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Review of Accounting Studies

Erschienen in:

01.09.2010

Signaling firm value to active investors

verfasst von: Tim Baldenius, Xiaojing Meng

Erschienen in: Review of Accounting Studies | Ausgabe 3/2010

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Abstract

Active investors provide risk-sharing and value-adding effort in form of advising, networking, monitoring, etc. This paper demonstrates a conflict between two key objectives for high-quality entrepreneurs: to elicit such investor effort and to signal the firm’s type by retaining shares. This conflict may give rise to stable (and economically meaningful) pooling equilibria for startup firms. More established firms, with access to multiple signals, can always realize both of these objectives but may still decide to forego investor effort if eliciting it would require them to deviate substantially from the cost-minimizing signal mix. In comparison with otherwise identical pure-exchange settings (with passive investors), we find that the potential for investors to be active always increases the signaling cost in case of noncontractible investor effort, whereas the effect is ambiguous if investor effort is contractible. At the same time, we identify conditions under which signaling is welfare-enhancing as it helps guide investors’ effort towards more promising ventures.

Vorheriger Artikel Discussion of “Are CEOs compensated for value destroying growth in earnings?”

Nächster Artikel Discussion of “Signaling firm value to active investors”

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See Gorman and Sahlman (1989), Hsu (2004), Gompers and Lerner (2006, p. 160), and Bottazzi et al. (2008) on how venture capitalists add value to operations, and Hellmann and Puri (2002) and Schmidt (2003) on complementarities.

In Kaplan and Stromberg (2004) the founder can threaten to walk away from the firm, which creates a holdup problem of a different nature than that in our model.

The pooling equilibrium satisfies Cho and Kreps’s (1987) “Intuitive Criterion.” In earlier pure-exchange signaling models pooling equilibria were routinely eliminated by this refinement.

In our model the introduction of the second signal eliminates any pooling equilibria that might have been present under univariate signaling.

There is a sizeable literature on multivariate signaling, e.g., Milgrom and Roberts (1986), Grinblatt and Hwang (1989), and Sarath and Natarajan (1996).

Our model with noncontractible effort is related to the “spot market” scenario in Garicano and Santos (2004), yet there are a number of differences. Most important, in Garicano and Santos, the compensation one agent pays to the other is a contractual choice variable. In contrast, in our model it is determined by the ownership structure, which is also used to signal base earnings. Huddart and Liang (2005) also study incentives in partnerships.

Convertible debt is common in venture financing. Yet, as shown by Kaplan and Stromberg (2003, p. 286), the widespread participating preferred securities are “better categorized as … straight preferred stock and common stock than as a position of convertible preferred.”

Discrete investor effort is a matter of technical convenience. The key tension in the model remains intact with continuous effort, except for the existence of pooling equilibria in Sect. 5.

The assumption that $\Upphi\geq 1$ ensures that the investor is willing to exert effort in a pooling equilibrium and therefore is important when establishing that pooling equilibrium is preferred by high-type founders (Sect. 5), but it does not otherwise affect our results. In particular, the existence of stable pooling equilibria does not depend on $\Upphi \geq 1.$

Risk neutrality is a standard assumption in IPO settings but less innocuous in our setting, as active investors are usually imperfectly diversified. Key to our story is that the investor provides some risk sharing; risk neutrality is assumed for simplicity.

An alternative model specification is conceivable where the investor has the bargaining power and offers a screening contract to the founder. As long as the contract variable used to screen firm types is firm shares, the moral hazard/holdup problem that is at the heart of our model would resurface. See Hellwig (1987) for a comparison of these two model classes.

Note that for high K, the share price may be negative, which would amount to a monetary net transfer from the founder to the investor. We thank a referee for pointing this out.

Program ${\mathcal{P}}_1$ omits the additional regularity condition that α ≤ 1. It is easy to show that this constraint is always slack in the optimal solution.

It is a matter of straightforward algebra to show that

$$ \alpha_N(K)=\frac{1}{\rho \sigma^2}\left[\sqrt{(Z(K))^2+2 \rho \sigma^2 [\Updelta \theta +(\phi_H-1)K]}- Z(K)\right], \ \hbox{for}\ Z(K)\equiv \Updelta\theta +(\Updelta\phi) K. $$

At times we will write out α_N(·) as an explicit function of K and σ². But, to save on notation, we shall drop one or both of the functional arguments whenever there is no potential for confusion.

L’s temptation to mimic H is driven also by the base earnings differential $ \Updelta\theta.$ A qualitatively similar result as in Proposition 1 can be shown, in that a high $\Updelta\theta $ calls for a high level of $\alpha ^{{**}}. $ In the subsequent analysis, however, we will confine attention to risk as the main conditioning variable.

Since H never has incentives to mimic L, there is no need to consider renegotiation of any inefficient (H, k = 0) subgames.

In contrast, if the investor has the bargaining power at Date $2 \frac{ 1}{2}$, then renegotiation does not affect the solution in Sect. 3 as it leaves the nonmimicry constraint (4) unchanged.

