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An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: |
| Time | Salary | ||||
| 0 | $ | 6,400,000 | |||
| 1 | 5,000,000 | ||||
| 2 | 5,500,000 | ||||
| 3 | 6,000,000 | ||||
| 4 | 7,400,000 | ||||
| 5 | 8,100,000 | ||||
| 6 | 8,900,000 | ||||
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All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate the terms. He wants a $9.9 million signing bonus payable today and a contract value increase of $1,900,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the discount rate is 5.4 percent compounded daily, what is the amount of his quarterly check? Assume 365 days in a year. |
SOLUTION:
AT FIRST WE SHALL CALCULATE EAR( EFFECTIVE ANNUAL RATE)
FORMULA : [1+(DISCOUNT RATE/365)]^365 - 1]
= [1+(.054/365)]^365 - 1]
=5.55%
NEXT WE SHALL FIND THE PRESENT VALUE FOR SALARY STRUCTURE BASED ON EAR
| Time | Salary | PV FACTOR @5.55% | PV VALUES |
| 0 | 6,400,000 | 1 | 6400000 |
| 1 | 5,000,000 | 0.9474 | 4737000 |
| 2 | 5,500,000 | 0.8976 | 4936800 |
| 3 | 6,000,000 | 0.8504 | 5102400 |
| 4 | 7,400,000 | 0.8057 | 5962180 |
| 5 | 8,100,000 | 0.7633 | 6182730 |
| 6 | 8,900,000 | 0.7232 | 6436480 |
| TOTAL | 39757590 |
NOW, THE PLAYER WANTS THE CONTRACT VALUE TO INCREASE TO &1,900,000/- AND A BONUS OF $9.9 MILLION
NOW PV FOR NEW CONTRACT WILL BE = $39,757,590 + 1,900,000 - 9,900,000 = $31,757,590
NEXT, SINCE ITS A QUARTILE CHECK, WE SHALL RECOMPUTE THE EAR QUARTERLY.
EAR(QUARTERLY) = [1+(DISCOUNT RATE/365)]^365/4 - 1]
= [1+(.054/365)]^365/4 - 1]
EAR QUARTERLY = 1.359%
SINCE ITS COMPUTED DAILY, WE SHALL FIND THE PVA(PRESENT VALUE ANNUITY )
PVA = $31,757,590= C{[1 - (1/1.01359)^24] / .01359}
AMOUNT OF QUARTERLY CHECK = $1,559,628.054
HERE N=24(6YEARS * 4 QUARTILES EACH)
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