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Keywords:

  • divestment;
  • moral hazard;
  • IPO;
  • venture capitalists

Abstract

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

Abstract:  An entrepreneur who wants to divest his firm suffers a time-inconsistency problem: divesting a stake creates an incentive to divest further since he does not internalize the arising agency costs for the stake already sold. This paper shows that this leads to excessive divestment in equilibrium and entails efficiency losses which can offset any potential divestment gains. As a result, firms may stay private even if there are large gains from going public. We show that venture capitalists can reduce these inefficiencies. This is because they have influence over a firm's divestment decisions and can distinguish between an excessive and a desirable dilution of equity (such as in response to liquidity shocks). We also show that the divestment inefficiency gives rise to an optimal time of going public, which trades off the gains from going public early (higher divestment gains) with its costs (higher divestment inefficiency).


1. INTRODUCTION

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

An IPO enables an entrepreneur for the first time to sell his firm to a well dispersed and diversified group of investors. The cost of not using a public placement or delaying it is large. Kahl et al. (2003), for example, estimate that an entrepreneur whose firm represents 50% of his wealth and who is restricted from selling the firm for five years, would be better off selling it for 30% to 80% of its value. Similarly, Meulbroek (2000) finds for a sample of internet IPOs that the required return for an undiversified investor is twice as large as for a diversified investor.

This raises a number of interesting questions. First, given these substantial potential gains from selling the firm to diversified investors, why then do so many companies choose to remain private? Even in the most developed financial markets, many large firms are not public. In many financial systems, such as Germany and Italy, public companies are the exception rather than the rule. Second, firms that go public are typically rather old. For example, Pagano et al. (1998) report an average age of 33 years for firms that went public in Italy (similar numbers are obtained by Rydqvist and Högholm, 1995, for Sweden) and in the US the average age of firms that go public is about eleven years (Gompers, 1996). This suggests large foregone gains through delaying diversification. Why do firms wait such a substantial time before going public? Third, and even more puzzling, when entrepreneurs finally have the opportunity to sell to a diversified pool of investors at the IPO, they again delay divestment. For example, for the US, Mikkelson et al. (1997) find that an entrepreneur divests on average 24% of his firm at the IPO but sells a further 26% in the next ten years; for the UK, Brennan and Franks (1997) find that 7% is divested at the IPO and another 7% in the seven subsequent years (similar results are obtained in Harjoto and Garen, 2005; and Berry et al. 2006). Fourth, yet another stylized fact indicating foregone diversification gains is that firms that go public often use venture capitalists (VC) in the early life of the firm. Why do firms choose to sell initially to a more undiversified group of investors, given that these should require a higher return?

This paper offers a common explanation for these stylized facts, based on the time-inconsistency problem in entrepreneurial divestment (e.g., Stoughton and Zechner, 1998; and DeMarzo and Uroševic, 2006). Initial divestment reduces an entrepreneur's incentives to exercise effort. Investors anticipate this and reduce the price they are willing to pay for a stake in the firm, forcing the entrepreneur to internalize the agency costs of lower effort. However, once he has sold a stake in the firm, these costs are no longer borne by the entrepreneur in full. This induces him to sell further stakes in the firm, causing the time-inconsistency.

We show that the time-inconsistency problem can create substantial inefficiencies for the entrepreneur by ultimately causing him to sell too much and too late of the firm. The main idea of the paper is then that these inefficiencies depend on the different modes of firm financing and also vary over the life cycle of the firm. They may hence influence a firm's dynamic financing choices.

For a public firm, selling opportunities are plenty and the time-inconsistency problem is pronounced. We show that when entrepreneurs are free to sell stakes at any time after going public, any potential diversification gains from selling to diversified investors are exactly offset by losses arising from the inefficiency of the entrepreneur's divestment plan. We argue that this may explain why entrepreneurs apparently forego large diversification gains by not selling their firm publicly. We also argue that this inefficiency can explain why entrepreneurs choose to delay diversification by divesting subsequent to the IPO (as the evidence suggests) rather than selling the whole amount at the IPO.

However, an entrepreneur's ability to freely sell shares in his public firm is in practice limited. For example, IPOs are typically accompanied by lock-up agreements that prohibit initial owners from selling their shares during a specified period. Moreover, there are usually trading rules for insiders.1 Such restrictions act as a commitment device for the entrepreneur (as shown by DeMarzo and Uroševic, 2006) and reduce the inefficiency, hence making the gains from divestment positive.

We show that the gains from going public vary then over the life cycle of the firm. The reason is as follows. For young firms it usually takes considerable time before the substantial investments made at the startup result in cash-flows. Therefore, in the early stages in the life of the firm an undiversified entrepreneur has a high incentive to divest his firm because otherwise he would have to wait for a long time to receive the cash-flows. As a consequence, an entrepreneur would also divest a large amount subsequent to the IPO if he goes public. Investors will be aware of this and in anticipation of a further effort reduction by the entrepreneur pay only a low price for the firm at the IPO. This in turn makes the gains from going public initially low. As time passes, however, the entrepreneur's incentives to divest are lowered. This reduces the time-inconsistency problem and leads to an increase in the gains from going public. Hence, instead of selling his firm soon after the start-up, an entrepreneur may wait until he does an IPO.

We also show that the high efficiency losses from going public provide a rationale for using venture capitalists (VCs) in the early life of the firm. The reason is that during their involvement in the firm (that is, typically, until the IPO), VC's have a comparative advantage over arms-length investors in that they have better insight into the financing needs of the firm. They may thus only inject new capital when there are unexpected financing requirements at the firm but stop the entrepreneurs from raising equity otherwise in order to prevent an inefficient dilution of his stake. Because of this role for VCs, entrepreneurs may find it optimal to involve VCs in the early stages of the firm when the time-inconsistency problem is high. This is even though VC financing is more costly as they have to be compensated for their efforts.

