Entrepreneurial Finance and Non-diversifiable Risk Chapter 1

Entrepreneurial Finance and Non-diversifiable Risk Abstract Entrepreneurs face significant non-diversifiable business risks. We build a dynamic incompletemarkets model of entrepreneurial finance to demonstrate the important implications of nondiversifiable risks for entrepreneurs’ interdependent consumption, portfolio allocation, financing, investment, and business exit decisions. The optimal capital structure is determined by a generalized tradeoff model where leverage via risky non-recourse debt provides significant diversification benefits. More risk-averse entrepreneurs default earlier, but also choose higher leverage, even though leverage makes his equity more risky. Non-diversified entrepreneurs demand both systematic and idiosyncratic risk premium. Cash-out option and external equity further improve diversification and raise the entrepreneur’s valuation of the firm. Finally, entrepreneurial risk aversion can overturn the risk-shifting incentives induced by risky debt. Keywords: Default, diversification benefits, entrepreneurial risk aversion, incomplete markets, private equity premium, hedging, capital structure, cash-out option, precautionary saving 1 Introduction Entrepreneurship plays an important role in fostering innovation and economic growth (Schumpeter (1934)). For reasons such as incentive alignment and informational asymmetry between the entrepreneur and financiers, entrepreneurs typically hold a significant non-diversified equity position in their businesses, and thus bear non-diversifiable entrepreneurial business risk.1 For example, using data from the survey of consumer finance, Gentry and Hubbard (2004) report that active businesses on average account for 41.5 percent of entrepreneurs’ total assets. Moskowitz and Vissing-Jorgensen (2002) document that about 75 percent of all private equity is owned by households for whom it constitutes at least half of their total net worth. Entrepreneurs are both producers and consumers. Like firms, they need to make invest- ment/capital budgeting, financing, and business exit decisions. Like consumers, they also manage household finance and have preferences for intertemporal consumption smoothing. The nondiversifiable idiosyncratic risk that the entrepreneurs bear from their businesses makes the business decisions and household decisions interdependent. We integrate intertemporal household finance (consumption-smoothing, portfolio choice) with corporate finance, and provide a utility-maximizing framework to analyze the entrepreneurial firm’s capital budgeting/investment, capital structure, and business exit decisions. We model an infinitely-lived risk-averse entrepreneur who has access to an illiquid non-tradable investment project. The project requires a lump-sum investment to start up, and generates stochastic cash flows that bear both systematic and idiosyncratic risks. If he chooses to take on the project, the entrepreneur sets up a firm with limited liability. Our baseline model analyzes the tradeoff between inside equity and external risky debt. Our focus on this tradeoff is motivated by the following empirical evidence. Heaton and Lucas (2004) document the high concentration of equity ownership in entrepreneurial firms and the importance of debt as a source of outside funding using data from the Survey of Small Business Finances (SSBF). For example, they report that the principal owner holds on average 81 percent of the firm’s equity, and the median owner wholly owns the firm. These findings are consistent with results from earlier Fed surveys of small businesses, as reported in Berger and Udell (1998), Cole and Wolken (1996), and Petersen and Rajan (1994). Using a large data set of public and private 1 Bitler, Moskowitz and Vissing-Jorgensen (2005) provide evidence that agency considerations play a key role in explaining why entrepreneurs on average hold large ownership shares. firms in the United Kingdom, Brav (2009) finds that private firms rely almost exclusively on debt financing, have higher leverage ratios, and tend to avoid external capital markets, compared to their public counterparts. Furthermore, Leland and Pyle (1977) show that debt often dominates equity in settings with asymmetric information because debt is less information-sensitive. After the firm is set up, the entrepreneur decides when to default on his debt (if the business does sufficiently poorly), and when to cash out by selling the firm (if the business is doing sufficiently well). In addition to the business exit decisions, he also