Entry strategies of partnerships versus conventional firms.

AuthorMoretto, Michele
  1. Introduction

    According to the U.S. Census taxonomy, firms can be classified in two broad categories: nonemployer and employer.

    "Nonemployers are businesses without paid employees. Most Nonemployers are self-employed individuals operating very small unincorporated businesses" (U.S. Census Bureau 2003).

    The nonemployer category accounts for nearly three fourths of all businesses and contains enterprises of three distinct legal or organizational forms or both: individual proprietorship, partnership, and corporation, (1) all without employees. Among them, the most common are the first two.

    Employers are enterprises that maximize profit and display separation between employees and owners. We may dub them conventional firms (as in Pencavel and Craig 1994) or, simply, firms.

    Because nonemployers do not live, on average, longer than employers, (Taylor 1999, Parker 2004), we can proxy net entry between 1997 and 2001 in the United States using the number of establishments. Nonemployer net entry is more than twice that of employer. Between the U.S. Censuses (2) of 1997 and 2001, the number of nonemployers grew by 10% compared with 3% of employers. Moreover, nonemployer business is smaller (average receipt is $43,638 in 2002) than employer business ($3,872,141). (3) Last but not least, nonemployers are quite common in expanding sectors, such as services and advanced industries.

    U.S. Census data show that the most dynamic and fastest growing group among the nonemployers is partnerships. (4) It is on this more popular and successful subcategory that we concentrate our study, the main aim of which is the comparison of entry strategies and sizes of conventional firms (Fs) and partnerships (PAs). Our interest in PAs is due to their diffusion in advanced industries and their apparent flexibility resulting from small dimension and swift entry policies.

    We conduct our analysis by taking advantage of the similarities between the internal organization of a PA and that of a labor-managed enterprise, (5) in which owners and employees coincide and share the governance of the firm on an equal level, maximizing individual dividend.

    Our contribution is cast within real option literature, which started with the seminal works of Brennan and Schwartz (1985) and McDonald and Siegel (1986). On the basis of the analogy between security options and the opportunities to invest in real assets, (6) these contributions underline the crucial role of investment timing when there are sunk costs and uncertainty over future rewards. Irreversibility and uncertainty induce entry only when the investment value exceeds that of the option to wait, once we apply the "bad news principle of irreversible investment" (Bernanke 1983).

    In a dynamic setting, in which a new venture project is carried out at distinct times and at distinct entry-trigger market prices, most differences between the PA and the F are due to uncertainty and sunk costs. The PA enters at less favorable conditions than the F because the trigger price increases in peculiar fashions for the two enterprises as uncertainty unfolds. Higher risk makes the investment return more volatile, and the value of the entry option goes up, as well as the incentive to wait.

    In a PA, each member shares the enterprise risk with colleagues and bears only a fraction of the corresponding cost. The consequence is a higher value of the investment option without any increase in the incentive to delay entry.

    In Fs, the entire risk is borne by shareholders. Therefore, entry might occur later.

    Our theoretical research on PAs and Fs provides fresh interpretations of two facts observed in U.S. data: (i) the smaller dimension of PAs, in terms of average receipts, and (ii) the recent growth of PAs during a period of intense financial volatility. (7)

    The paper is organized as follows: In the next section, we set up the basic entry option model for the two types of enterprise. In the third and fourth sections, we find their stock market values. In section 5, we compare their different entry strategies. In section 6, we assess the effect of uncertainty on entry and optimal size. In section 7, we supplement the theoretical inquiry with a numerical example. Section 8 concludes.

  2. A Start-Up Option

    We first go through the entry strategies of the two firms that are supposed to own a startup option that allows them to begin producing a good and then sell in on the market. To this purpose, each firm has to bear a sunk cost, which is internally financed. Workers of F get the market unit wage w, which is the opportunity cost of joining the PA. Firms operate in an uncertain market environment. Decisions are taken on an infinite time horizon: in the PA by members, in the F by shareholders.

    We begin by comparing entry policies and options. Each enterprise is supposed to own an infinitely lived investment project. We model entry with a set of common assumptions plus some specific hypotheses referring to each enterprise.