There is an extensive literature on the decision to go public and the timing of an IPO (for a comprehensive survey see Pagano et al., 1998; and Helwege and Packer, 2003).2 Many contributions stress the informational aspects of stock market trading and relate it to the timing of going public (Ellingson and Rydqvist, 1997; Chemmanur and Fulghieri, 1999; Subrahmanyam and Titman, 1999; and Maksimovic and Pichler, 2001). For example, in Chemmanur and Fulghieri (1999) the entrepreneur faces a trade-off between lower financing costs (compared to venture capitalist financing) and higher informational costs when going public. Ellingson and Rydqvist (1997) present a model in which trading at the stock market produces information that helps to reduce adverse selection. The initial owner may therefore prefer to sell first a part of the stake at the IPO and sell further shares later under more favorable informational conditions. Other papers are based on a change of control as motive for going public (Zingales, 1995; and Mello and Parsons, 1998). These papers argue that the initial owner maximizes the proceeds from selling the firm by differentiating between investors, which usually leads to selling the firm in different stages. For example, in Mello and Parsons (1998) the initial owner uses the IPO to sell shares to small and passive investors, while the marketing of controlling blocks occurs separately.3 The present paper differs from these and other contributions by offering a theory of going public (and, more generally, the life cycle of the firm) based on the dynamic inefficiency of an entrepreneur's divestment plan.4

The time-inconsistency problem of the optimal trading plan of an entrepreneur (or, more generally, a large shareholder) has been emphasized in several contributions. Kihlstrom (1998) has shown that there is an analogy to the Coase-conjecture of a monopolist with durable goods (e.g., Hörner and Kamien, 2004; and Basak and Pavlova, 2004). The monopoly power of a large shareholder (who is a monopolist in the sense that he can affect state prices in the economy) is eroded in a multiple period framework since in each period the shareholder has an incentive to sell his firm (the good) in order to exploit his monopoly power. DeMarzo and Uroševic (2006) have established such a result for when there is additionally moral hazard. They show that in the absence of commitment and if moral hazard is not important, the standard Coase-result obtains in that the large shareholder immediately trades down to the competitive outcome. However, if moral hazard is sufficiently important (as in our paper), the large shareholder trades the firm in every period.

Our model relates to DeMarzo and Uroševic (2006) as follows. First, the focus of their paper is on deriving the optimal time-consistent trading strategy. Our paper, using a much simplified setup, focuses on the implications of the inefficiency of the time-consistent trading strategy for an entrepreneur's financing decisions over the life cycle of the firm. That is, the decision on whether to use venture financing, to stay private or to go public etc. Second, while inefficiencies feature in both approaches, their source differs. In DeMarzo and Uroševic (2006) the main inefficiency arises due to the large shareholder having monopoly power. Time-inconsistency then improves efficiency because it helps to erode monopoly power (the Coase-conjecture). In contrast, there is no monopoly power in our framework and time-inconsistency reduces efficiency by leading to an inefficient spreading of divestment over time. This leads to different policy implications.5 Third, in our framework there is a time lag between investment at the firm's start-up and production (while in DeMarzo and Uroševic production is instantaneous), which drives our results on the financing life cycle.

The remainder of this paper is organized as follows. Section 2 develops a fully dynamic framework of divesting a public firm, showing the dynamic inefficiency of the time-consistent plan. Section 3 analyzes the decision to go public. In Section 4 the rationale for VCs is considered. The final section concludes.

2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

Our analysis aims to capture two main characteristics of young entrepreneurial firms. First, there is likely to be a substantial moral hazard problem. Second, there is typically a lag between the initial investments in the firm, and the time the pay-offs materialize. This is because at the start-up, the entrepreneur dedicates a considerable amount of human and physical capital. He has to develop the business idea, set up a plant, buy machinery, hire workers etc. The returns on these investments are initially low (firms typically have negative cash-flows in the first years after their foundation) and it takes time for them to materialize in full. Such a lag between investment and production surely also exists for mature firms but is less pronounced then. It is also less important since mature firms will have cash-flows from previous investments compensating for investment outlays.

These characteristics create an essential trade-off. Due to the time lag between investment and return, entrepreneurs have a strong desire to cash-in on their firm's future production (they are undiversified and likely to be cash-constrained) but doing so creates inefficiencies from moral hazard. We model this trade-off as follows. An entrepreneurial firm is founded at t=0 but production in the firm materializes only at t = n. We think of n as the time until the firm matures, perhaps between 5 and 50 years, depending on its business (for example, a biotechnology firm is likely to have a larger n than a firm that produces machinery). After that date, there is no longer a lag between investment and production and the trade-off disappears. For our purpose, we simply assume that the firm then simply ceases to exist.

There are two factors to production, capital k and entrepreneurial effort e. We can then write the production function as inline image, where inline image and inline image are the sequence of inputs chosen. Capital is observable and contractible. As we want to focus on the moral hazard issue, we take the sequence of capital investments as exogenously given.6 Effort is unobservable and not contractible. Since there is only a single production date, the number of effort choices and their timing do not matter: an entrepreneur simply anticipates the final stake in the firm that arises from his divestment strategy and set effort(s) accordingly. For concreteness, we hence only consider a single effort choice, taking place at t = n (just before production).

Thus, our production function simplifies to inline image. This setup differs from other models used in the literature (as, for example, in DeMarzo and Uroševic, 2006), where there are multiple production dates and where inputs lead to instantaneous production, i.e., ft(kt, et) for inline image. While adding multiple production dates would not alter the basic mechanisms of our model, the lag between investment and production is essential for our results on the divestment life cycle.