chooses consumption and allocates his liquid wealth between a riskless asset and a diversified market portfolio (as in Merton (1971)). While the entrepreneur can hedge the systematic component of his business risks using the market portfolio, he cannot diversify the idiosyncratic risks. Moreover, both default and cashing out options are costly. Therefore, the entrepreneur faces incomplete markets, and the idiosyncratic risk exposure has important effects on the entrepreneur’s interdependent consumption, investment, financing, and business exit decisions. While the entrepreneur can hedge the systematic component of his business risks using the market portfolio, he cannot diversify the idiosyncratic risks. Moreover, exit via default or cashing out is costly. Therefore, the entrepreneur faces incomplete markets, and the idiosyncratic risk exposure will have important effects on the entrepreneur’s interdependent consumption, investment, financing, and business exit decisions. Our main results are as follows. The default option embedded in non-recourse debt allows the entrepreneur to limit his liability when walking away from his business. Intuitively, the entrepreneur is long a default (put) option (i.e., a state-contingent sale of the firm to the financier), which is an insurance to the entrepreneur against the firm’s potential poor performance in the future. Because the entrepreneur is exposed to the idiosyncratic risk from his concentrated ownership position in the firm, the diversification benefits of external risky debt are important when markets are incomplete. The diversification benefits of debt are large. Even without the tax benefits of debt, the entrepreneurial firm still issues a significant amount of debt. The diversification benefits also lead to a seemingly counterintuitive prediction: more risk-averse entrepreneurs choose higher leverage. On the one hand, higher leverage increases the risk for the entrepreneur’s equity stake. On the other hand, higher leverage/debt implies less equity exposure to the entrepreneurial project, making the entrepreneur’s overall portfolio (including both his private equity in the firm and his liquid financial wealth) less risky. This overall portfolio composition effect dominates the high leverage effect within the firm. The more risk-averse the entrepreneur, the stronger the need to reduce his firm risk exposure, therefore the higher the leverage. The non-diversifiable risk and concentrated wealth in the business make the entrepreneur value his equity less than do diversified investors. The entrepreneur demands an extra premium for bearing the idiosyncratic risks of the firm. Thus, compared to a well-diversified firm, the entrepreneur tends to default earlier on his debt. While equity is a call option on firm assets, and hence is convex in firm cash flows, in our model, the private value of equity is not necessarily globally convex. When risk aversion and/or idiosyncratic volatility are sufficiently high, the entrepreneur’s precautionary saving demand can make his private value of equity concave in cash flow. This finding has important implications for risk shifting, an agency problem induced by risky debt. Jensen and Meckling (1976) point out that managers of public firms have incentives to invest in excessively risky projects after debt is in place because of the convexity feature of equity. In our model, when the degree of risk aversion is high enough, the entrepreneur’s private value of equity (locally) decreases with the idiosyncratic volatility of the project. Thus, he may prefer to invest in a low idiosyncratic volatility project with debt in place, overturning the asset substitution result of Jensen and Meckling (1976). We find that, when the firm is not in distress, very low risk aversion is enough to make the entrepreneur prefer safer projects. Our model thus provides a potential explanation for the lack of empirical and survey evidence on asset substitution and risk-shifting incentives. The standard option valuation analysis is no longer applicable to the default and cash-out options in our setting because these options are non-tradable and their underlying assets are illiquid. Under the assumption of constant absolute risk aversion (CARA) utility, we provide an analytically tractable framework to value these options. We also derive an analytical formula for the idiosyncratic risk premium demanded by the entrepreneur. The key determinants of the idiosyncratic risk premium are risk aversion, idiosyncratic volatility, and the sensitivity of entrepreneurial value of equity with respect to