Beijing University of Aeronautics and Astronautics, BUAA
Lottery Winnings – Looks Can Be Deceptive!
Submitted to: Prof. BAI MING
Date of submit: 02/November/2015
An anonymous from Michigan has stepped forward as the winner of the most recent $181,5 million The Big Game Lottery. Lucky Guy! Now comes the hard part. But what happens when you actually win?
Normally the answer appears to be "take all the money up front immediately and subsequently squander every available penny on frivolous ...view middle of the document...
The annual payments come with a maximum assurance and may even be larger than you expected if the market does well.
2. If you decide to select the annuity option, how much money would you receive each year after taxes?
Under the annuity option, the winner is paid the advertised prize money in 26 equal parts after taxes are withheld. The calculation is as follows:
Before tax annuity= $ 181 500 000/26= $ 6 980 769, 23
After tax annuity = $ 6 980 769, 23 – 0,322($ 6 980 769, 23) = $ 4 732 961, 54
Where 0,322 is total tax rate (28% + 4.2%)
* 3. Is the State of Michigan justified in advertising the prize amount as $363 million? Explain.
On the one hand, we think that it is not really justified: the whole amount of the prize might be $363 million, but there is no warning about how it is divided in case of multiple winners. Apart from that, if the winner wants to take the prize in cash, he will just get the 50% of the whole amount (before taxes). To sum up, the prize amount is over stated.
On the other hand, we should realize that it is being used for the advertisements of the lottery: the state wants as many people as possible to join the game and therefore increase its own benefits. So, as a marketing campaign, to advertise the lottery using the higher prize amount can be justifiable.
* 4. If the only option available were an annuity payment plan, what could Larry do to maximize the value of his winnings assuming that the risk-free rate of interest is 5%.
Larry could sell off the Annuity to the professional firms in exchange for a lump sum and then invest the money in buying stocks or bonds. Larry can face many different situations according the discount interest that professional firms will cut. Here are present value (or the amout of money that Larry could get selling his annuity and being charged with different rate). To calculate it the following formula was used:
PV=A*(1+i)N-1i*(1+i)N, where n=26, A=4 732 961, 54
Then we assuming that Lurry invests the lump sum he got from the firm with the annual interest rate of 11% for the same 26 years, we also assume that Larry's future income will be charged with 25% of income tax rate.
, where n=26, i=11%
RATE | PRESENT VALUE | | Rate | Duration | Future Value | FV After Tax |
0,05 | 68037191,40 | | 0,11 | 26 | 1025991649,09 | 769493736,8 |
0,10 | 43358397,64 | | 0,11 | 26 | 653838775,25 | 490379081,4 |
0,15 | 30719588,28 | | 0,11 | 26 | 463247238,58 | 347435428,9 |
0,20 | 23458081,17 | | 0,11 | 26 | 353744693,08 | 265308519,8 |
0,30 | 15759338,41 | | 0,11 | 26 | 237648692,84 | 178236519,6 |
If Larry decided do not sell the anuuity he won and just invests the annuity with the 5%...