A professional baseball player signs a contract for $165 million to play with a

Question

A professional baseball player signs a contract for $165 million to play with a team for 7 years. He and his team agree that the contract will be spread out so that the player is paid beyond the 7 years. The payment plan for the contract is as follows: $16 million each year for years 1 through 7 $3.2 million each year for the next 8 years $1.3 million each year for the next 4 years. You should assume that the baseball team will pay the player annually at the end of each year and that he will receive the first $16 million at the end of the first year The player receives money for 19 years. The player had previously rejected a contract that would have paid $154 million for 7 years in which the $154 million would be paid in 7 equal installments (i.e., $22 million per year). The first payment would be made at the end of the first year. Assume the player will invest every dollar that he receives in an account that pays 4.2% interest compounded annually. Enter the amount in millions of dollars of the contract that would result in the most money at the end of 19 years for the player."

Explanation / Answer

Contract 1:

$16 million each year for years 1 through 7
$3.2 million each year for the next 8 years
$1.3 million each year for the next 4 years

Interest Rate = 4.20%

Future Value of Payments = $16*1.042^18 + $16*1.042^17 + $16*1.042^16 + ... + $16*1.042^12 + $3.2*1.042^11 + $3.2*1.042^10 + ... + $3.2*1.042^4 + $1.3*1.042^3 + $1.3*1.042^2 + $1.3*1.042 + $1.3
Future Value of Payments = $16 * 1.042^12 * (1.042^7 - 1) / 0.042 + $3.2 * 1.042^4 * (1.042^8 - 1) / 0.042 + $1.3 * (1.042^4 - 1) / 0.042
Future Value of Payments = $208.31 + $35.01 + $5.54
Future Value of Payments = $248.86

So, value of payment at the end of 19 years is $248.86 million

Contract 2:

$22 million for 7 years

Interest Rate = 4.20%

Future Value of Payments = $22*1.042^18 + $22*1.042^17 + $22*1.042^16 + ... + $22*1.042^12
Future Value of Payments = $22 * 1.042^12 * (1.042^7 - 1) / 0.042
Future Value of Payments = $286.42

So, value of payment at the end of 19 years is $286.42 million

So, Contract 2 will provide more money at the end of 19 years.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.