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: $1.32 million

Year 2: $1.97 million

Year 3: $2.23 million

Year 4: $2.83 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 $1.90 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 12.00 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)

Explanation / Answer

We have

Present value of Annuity Due = A*[(1-(1+r)-n)/r] * (1+r)

Where

A - Annuity payment = ?

r - rate per period = 12%

n - no. of periods = 5

1.90 million = A*[(1-1.12-5)/.12] * 1.12

= A * [(1-.5674)/.12] * 1.12

= A * 4.0376

A = 1.90 million / 4.0376

= .4706 millions

= .47 millions

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