For brevity we suppress from now on the time index t and the (exogenous) capital inputs inline image. Hence we can write the production function as f(e). We also assume linear production, f(e)= e, and quadratic effort costs, c(e)= e2/2.

The entrepreneur maximizes wealth and discounts the firm's cash-flows at a rate of inline image(inline image). There are a large number of investors who maximize wealth but do not discount cash-flows (their discount factor is 1). We interpret this as a reduced form of a model where, because of borrowing constraints, the entrepreneur's valuation of the firm's cash flows is lower than that of investors (we later introduce an extension where the entrepreneur's valuation is endogenized).

We consider a situation where at t=0 an entrepreneur goes public and sells cash-flow rights (shares in his firm) to investors. After the IPO, there are l trading periods in each time period, thus nl trading periods in total. We assume that l is a large number (technically, we let l go to infinity). However, the IPO is succeeded by a lock-up period of duration m, thus the entrpreneur cannot trade for ml trading periods. After the lock-up period the entrepreneur can trade freely in each (trading) period. Denoting the period price with inline image we can then write the entrepreneur's objective function as:

  • image

where inline image is the entrepreneur's stake in the firm before the IPO (in this section equal to one) and inline image his stake after the IPO. The entrepreneur's return thus consists of the revenues from selling the firm at the IPO (first term), the discounted revenues from selling after the lock-up period (second term) and the discounted net benefit from production (last term).

Selling the firm creates moral hazard since the entrepreneur participates less in the firm's pay-off and has, therefore, less incentives to exercise effort. Although investors cannot observe effort, it is assumed that they can observe how much of the firm is sold at each s by the entrepreneur. This is realistic for IPOs, where the amount of shares offered is fixed or governed by rules. For secondary market trading, disclosure requirements for insiders and quantitative trading restrictions that are commonplace make trading de facto observable ex-post. For example, in the US, officers and directors or owners of more than 10% of a stock have to disclose their trading. Coupled with the fact that market liquidity is imperfect, this prevents an entrepreneur from divesting large stakes unnoticed, thus effectively ensuring observability.7

Hence, investors lower their valuation for the firm when the entrepreneur reduces his stake in anticipation of a lower effort choice. As a consequence, the entrepreneur faces a trade-off between the gains from divestment (given by the differences in the discount factors inline image) and distortions arising from moral hazard, which he internalizes through the lower price for his firm.

Since investors are rational, the price inline image they pay for the firm at s will reflect their anticipation of the entrepreneur's final stake, conditional on the stake inline image the entrepreneur retains at s.8 This is what causes the time inconsistency problem: the share price at s also depends on the (anticipated) subsequent divestment decisions.

We characterize the entrepreneur's time-consistent optimization problem as follows. We denote an entrepreneur's optimal stake at time s as function of his stake at time s−1 by inline image. Since there is a finite horizon, this function is defined uniquely. From this we can define the function inline image, which is the stake held by the entrepreneur at period s+ k given that his stake in the firm at time s was inline image can be (implicitly) defined using iterations of inline image:

  • image

We denote further the utility of an entrepreneur at s with a stake before divestment of inline image by inline image.

The time consistent equilibrium (i.e., the Markov-perfect equilibrium) is then a sequence of functions inline image such that the entrepreneur maximizes utility by choosing the amount to sell in each period inline image:

  • image(1)

subject to:

  • image(2)

Condition (i) requires the entrepreneur's effort choice to be incentive compatible. Condition (ii) states that the final vaue of the firm reflects the entrepreneur's incentive compatible effort. Condition (iii) fixes the entrepreneur's starting stake at 1. Condition (iv) is the assumed production function and condition (v) states that investors price the firm rationally. Finally, condition (vi) states that the entrepreneur cannot divest during the lock-up period.

The solution to the problem can be found through backward induction. Following this we let the number of trading periods per unit of time (that is, the trading intensity), l, go to infinity. The following proposition characterizes the resulting time-consistent divestment path and entrepreneurial utility:

Proposition 1:  (i) The entrepreneur divests a stake of inline image at the IPO; (ii) after the expiration of the lock-up the entrepreneur divests at each instant of time inline image; (iii) the entrepreneur retains a share of inline image after the last trading period; (iv) the utility of the entrepreneur is inline image.

Proof:  See Appendix A.     ▪

The reason why the entrepreneur divests at each trading opportunity is the following: after he has sold an amount of the firm, he has an incentive to sell more of it because he does not internalize the inefficiency losses on the stake already sold. In that way, any divestment creates a new incentive for divestment and leads to a positive divestment path.

Since between inline image no production takes place, the question arises where the variation in the entrepreneur's optimization problem over time (which causes the divestment path) comes from. The answer is that because of discounting, the entrepreneur strictly prefers to sell the firm sooner rather than later. At each trading opportunity, there is hence a trade-off between divesting now or at the next trading opportunity: because of inline image he prefers revenue now; but this will trigger additional sales at the next trading opportunity (because of time inconsistency), which in turn will lead to a less efficient effort choice. By contrast, if there were no discounting between trading opportunities (for example, if the entrepreneur were allowed to trade several times within a very short period only), there would be no costs in delaying the sale of the firm. The entrepreneur would then only sell at the last trading opportunity.

One may wonder whether Proposition 1 hinges on our assumption that the entrepreneur has an exogenously given valuation of the firm. It may generally be expected that an entrepreneur's valuation depends on his divestment behavior. For example, if the entrepreneur is borrowing constrained, the revenues from divestment in a period will affect his consumption and hence also his marginal utility in the same period. We show in Appendix B that Proposition 1 (qualitatively) continues to hold in such a setting.

