Newman Long has just learned he has won a $514,700 prize in the lottery. The lot
ID: 2531622 • Letter: N
Question
Newman Long has just learned he has won a $514,700 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Newman takes all the money today, the state and federal governments will deduct taxes at a rate of 47% immediately. (2) Alternatively, the lottery offers Newman a payout of 20 equal payments of $36,400 with the first payment occurring when Newman turns in the winning ticket. Newman will be taxed on each of these payments at a rate of 25%. Click here to view factor tables Compute the present value of the cash flows for lump sum payout. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) Lump sum payout 272791 Assuming Newman can earn an 8% rate of return compounded annually on any money invested during this period, compute the present value of the cash flows or annuity payout (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to O decimal places, e.g. 458,581.) Present value of annuity payout Which pay-out option should he choose?Explanation / Answer
Present value of lump sum payout = $514700 x 57% = $272,791.
Present value of Annuity Payout:
Value of each annuity payout = 36400 - (36400 x 25%) = 36400 - 9100 = $27,300
Present value of annuity payout is calculated as follows:
Total Discounted Cash Flow = $27300 + $262177 = $289,477.
So the present value of annuity = $289,477
Conclusion: Newman Long will choose a payout of 20 equal payments @ tax rate of 25%
Note:
1. Since the first payment is received immediately its present value is the same.
2. After the first payment he will get 19 more equal payments for 19 years. So the annuity factor for 19 years @8% is taken for calculation.
At the end of year Cash Flow Present value annuity factor Discounted Cash Flow 0(Immediately) 27300 1 27300 1 - 19 27300 9.60356 262177