In: Finance
An All-Pro offensive lineman is in contract negotiations. The team has offered the following salary structure (note: today is Year=0). The appropriate discount rate is 12% per year, compounded monthly.
Year |
Salary ($) |
1 |
$3,500,000 |
2 |
$4,000,000 |
3 |
$4,500,000 |
4 |
$5,000,00 |
a) The lineman wants the timing of the payments modified. (He is happy with the overall value of the contract – so no increase in overall value, measured in PV terms -- is needed.)
Instead of the initial terms offered, he would like to receive a $3,000,000 signing bonus, today. In addition, he wants the remaining overall value of the contract paid out in equal quarterly installments (beginning one quarter from today) over the next four years (last payment at t=4. So, there are 16 quarterly payments). What payment amount should he receive each quarter (for the next four years)?
b) The lineman has changed his mind. He now wants the overall value of the contract increased by $2,000,000. In addition, he wants to receive quarterly payments (over the next four years) that grow by 2% each quarter. If the first quarterly payment is received one quarter from today and the last is received at t=4, what amount should he receive in the first quarterly payment (received 3 months from today)?
Please fully answer the question and show your work. Also, provide the formulas used to solve this problem.
The problem is related to Calculation of Present Value.
Year | Amount | Discount Factor | Calculation of Pv | ||
1 | 3500000 | 1.136 | 3976000 | ||
2 | 4000000 | 1.291 | 5164000 | ||
3 | 4500000 | 1.467 | 6601500 | ||
4 | 500000 | 1.667 | 833500 |
Total Present Value= 16575000
In order to calculate the present factor, the following formula has to be applied
Present Factor or Discount Factor= (1/1-discount factor)
In the above problem discount rate is equal to 12% per year, instead of yearly basis the lineman requires it on a quarterly basis of calcuations for installments.
a) if he recieves $3000,000 , then how much amount he recieves quarterly
=3000000*1/16*1/4 =$ 46875
Each quarter he should recieve $ 46875 for the next four years.
b) Given :- Previously $3000000 and now the overall contract increased by $2000000.
3000000+2000000*1/16*1/4= S78185
In each Quarter he should recieve 2% growth in payments for each quarter
78185*2/100= $1562.5
Hence overall first payment is 78175+1562.5= $79737.5