On march 17, 2016 you won 527.25 million in the Powerball lottery. The Multi-State Lottery Association gave you the choice of 30 equal annual payments with the first payment of 17.575 million due on the day you claimed your prize. The remaining 29 payments follow at on year intervals. Alternatively, you can elect to take a lump sum payout on the day you claim your prize.
1: in general, how would you decide between future annual payments and a lump sum payout?
The present value of future cash flow for 29 years and today value will be compared with the lump sum payment being made today, if the present value is more than lump sum payment then the future cash annual payments will be accepted otherwise the lump sum payment will be accepted.
2: Determine the lump sum payout that you would be offered if the Multi-State Lottery association uses a discount rate of 4%.
PVIF at 4% for 29 years = (1-1/1.0429)/.04 = 16.9837
The PV of 29 payments = 17.575*16.9837 = = 298.489 million + 17.575 = 316.064 will be the lump sum payout.
3: Assuming that the total payments remain unchanged, would you prefer that the payments increase, decrease or remain constant through time? Explain your response.
The more payment in the starting years will create the more present value of future cash flow, therefore I would like to accept higher amount of payments in the beginning years and then lower amount of payments in the later years.
4: Assume instead the Lottery has offered you a payment of $21.7 million on the day you claim your prize and 19 additional payments at one year intervals each increasing by 2%. Prepare an Excel spread sheet to answer the following questions. In order to receive credit for your answers, you must attach a copy of your spreadsheet using the "show formulas" option. You must also use Excel's NPV function to calculate the present values.
a: Calculate the 19 additional annual payments using the future value formula.
b: Assuming a discount rate of 2%, calculate the lump sum payout you would receive. How do you know this answer is correct?
434 million
As it is equal to 21.70*20 = 434, because the discount rate and the growth rate of 2% are the same.
c: Assuming a discount rate of 4% determine the lump sum payout.
363.16 million
d: Assuming a discount rate of 8% determine the lump sum payout.
266.07 million
e: Assuming the Multi-State Lottery Association offer you a lump sum payout of million, determine the discount rate used by the Multi-State Lottery Association to compute the payout. Round your answer to the nearest percent.