Question

An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: Time Salary 0 $ 6,100,000 1 4,700,000 2 5,200,000 3 5,700,000 4 7,100,000 5 7,800,000 6 8,600,000 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 signing bonus of $9.6 million payable today and a contract value increase of $1,600,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is an APR of 5.1 percent compounded daily, what is the amount of his quarterly check? Assume 365 days in a year. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Quarterly check amount $

Answer 1

First we have calculate Effective annual rate (EAR) to calculate the PV of the present salary
EAR=(1+(5.1/365)%)^365-1			0.052319144	or	5.2319%
To Calculate the quaterly pay check first we calculate PV of the present salary
Time	Salary	Dis. Fact. =1/(1+5.2319%)^n	PV
0	6,100,000	1.00000	6,100,000
1	4,700,000	0.95028	4,466,326
2	5,200,000	0.90304	4,695,788
3	5,700,000	0.85814	4,891,394
4	7,100,000	0.81547	5,789,869
5	7,800,000	0.77493	6,044,460
6	8,600,000	0.73640	6,333,066
Total PV of the present Salary(Present Contract)			38,320,903
Add: Increase in the contract			1,600,000
Total Value of the New Contract			39,920,902.92
Less: Payment of bonus now			9,600,000.00
Pv of the money for which quaterly cheque to be paid			30,320,902.92
We have to find out Quaterly EAR
EAR=(1+(5.1/365)%)^91.25-1			0.012831	or	1.2831%
Calulation of the quaterly installment
=(30320902.92*1.2831%*(1+1.2831%)^24)/((1+1.2831%)^24-1)					1,475,887
Quaterly Instalment would be $1,475,887