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

Instead of accepting the contract, the baseball player asks his agent to negotiate a contract which 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)?

Answers

Answer 1
It would be year 4 2.4 million
Answer 2

The player's annual salary is $2 million. If All cash flows are discounted at 10 percent. If the team were to agree to the player's terms.

What is meant by the value of an annuity?

A stream of identical future payments is worth in dollars today what is known as the present value of an annuity. To put it another way, it's the sum of the investments you would need to make today to equal the total of the annuity payments after accounting for the time value of money.

Given,

Cash Flow(CF)      Year 1            Year 2     Year 3      Year 4      Year 5

(Amt in million)       $1.2               $1.6         $2.0        $2.4           $2.8

Discounted rate = 10%

Additional cash Inflow = $1 million

Required to find annual salary =?

First, we have to find the Present value = CF1/(1+r)¹ + CF2/(1 + r)² + CF3/(1+r)³ + CF4/(1+r)⁴ + CF5/(1+r)

Present value = 1.2/(1+0.1)¹ + 1.6/(1+0.1)² + 2/(1+0.1)³ + 2.4/(1+0.1)⁴ + 2.8/(1+0.1)⁵

Present Value = 7.293 million

Now Increase Pv by 1 million + 7.293 = 8.293 million.

PMT = (PV)/(1+r)*(1-(1/(1+r)ⁿ)) x (1+r)

PMT = 8.293/(1/0.1) x (1-(1/(1+0.1)⁵)) x (1+0.1)

PMT = 1.98 which is 2.0 million approx.

Thus, The player's annual salary is $2 million.

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