A creative general manager has offered two different contracts to a vain quarterback. The contracts are shown below:


CONTACT ACONTRACT B

YEAR

SALARY

YEAR

SALARY

0

$503,700.00

0

$303,650.00

1

$503,700.00

1

$303,650.00

2

$503,700.00

2

$802,150.00

3

$503,700.00

3

$802,150.00

4

$503,700.00

4

$802,150.00


The newspapers report the total dollars of the contract, so contract A will pay a total of $2,518,500.00, while contract B will pay $3,013,750.00. The player will select contract B as it has more publicity. The team can earn 8.00% on their investments, so let's determine the value of each contract.

To determine the value of each contract, we need to calculate the **present value** (PV) of the contracts. This is done by discounting each payment back to the present using the team's rate of return on investments, which is 8%. Here's the step-by-step process:

### Formula for Present Value:
\[
PV = \frac{C}{(1 + r)^t}
\]
Where:
- $C$ is the cash flow in a given year (i.e., salary),
- $r$ is the interest rate (8% or 0.08),
- $t$ is the time in years.

### Contract A

Contract A pays $503,700$ every year for 5 years, so we will compute the present value for each year's payment and sum them up.

\[
PV_A = \sum_{t=0}^{4} \frac{503,700}{(1 + 0.08)^t}
\]

### Contract B

Contract B pays:
- $303,650 in years 0 and 1
- $802,150 in years 2, 3, and 4

Thus, we calculate the present value for each of these payments as well:

\[
PV_B = \frac{303,650}{(1 + 0.08)^0} + \frac{303,650}{(1 + 0.08)^1} + \frac{802,150}{(1 + 0.08)^2} + \frac{802,150}{(1 + 0.08)^3} + \frac{802,150}{(1 + 0.08)^4}
\]

Let me calculate the present values for each contract.The present value of each contract, given the 8% rate of return, is:

- **Contract A**: $2,172,018.29
- **Contract B**: $2,498,898.47

Even though the total dollars for Contract B are higher, the present value calculation shows that Contract B is still worth more in today's dollars compared to Contract A, which would justify the player's preference for Contract B.

Would you like further details on the calculations, or do you have any questions?

Here are some follow-up questions for deeper understanding:

1. What would happen if the interest rate were higher or lower? How would it affect the present values?
2. Can we calculate the difference between the two contracts' present values at different interest rates?
3. How would adding a signing bonus to either contract impact its present value?
4. How does the concept of time value of money influence long-term contracts like these?
5. Why is it important to consider present value rather than just the total sum of payments?

**Tip:** Always use present value to assess future cash flows when investment returns or interest rates are involved.

A creative general manager has offered two different contracts to a vain quarterback. The contracts are shown below:

Contract A: 
Year 0: $503,700.00
Year 1: $503,700.00
Year 2: $503,700.00
Year 3: $503,700.00
Year 4: $503,700.00

Contract B: 
Year 0: $303,650.00
Year 1: $303,650.00
Year 2: $802,150.00
Year 3: $802,150.00
Year 4: $802,150.00

The newspapers report the total dollars of the contract, so contract A will pay a total of $2,518,500.00, while contract B will pay $3,013,750.00. The player will select contract B as it has more publicity. The team can earn 8.00% on their investments, so let's determine the value of each contract.

Understand how to calculate the present value of two sports contracts using an 8% discount rate. This problem involves concepts like discounting cash flows and the time value of money, providing a detailed analysis suitable for high school students in Grades 11-12.

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