A baseball player is offered a 5-year contract that pays him the following amounts: Year 1: $1.40 million Year 2: $1.51 million Year 3: $2.25 million Year 4: $2.59 million Year 5: $3.17 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 $1.54 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 10.00 percent. If the team were to agree to the player's terms, what would be the player's annual salary (in millions of dollars)

The present value of the player's future cash flows (salaries) is the current value or the value in today's dollars. It is computed by discounting the future values at the appropriate discount rate.

The present value can be computed using the Present Value formula, an online finance calculator, or the PV factor table.

Formula

PV = FV \frac{1}{(1+r)^{n}}

Where:

PV = present value

FV = future value

r = rate of return

{n} = number of periods

Data and Calculations:

Discount rate = 10%

Period of salary = 5 years

Period Cash Flows PV Factor Present Value

Year 1: $1.40 million 0.909 $1,272,600 ($1.4 x 0.909)

Year 2: $1.51 million 0.826 1,247,260 ($1.51 x 0.826)

Year 3: $2.25 million 0.751 1,689,750 ($2.25 x 0.751)

Year 4: $2.59 million 0.683 1,768,970 ($2.59 x 0.683)

Year 5: $3.17 million 0.621 1,968,570 ($3.17 x 0.621)

Additional present value required 1,540,000

Total present value = $9,287,150

Annual salary (in millions of dollars) = $1.89743 million ($9,287,150/5).

Thus, the player's annual salary (in millions of dollars) is $1.89743 million.

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