IShine Co. is a gold producer. It is a stock company with 100 million shares outstanding and has no debt.
Its value next year is either $1000m if gold price is low with a probability of 60% or $1600m if gold price is high with a 40% probability. If IShine hedges its gold price, the firm value can be stabilized at $1260m.
Jack, IShine's chief risk officer, is risk averse and has a utility function of U = Squareroot W where U is Jack's utility and W is Jack's wealth all coming from his employment income. Currently, Jack is paid a flat salary of $250,000.
1. What's Jack's utility with this flat salary?
2. If IShine changes its pay program and plans to pay Jack some proportion x of the firm value, which is called "performance pay", what value of x will make Jack indifferent between flat salary and performance pay without hedging?
3. With performance pay with x calculated from (2), will Jack hedge gold price risk? Justify your answer with calculation.
4. If Jack is granted y call options with strike price $12.40, how many call options y should be granted to Jack to make him indifferent between flat salary and stock option plan without hedging? Suppose each call option has the right to purchase one share at the strike price.
5. With stock option plan with y calculated from (4), will Jack hedge gold price risk? Justify your answer with calculation.