    ASSUMPTION 1. The project, corresponding to the start-up decision, is of finite size and requires an exogenous investment I to be borne if the enterprise enters, by shareholders in F and by partners in PA.

    ASSUMPTION 2. Once entered, the investment becomes irreversibly sunk. It can be neither changed, temporarily stopped, or shut down. (8)

    ASSUMPTION 3. Once the project is implemented, the instantaneous short-run revenue of the project is

    R([p.sub.t]; [L.sub.t]) [equivalent to] [p.sub.t]Q([L.sub.t]), (1)

    where [p.sub.t] is the market output price, [L.sub.t] is labor, Q([L.sub.t]) is the short-run production function, with the usual properties: Q(0) = 0, Q'([L.sub.t]) > 0, Q" ([L.sub.t])

    ASSUMPTION 4. The uncertain market price evolves according to the following trendless stochastic differential equation:

    [dp.sub.t] = [sigma][p.sub.t] [dB.sub.t] with [sigma] > 0 and [p.sub.0] = p, (2)

    where [dB.sub.t] is the standard increment of a Wiener process (or Brownian motion), uncorrelated over time and satisfying the conditions that E([dB.sub.t]) = 0 and E([dB.sup.2.sub.t]) = dt (Dixit 1993). Therefore E([dp.sub.t]) = 0 and E([dp.sup.2.sub.t]) = [([sigma][[pi].sub.t).sup.2] dt, i.e., starting from the initial value[p.sub.0], the random position of the price [p.sub.t] at time t > 0 has a normal distribution with mean [p.sub.0] and variance [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which increases as we look further and further into the future. The process "has no memory" (i.e., it is Markovian), and hence (i) at any time t, the observed [p.sub.t] is the best predictor of future prices and (ii) [p.sub.t] moves at any t + 1 upward or downward with equal probability. By the Markov property of the process [p.sub.t], the results do not change qualitatively assuming a positive (or negative) price trend.

    ASSUMPTION 5. The market unitary wage w is constant.

    ASSUMPTION 6. For the PA, the investment is set and financed by the founding members, as if there were a market for memberships operating according to standard financial canons (Sertel 1993, 1997). For the F, shareholders are involved.

    ASSUMPTION 7. Members of the PA are homogeneous. They invest in the project and maximize the discounted value of expected individual net dividends. They receive an income that can be thought of as a kind of "supplemented wage," equal to dividends plus the opportunity cost of being a member (i.e., the market wage w).

    ASSUMPTION 8. In Fs, the entrepreneur maximizes the discounted value of expected cash flows. In PAs, the objective is the individual discounted value of expected cash flows. This assumption is consistent with canonical modeling of profit-maximizing conventional firms and labor-managed enterprises (Bonin and Putterman 1987).

    ASSUMPTION 9. Size (L), corresponding to the number of members for the PA and to labor force for the F, is set at entry and held fixed afterwards. As a matter of fact, new enterprises are usually small. It seems plausible to assume that, at their entrance, they choose the size of the labor force to hire and shun from adjusting it to variation of demand, preferring alternative ways that do not damage fresh internal organization.

  3. The Value of a Partnership

    If the market price of the product is high enough, PA enters setting the optimal size (L). The decision process requires a backward procedure. First, for any L, the value of the individual option to enter has to be computed. Subsequently, we have the choice of L that maximizes the individual option value at entry. The discounted value of expected net individual dividend is

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

    where [E.sub.0](x) is the expectation operator, with the information available at time 0, [rho] is the riskless interest rate (9) and w/[rho] is the discounted flow of the market wage (i.e., the minimum that the PA grants its members). This salary corresponds to a participation constraint: Below it, members are better off supplying their labor in the market rather than founding a new PA.

    Members of a PA of size L decide whether and when to start the new project by solving an optimal stopping time problem and choosing the investment timing, which maximizes

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

    By Assumption 7, PA associates are homogeneous. Each one holds an option to invest corresponding to Equation 4 and has an interest in exercising it cooperatively at the same time because members have just founded the firm of the...

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