Sensitivity analysis of incentive compatible compensation contract

After class today, a Finance 4335 student asked me a particularly interesting question about the class problem; specifically, how much bonus is too much to offer? Clearly (based upon parts 4-5 of this class problem), if the firm is intent on hiring the CEO, then increases in her cost of effort require higher bonuses. For example, if the cost of effort is $200,000, then the minimum bonus comes to $701,038 (compared with a minimum bonus of $429,298 when the cost of effort is only $50,000). Under either of those cost of effort scenarios, the CEO will optimally work hard and expected profits net of CEO compensation (see the section of the spreadsheet labeled “Profit after proposed compensation”) are higher compared with the ‘Go Through Motions” scenario. However, if the CEO’s cost of effort is $500,000 (as it is in part 5), then the bonus comes out to $1,287,876. Even though expected profit net of CEO compensation remains higher under the “Work Hard” scenario, it turns out that the CEO will choose instead to go through the motions rather than work hard, since expected utility is 1,280.73 under ‘Go Through Motions” compared with 1,224.74 under “Work Hard”. In this case, the firm would definitely not want to hire a part 5 CEO and instead find a CEO who has a lower cost of effort (e.g., C = $200,000 or less as shown in parts 2-4).

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