A baseball player is offered a 5-year contract that pays him the following amoun

Question

A baseball player is offered a 5-year contract that pays him the following amounts:

Year 1: $1.2 million
Year 2: 1.6 million
Year 3: 2.0 million
Year 4: 2.4 million
Year 5: 2.8 million

Under the terms of the agreement all payments are made at the end of each year. Instead of accepting the contract, the baseball player asks his agent to negotiate a contract that has a present value of $1 million more than that which has been offered. Moreover, the player wants to receive his payments in the form of a 5-year annuity due. All cash flows are discounted at 10 percent. If the team were to agree to the player’s terms, what would be the player’s annual salary (in millions of dollars)?

What are the steps to solve this answer?

Explanation / Answer

PVCFs = PVCF1 + PVCF2 +.......+ PVCFn

           = $1200000 (1 + 0.10)-1 + $1600000 (1 + 0.10)-2 + $2000000 (1 + 0.10)-3 + $2400000 (1 + 0.10)-4

               + $2800000 (1 + 0.10)-5

           = 1200000 / (1.10) + 1600000 / (1.21) + 2000000 / (1.331) + 2400000 / (1.4641) + 2800000 / (1.61051)

           = 1090909 + 1322314 + 1502630 + 1639232 + 1738580

          = $7293665

Therefore, PV is $1000000 more than that which has been offered.

PVADue = $7293665 + $1000000 = $8293665

PVADue = Pmt [(1 - (1 + r)-n) / r] * (1 + r)

$8293665 = Pmt [(1 - (1 + 0.10)-5 ) / 0.10] * (1 + 0.10)

8293665 = Pmt [(1 - 1/1.61051) / 0.10] * 1.10

8293665 = Pmt [(1 - 0.62092) / 0.10] * 1.10

8293665 = Pmt [0.37908 / 0.10] * 1.10

8293665 = Pmt * 3.7908 * 1.10

Pmt = 8293665 / (3.7908 * 1.10)

Pmt = 8293665 / 4.16988

Pmt = $1988946

Therefore, If the team were to agree to the player's terms, player's annual salary would be $1988946

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