Lyft launched its IPO on April 1^st 2019 with a share price of $72. Before the IPO, Lyft's board of directors was likely trying to decide how to compensate CEO Logan Green to provide an incentive for him to increase the firm's performance and share price after it went public. Let's say the board was considering two possibilities such that they were deciding between providing one million dollars worth of shares of the firm stock at $72 per share or one million dollars worth of call options with a strike price of $72 and a maturity and vesting date one year after the IPO. To keep things simple, let's say CEO Logan Green can choose between providing two levels of effort: regular effort or high effort. He has been exerting regular effort all along. He could switch to high effort which would be much more costly for him as he would have to work even longer hours, but the extra effort would likely result in better performance for the firm. The goal of the board's incentive compensation is to convince the CEO to exert high effort, and we want to consider the incentive created by giving him either shares of stock or stock options.

To determine the incentive created under shares versus options, we first have to know how many shares or options the one million dollars of incentive compensation would provide. We already know the price of a share of stock ($72), but we have to determine the price of the option to know how many options to provide. Remember that we determine the price of an option by considering the various values the stock price might be at the time of the option maturity. Let's say the board assumes the CEO will exert regular effort and under that level of effort works with market analysts to predict the value of a share of the stock one year after the IPO. They conclude the share price one year after the IPO has the following probabilities: a 30% chance of $42 per share, a 10% chance it is $35 per share, a 30% chance it is $60 per share, a 20% chance of it being $74 per share, and a 10% chance if it being $80 per share.

Questions Begin Here.

a. If the board decided to give one million dollars worth of shares of the stock, how many shares would the CEO receive?

b. Given the predicted probabilities of future share price at the time of option maturity, what is the price of the option?

c. How many options will the firm give the CEO if they want to provide the one million dollars worth of incentive compensation in the form of options?

Now that we know how many shares or options the CEO will receive and the value of those shares and options at the time of the IPO, we can think about the incentive created under each compensation plan for the CEO to exert extra effort. We already know the potential future values of the share price under regular effort. Let's assume if Logan Green decides to exert extra effort, he improves the chances of the share price being better one year after the IPO. Under extra effort, the probabilities of future share prices one year after the IPO are as follows: a 5% chance of being $42, a 10% chance of being $60, a 20% chance of $74, 30% of $80, and 35% of $85.

Let's first determine the incentive created to exert extra effort if the CEO receives shares of stock as compensation.

d. What is the expected value of the stock price in one year if the CEO maintains regular effort?

e. What is the expected value of the stock price in one year if the CEO exerts extra effort?

f. Given how many shares of stock he received as incentive compensation, what is the monetary value of exerting extra effort if he is compensated through shares of stock?

Now let's determine the incentive created to exert extra effort if the CEO receives options as incentive compensation. We've already determined the value of the option under regular effort.

g. What is the value of the option if the CEO exerts extra effort?

h. Given how many options the CEO received, what is the monetary value of exerting extra effort if he is compensated through stock options?

i. If the board wants to encourage the CEO to exert extra effort, which form of incentive compensation should it employ?