10 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE maximize his expected return subject to(IC) and(Ir) maxa()∑。p(a,s)[B(s)-u(s) (s)≥0,a≥0 p(a,s)U((s)-v(a)≥∑p(b,s)U((s)-v(b),vb (IR) sp(a,s)U((s)-v(a)≥元 We can use this model of effort to illustrate the so-called debt overhang problem, if an entrepreneur has a pre-existing debt he may not wish to un- dertake a project with positive net present value. It is easiest to fit this into our present framework by representing the investment as effort that must be undertaken by the entrepreneur. Suppose that r is the face value of the debt The status quo is represented by a probability distribution p, which has zero cost of effort. The new project will result in a probability distribution p which has a positive cost c. We assume that p dominates p in the sense of first-order stochastic dominance and ∑p(s)(s)->∑叭(s)B(s) (4.1) However, the entrepreneur will undertake the new project only if ∑p()max{(s)-r,0-c≥∑s)max{(s)-r,0(42) and condition(4. 1)does not necessarily entail(4.2). In fact, it is easy to find examples in which the new project will not be undertaken. We can even find conditions under which it might be optimal for the bondholder's to forgive the debt in order to encourage greater effort(investment)on the part of the 4.4 Debt and Equity as Incentive Devices Grossman and Hart(1982) emphasizes the incentive effects of debt: a man ager whose firm is loaded with debt knows that shirking may result in an inability to service the debt. Insolvency or liquidation will be costly for the manager: he loses perquisites of his present job, is forced to search for an- other, and once he finds another job he may earn less because his reputatio has been damaged. This is equivalent to adding a non-pecuniary benefit10 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE maximize his expected return subject to (IC) and (IR): max(a,w(·)) P s p(a, s) [R(s) − w(s)] s.t. w(s) ≥ 0, a ≥ 0 (IC) P s p(a, s)U(w(s)) − ψ(a) ≥ P s p(b, s)U(w(s)) − ψ(b), ∀b (IR) P s p(a, s)U(w(s)) − ψ(a) ≥ u. ¯ We can use this model of effort to illustrate the so-called debt overhang problem, if an entrepreneur has a pre-existing debt he may not wish to un￾dertake a project with positive net present value. It is easiest to fit this into our present framework by representing the investment as effort that must be undertaken by the entrepreneur. Suppose that r is the face value of the debt. The status quo is represented by a probability distribution p, which has zero cost of effort. The new project will result in a probability distribution p0 , which has a positive cost c0 . We assume that p0 dominates p in the sense of first-order stochastic dominance and X s p0 (s)R(s) − c0 > X s p(s)R(s). (4.1) However, the entrepreneur will undertake the new project only if X s p0 (s) max{R(s) − r, 0} − c0 ≥ X s p(s) max{R(s) − r, 0} (4.2) and condition (4.1) does not necessarily entail (4.2). In fact, it is easy to find examples in which the new project will not be undertaken. We can even find conditions under which it might be optimal for the bondholder’s to forgive the debt in order to encourage greater effort (investment) on the part of the entrepreneur. 4.4 Debt and Equity as Incentive Devices Grossman and Hart (1982) emphasizes the incentive effects of debt: a man￾ager whose firm is loaded with debt knows that shirking may result in an inability to service the debt. Insolvency or liquidation will be costly for the manager: he loses perquisites of his present job, is forced to search for an￾other, and once he finds another job he may earn less because his reputation has been damaged. This is equivalent to adding a non-pecuniary benefit