Problem 6-59 Calculating Annuity Values [L01] An All-Pro defensive lineman is in

Question

Problem 6-59 Calculating Annuity Values [L01] An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: Time Salary 0 $%6,000,000 1 $4,600,000 2 5,100,000 3 $%5,600,000 4 $7,000,000 5 7,700,000 6 $8,500,000 All salaries are to be paid in lump sums. The player has asked you as his agent to renegotiate the terms. He wants a $9.5 million signing bonus payable today and a contract value increase of $1,500,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is 5 percent compounded daily, what is the amount of his quarterly check? Assume 365 days in a year. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Quarterly check amount

Explanation / Answer

To find the quarterly salary for the player, we first need to find the PV of the current contract. The cash flows for the contract are annual, and we are given a daily interest rate. We need to find the EAR so the interest compounding is the same as the timing of the cash flows. The EAR is:   

EAR = [1 + (0.05/365)]365 – 1 = 5.12%

The PV of the current contract offer is the sum of the PV of the cash flows. So, the PV is:

PV $6,000,000 + $4,600,000/1.0512 + $5,100,000/1.05122 + $5,600,000/1.05123
+ $7,000,000/1.05124 + $7,700,000/1.05125 + $8,500,000/1.05126

PV = $37,843,159.80

The player wants the contract increased in value by $1,500,000 so the PV of the new contract will be:

PV = $37,843,159.80 + 1,500,000 = $39,343,159.80

The player has also requested a signing bonus payable today in the amount of $9.5 million. We can simply subtract this amount from the PV of the new contract. The remaining amount will be the PV of the future quarterly paychecks.

$39,343,159.80 – $9,500,000 = $29,843,159.80

To find the quarterly payments, first realize that the interest rate we need is the effective quarterly rate. Using the daily interest rate, we can find the quarterly interest rate using the EAR equation, with the number of days being 91.25, the number of days in a quarter (365 / 4). The effective quarterly rate is:

Effective quarterly rate = [1 + (0.05/365)]91.25 – 1 = 0.01257, or 1.257%

Now we have the interest rate, the length of the annuity, and the PV. Using the PVA equation and solving for the payment, (Note: Using number of periods as 24, as we have 6 years and 4 quarters in a year) we get:

PVA = $29,843,159.80 = C{[1 – (1/1.0125724)] / 0.01257}

(Note: To calculate PVA use the formula or use PMT function in excel)

C = $1,448,186.10

Hence, the amount of quarterly check is $1,448,186.10

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