Question

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

Year 1: $1.41 million

Year 2: $1.67 million

Year 3: $2.12 million

Year 4: $2.79 million

Year 5: $3.46 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 $1.70 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 11.00 percent. If the team were to agree to the player's terms, what would be the player's annual salary (in millions of dollars)? (Express answer in millions. $1,000,000 would be 1.00)

Answer 1

Step-1, Calculation of the Present Value of the 5 year cash flow

Year	Cash Flows ($ in Millions)	Present Value Factor at 11%	Present Value of the cash flow ($ in Millions)
1	1.41	0.90090	1.27027
2	1.67	0.81162	1.35541
3	2.12	0.73119	1.55013
4	2.79	0.65873	1.83786
5	3.46	0.59345	2.05334
TOTAL			$8.06701

Therefore, the Total Contract amount = Present Value of the cash flows + $1.70 Million

= $8.06701 Million + $1.70 Million

= $9.76701 Million

Step-2, Calculation of the Annual Salary Payment using Present Value annuity due formula

Present Value of an Annuity Due is calculated by using the following formula

Present Value of an Annuity Due = (1 + r) x P x [{1 - (1 / (1 + r) n} / r]

Interest Rate (r) = 11%

Number of Periods (n) = 5 Years

Present Value of annuity Due = $9.76701 Million

Annual Payment (P) = ?

Present Value of an Annuity Due = (1 + r) x P x [{1 - (1 / (1 + r) n} / r]

$9.76701 = (1 + 0.11) x P x [{1 - (1 / (1 + 0.11)⁵} / 0.11]

$9.76701 = 1.11 x P x [{1 - (1 / 1.68505)} / 0.11]

$9.76701 = 1.11 x P x [{1 - 0.593451} / 0.11]

$9.76701 = 1.11 x P x 3.69589

$9.76701 = P x 4.102445

P = $9.76701 / 4.102445

P = $2.381 Million

“Therefore, the player's annual salary would be $2.381 Million”