8 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE Suppose that p(, ) is a mean-preserving spread of P(b, ) Then, for any number r ∑p(a,s)max{R()-r,0≥∑p(,smax{B(s)-r,0 This follows immediately from the proposition and the fact that the functi f(s)= max(R(s)-r, 0 has non-decreasing differences. In other words the entrepreneur has a preference for risk(a preference for mean-preserving The principal on the other hand wants to maximize > pla, s)V(min(, R(s))) At any solution of the principal-agent problem, the participation constraint should be satisfied with equality: s P(a, s)w(s)= sp( a snax r,0=i. Thus, in the absence of the incentive problem the principal seeks to maximize ∑pa,sV(min{,R(s)) subject to p(a, s)max(R(s)-r,Of For example, if the principal is risk neutral he would always prefer a project with a higher expected value. But once the incentive constraint is imposed the risk shifting preferences of the agent have to be taken into account 4.3 Debt Overhang The risk taking or asset substitution problem is not the only one. Myers (1977)pointed out that firms rather than accepting negative NPV projects have an incentive to forego positive NPv projects. This incentive results from a debt overhang problem. The reason this arises is that equityholders with existing debt have to share the rewards of new projects with bondholders To see how this works consider another simple example 4.3.1 A Simple Example of Debt Overhang The firm has no cash and has debt of S10.000 The firm does nothing8 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE Suppose that p(a, ·) is a mean-preserving spread of p(b, ·). Then, for any number r, X s p(a, s) max{R(s) − r, 0} ≥ X s p(b, s) max{R(s) − r, 0}. This follows immediately from the proposition and the fact that the function f(s) = max{R(s) − r, 0} has non-decreasing differences. In other words, the entrepreneur has a preference for risk (a preference for mean-preserving spreads). The principal on the other hand wants to maximize P s p(a, s)V (min{r, R(s)}). At any solution of the principal-agent problem, the participation constraint should be satisfied with equality: P s p(a, s)w(s) = P s p(a, s) max{R(s) − r, 0} = ¯u. Thus, in the absence of the incentive problem the principal seeks to maximize X s p(a, s)V (min{r, R(s)}) subject to X s p(a, s) max{R(s) − r, 0} = ¯u. For example, if the principal is risk neutral he would always prefer a project with a higher expected value. But once the incentive constraint is imposed, the risk shifting preferences of the agent have to be taken into account. 4.3 Debt Overhang The risk taking or asset substitution problem is not the only one. Myers (1977) pointed out that firms rather than accepting negative NPV projects have an incentive to forego positive NPV projects. This incentive results from a debt overhang problem. The reason this arises is that equityholders with existing debt have to share the rewards of new projects with bondholders. To see how this works consider another simple example. 4.3.1 A Simple Example of Debt Overhang The firm has no cash and has debt of $10,000. The firm does nothing: