ook: Introduction: What This Book Is About $($Ch $01)$

Individual Problems

$1-1$ Goal Alignment at a Small Manufacturing Concern

The owners of a small manufacturing concern have hired a vice president to run the company with the expectation that he will buy the company after five years. Compensation of the new vice president is a flat salary plus $75\%$ of the first $$150,000$ profit, and then $10\%$ of profit over $$150,000.$ Purchase price for the company is set at $4\mathrm{.}5$ times earnings $($profit$),$ computed as average annual profitability over the next five years.

a$.$ Plot the annual compensation of the vice president as a function of annual profit.

b$.$ Assume the company will be worth $$10$ million in five years. Plot the profit of buying the company as a function of annual profit.