Suppose in Example 9.3 that net income turns out to be $25, despite the assumption that net income can only be one of $115 and $40. How could this happen, and what does it say about the completeness of the compensation contract in the example? How might the manager react to this lower net income number?

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Example 9.3 Net Income as a Performance Measure To illustrate the use of net income in compensation contracts, we extend Example 9.2. Recall from Table 9.2 that if the manager works hard (a,) the probability of the high pay- off ($100) is 0.6, with 0.4 probability of the low payoff ($55). If the manager shirks (a), the probabilities of the high and low payoffs are 0.4 and 0.6, respectively. As explained at the time, the reason why the payoff can be low even if the manager works hard, and vice versa, is because of the various risks faced by the firm. Despite hard work, bad eco- nomic times may result in the low payoff. Alternatively, good times may rescue the man- ager who shirks. These risks can be reduced by manager effort, but cannot be eliminated, as reflected in the 0.4 probability of low payoff given a, and the 0.4 probability of high payoff given a,. In sum, while the manager can increase the probability of the high pay- off by working hard, a high payoff cannot be guaranteed. Nor can it be guaranteed that shirking will result in a low payoff. Furthermore, noisy net income introduces a second source of compensation risk for the manager-given the ultimate payoff, compensation will still vary depending on which net income is realized. To reflect the noise in net income, assume the following: An Analysis of Conflict 321 If the payoff is going to be $100, net income for the current period will be $115 with probability 0.8 and $40 with probability 0.2 If the payoff is going to be $55, net income for the current period will be $115 with probability 0.2 and $40 with probability 0.8 The noise in net income could result from the random effects of internal control failure and recognition lag, as discussed earlier. There are thus two possible net income numbers. The manager who works hard requires a 0.3237 share of net income to attain reservation utility of 3. This is verified as follows: EU (a) 0.6/0.8 V0.3237 x 115 +0.2 V0.3237 x 40 +0.40.2 V0.3237 x 115 +0.8 V0.3237 x 40 - 2 0.6 0.8 V37.2255 +0.2 V12.9480 +040.2 37.2255 +0.8 12.9480-2 = 0.6 x 5.6007 +0.4 x 4.0989-2 -3.3604 +1.6396-2 -3.00