An interesting question is also why does the entrepreneur not trade immediately down to his final stake once the lock-up period has expired, as the Coase-conjecture would predict to happen in continuous time? The reason is that our results are driven by a different friction (moral hazard) than the Coase-conjecture (monopoly power). In the Coase-setting, if the firm sells the competitive quantity in the first period, there are no more incentives to sell in later rounds. In our setting, however, the entrepreneur always has an incentive to sell in later rounds, regardless of the initial quantity sold. This is because unless he has sold the complete firm (which cannot be an equilibrium outcome here since effort is essential in the production process), his valuation of the firm is lower than the one of investors.

The next result inline image that entrepreneurial divestment is not efficient, in the sense that a social planner who has to respect the limited availability of assets (shares) and the unobervability of effort cannot improve upon the allocation.

Result 1:  The time-consistent divestment (i) is inefficient (i.e., there are divestment paths that give an entrepreneur higher pay-offs), (ii) entails more divestment than what is optimal.

Proof:  See Appendix A.     ▪

The reason for the inefficiency is the time inconsistency of the entrepreneur's efficient divestment plan. Intuitively, given his strictly higher time preference compared to investors, the optimal outcome would require that the entrepreneur sells only at the IPO and not thereafter. However, this is not time-consistent, since, as discussed above, once he has divested a stake in the firm, he finds it optimal to divest further at the next trading opportunity.

As a result, there is an inefficient timing of divestment. Moreover, since once he has sold a stake in the firm, he does not fully internalize the inefficiencies stemming from a further reduction in his stake, he poses a negative externality to existing shareholders at the time of trading. As a consequence, he divests in total more than the efficient amount (note, however, that the entrepreneur ends up paying for divesting excessively because existing shareholders anticipate this future divestment and require a discount for buying the firm).

Note that this inefficiency is different from the one in DeMarzo and Uroševic (2006). While here the time-inconsistency itself leads to an inefficient divestment, in DeMarzo and Uroševic (2006) the inefficiency arises from the monopoly power of the entrepreneur and is actually reduced by the time-inconsistency.

The results also contrast with previous results in the literature that have considered efficieny in a one-trade setup. Although there, moral hazard prevents the first best from being achieved (which would require that the entrepreneur sells the whole firm), the outcome after trading is efficient in the sense that a social planner who has to respect the limited availability of assets (shares) and the unobservability of effort cannot improve the allocation. This result holds under relatively general conditions.9 The reason for it is that efficiency losses arising from moral hazard are fully internalized by the entrepreneur through the lower price he obtains when selling the firm. This is no longer the case in the multi-period setup, since divestment by an entrepreneur in one period, also affects future incentives to divest.

Result 2 shows next that efficiency can be improved by increasing the length of the lock-up period.10 It also shows that firm value increases as well as a result.

Result 2:  Committing not to trade for a longer period of time after the going public (that is, increasing m) (i) improves the pay-off for an entrepreneur who goes public and, (ii) increases firm value at the IPO.

Proof:  See Appendix A.     ▪

The intuition behind the result is straightforward. Entrepreneurial utility improves since an increase in the lock-up reduces the time inconsistency. Since time-inconsistency also goes along with excessive divestment (Result 1), the entrepreneur's final stake increases as a result. This lowers moral hazard problems and hence increases the value of the firm at the IPO.

Since the only source of the inefficiency in our framework is a time-inconsistency, full commitment by the entrepreneur would restore efficiency. However, this is not likely to be a practical solution. First, entrepreneurs simply seem to lack the ability to commit to trades for long periods: any kind of long-term commitment by entrepreneurs not backed up by an institutional arrangement, is rarely observed for public firms. Even the lock-up period itself is usually governed by stock exchange rules and/or the IPO underwriter and not purely a commitment from the entrepreneur himself. Second, even if an entrepreneur is able to commit, he may not want to do so because this would imply a loss of flexibility. For example, the entrepreneur may want to adjust his stake in response to a liquidity shock or a change in market sentiment.

Another interesting question is the impact of the number of time periods on the utility of the entrepreneur and on firm value.

Result 3:  An increase in the number of periods until production (that is, an increase in n) (i) reduces the pay-off for an entrepreneur who goes public and, (ii) reduces firm value at the IPO.

Proof:  See Appendix A.     ▪

The reason for this result is as follows. A larger amount of time until production means that there are more trading periods during which the entrepreneur can sell his firm. The incentives to sell at a trading period are unchanged as discounting between two periods remains unchanged.11 Hence, the total stake the entrepreneur sells increases. This means that less effort is exerted at the final date and hence results in a lower firm value at the IPO. Since less effort also implies higher inefficiencies, entrepreneurial utility falls as well.

There is no underpricing of the IPO issuance in our model. This is because due to arbitrage by (small) investors, the price before the IPO and after the lock-up period is the same. However, IPO underpricing can be generated by assuming that at the IPO shares are sold to a large shareholder. This shareholder subsequently monitors the entrepreneur and thus helps to induce better effort (e.g., Stoughton and Zechner, 1998). Since monitoring is costly, the entrepreneur needs to realize a gain during the lock-up period in order to be compensated for the these costs. It can be shown that this creates a rationale for using large shareholders which can indeed create underpricing in our model.12

3. THE DECISION TO GO PUBLIC

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

Different modes of financing will entail different trading opportunities. For example, an entrepreneur in a public firm has arguably more selling possibilities than one in a private firm. Therefore, the inefficiencies that arise when there are multiple trading opportunities may also influence financing choices. This section analyzes how the principal time inconsistency of the divestment plan affects entrepreneur's decisions to go public and how it can make the latter vary over the life cycle of his firm.