cash flow. The dynamic properties of the idiosyncratic risk premium are quite different from the systematic risk premium, especially when the firm is close to default or cash-out. Moreover, ignoring the idiosyncratic risk premium can lead to substantial downward bias in the estimates of the leverage ratio of entrepreneurial firms. Finally, we extend our model to allow the entrepreneur to issue costly external equity. The more external equity issued, the smaller the entrepreneur’s idiosyncratic risk exposure, but it also creates an incentive problem for the entrepreneur, which lowers the expected growth rate of revenue. We show that the entrepreneur’s dependence on external debt for diversification decreases when he has access to external equity. Intuitively, external equity is more effective than debt in transferring idiosyncratic risks to outside investors. The entrepreneur maximizes his ex ante private value of the firm by trading off the diversification benefits of equity against the costs of incentive problems. This paper builds on the insight of Heaton and Lucas (2004), who are the first to model the diversification benefits of risky debt in a static model with asymmetric information (as in Leland and Pyle (1977)). We study the entrepreneur’s consumption, portfolio choice, (debt/equity) financing, and exit (default/cash-out) decisions in a dynamic trade-off model. Our model is tractable and allows for analytical characterization of the dynamics of debt, equity, and the systematic and idiosyncratic risk premium demanded by the entrepreneur. We also incorporate a range of realistic features for entrepreneurial financing, including taxes, cash-out options, and external equity. We integrate incomplete markets and diversification benefits into the tradeoff model of Leland (1994), thus bringing a new dimension to the structural credit risk/capital structure models.2 Our generalized tradeoff model not only applies to entrepreneurs, but also to public firms with under-diversified managers. Our model is related to the incomplete-markets consumption smoothing/precautionary saving literature.3 For analytical tractability reasons, we adopt the CARA utility specification as in Merton (1971), Caballero (1991), Kimball and Mankiw (1989), and Wang (2006). Our model contributes to this literature by extending the CARA-utility-based precautionary saving problem to allow the entrepreneur to reduce his idiosyncratic risk exposure via exit strategies such as cash-out and default. This paper is also related to the real options literature.4 The closest paper is Miao and Wang (2007), who analyze the impact of the entrepreneur’s non-diversifiable idiosyncratic risks on his growth option exercising decision. The present paper analyzes the entrepreneurial firm’s investment and financing (internal versus external, debt versus equity), and endogenous default and cash-out decisions. 2 See Leland (1994), Goldstein, Ju, and Leland (2001), Strebulaev (2007), Hackbarth, Miao, and Morellec (2006), Bhamra, Kuehn, and Strebulaev (2008), Chen (2008), and earlier work of Black and Cox (1976), and Fischer, Heinkel, and Zechner (1989). 3 Hall (1978) initiated the Euler equation approach to study intertemporal consumption behavior. See Deaton (1992) and Attanasio (1999) for surveys. 4 See Brennan and Schwartz (1986), McDonald and Siegel (1986), Abel and Eberly (1994), and Dixit and Pindyck (1994). 2 Model setup Investment opportunities An infinitely-lived risk-averse agent has a take-it-or-leave-it project at time 0, which requires a one-time investment I. The project generates a stochastic revenue process {yt : t ≥ 0} that follows a geometric Brownian motion (GBM): dyt = µyt dt + ωyt dBt + ǫyt dZt , y0 given, (1) where µ is the expected growth rate of the revenue, Bt and Zt are independent standard Brownian motions, which are the sources of market (systematic) and idiosyncratic risks of the private business, respectively. The parameters ω and ǫ are the systematic and idiosyncratic volatility parameters of the revenue growth. The total volatility of revenue growth is σ= p ω 2 + ǫ2 . (2) As we will show, these different volatility parameters ω, ǫ, and σ have different effects on the entrepreneur’s decision making. In addition, the agent has access to standard financial investment opportunities as in Merton (1971).5 The agent allocates his liquid financial wealth between a riskfree asset which pays a constant rate of interest r and a diversified market portfolio (the risky asset) with returns Rt satisfying: dRt = µp dt + σp dBt , (3) where µp and σp are the expected return