studyhow the value of the firm taken public influences the IPO and especially theshares retained. The comparison is not trivial as the underpricing is determineddifferently in the early stage investors case and in the venture capitalists.

Consider the case where the new investment profitability is at the minimumand thus there is no underpricing. The venture capitalist concedes part of theprofits to the entrepreneur to induce effort exertion, and hence his profitabilityis reduced to i+1 . Hence for the same level of new investment profitability,

the venture capitalist is gaining less and therefore prefers to sell fewer sharesinto the IPO. It follows that the venture capitalist tends to sell fewer shares forthe same firm value and the same investment profitability than the early stageinvestor.

When the new venture profitability is low and the venture capitalist under-prices less than the early stage investor, the amount of shares retained is evenhigher: not only does the venture capitalist tend to retain more shares becausehe has a smaller fraction of the new investment opportunity, but as he under-prices less (as we saw above), he retains more shares because he wants to set ahigher price.

For higher new venture profitability, the venture capitalist underprices morethan the early stage investor; however given that he gets only a fraction of the
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46 S. Rossetto

These empirical predictions are new and no study to date focused on thedifferences in the amount of shares retained by the venture capitalist versus theearly stage investor over time. There is however a general consensus in liter-ature that the amount of shares retained by the venture capitalist is generally

higher than the one retained by the early stage investor and this is in line withthe predictions of the model (Gompers and Lerner 1999).

5 Conclusions

This paper models an investors exit strategy from a private equity investment,when exit is driven by the need to free up funds for new investment oppor-tunities. It thus links the availability of new investment opportunities to IPO

decisions of early stage and VC investors. In doing so, the model addressestwo unresolved empirical puzzles surrounding IPOs, namely that (i) IPO un-derpricing tends to increase during hot issue periods, and (ii) VC backed IPOsare underpriced less than non-VC backed ones during normal periods, but sur-prisingly, are underpriced more during hot issue periods. Neither of the twophenomena have been explained in a satisfactory manner and this paper pro-vides a single explanation for both.

Firstly, it is shown that the widely observed increase in IPO underpricingduring hot issue periods can be explained by the arrival of highly profitable

new investment opportunities. When such opportunities arise, an early stage orVC investor is more eager to raise funds by exiting from existing investmentsthrough an IPO. He is therefore willing to underprice the offering more stronglycompared to a situation in which new investment opportunities are only mod-erately profitable. Secondly, the paper draws a distinction between early stageinvestors and VC investors based on Gompers (1995)s finding that VCs tend toinvest in companies with more severe moral hazard problems. This paper showsthat underpricing in the presence of a moral hazard problem between the ven-ture capitalist and its portfolio firm becomes more sensitive with respect to the

profitability of the new investment opportunity. This is because the stake thatthe VC can invest in such an opportunity depends itself on its profitability. Asa result, the VCs payoff from the new investment becomes a convex functionof its underlying profitability. This affects the VCs underpricing strategy in theIPO. When new investments are very profitable, i.e., during a hot issue market,the VC is extremely eager to raise funds via an IPO of an existing company andtherefore underprices the offering more than an early stage investor with a simi-lar investment opportunity. Conversely, when new investment opportunities areonly moderately profitable, the VC would only invest a small stake in the newventure and therefore have a reduced need to raise funds through an IPO. Hetherefore underprices an IPO less than an early stage investor during normalperiods. The models also predict that during hot issue markets when under-
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The model could be extended in various directions. One natural extensionis to adapt the model to a dynamic setting where the new investment opportu-nities arrive randomly. This could offer insights into how IPOs vary over time.Extending the model to a general equilibrium framework would instead explic-

itly allow the cyclicality of IPOs to be linked to other economy wide variables,such as technology shocks.

Appendix

Proof (Proposition 1) The proof proceeds in two steps.

1. I first find the unique reactive separating equilibrium when there is onlyasymmetry of information on the firm value.

2. I find the optimal price and shares retained in case of double asymmetry ofinformation.

Part 1. When the new profitability of the investment opportunity is commonknowledge, the early stage investor signals the firm value through the fractionof shares sold. If the early stage investor chooses not to signal the firm value, hefaces the lemons problem and P = L. Hence, he prefers to signal by limitingthe amount of shares sold.

The early stage investor chooses to maximize his objective function taking

into consideration that affects how outside investors perceive the firm value.Hence the first order condition is:

dW

d= V() + V () V = 0. (15)

To obtain an informationally consistent price function I impose the self fulfill-ing belief condition V() = V. Rearranging Eq. (15), the first order conditionbecomes

(

1+

) V(

)+

V

(

)=

0. (16)It follows that the family of optimal candidate signaling schedules is the

equation that solves the above differential equation. In order to find the Paretooptimal schedule, the constant of integration has to be such that when the earlystage investor investor sells all his holding, the firm value is equal to the mini-mum firm value, L. Indeed, the schedules where V(1) < L allow for arbitrage.Those where V(1) > L are Pareto dominated by V(1) = L as the early stageinvestor could receive higher proceeds to reinvest in the latter case. Hence,V(1) = L. So the Pareto-dominant price schedule is:

V() = 1+1 L. (17)
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48 S. Rossetto

the unique reactive equilibrium when there is asymmetry of information onlyon the firm value.