The decision to go public is modelled as follows. At any point in time during the life of the firm, the entrepreneur can take the firm public. Going public incurs costs (e.g., due to underwriter fees). These costs consist of a fixed part, cF >0, and a variable part which is a fraction cV(0< cV <1) of the value of the IPO. Denoting the stake retained by the entrepreneur after the IPO with inline image, the IPO value is inline image, that is, the share of the firm sold at the IPO times the IPO price. The total IPO costs are hence:

  • image(3)

Once the firm is public, after expiration of the lock-up period the entrepreneur can trade the firm continuously until the end of the trading period, that is he can divest for inline image. By contrast, when the firm is private we assume that it cannot be sold at all.

The following proposition shows that if the entrepreneur cannot commit to trading in the public phase (m=0) the cost of time-inconsistency is so large that an entrepreneur never goes public. An interpretation of this proposition is that due to the time-inconsistency, an entrepreneur may be better off by placing the shares privately, i.e., to large shareholders who can make the entrepreneur internalize inefficiencies or commit not to go public.13

Proposition 2:  In the absence of commitment (m=0), the entrepreneur does not go public.

Proof:  See Appendix A.     ▪

We show next that the time-inconsistency problem makes the gains from going public vary over time. We assume partial commitment in the form of an (exogenously given) lock-up period, which is partial in the sense that it does not cover the whole trading period. Specifically, we assume that the entrepreneur can commit not to trade for a constant fraction d (0< d<1) of the public phase of his firm. Furthermore, we consider a firm whose production takes place after a large amount of time (n is large). Denote with br) the gains (gross of IPO costs c) for this firm from going public r periods before production takes place (i.e., we have r= n− t). The gains from going public b(r) are thereby defined as the difference in utility of going public at t= r (denoted ugp(r)) and the utility of staying private in all following periods (denoted up(r)).

Proposition 3:  Under partial commitment the gains from going public before IPO costs, b(r)= ugp(r)− up(r), follow a hump shape on inline image (i.e., have a unique locale extrema, which is a maximum) and are 0 for r=0 and inline image.

Proof:  See Appendix A.     ▪

The intuition behind Proposition 3 is as follows. In the early stages of the life of the firm production is still far off (r large). The entrepreneur then has a strong motive to sell his firm because he discounts the cash flows from production a lot. Investors at an IPO would be aware of this and anticipate that he will sell heavily after the expiration of the lock-up period and in the subsequent trading periods. Therefore, they would only pay a low price at the IPO. This makes the gains from going public initially low (although the potential gains from going public, which are given by the differences in the present value of production, are high!). As time passes, production is discounted less (r decreases) and time inconsistency is reduced because the entrepreneur then has a greater interest in keeping a stake in the firm. Investors will then increase the price they pay for the firm, making the gains from going public increase. As the time of production approaches, however, the relative valuation of the firm by the entrepreneur vis-à-vis investors increases (since production is discounted less). This effect eventually outweighs the reduction in the time inconsistency problem and after reaching their maximum, the gains from going public fall. At the end of the trading period, the gains from going public are obviously zero.14

Thus, Proposition 3 may explain why, even though the gains from divesting are highest if a firm goes public immediately after its foundation, entrepreneurs may wait until they go public. The reason is that the gains from going public increase if entrepreneurs wait (provided r is large enough) since the time-inconsistency is reduced (this follows from the hump-shape of b(r)).15,16 If this is not offset by higher IPO-costs, going public will then become more attractive for entrepreneurs.

It can be shown that in our setup, higher IPO-costs can never offset higher gains. This is obvious for the fixed component of the IPO costs. The following lemma, moreover, implies that it is also the case for the variable part. The lemma shows that they are a fraction of the gains from going public. Thus, when the gains rise over time, the IPO costs rise by less (in absolute terms) and hence the net benefits from going public increase.

Lemma 1:  When the gains from going public increase, the variable IPO costs increase by less.

Proof:  See Appendix A.     ▪

We can thus conclude:

Proposition 4:  In the presence of IPO-costs, entrepreneurs may not go public at the time of foundation (where the potential benefits from divestment are the largest) but at a later stage.

4. VENTURE CAPITALISTS

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

The inefficiency of the entrepreneur's divestment plan also provides a rationale for using venture capitalists (VC) in the early life of the firm (and taking the firm public at a later stage). The reason is that due to the time inconsistency problem entrepreneurs have incentives to dilute their stake in the firm more than is efficient. Outsiders are thus unwilling to provide additional funds to the firm (prior to the IPO) since they may fear that the entrepreneur uses them simply to reduce his stake in the firm. VCs by contrast have a comparative advantage over arms-length financiers in that they have better insight into firms and can hence better distinguish between an inefficient dilution of equity and a desirable dilution, arising for example, due to unexpected financing needs at the company.

We model this through a liquidity shock that may hit the firm before the IPO. Arms-length financiers cannot observe this shock. They may hence not provide financing to the firm since they may be concerned that the entrepreneur may wrongly report that the liquidity shock has hit and use the additional funds to reduce his stake in the firm (which induces inefficiencies due to lower effort in the final period). The VC, by contrast, can observe the liquidity shock and can hence provide additional financing to the entrepreneur only if the liquidity shock hits.

In order to analyze the role of VCs we now assume that after the startup of the firm, the entrepreneur can decide to involve a VC. If he does so, the entrepreneur and the VC agree on the stake the VC takes in the firm (denoted inline image) and the time tvc at which they plan to take the firm public. Moreover, until the time of IPO, the VC and the entrepreneur act in concert. That is, the VC only injects new capital if that is efficient. Involving the VC in the firm incurs costs k. These costs summarize the effort which is needed to monitor the production in the firm and to be able to recognize the true occurrance of a liquidity shock. They may also include the costs of selling to a relatively undiversified investor, as opposed to a diversified fringe.

