Sep 19, 2017


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(asymmetric information about the value of assets in place and the negative stock price reaction to equity offerings with a continuum of types). Consider the privately-known-prospects model of Application 2 in Section 6.2.2, but with a continuum of types. The entrepreneur already owns a project, which with probability p yields profit R and probability 1 − p profit 0. The probability p is private information of the borrower. From the point of view of the investors, p is drawn from cumulative distribution F(p) with continuous density f (p) > 0 on some interval [p ¯ , p]¯ . Assume that the distribution has monotone hazard rates:

(This assumption, which is satisfied by most usual distributions, is known to imply that the truncated means m−(p) and m+(p) have slope less than 1:

The model is otherwise as in Section 6.2.2. A seasoned offering may be motivated by a profitable deepening investment: at cost I, the probability of success can be raised by an amount τ such that

τR > I

(of course, we need to assume that p¯ + τ ≤ 1). The entrepreneur has no cash on hand, is risk neutral, and is protected by limited liability. The investors are risk neutral and demand a rate of return equal to 0.

(i) Show that in any equilibrium, only types p p∗, for some cutoff p∗, raise funds and finance the deepening investment.

(ii) Show that p∗ > p ¯ and that if p∗

Show that if the benefits from investment are “not too large,” in that

then indeed p∗ ∗ Pareto-dominates (is better for all types than) the other equilibria. (iii) Is there a negative stock price reaction upon announcement of an equity issue? (iv) Focusing on an interior Pareto-dominant equilibrium, show that, when τ increases, the volume of equity issues increases.

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