Part 2. When the new opportunitys profitability is lowest, = L, the earlystage investor has no reason to set a price different from the firm value and

incur any underpricing. In this case the solution of the signaling problem canbe reduced to the case of known profitability. Define with VL the schedule incase of lowest new venture profitability. Hence:

VL () = 1+ 1L L. (18)

When > L, the early stage investor chooses a price such that he maximizes

his utility taking into account that is not known to outside investors. DefineD = V P, the first order condition of the early stage investors maximizationproblem is:

W

D=

V (D) 1

= 0, (19)

such that V(0) = VL () in order to have the Pareto dominant schedule.Solving this differential equation, I obtain:

V(D) = V(L) + D. (20)

Applying this result to the objective function, I can write

max

W = max

(VL () + D D) + (1 ) V. (21)

The first order condition together with the self-fulfilling belief condition,V = V(, D) = VL () and = (, D), is:

W

=

LD 1

L ( L)

L= 0. (22)

Rearranging Eqs. (20) and (22), I obtain Eqs. (3) and (4). They satisfy thesix conditions ofEngers (1987) which guarantee that this is the unique Pareto
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Proof (Proposition 2) The maximization problem of the venture capitalist is:

max

i

0

f (i | e) i i+1 (iK D) + (1 ) iK di K (23)

s.t. maxe

0

f (i | e) (1 i) iKdi e (24)

0

f (i | e) (1 i) iKdi e (25)

0

f (i | e) i

i+1 (iK D) + (1 ) iK

di K (26)

0 i 1 (27)

where Eq. (24) is the maximization problem of the entrepreneur in terms ofeffort exerted, condition (25) is the individual rationality constraint of the entre-preneur and condition (26) is the individual rationality constraint of the venturecapitalist himself. This last condition is relevant only in terms of venture selec-

tion: the venture capitalist wants to invest only if the rate of return is greaterthan 1.

Given assumption i (e) > i/e whenever the entrepreneurs rationality con-straint (25) is satisfied, he exerts maximum effort. Moreover, the entrepreneursindividual rationality constraint becomes less binding as e increases. Since theventure capitalists objective function is increasing in e, e is the optimal choiceand

i = 1 e

(e)i K. (28)

Proof (Proposition 3) The proof follows the same steps as in the proof ofProposition 1. Similarly it can be shown that when there is asymmetry of infor-mation only on the firm value, the venture capitalist chooses to signal troughthe fraction of shares sold. The first order condition is:

W

= V +

e

K

1 i+1V() + e

K

1 i+1V () = 0. (29)

Adding the self full-filling belief condition, V = V(), and the financing condi-tion, K = V()i+1

, the above equation becomes
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50 S. Rossetto

The Pareto dominant schedule is the one where V(1) = L. Hence

V() =ei+1L

ei+1 L(1 i+1) ln . (31)

This is a reactive Pareto dominant equilibrium as again the six conditions ofRiley (1979) are satisfied.

Considering the asymmetry of information on both terms, I first solve theoptimization problem with respect to D considering the constraint that whenthere is no underpricing, the level of participation of the venture capitalist is atthe minimum, i+1 = L. Hence, V(D, ) = VL () + D. Inserting this in themaximization problem, it becomes

max

W =

e1 i+1

K

VL () + (1 ) V. (32)

Adding the conditions that V = VL () + D and that K =VLi+1

, the first order

condition becomes

W

= D +

eL(i+1 L)

(1 i+1)(eL L(1 L) ln )= 0. (33)

This yields to

i+1 (, D) = 1 e (1 L) L

e(L + LD) DL(1 + L) ln , (34)

= L

1 +

(1 L) D

V (1 L) D

. (35)

Given the construction of the two schedules, this is the unique Pareto dominantequilibrium. Rearranging Eqs. (31) and (35), Eqs. (11) and (12) are obtained.

However, as 1, this schedule applies only when VL (1L)L(1) . When thiscondition does not hold, the venture capitalist investor sells all the shares atP = L.

Proof (Proposition 4) The percentage underpricing with respect to the IPOprice of the venture capitalist is given by

dVC =i+1 L

L 1 i+1

. (36)

Denote with the the venture capitalist chooses given . Using Eq. (6) andconsidering that for L there is no underpricing, the above expression becomes
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The percentage underpricing with respect to the IPO price of the early stageinvestor is given by

dESI = L

L. (38)

It follows that dVC > dESI if and only if

> LV e

VL L e. (39)

Note that the fraction on the right hand side is always bigger than one because > L .

Acknowledgements This paper is a revised version of Chapter 4 of my Ph.D. dissertation at the

University of Amsterdam. I am grateful to the editor and to an anonymous referee. I thank BrunoBiais, Arnoud Boot, Zhaohui Chen, Stijn Claessens, Alexander Gmbel, Ulrich Hege, Frank deJong, Jos Jorge, Enrico Perotti, Jean Charles Rochet, Dimitri Tsomocos, Lucy White and BillWilhelm for helpful insights and discussions. I would also like to thank participants at the AFA2006in Boston, the ESSFM Studienzentrum Gerzensee, the ISCTE conference in Lisbon and at the sem-inars at the University of Amsterdam, ESSEC, Universidad Carlos III and Sad Business School.I would like to thank the Wharton School, where part of this research project was carried out, fortheir kind hospitality.

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price of rapid exits in vc

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