Early in $2019,$ Bryce Harper signed a $13-$year, $$330$mm contract with thePhiladelphia Phillies. He also turned down a more complicated contract withthe Washington Nationals. It turns out that the Nationals offered a contractwith a lot of deferred money. The purpose of this question is to compare thevalue of the two contracts.

Because the contracts have some differences, we will make somesimplifying assumptions, particularly for the Nationals contract. Assume a$6\%$ discount rate $($annual rate that is annually compounded$)$

a$.$First, calculate the present value of the Phillies$$ offer which will pay him$$25\mathrm{.}385$ million each year from t $=1$ to t $=13.$

b$.$Second, calculate the present value of the Nationals$$ offer whichconsists of two parts. The contract will pay him $$20$ million each yearfrom t $=1$ to t $=10$ and then pay him $$10$ million from t $=11$ to t $=34($thedeferred part of the contract.

c$.$Which offer should he take? What interest rate would make himindifferent between the two offers?

d$.$Go back to your answer for the first part of c in which you decidedwhich contract he should sign. If the team that signed him estimates thatthe present value of the additional positive cash flows that they willreceive for having him on their team $($additional ticket sales, jerseys,television revenue, etc.$)$ will be $$250$ million. Should the team havemade the offer to Harper? Why?