and volatility of the risky asset, respectively, and Bt is the standard Brownian motion introduced earlier. Let η= µp − r σp (4) denote the after-tax Sharpe ratio of the market portfolio, and let {xt : t ≥ 0} denote the entrepreneur’s liquid (financial) wealth process. The entrepreneur invests the amount φt in the market portfolio (the risky asset) and the remaining amount xt − φt in the riskfree asset. Entrepreneurial firm If the entrepreneur decides to start the project, he runs it by setting up a limited-liability entity, such as a limited liability company (LLC) or an S corporation. The LLC 5 It is straightforward to consider entering the labor market as an alternative to running entrepreneurial business, which provides an endogenous opportunity cost of taking on the entrepreneurial project. Such an extension does not change key economics of our paper in any significant way. or S corporation allows the entrepreneur to face single-layer taxation for his business income and makes the debt non-recourse. We may extend the model to allow for personal guarantee of debt to varying degrees. This feature effectively makes debt recourse to varying degrees. The entrepreneur finances the initial one-time lump-sum cost I via his own funds (internal financing) and external financing. In the benchmark case, we assume that the only source of external financing is debt. See Petersen and Rajan (2002), Heaton and Lucas (2004), and Brav (2009) for evidence that debt is the primary source of financing for most entrepreneurial firms.6 One interpretation of the external debt is bank loans. The entrepreneur uses the firm’s assets as collateral to borrow, so that the debt is secured. We assume that debt is issued at par and is interest-only (consol) for tractability reasons as in Leland (1994) and Duffie and Lando (2001). Let b denote the coupon payment of debt and F0 denote the par value of debt. Debt is priced competitively in that the lender breaks even on the risk-adjusted basis. We further assume that debt is only issued at time 0 and remains unchanged until the entrepreneur exits. Allowing for dynamic capital structure before exit will not change the key economic tradeoff that we focus on: the impact of idiosyncratic risk on entrepreneurial financing decisions. After debt is in place, at any time t > 0, the entrepreneur has three choices: (1) continuing his business; (2) defaulting on the outstanding debt, which leads to the liquidation of his firm; (3) cashing out by selling the firm to a diversified buyer. While running the business, the entrepreneur receives income from the firm in the form of cash payments (operating profit net of coupon payments). Negative cash payments are interpreted as cash injections by the entrepreneur into the firm. Notice that trading riskless bonds and the diversified market portfolio alone does not help the entrepreneur diversify the idiosyncratic business risk. He can sell the firm and cash out, which requires a fixed transaction cost K. The default timing Td and cash-out timing Tu are not contractible at time 0. Instead, the entrepreneur chooses the default/cash-out policy to maximize his own utility after he chooses the time-0 debt level. Thus, there is an inevitable conflict of interest between financiers and the entrepreneur. The choices of default and cash-out resemble American-style put and call options on the underlying non-tradeable entrepreneurial firm. Since markets are incomplete for the entrepreneur, we cannot price the entrepreneur’s options using the standard dynamic replication argument (Black-Scholes-Merton). 6 In Section VII, we introduce external equity as an additional source of financing. At bankruptcy, the outside lender takes control and liquidates/sells the firm. Bankruptcy ex post is costly as in standard tradeoff models of capital structure. We assume that the liquidation/sale value of the firm is equal to a fraction α of the value of an all equity (unlevered) public firm, A (y). The remaining fraction (1 − α) is lost due to bankruptcy costs. We also assume that absolute priority is enforced, and abstract away from any ex post renegotiation between the lender and the entrepreneur. Before the entrepreneur can sell the firm, he needs to retire the firm’s debt obligation at par F0 . We make the standard assumption that the buyer is well diversified. He will optimally relever the firm as in the complete-markets model of Leland (1994). The value of the firm after sale is the value of an optimally levered public firm, V ∗ (y). After the entrepreneur exits from his business (through default or cash-out), he “retires” and lives on his financial income. He then faces a standard complete-markets consumption and portfolio choice problem.7 Taxes We consider a simple tax environment. The entrepreneurial firm pays taxes on his business profits at rate τe . When τe > 0, issuing debt has the benefit of shielding part of the entrepreneur’s business profits from taxes. For a public firm, the effective marginal tax rate is τm . Unlike the entrepreneurial firm, the public firm is subject to double taxation (at the corporate and individual levels), and τm captures the net tax rate (following Miller (1977)). Finally, τg denotes the tax rate on the capital gains upon sale. Naturally, higher capital gain taxes will delay the timing of cash-out. Entrepreneur’s objective The entrepreneur derives utility from consumption {ct : t ≥ 0} ac- cording to the following time-additive utility function: Z ∞  E e−δt u (ct ) dt , (5) 0 where δ > 0 is the entrepreneur’s subjective discount rate and u( · ) is an increasing and concave function. The entrepreneur’s objective is to maximize his lifetime utility by optimally choosing consumption (ct ), financial portfolio (φt ), and whether to start his business. If he starts his business, he also chooses the financing structure of the firm (coupon b), and the subsequent timing decisions of default and cash-out (Td , Tu ). 7 Extending our model to allow for sequential rounds of entrepreneurial activities will complicate our analysis. We leave this extension for future research. In general, incomplete markets imply that the entrepreneur cannot fully diversify his business risk and hence cannot fully separate his investment from consumption decisions. Indeed, provided that u′ (c) is convex, the entrepreneur’s precautionary motive will determine his intertemporal consumption smoothing.8 3 Model solution First, in Section III.A, we report the complete-markets solution for firm value and financing decisions when the firm is owned by diversified investors. Then, we analyze the entrepreneur’s interdependent consumption/saving, portfolio choice, default, and initial investment and financing decisions. The complete-markets solution of Section III.A serves as a natural benchmark for us to analyze the impact of non-diversifiable idiosyncratic risk on entrepreneurial investment, financing and valuation. 3.1 Complete-markets firm valuation and financing policy Consider a public firm owned by diversified investors. Because equityholders internalize the benefits and costs of debt issuance, they will choose the firm’s debt policy to maximize ex ante firm value by trading off the tax benefits of debt against bankruptcy and agency costs. The results in this case are well-known.9 In Appendix A, we provide the after-tax value of an unlevered public firm A(y) in equation (A.19), and the after-tax value of a public levered firm V ∗ (y) in equation (A.21). Next, we turn to analyze the entrepreneur’s decision problem before he exits from his business. 3.2 Entrepreneur’s problem The significant lack of diversification invalidates the standard finance textbook valuation analysis for firms owned by diversified investors. As a result, the standard two-step complete-markets (ArrowDebreu) analysis10 (i.e., first value maximization and then optimal consumption allocation) no longer applies. This non-separability between value maximization and consumption smoothing has important implications for real economic activities (e.g., investment and capital budgeting) and the valuation of claims that an entrepreneur issues to finance his investment activities. 8 Leland (1968) is among the earliest studies on precautionary saving models. Kimball (1990) links the degree of precautionary saving to the convexity of the marginal utility function u′ (c). 9 For example, see Leland (1994), Goldstein, Ju, and Leland (2001), and Miao (2005). 10 Cox and Huang (1989) apply this insight to separate intertemporal portfolio choices from consumption in continuous-time diffusion settings. We solve the entrepreneur’s problem by backward induction. First, we summarize the entrepreneur’s consumption/saving and portfolio choice problem after he retires from his business via either cashing out or defaulting on debt. This “retirement-stage” optimization problem is the same as in Merton (1971), a dynamic complete-markets consumption/portfolio choice problem. Second, we solve the entrepreneur’s joint consumption/saving, portfolio choice, and default decisions when the entrepreneur runs his private business. Third, we determine the entrepreneur’s exit decisions (his cash-out and default