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

Year 1: $1.18 million

Year 2: $1.85 million

Year 3: $2.00 million

Year 4: $2.75 million

Year 5: $3.11 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 $1.92 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)? (Express answer in millions. $1,000,000 would be 1.00)

To find the player's new annual salary, we need to determine the present value (PV) of both the original contract and the desired contract with the 5-year **annuity due** structure.

### Step 1: Present Value of the Original Contract
The cash flows for the original contract are:
- Year 1: $1.18 million
- Year 2: $1.85 million
- Year 3: $2.00 million
- Year 4: $2.75 million
- Year 5: $3.11 million

To calculate the present value (PV) of these cash flows, we use the formula for the present value of a lump sum payment:

\[
PV = \frac{C}{(1 + r)^t}
\]

Where:
- $ C $ is the cash flow for the given year,
- $ r $ is the discount rate (10% or 0.10),
- $ t $ is the time in years.

Let's calculate the present value of each cash flow.

### Step 2: Total Present Value of the Original Contract
We will sum the present values of all 5 cash flows.

### Step 3: Present Value of the Desired Contract
The new contract is an annuity due, which means payments are made at the beginning of each year. The player wants the present value of this annuity due to be $1.92 million more than the present value of the original contract.

The present value of an annuity due is given by:

\[
PV = C \times \left(1 + r\right) \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]
\]

Where:
- $ C $ is the annual payment (what we need to find),
- $ r = 0.10 $,
- $ n = 5 $ (the length of the contract in years).

We know that the present value of the new contract needs to be:

\[
PV_{\text{new}} = PV_{\text{original}} + 1.92
\]

By calculating the present value of the original contract and substituting it into this equation, we can solve for the new annual salary $ C $.

Let me compute everything step by step.The present value of the original contract is approximately **$7.91 million**. To meet the player's demand of increasing the present value by $1.92 million, the player's new annual salary under the 5-year annuity due structure would be approximately **$2.36 million** per year.

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:
1. How does the calculation change if the discount rate is different?
2. What is the difference between an ordinary annuity and an annuity due?
3. How would the player's annual salary change if the contract duration was extended?
4. What impact does a higher or lower present value have on future salary expectations?
5. How do real-world factors such as taxes affect the present value of contracts?

**Tip:** When working with annuities, the timing of payments (beginning vs. end of the period) can significantly affect the present value calculation.

A baseball player is offered a 5-year contract that pays him the following amounts: Year 1: $1.18 million, Year 2: $1.85 million, Year 3: $2.00 million, Year 4: $2.75 million, Year 5: $3.11 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 $1.92 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)?

Solve a real-world problem involving a 5-year baseball contract with a present value increase of $1.92 million. Learn how to calculate the player's annual salary using present value and annuity due concepts, with cash flows discounted at 10%. Ideal for finance students.

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