You have been hired as an agent representing Johnny Baseball. Johnny doesn't care about risk, but he faces an interest rate of 10% a year.

Johnny has an offer of $10 million a year for the four years 0 through 4 from the Red Sox.

1. The Guardians are going to make Johnny an offer where he plays in the minor league for years zero and one at $1 million and then plays for 3 years at a constant salary. How large does that salary need to be for Johnny to take it over the Red Sox offer?

Johnny's prospects are uncertain. If Johnny were to strike a new 3-year contract after two years of play on the open market, there is a 50% it would be for $10m a year, a 25% chance it would be for $15 million a year, and a 25% change it would be for $5m. These are the values to the Guardians and the values he could get on the open market.

1. The Guardians want to offer Johnny a contract that pays a fixed amount per year for years 0 and 1, and then gives the team the option (but not obligation) to sign him for $10m a year for year 2 through 4. How large does that fixed amount in year 0 and 1 need to be for Johnny to take it over the Red Sox offer?

1. The Guardians want to offer Johnny a contract that pays a fixed amount per year for years 0 and 1, and then gives Johnny the option (but not obligation) to sign up for $10m a year for years 2 through 4. How small can the fixed amount in year 0 and 1 be for Johnny to take it over the Red Sox offer?