$7.$ Ken Griffey III, a professional baseball player, is deciding between two contract offers. The Red Sox have offered Griffey an eight$-$year contract that would pay $$12$ million per year for the first two years, and $$8$ million per year for the remaining six years. The Yankees have also offered Griffey an eight$-$year contract. They would pay $$6\mathrm{.}0$ million per year for each of the eight years, and would also make deferred payments of $$5$ million per year for another eight years after the contract period finished. Assume that each payment is made at the end of the year. Griffey has determined that he will accept the contract with the highest present value.

$($a$)$ Assume that this offer occurs in a low interest rate environment, that that Griffey is willing to discount the future cash flows at a rate of $2\%$ per year. What is the NPV of each contract offer?

$($b$)$ Assume that this offer occurs in a high interest rate environment, that that Griffey will discount the future cash flows at a rate of $8\%$ per year. What is the NPV of each contract offer?

$($c$)$ Explain why the results in part $($b$)$ differ from part $($a$)$ in the manner that they do$.$