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Small Business Economics

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23-11-2019

On the optimal investment finance of small businesses

Author: Mario Tirelli

Published in: Small Business Economics | Issue 4/2021

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Abstract

Small businesses are frequently characterized by “information opacity” which results from several information asymmetries combined. Certain firm and institutional characteristics (e.g., their young age, small capitalization, and simplified accountancy requirements) make it hard for outside investors to verify their financial situation (net worth) and investment decisions at different stages of their realization. This work derives the (second-best) efficient investment and financial policies of small businesses when their opacity results in a possible adverse selection on entrepreneurs’ initial net worth and in a double-moral hazard, on the firm investments and on the release of information on their realized earnings. Finally, these (second-best) efficient policies are compared with those documented in much of the empirical evidence on small companies.

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These types of requirements have recently been reaffirmed in the EU Responsible Business Package, also for limited liability companies (see European Parliament (2013). In addition, depending on their dimension (small or micro firms), the Directive allows EU Members to introduce further significant simplifications at national level. Similarly, private US small companies are not required to release financial information on their 10-K forms; this applies also to those in the legal form of limited liability companies. The SEC has recently introduced some consistent simplifications also on “smaller reporting (public) company(s).”

Carpenter and Petersen (2002a) document that the growth of most small firms is constrained by the size of internally generated finance. See also the up-to-date review in Hubbard (1998). Jõeveer (2013) finds evidence that the liabilities used for firm financing (“narrow leverage”) by small, unlisted, companies are positively correlated with their tangible assets.

In the absence of available business collateral, a substantial proportion of small business owners pledge personal commitments to obtain outside credit (business loans). Personal commitments by lenders can be personal collateral and/or personal guarantees. As a result, the risks of small business ownership and of owner’s personal finance may lack of a separation. This has been, for example, held responsible of the credit crunch in the early 1990s, by Bernanke and Lown (1991).

Myers and Rajan (1998) have shown that transformation of risk reduces debt capacity (see also Guiso (2003)).

The empirical literature on family firms achieves different conclusions in terms of their efficiency and growth performance. The diffuse presence of family firms is alternatively considered to be driven by “competitive advantages,” highlighting their superior efficiency, or by “cultural” factors, highlighting certain opportunistic behaviors of the founder (or heirs). See, e.g., Bertrand and Schoar (2006); Amit and Villalonga (2014), for a survey.

See also Brown et al. (2012) for evidence on European firms.

This latter work indicates that European firms, intensively active in R&D, mostly finance their investment through internal finance and that their stock issue ratio is 18.1% when young and only 2.5% when they become mature.

This modeling choice of earnings does also replicate the reduced-form, due to Mirrlees (1974) (see also Hölmstrom (1979)) and it has proved to give simpler characterizations of the optimum than those found using the state-space approach. The state-space approach would write firm’s earning as the outcome of investment/effort x and a random variable \(\widetilde {\theta }\), say, \(\pi =\widetilde {\theta }f(x)\). From the latest and for a given a distribution of \(\widetilde {\theta }\), one can deduce the distribution of π. Though, the two approaches need not give the same results. An equivalence is obtained under the conditions established in Poblete and Spulber (2012).

The fact that “soft” capital increases the probability that the firm achieves higher earnings and a higher expected value is used, for example, in Gertler and Rogoff (1990), Gertler and Hubbard (1988), and Greenwald and Stiglitz (1990). Similarly, a higher R&D expenditure increases the probability to innovate and grow at a higher rate, in most contemporary Schumpterian growth models (see, e.g., Aghion & Howitt, 1992, 2005).

This kind of stochastic decreasing return property is common in the moral hazard literature, when the the “first-order approach” is exploited. See Rogerson (1985).

See Rogerson (1985) and, for other examples and discussion LiCalzi and Spaeter (2003). Let G(π, x) be an exponential for π in \([0,\bar \pi ]\) and equal to one for \(\pi >\bar \pi \). Examples of the conditional cdf and pdf of this distribution, respectively, are \(G(\pi |x)=[x^{2} \pi e^{x \pi /\bar \pi }]/[\bar \pi (1+(x-1)e^{x})]\) and \(g(\pi |x)=e^{x (\pi /\bar \pi -1)}(\bar \pi +x \pi )/\bar \pi ^{2}\).

We impose P_l ≥ 0 only when final earnings can be verified at no cost (Theorem 1 below), not in the more general case of costly state verification (Theorem 2).

