Problem 1. (10 points) It always makes the papers when a well-known sports star signs a multi-million-dollar contract (such as the payment schedule for a football player who has signed a 10-year, $130 million contract extension that guarantees him an NFL-record $37 million in bonuses.). The contract also comes with two categories of signing bonuses. The initial signing bonus ($30 million) can be pro-rated only over the first six years of the contract. Then the second roster bonus of $7,002,000 can be pro-rated over the final nine seasons of the contract. With the salary and signing bonus paid at the beginning of each season, the net annual payment schedule looks like Table 1. a) How much is the player's contract actually worth at the time of signing, at an interest rate of 6%? b) For the initial signing bonus and the second roster bonus, suppose that the ball club allows the player to take either the pro-rated payment option as just described ($30 million over five years) or a lump- sum payment option in the amount of $23 million at the time he signs the contract. Should the player take the lump-sum option instead of pro-rated one? Table 1 Beginning Base Salary Pro-rated Signing Bonus Total Annual Payment of Season 1 $600,000 $5,000,000 $5,600,000 2 $1,400,000 $5,000,000 + $778,000 $7,178,000 3 $6,000,000 $5,000,000+ $778.000 $11,778,000 4 $7,000,000 $5,000,000+ $778,000 $12,778,000 5 $9,000,000 $5,000,000+ $778,000 $14,778,000 6 $10,500,000 $5,000,000+ $778,000 $16,278,000 7 $13,500,000 $778,000 $14,278,000 8 $13,000,000 $778,000 $13,778,000 9 $15,000,000 $778,000 $15.778,000 10 $17,000,000 $778,000 $17,778,000