boundaries) by comparing his value functions just before and after retirement. Finally, we solve the entrepreneur’s initial (time-0) investment and financing decisions taking his future decisions into account. Conceptually, our model setup applies to any utility function u(c) under technical regularity conditions. For analytical tractability, we adopt the CARA utility throughout the remainder of the paper.11 That is, let u (c) = −e−γc /γ, where γ > 0 is coefficient of absolute risk aversion, which also measures precautionary motive. We emphasize that the main results and insights of our paper (the effect of non-diversifiable idiosyncratic shocks on investment timing) do not rely on the choice of this utility function. As we show below, the driving force of our results is the precautionary savings effect, which is captured by utility functions with convex marginal utility such as CARA. While CARA utility does not capture wealth effects, it helps reduce the dimension of our double-barrier free-boundary problem, which makes the problem much more tractable compared to constant relative risk aversion (CRRA) utility. Consumption/saving and portfolio choice after exit. After exiting from his business (via either default or cash-out), the entrepreneur no longer has any business income, and lives on his financial wealth. The entrepreneur’s optimization problem becomes the standard complete-market consumption and portfolio choice problem (e.g., Merton (1971)). We summarize the results in Appendix B. Entrepreneur’s decision making while running the firm. We summarize the solution for consumption/saving, portfolio choice, default trigger yd , and cash-out trigger yu in the following theorem. 11 The CARA utility specification proves tractable in incomplete-markets consumption-saving problems with labor income. Kimball and Mankiw (1989), Caballero (1991), Svensson and Werner (1993), and Wang (2006) have all adopted this utility specification in various precautionary saving models. Miao and Wang (2007) use this utility specification to analyze a real option exercising problem when the decision maker faces uninsurable idiosyncratic risk from his investment opportunity. Theorem 1 The entrepreneur exits from his business when the revenue process {yt : t ≥ 0} reaches either the default threshold yd or the cash-out threshold yu , whichever comes first. Prior to exit, for given liquid wealth x and revenue y, he chooses his consumption and portfolio rules as follows:   δ−r η2 + , (6) c (x, y) = r x + G (y) + 2γr 2 γr 2 ω η − yG′ (y) , (7) φ (x, y) = γrσp σp where G(·) and yd solve the free boundary problem given by the differential equation: rG(y) = (1 − τe ) (y − b − w) + (µ − ωη)yG′ (y) + σ 2 y 2 ′′ γrǫ2 y 2 ′ 2 G (y) − G (y) , 2 2 (8) subject to the following (free) boundary conditions: G(yd ) = 0 (9a) G′ (yd ) = 0 (9b) G(yu ) = V ∗ (yu ) − F0 − K − τg (V ∗ (yu ) − K − I) (9c) G′ (yu ) = (1 − τg )V ∗′ (yu ) (9d) where complete-markets firm value V ∗ (y) is defined in (A.21), and the value of external debt F0 = F (y0 ) is given in (C.6). Equation (6) states that consumption is equal to the annuity value of the sum of financial wealth x, certainty equivalent wealth G(y), and two constant terms capturing the effects of the expected excess returns and the wedge δ−r on consumption. The key is to note that G(y) is the risk-adjusted subjective valuation of the entrepreneur’s business project. Equation (7) gives the entrepreneur’s portfolio holding, where the first term is the standard mean-variance term as in Merton (1971), and the second term gives the entrepreneur’s hedging demand as he uses the market portfolio to dynamically hedge the entrepreneurial business risk. The differential equation (8) provides a valuation equation for the certainty equivalent wealth G(y) from the entrepreneur’s perspective. In the standard CAPM model, only systematic risk demands a risk premium under the complete-markets setting. Since the systematic volatility of revenue growth is ω, the risk-adjusted expected growth rate of revenue in the CAPM model is ν = µ − ωη. (10) If we drop the last nonlinear term in (8), the differential equation becomes the standard pricing equation: setting the instantaneous expected return of an asset under the risk-neutral measure (RHS) equal to the riskfree rate (LHS). The last term in (8) captures the additional discount due to the non-diversifiable idiosyncratic risk. Intuitively, the higher the risk aversion parameter γ or the idiosyncratic volatility ǫy, the larger the discount on G(y) due to idiosyncratic risk. The next section provides more