When π ≤ z_l and the payment prescribes a full appropriation of the firm’s net worth, we have “bankruptcy states” (see, e.g., Gale and Hellwig (1985)).

In words, given R, the type of restriction we impose on g is one such that, when x is closed to zero, a slight increase of investment induces a strong increase in the expected value of earnings, by producing a significant redistribution of the probability weights, from low to high earning realizations.

Restricting to direct mechanism is without loss of generality and follows from a standard application of the Revelation Principle.

In fact, (CC) ensures that the entrepreneur \(\widehat {a}\) “commits” to the investment policy designed for him/her by the principal; thereby preventing moral hazard. (IC) ensures that the contract designed for \(\widehat {a}\) is incentive-compatible, thereby preventing that \(\widehat {a}\) deviates and choose a contract conceived for a different type.

The role played in our model by investment in “soft” capital replaces that of effort in Innes (1990). Effort is physical: it is subject to a physical limit and produces some subjective disutility. Instead, investments are limited by the entrepreneur’s availability of funds (internal and external) and are sensitive to market conditions: the market interest rate R and liquidity conditions, which we discuss below (see Corollary 1).

We thank an anonymous referee for raising this issue.

In an equilibrium setting with flexible prices and a fixed \(\widehat {B}\), R adjusts to clear the credit market, avoiding credit rationing. Yet, for a low \(\widehat {B}\), the rise of R would spill over on the cost of all financial contracts offered by the intermediaries to the firms; thereby, disciplining their demand of outside funds and inducing a drop on their investments.

The reader should be aware that this reasoning is a partial equilibrium one. In a general equilibrium context, one should consider that R adjusts to clear the “formal” credit market. Hence, that R adjusts to a fall of the fund supply, but also to any change of the fund demand, which here depends on the contracts offered by the intermediaries to the entrepreneurs.

Notice that we say that an agent experience “credit rationing” when, at the current contractual condition, she would rather have more credit. In Theorem 1, firms who underinvest are not “credit rationed” simply because, at the contract they sign, they obtain as much fund as they demand.

I thank an anonymous referee for raising this question.

A proof is available from the author.

Assuming, instead, that this cost takes the form of a constant fee would not substantially change any of the following analysis.

These last two elements modify the informal description of our direct mechanism, in the previous section.

See Lemma 2.1 in Townsend (1979).

In the verification region, P(π) has a slope equal to (1 + λ)^− 1 < 1.

Up-to-date surveys on these studies are in Hubbard (1998) and Stein (2003).

Among earlier influential articles on the cash flow sensitivity of R&D expenditure by small firms, see also Himmelberg and Petersen (1994).

They argue that this may be because bank finance is not entirely external, and that the owners personally guarantee the loan in the event of default. See also Gregory et al. 2005 and La Rocca et al. 2011

See also Lewis and Sappington (2001) and the references therein.

Apart from Innes (1990), our formulation is common to many other contributions in the literature on optimal security design (see, for example, problem (2) in Gale and Hellwig (1985). It is mostly natural under perfect competition on financial markets. This distinction is not purely semantic: the introduction of incentive-compatibility constraints makes the underline optimal design problems non-concave; hence, the solution attained from its primal and dual formulations may not just consist in a different sharing rule of social surplus.

For example, in Chan & Thakor. cit. the mechanism-design problem restricts the space of contracts to that of bank loans. Moreover, they assume that agents/borrowers have unlimited collateral that can be used to finance an investment of exogenously fixed amount.

Notice that \(\frac {d}{dz}D_{x}\mathbb {E}[\boldsymbol {P}|x]\equiv {\int \limits }_{z}^{\infty } g_{x} d \pi >0\), because g_x > 0 for a.a. π ≥ z, by definition of z above (and Assumption 1).

Later, we use the notation \((a^{\prime }(\ell ),x(\ell ))\equiv (a^{\prime }(\ell ,\ell ),x(\ell ,\ell ))\).

Deviations within A^nb have clearly no reason to occur.

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Title: On the optimal investment finance of small businesses
Author: Mario Tirelli
Publication date: 23-11-2019
Publisher: Springer US
Published in: Small Business Economics / Issue 4/2021
Print ISSN: 0921-898X
Electronic ISSN: 1573-0913
DOI: https://doi.org/10.1007/s11187-019-00283-1

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