4.3. DEBT OVERHANG The firm will go bankrupt The firms investment opportunity Invest $2,000 and receive return $11,000 with certainty(ignore discount- xpected return=-2,000+11,000=+89,000 E This is clearly a very attractive project. Is it worth the firm doing it? The firm does the project Value of bonds=$10000 Payoff to Equityholders =-2,000+1,000=-$1,000 The will not be prepared to put up the money for investment since even though it's a very good project they lose money from doing it Even if the firm has $2,000 cash on hand they would not do the project since the shareholders would be better off to pay the money as a dividend This example illustrates the conclusion that if business risk is held con- stant, any increase in firm value is shared among bondholders and stockhold- Thus, only if bondholders are willing to put up most of the money will the firm undertake the investment. However, bondholders may get very imperfect information. They may not be able to tell whether its this type of project or the type that we had in the previous example. As a result of this asymmetric information the project will not be undertaken 4.3.2 A Formal Model of Debt Overhang The manager in this example chooses a level of effort a that results in a probability distribution p(a, s)over the outcomes s. There is no investment required. The manager's utility function is U(c-v(a). The contract between the shareholder and the manager specifies a reward w(s) as a function of the state s. Limited liability implies that w(s)20. The manager will choose the effort that maximizes his expected utility >spla, s)U(w(s)-v(a).The shareholder chooses the incentive scheme w( to provide the manager with an incentive to pursue his(the shareholders)interests The interaction of the n and shareholder can be written principal-agent problem in which the shareholder chooses the effort level to4.3. DEBT OVERHANG 9 The firm will go bankrupt. The firm’s investment opportunity: Invest $2,000 and receive return $11,000 with certainty (ignore discount￾ing). Expected return = -2,000 + 11,000 = +$9,000 This is clearly a very attractive project. Is it worth the firm doing it? The firm does the project: Value of bonds = $10,000. Payoff to Equityholders = -2,000 + 1,000 = -$1,000. The will not be prepared to put up the money for investment since even though it’s a very good project they lose money from doing it. Even if the firm has $2,000 cash on hand they would not do the project since the shareholders would be better off to pay the money as a dividend. This example illustrates the conclusion that if business risk is held con￾stant, any increase in firm value is shared among bondholders and stockhold￾ers. Thus, only if bondholders are willing to put up most of the money will the firm undertake the investment. However, bondholders may get very imperfect information. They may not be able to tell whether its this type of project or the type that we had in the previous example. As a result of this asymmetric information the project will not be undertaken. 4.3.2 A Formal Model of Debt Overhang The manager in this example chooses a level of effort a that results in a probability distribution p(a, s) over the outcomes s. There is no investment required. The manager’s utility function is U(c)−ψ(a). The contract between the shareholder and the manager specifies a reward w(s) as a function of the state s. Limited liability implies that w(s) ≥ 0. The manager will choose the effort that maximizes his expected utility P s p(a, s)U(w(s) − ψ(a). The shareholder chooses the incentive scheme w(·) to provide the manager with an incentive to pursue his (the shareholder’s) interests. The interaction of the manager and shareholder can be written as a principal-agent problem in which the shareholder chooses the effort level to