The liquidity shock occurs with probability inline image before the IPO. If the liquidity shock occurs then an amount l has to be injected into the firm's technology, otherwise the technology becomes worthless (that is, the output at the final date is then zero). We also assume that the shock is a pure liquidity shock, that is, if it hits and the liquidity injection is provided, final date output is increased equivalently by l. It follows that undertaking the liquidity injection is always worthwhile, hence when the VC is involved it will always be provided.

The alternative to VC-financing is for the entrepreneur to obtain arms-length finance at t=0. In this case he would sell an initial stake to these financiers and agree with them on a time of going public tgp. Because arms-length financiers cannot observe the liquidity shock, they cannot contract with the entrepreneur on a liquidity injection conditional on its arrival. Since due to the time-inconsistency problem the entrepreneur always has an incentive to (inefficiently) raise new equity in order to dilute his stake, the entrepreneur cannot credibly communicate the arrival of the liquidity shock to the financiers. Thus, there can only be pooling outcomes where outside financiers either always provide additional financing or never provide additional financing. We focus on the first case, that is, from an ex-ante perspective, it is optimal in the case of arms-length financing for the entrepreneur to commit not to raise new equity until the IPO.17

Proposition 5:  When the likelihood of a liquidity shock inline image is sufficiently high and the costs of VC-financing k are sufficiently low, the entrepreneur favours VC-financing over other forms of financing.

Proof:  See Appendix A.     ▪

The proposition shows that involving a VC can be desirable, even when there are costs of doing so. This is, as explained earlier, because VCs can overcome time-inconsistency problems prior to the IPO. Interestingly, the proposition suggests that the benefits from using VC increases when there is a substantial uncertainty about future liquidity needs (inline image is high). We should thus expect that firms that are more prone to liquidity shortages are more likely to make use of VCs.

5. SUMMARY

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

This paper has presented a dynamic theory of entrepreneurial divestment. We have suggested that different forms of divestment and their timing can be explained as the optimal response to an inefficiency arising from a time-inconsistency of an entrepreneur's optimal divestment plan. Our simple model can produce a plausible dynamic financing pattern of the firm, with private financing, venture financing, and public financing (consisting of an IPO followed by a lock-up period and subsequent divestment in the secondary market). In particular, our theory can explain why firms may wait substantially before going public or why firms may stay private altogether, even though there are substantial potential gains from going public.

Our theory also has interesting empirical predictions. As the abovementioned dynamics are driven by time-inconsistency problems, our theory suggests that financing patterns should differ between firms that differ with respect to the severity of their time-inconsistency problem. For instance, for firms where entrepreneurial effort is difficult to observe and where it takes a long time for output to fully materialize, this problem is likely to be more pronounced. This may, for example, be the case in R&D intensive or high-tec firms. Our theory then, for instance, suggests that for these firms divestment is more staggered over time and, furthermore, that they are more likely to use VC-financing.

Appendices

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES

APPENDIX A

Proofs

Proposition 1:  From 2(i) it follows that inline image. Using 2(ii)-(iv), the entrepreneur's optimization problem at s= nl is:

  • image

from which follows that:

  • image

Using again 2(i)-(v), we get the optimization problem at each inline image:

  • image

The FOC for inline image is (from differentiating at s= k wrt. inline image):

  • image

Note that because of the FOC for inline image, the last term is zero (envelope theorem). Hence the FOC simplifies to:

  • image

Dividing by inline image gives:

  • image(4)

Next we show that (4) implies that:

  • image(5)

for inline image.

Proof by induction:  Base case: For s= nl−1 we find from (5) that inline image, which holds as shown above. Induction: We show that if the claim holds for s= k, then it also holds for s= k−1. Using inline image to substitute inline image and inline image in the FOC for inline image (equation (4)) we get:

  • image

Rearranging gives inline image, which completes the proof by induction.

From (5) we then have that inline image. Hence, using again (5), we get:

  • image(6)

for inline image and inline image. Indexing per time-period (t= s/l) instead of trading period (s) this can be written as inline image. Using inline image, we get for inline image: inline image. Hence inline image and inline image.

The entrepreneur's utility (gross of IPO costs) is then:

  • image

Using inline image for t>m and inline image we obtain:

  • image

Differentiating wrt. inline image and rearranging we find that the optimal after-IPO stake is inline image. Substituting back into utility gives:

  • image

and using inline image we obtain:

  • image

     ▪

Proof of Result 1 (i) Consider the following alternative divestment path inline image (that is, there is only divestment at the IPO). Since this path implies the same inline image as the time-consistent solution, effort, production and the share price do not change. Therefore, since investors do not discount time they still break even. However, the entrepreneur now receives all revenues from selling the firm at t=0, hence his utility has increased. (ii) From (i) it is clear that an efficient divestment path inline image requires that trading only take place at t=0, i.e. inline image for all inline image. Dropping the time subscript, efficient divestment has therefore to satisfy:

  • image

s.t. to (2). Using inline image (from 2(i)) and inline image, the FOC is inline image. Hence inline image, which is larger than inline image for inline image and inline image.     ▪

Proof of Result 2:  (i) From the proof of Proposition 1 we have that:

  • image

Hence inline image. (ii) From Proposition 1 we have that:

  • image

It follows that inline image and since inline image the market value of the firm increases.     ▪

Proof of Result 3:  (i) Follows from differentiating ugp (from Proposition 1) with respect to n. (ii) Follows from differentiating inline image (from Proposition 1) with respect to n and recalling that inline image.     ▪

Proof of Proposition 2:  Using that inline image is the utility from going public n periods before production, the entrepreneur's utility from taking his firm public r-periods before production is for the case of m=0:

  • image

His utility from remaining private until production arrives (i.e., inline image) is inline image. Hence for any r we have ugp − c< up. Therefore, the entrepreneur will never go public.     ▪

Proof of Proposition 3:  From Proposition 2 and Result 2 we have that inline image and inline image. Hence b(0)= ugp(0)− ugp(0)=0 and inline image. To show the hump-shape of b(r) we have to show that (i) b(r) has a locale extrema on inline image (existence of extrema), (ii) whenever there is a r with inline image we have inline image (each extrema is a maximum and, by continuity, there is only one maximum). (i) follows from inline image and from b(1)>0. (ii) follows from applying standard calculus (not for publication: calculations on additional sheet).     ▪

Proof of Lemma 1:  The ratio of the variable IPO costs to the gains from going public are given by:

  • image

We thus have inline image.     ▪

Proof of Proposition 5:  We start by deriving the utility from using the VC in the absence of liquidity shocks. This utility consists of two parts. First, there is the revenue from the sale of a stake of the firm to the VC at inline image, where p is the price at which the VC buys a unit of the firm. Second, there is the usual revenue from selling at the IPO and at later periods. From Proposition 1 we have that the gains from going public at time t in the absence of a VC net of IPO costs and discounted to date 0 are:

  • image

Analogous, the gains with VC are then:

  • image

The price p can be determined from the fact that the VC has to break even. His revenue at the IPO is inline image since the IPO price will reflect the entrepreneur's final stake. Using inline image (see proof of Proposition 1), this can be written as inline image. Given VC-costs k we thus have that the VC's date 0 payment to the entrepreneur has to fulfill:

  • image

The entrepreneur's utility is thus given by:

  • image

From this we can see that the optimal VC stake has to maximize inline image. From differentiating inline image with respect to inline image and setting equal to zero, we obtain for the optimal stake VC stake inline image:

  • image

Plugging this back into uvc(t) gives:

  • image

Consider now the situation where a liquidity shock of size l hits. In this case the VC provides financing of an amount of l to the firm. We assume that this financing is in the form of debt (this is the simplest way of modelling the VC's claim since it does not yield additional distortions in the effort choice). Competitive pricing requires that the VC obtains in return a claim of l of the final date output. The entrepreneur's effort problem at the final date is then to maximize the returns on production, e+ l, minus the pay-offs to equity and debt, inline image and l, minus effort costs e2/2. Thus he maximizes inline image, which is the same as in the absence of the liquidity shock. Hence his effort choice is unchanged and the firm's price is the same as well. It follows that also his utility is the same (intuitively, this is because the liquidity shock only transfers production across periods and hence does not reduce the overall value of the project). It follows that uvc(t) above also applies when there is as a positive likelihood of liquidity shocks.

The utility from arms-length financing can be derived as follows. At t=0 the entrepreneur sells a stake of inline image. He agrees with the financiers on a going public date tal. We focus on the case where it is optimal for the entrepreneur (ex-ante) to agree with outside financiers that additional equity cannot be raised until the IPO (the entrepreneur profits from this through a higher price at which he can sell initial stakes to outside financiers). Intuitively, this case will arise whenever the liquidity shock l is relatively high since in this case the cost of unnecessary equity dilution if the liquidity shock does not arrive is large.

Thus, whenever the entrepreneur truly experiences the liquidity shock his firm becomes worthless. His utility from taking the firm public in case the liquidity shock does not arrive is then (analogous to the previous calculations for the VC case):

  • image

If the shock arrives, his utility is zero since then the technology becomes worthless. What does this imply for the price at which he can sell the initial stake at t=0? Since arms-length financiers have to break even, the price will reflect the expected value of the firm. The latter is given by:

  • image

Thus, the entrepreneur's total utility is:

  • image

The optimal arms-length stake hence maximizes inline image, which is the same expression as for the VC case. We thus have:

  • image

Plugging this into ual(t) gives:

  • image

Comparing to the utility from VC financing in the previous proposition, we can see that the optimal time of going public in the arms-length case is the same as in the VC case. Denote this time with inline image. We thus have for the difference in utility between VC and arms-length financing:

  • image

From comparing the term in brackets with the expression for inline image we can see that inline image. Hence the expression in the brackets is positive. It follows that VC financing is always used if the VC-costs k are sufficiently small or if inline image is sufficiently large. By contrast, for small inline image and high k, VC financing is not preferred.     ▪

APPENDIX B

Endogenous Firm Valuation

In the baseline model a higher valuation of the firm by investors was generated by assuming that investors do not discount the firm's cash-flows, while an entrepreneur does so at a (constant) rate. Thus, the valuation differential between entrepreneurs and investors was given. One may, however, expect the relative valuation of the firm to depend on the entrepreneur's consumption, and thus also on the divestment path itself. In the following we endogenize the entrepreneur's valuation of the firm and show that Proposition 1 (qualitatively) continues to hold.

We assume that an entrepreneur cannot borrow against the future output of the firm (that is, the entrepreneur is borrowing constrained). For simplicity, we also assume that the entrepreneur cannot save and that he has no other endowments. His consumption in any period thus has to be solely financed from the revenues from selling the firm in the same period. Entrepreneurs have time-separable risk-averse utility u(c) (with inline image and inline image). Investors, by contrast, are not borrowing constrained and thus have a constant marginal valuation of the firm. We set their marginal valuation to 1. The entrepreneurs utility is thus given by:

  • image(1)

At date n, after the final divestment opportunity, the entrepreneur chooses effort in order to maximize inline image. From differentiating it follows that optimal effort is inline image, as in the baseline model. Final period consumption is thus inline image. From differentiating with respect to inline image, it follows that the optimal final stake is inline image. Hence, as in the baseline model, there is no selling in the final period. We can thus write the entrepreneur's utility as:

  • image(8)

The FOC of the entrepreneur at t= k (k< n) is:

  • image(9)

Combining with the FOC inline image, one can see that the last term is zero (this is the envelope theorem). Hence the FOC simplifies to:

  • image(10)

Rearranging gives:

  • image(11)

We assume that in equilibrium we have inline image (we show later that this always must be the case). Writing the FOC for t= n−1 gives:

  • image(12)

Suppose that the entrepreneur does not sell at inline image. We then have that the left-hand side of the above equation is zero. The right hand side is larger than zero since cn−1=0 but cn >0 and hence inline image. Since the left-hand side is decreasing in inline image (since inline image due to inline image) and the right-hand side is increasing in inline image (since inline image), it follows that there is a unique inline image with inline image (that is, the entrepreneurs sell a positive stake at t= n−1). Note that from (12) it then follows that inline image.