detailed analysis on the impact of idiosyncratic risk on G(y). Equation (9a) comes from the value-matching condition for the entrepreneur’s default decision. It states that the private value of equity G(y) upon default is equal to zero. Equation (9b), often referred to as the smooth-pasting condition, can be interpreted as the optimality condition for the entrepreneur in choosing default. Now we turn to the cash-out boundary. Because the entrepreneur pays the fixed cost K and triggers capital gains when cashing out, he naturally has incentive to wait before cashing out. However, waiting also reduces his diversification benefits ceteris paribus. The entrepreneur optimally trades off tax implications, diversification benefits, and transaction costs when choosing the timing of cashing out. The value-matching condition (9c) at the cash-out boundary states that the private value of equity upon the firm’s cashing out is equal to the after-tax value of the public firm value after the entrepreneur pays the fixed costs K, retires outstanding debt at par F0 , and pays capital gains taxes. The smooth-pasting condition (9d) ensures that the entrepreneur optimally chooses his cash-out decision. Initial financing and investment decisions. Next, we complete the model solution by endo- genizing the entrepreneur’s initial investment and financing decision. The entrepreneurial firm has two financial claimants: inside equity (entrepreneur) and outside creditors. The entrepreneur values his ownership at a certainty equivalent value G(y). Diversified lenders price debt in competitive capital markets at F (y), which does not contain the idiosyncratic risk premium because outside investors are fully diversified. Thus, the total private value of the entrepreneurial firm is S(y) = G(y) + F (y). (11) We may interpret S(y) as the total value that an investor needs to pay in order to acquire the entrepreneurial firm by buying out the entrepreneur and the debt investors. At time 0, the entrepreneur thus chooses debt coupon b to maximize the private value of the firm: b∗ = argmax S (y0 ; b) . (12) b Intuitively, the entrepreneur internalizes the benefits and costs of debt financing, and markets competitively price the firm’s debt. In Appendix B, we show that (12) indeed arises from the entrepreneur’s utility maximization problem stated in (B.18). Note the conflicts of interest between the entrepreneur and external financiers. After debt is in place, the entrepreneur will no longer maximize the total value of the firm S(y), but his private value of equity G(y). Theorem 1 has already captured the conflict of interest between the entrepreneur and outside creditors. The last step is to characterize whether the agent wants to undertake the project. He makes the investment and starts up the firm at time 0 if his life-time utility with the project is higher than that without the project. This is equivalent to the condition that S (y0 ) > I. We may interpret our model’s implication on capital structure as a generalized tradeoff model of capital structure for the entrepreneurial firm, where the entrepreneur trades off the benefits of outside debt financing (diversification and potential tax implications) against the costs of debt financing (bankruptcy and agency conflicts between the entrepreneur and outside lenders). The natural measure of leverage from the entrepreneur’s point of view is the ratio between the public value of debt F (y) and the private value of firm S(y), L(y) = F (y) . S(y) (13) We label L(y) as private leverage to reflect the impact of idiosyncratic risk on the leverage choice. Note that the entrepreneur’s preferences (e.g., risk aversion) influence the firm’s capital structure. The standard argument that shareholders can diversify for themselves and hence diversification plays no role in the capital structure decisions of public firms is no longer valid for entrepreneurial firms. So far, we have focused on the parameter regions where the entrepreneur first establishes his firm as a private business and finances its operation via an optimal mix of outside debt and inside equity. We now point out two special cases. First, when the cost of cashing out is sufficiently small, it is optimal for the entrepreneur to sell the firm immediately (yu = y0 ). The other special case is when asset recovery rate is sufficiently high, or the entrepreneur is sufficiently risk averse, so that he raises as much debt as possible and defaults immediately (yd = y0 ). Both cases lead to immediate exit. In our analysis below, we consider parameter values that rule out these cases.