Problem 6-59 Calculating Annuity Values (LO1] An All-Pro defensive lineman is in

ID: 2816095 • Letter: P

Question

Problem 6-59 Calculating Annuity Values (LO1] An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: Salary ime 0$5,900,000 1$4,500,000 2 $5.000000 3 $5.500,000 4 $6,900,000 5 $7600000 6 $8,400,000 All salaries are to be paid in lump sums. The player has asked you as his agent to renegotiate the terms. He wants a $9.4 million signing bonus payable today and a contract value increase of $1,400,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is 4.9 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, 3216.) 19 of 25

Explanation / Answer

First calculate the PV of the current contract. The cash flows are given on annual basis with daily interest rate.

Then calculate the EAR to convert it into annual interest rate

EAR = [1+(0.049/365)]^365 -1

=(1.000134)^365-1

=1.050122- 1

=0.050122 or 5.01%

Now calculate the PV of contract value

Year

Salary

PVIF @5.01%

5,900,000

5900000

4,500,000

0.9524

4285800

5,000,000

0.907

4535000

5,500,000

0.8638

4750900

6,900,000

0.8227

5676630

7,600,000

0.7835

5954600

8,400,000

0.7462

6268080

37371010

It is given in the question that the player wants to increase the value by $1400000.

In this case the PV of new contract will be = 37371010+1400000 = 51371010

It is given that he wants a $9.4 million signing bonus payable today. Hence deduct the amount from the new PV =51371010- 9,400,000 = 41971010

Calculation of the value of pay check with quarterly interest rate:

EAR = [1+(0.049/365)^365/4 - 1

=(1.000134)^91.25-1

=1.0123-1=0.012

Amount of check = 41971010 = A[1-(1/1.0123)^24] / 0.0123

41971010 =A[1-(0.9878^24] / 0.0123

41971010 =A[1-0.7457] / 0.0123

41971010 =A[0.2543/ 0.0123]

41971010 =A(20.67)

41971010 =41971010 = A(20.6728)

A = 2030252.8

Therefore the amount of his quarterly check is 2030252.8