Question

An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: Time Salary 0 $ 5,700,000 1 $ 4,300,000 2 $ 4,800,000 3 $ 5,300,000 4 $ 6,700,000 5 $ 7,400,000 6 $ 8,200,000 All salaries are to be paid in lump sums. The player has asked you as his agent to renegotiate the terms. He wants a $9.2 million signing bonus payable today and a contract value increase of $1,200,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is 4.7 percent compounded daily, what is the amount of his quarterly check

Answer 1

The amount of his quarterly check is $1,439,900.81.

Step-by-step explanation:

Note: The data on the salary structure offered in the question are merged together. They are therefore sorted before answering the question as follows:

Time Salary

0 $ 5,700,000

1 $ 4,300,000

2 $ 4,800,000

3 $ 5,300,000

4 $ 6,700,000

5 $ 7,400,000

6 $ 8,200,000

The explanation of the answer is now given as follows:

The amount of his quarterly check can be calculated using the following 4 steps:

Step 1: Calculation of effective annual rate (EAR)

Note: There is a need to calculate this because the interest rate in the question is compounded daily.

The effective annual rate (EAR) can be calculated using the following formula:

EAR = ((1 + (i / n))^n) - 1 .............................(1)

Where;

i = Interest rate = 4.7%, or 0.047

n = Number of compounding days in a year = 365

Substituting the values into equation (1), we have:

EAR = ((1 + (0.047 / 365))^365) - 1

EAR = 0.0481188377107922, or 4.81188377107922%

Step 2: Calculation of present of the cash of the contract offer

PV of the cash flow of the contract offer = ($5,700,000 / (1 + EAR)^Time) + ($4,300,000 / (1 + EAR)^Time) + ($4,800,000 / (1 + EAR)^Time) + ($5,300,000 (1 + EAR)^Time) + ($6,700,000 / (1 + EAR)^Time) + ($7,400,000 / (1 + EAR)^Time) + ($8,200,000 / (1 + EAR)^Time)

PV of the cash flow of the contract offer = ($5,700,000 / (1 + 0.0481188377107922)^0) + ($4,300,000 / (1 + 0.0481188377107922)^1) + ($4,800,000 / (1 + 0.0481188377107922)^2) + ($5,300,000 (1 + 0.0481188377107922)^3) + ($6,700,000 / (1 + 0.0481188377107922)^4) + ($7,400,000 / (1 + 0.0481188377107922)^5) + ($8,200,000 / (1 + 0.0481188377107922)^6)

PV of the cash flow of the contract offer = $37,861,722.19

Step 3: Calculation of present of the new contract

PV of the new contract = PV of the cash flow of the contract offer - Signing bonus payable today + Contract value increase = $37,861,722.19 - $9,200,000 + $1,200,000 = $29,861,722.19

Step 4: Calculation of quarterly check

Since the first paycheck is three months from now, this can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

PV = PV of the new contract = $29,861,722.19

P = Quarterly check = ?

r = Quarterly interest rate = EAR / Number of quarters in a year = 0.0481188377107922 / 4 = 0.012029709427698

n = number of quarters = number of years * Number of quarters in a year = 6 * 4 = 24

Substitute the values into equation (2) and solve for P, we have:

$29,861,722.19 = P * ((1 - (1 / (1 + 0.012029709427698))^24) / 0.012029709427698)

$29,861,722.19 = P * 20.738735546182

P = $29,861,722.19 / 20.738735546182

P = $1,439,900.81

Therefore, the amount of his quarterly check is $1,439,900.81.