As chairman of the board of ASP Industries, you estimate that your annual profit is given by the table below. Profit (II) is conditional upon market demand and the effort of your new CEO. The probabilities of each demand condition occurring are also shown in the table.
It =$10 million
It =$15 million
It =$17 million
You must design a compensation package for the CEO that will maximize the firm”s expected profit. While the firm is risk neutral, the CEO is risk averse. The CEO”s utility function is
Utility = W5 when making low effort
Utility = W5 -100 when making high effort
where W is the CEO”s income. (The -100 is the “utility cost” to the CEO of making a high effort.) You know the CEO”s utility function, and both you and the CEO know all of the information in the preceding table. You do not know the level of the CEO”s effort at time of compensation or the exact state of demand. You do see the firm”s profit, however.
Of the three alternative compensation packages below, which do you as chairman of ASP Industries prefer? Why? Package
1: Pay the CEO a flat salary of $575,000 per year Package
2: Pay the CEO a fixed 6 percent of yearly firm profits Package
3: Pay the CEO a flat salary of $500,000 per year and then 50 percent of any firm profits above $15 million
The issue here is how to get your CEO to make high effort but not give away the company storethat is, too much in profits. For each package, first calculate whether the executive will make high or low effort. Then calculate firm profits under each effort to decide if the package works to your advantage. Then select that package which maximizes your profits. CEO Utility under the three packages: PACKAGE 1 :the CEO will give low effort to maximize utility: Low Effort: E(U) = ($575,000).5= 758.29 High Effort: E(U) = ($575,000).5-100 = 658.29. PACKAGE 2) the CEO will give high effort to maximize utility: Low Effort: E(U) = .3(.06×5,000,000).5+ .4(.06×10,000,000).5+ .3(.06×15,000,000).5= 758.76 High Effort: E(U) =.3(.06×10,000,000).5+ .4(.06×15,000,000).5+ .3(.06×17,000,000).-100 = 814.835 PACKAGE 3 : the CEO will give high effort to maximize utility: Low Effort: E(U) = .3(500,000).5+ .4(500,000).5+ .3(500,000).5= 707.11 High Effort: E(U) =.3(500,000).5+ .4(500,000).5+ .3(1,500,000).5-100 =762.40 Now calculate the expected firm profits under each plan net of expected compensation: PACKAGE 1 :Low Effort: E() = .30x$5m + .40x$10m + .30x$15m-($.575m) = $9.425million PACKAGE 2 :Low Effort: E() = .30x$5m + .40x$10m + .30x$15m-(.3x$.3m + .4x$.6m + .3x$.9m)= $9.4m High Effort: E() = .30x$10m + .40x$15m + .30x$17m-(.3x$.6m + $.4x$.9m+ .3x$1.02m) = $13.254m PACKAGE 3 :Low Effort: E() = .30x$5m + .40x$10m + .30x$15m-(.3x$.5m +$.4x$.5m + .3x$.5m)= $9.5m…
h Effort: E() = .30x$10m + .40x$15m + .30x$17m-(.3x$.5m + $.4x$.5m+ .3x$1.5m) = $13.3m To maximize the expected profits of ASP Industries, you recommend compensation PACKAGE 3 which uses a flat salary and then a large bonus when the firm does exceptionally well and makes $17 million. You prefer this package because itmaximizes firm expected profits net of compensationhere at a value of $13.30 million. Notice that if you just gave a very large bonus when the firm did exceptionally well, CEO risk aversion would lead him to make low effort–or more likely work for someone else. The flat salary offsets the disincentive effects of a risk-but motivating package. This is the usual form of executive compensation.Notice too that compensation is tied to firm profitability. When the worker gives high effort, always check that your profits are higher under high effort than under low effort. You might be getting high effort, but you are giving away too much so that you really prefer that the worker be lazy! Well not really, but you a giving away too much of firm profits to motivate your employees. If you find this to be a problem, then reduce compensation while keeping high effortuntil profits from high effort beat profits from low effort. Then you have a compensation plan that makes some sense.