Consider next the FOC at t= n−2:

  • image

Since we have:

  • image

the same arguments as for t= n−1 apply and we have that inline image and inline image. Through induction one can then show that inline image for all t< n. Hence the entrepreneur divests at each trading opportunity.

We show next that inline image. Suppose to the contrary that the entrepreneur follows a divestment path which generates inline image. The entrepreneur's effort choice is then zero and hence the price of the firm is zero as well. Thus, the entrepreneur does not obtain any revenue from selling the firm, and hence his consumption in each period is zero as well. The entrepreneur's utility is hence inline image. Consider now, alternatively, that the entrepreneur does not divest at all. He then has zero consumption in each period t< n but positive consumption at t= n: inline image. His utility is hence inline image. The entrepreneur is thus strictly better off by not divesting at all, hence inline image can never be the outcome of an equilibrium divestment path.

Summarizing, we have thus shown that the entrepreneur divests a positive stake at each trading possibility but keeps a positive amount after trading.

Footnotes
  • 1

    For example, in the US, SEC rule 144 restricts the public trading of non-registered shares through quantity and minimum holding period restrictions.

  • 2

    This paper, as most of the literature, focuses on IPO decisions by private owners. However, public firms may also be created by privatization of state-owned companies, see Megginson et al. (2004).

  • 3

    There is also a large literature on underpricing which generally emphasizes adverse selection (Chemmanur, 1993; Grinblatt and Hwang, 1989; and Welch, 1989). A notable exemption is Stoughton and Zechner (1998). In their model oversubscription of the IPO is used by the owner to differentiate between investors in order to reduce monitoring.

  • 4

    Our theory presumes that moral hazard is important for entrepreneurial divestment. Recent evidence is consistent with this. Ben-Dor (2003) show that moral hazard affects the amount of the firm divested by the entrepreneur at the IPO. Brav and Gompers (2003) study lock-up periods and conclude that they are used as a commitment device to alleviate moral hazard (as opposed to a signalling effect based on adverse selection). A similar conclusion is reached in Yung and Zender (2006).

  • 5

    For example, lock-up periods reduce efficiency in DeMarzo and Uroševic (but make entrepreneurs privately better off), while they increase efficiency in our setting. Similarly, the total amount of divestment is insufficient from a welfare perspective in DeMarzo and Uroševic, while it is excessive in the present paper. Among others, our analysis thus provides a rationale for measures which constrain the possibilities for entrepreneurs to divest stakes once public.

  • 6

    Endogenizing capital helps to alleviate the moral hazard problem (the entrepreneur can by investing more capital in the firm essentially commit himself to more effort in later periods) but does not affect the basic trade-off, see for example, Magill and Quinzii (2002).

  • 7

    For a more extensive discussion of the observability of trading see Kocherlakota (1998) and Magill and Quinzii (2002).

  • 8

    Note that since ps depends on inline image, the price in a trading period is affected by current divestment.

  • 9

    See, for example, Magill and Quinzii (2002). Admati et al. (1994) have shown that under certain conditions even the first-best asset allocation may be achieved.

  • 10

    A similar result is contained in DeMarzo and Uroševic (2006). Consistent with it, Brav and Gompers (2003) have provided evidence that the length of lock-up periods is related to moral hazard problems in the firm.

  • 11

    This would be different if we would instead increase the number of trading periods per unit of time (thus keeping n constant). In this case, on the one hand, the incentives to sell per trading period decline as there is less discounting of the next trading period. On the other hand, there are also more trading periods. The net effect on the final stake then becomes ambiguous (calculations available on request from the author).

  • 12

    Calculations available upon request from the author.

  • 13

    The proposition should be considered as the limiting case of the time-inconsistency problem since it assumes that there is continuous trading and no lock-up. If there were by contrast either a sufficiently small number of trading periods or a sufficiently long lock-up period, going public would always be desirable for sufficiently high divestment gains (that is, low inline image) and low going public costs.

  • 14

    It is noteworthy that Proposition 3 holds for any partial commitment level and for any discounting differences between entrepreneurs and investors. However, the proposition may not hold if there is a discrete number of trading periods.

  • 15

    Firms that are founded with a short time until production (r small), experience falling gains from going public. These firms would either go public immediately or remain private forever.

  • 16

    Note that such an increase in the gains from going public would not arise with a standard production function (i.e., without a time lag between investment and production) because there would then be no reduction in the time-inconsistency problem over time.

  • 17

    The results do not depend on this since in the other case there will also be inefficiencies from arms-length financing, this time arising because it causes inefficient dilution of equity in case the liquidity shock does not arrive.

REFERENCES

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  2. Abstract
  3. 1. INTRODUCTION
  4. 2. ENTREPRENEURIAL DIVESTMENT WHEN THE FIRM IS PUBLIC
  5. 3. THE DECISION TO GO PUBLIC
  6. 4. VENTURE CAPITALISTS
  7. 5. SUMMARY
  8. Appendices
  9. REFERENCES
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