You are the negotiator for a football club and are trying to negotiate a contract with a player. His agent has let you know that his player is seeking a five year contract paying him $$4$ million a year for five years. You make a counter$-$offer of $$3$ million a year for the first five years and offer to continue to pay him $$1$ million a year for the next five $($so that the total nominal value of the contract is $$20$ million$).$ The appropriate discount rate is $10\%$

$($a$)$ How much would the player lose in present value dollars if he accepted your offer? $5$ pts

$($b$)$ How much more would you have to pay over the last five years $($over and above the $$1$ million that you have offered him$)$ so as to allow the player not to lose in present value terms? $10$ pts