The owners of a small manufacturing concern have hired a vice president to run the company with the expectation that he will buy the com- pany 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 4.5 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. c. Does this contract align the incentives of the new vice president with the profitability goals of the owners? d. Redesign the contract to better align the incentives of the new vice president with the profit- ability goals of the owners.