To see this, note that $Y( \tilde \alpha)=(1-\tilde \alpha)\phi_H+\tilde{\alpha}{\phi_L-1}>(1-\tilde \alpha)\phi_H -1=0=Y(\alpha_0).$ Then $\tilde{\alpha}<{\alpha_0}$ follows directly from the fact that Y(α) is a decreasing function.

We suppress the functional dependence of $\tilde{K}$ on σ² to avoid clutter.

More generally, the “focal” pooling equilibrium is the one that ensures efficient risk sharing. If the active investor, too, were risk averse, then α > 0 in the focal pooling equilibrium.

If $\Upphi<1$ were to hold, contrary to our maintained assumption, then the pooling equilibrium would involve k = 0, and the payoff to each type of founder would be $U^{PE}(0,0)=\Uptheta.$

Specifically, equating the thresholds K ₁ and K ₂ as derived in the "Appendix" yields:

$$ \sigma_K^2=\frac{2 \Updelta\theta (\phi_H)^2(1-p \phi_H)} {\rho (1-\phi_H)^2 \phi_L}>0. $$

At $K=\tilde{K}$, one might expect the equilibrium α to drop to α_LP, the Leland-Pyle prediction in a pure-exchange model. Yet, this would not be an equilibrium in our setting: if retaining α_LP were a credible signal of the firm’s type being H, then the investor would choose k = K, because $\alpha_{LP}<\tilde{\alpha}$ whenever $\sigma^2>\tilde{\sigma}^2.$ Hence, H needs to retain $\tilde{\alpha}$ shares to ensure separation and k = 0.

In Martimort and Sand-Zantmann (2006) higher type firms receive less effort from the uninformed party because the authors assume the productivity of effort to be independent of firm type. In our model, in contrast, the complementarity between type and effort results in effort inputs always being (weakly) greater for high-type firms than for low-type firms.

While we use the payoff to H as the criterion for equilibrium selection, a Pareto-ordering (and thus a fortiori also a social welfare ordering) would result in the same prediction as Proposition 2 because L’s payoff is strictly greater under pooling than under the efficient separating equilibrium. In fact, by using H’s payoff as the selection criterion, we bias the analysis against pooling.

When K becomes large, pooling will again be an equilibrium. Then the payoff comparison between pooling with k = K and separating with k = 0 (depicted in Fig. 4a) carries over a fortiori to Fig. 4b: separating will now be even less attractive to H as it would require retaining even more shares ($\alpha_{LP}>\tilde \alpha$ when $\sigma^2<\tilde{\sigma}^2$).

In contrast, in Martimort and Sand-Zantmann (2006), the productivity of investor effort is independent of the firm’s type, which precludes any welfare-improving effect of signaling.

A forcing contract restricting the forecast to be either θ_H or θ_L would require that courts know the values (θ_H, θ_L). However, while these values may be common knowledge among founder and investor, they will often not be verifiable to the courts. We therefore ignore forcing contracts.

Among the various signals at firms’ disposal, our choice was guided by which appear to be of key importance in investor negotiations. Moreover, our setup permits comparisons with earlier pure-exchange studies such as Fan (2007). Replacing earnings forecasts with other signals that leave ownership unaffected (e.g., auditor quality) would yield qualitatively similar insights.

In Fan (2007) the misreporting cost comes out of the firm’s, and not the founder’s, pocket. This difference in assumptions does not qualitatively affect our results. Note that earnings forecasts can be reinterpreted as biased “disclosure” or as “earnings management” if the model is extended to two periods as follows. The firm operates for one period generating earnings of θ. Those earnings can be misreported by the founder. Then the game continues as described here with base earnings that are perfectly correlated across time.

Similar arguments as in Sect. 3 rule out any pooling equilibria with contractible effort.

For the special case of Assumption 1, below, this translates into $v<\bar{v}(K)\equiv 2\frac{(\phi_H-1)K+\Updelta\theta } {({\Updelta\theta} )^2}.$

Identifying the threshold value for operating risk involves polynomials of higher order and cannot be solved analytically. Invoking Assumption 1 with parameters {ρ = 0.1, ϕ_H = 2, ϕ_L = 0.5, θ_H = 2, θ_L = 1} shows that for σ² ≤ 5 and v ≤ 0.2, $\alpha^{**}(K)> \tilde {\alpha}$ for any K.

For given investor beliefs $(\hat{\theta} , \hat{\phi})$, the (α, m)-frontier that determines a binding nonmimicry constraint is strictly monotonic so that for any K there exists a unique m ^o(K).

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Titel: Signaling firm value to active investors
verfasst von: Tim Baldenius
Xiaojing Meng
Publikationsdatum: 01.09.2010
Verlag: Springer US
Erschienen in: Review of Accounting Studies / Ausgabe 3/2010
Print ISSN: 1380-6653
Elektronische ISSN: 1573-7136
DOI: https://doi.org/10.1007/s11142-010-9130-7

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