lottery case study

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Post on 28-Oct-2014




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+ Lottery Winnings

Looks Can Be Deceptive!

Financial ManagementSankar Akshay Goyal Jitesh Agarwal Srikanth Erraballi

+ Case Description

State Sponsored Lotteries

Annual Sales: Net Revenues: Retailer Commission: Lottery Prizes:

$1.69 bn $618.5 $120.3 mn $ 920.8 mn

The Big Game

7 States Georgia, Illinois, Maryland, Massacheusetts, Michigan, New Jersey & Virginia JackPot: Winning Amount: $5 mn -- $ 363 mn Annuitized Amount of $181.5 mn

The Michigan Lottery

Two Ways Annuity & Lump Sum

Income Tax: 27%State Tax: 4.6%

{ Amount> $5,000}

+Option 1: Annuity Payments

A total of $181.5 mn is paid over a period of 25 years through 25 equal installments.

Option 2: Cash Payment

60% of the total jackpot amount

+ Annuity Option

Future Value (FV) = $181.5 mn Present Value (PV) = 60% of $181.5 mn = $108.5 mn Number of Annuities = 25 FV = PV(CVF i,25yrs) $181.5 mn = $108.5 mn (CVF i, 25yrs)

=> i = 2%FV= A (CVFA2%, 25yrs) => A = $5.67 mn

+ Taxation on Annuity Option

Total Tax Percentage = 27% + 4.6% = 31.6%Annuity after tax deduction = (100 31.6)% of $5.67mn= $3.87828 mn

Net Amount received after 25 years = A (CVFA2%, 25yrs) Thus, net amount received after tax deduction = $124.22 mn

+ Lump Sum Option

Amount Receivable = 60% of $181.5 mn = $108.9 mnAmount receivable after tax deduction = $74.4876 mn Future Value of this amount invested at 2% for 25 years= $122.234 mn

+ Question 1

If you were one of the winners, which option would you select?


Since we get a greater amount through the annuity scheme, we would prefer to receive the lottery amount in annuities for a period of 25 years.

+ Question 2

If you decide to select the annuity option, how much money would you receive each year after taxes?


As has already been shown, the annuity receivable each year is $3.87828 mn.

+ Question 3

Is the state of Michigan justified in advertising the prize amount as $363 mn?


No. Since the winner receives only 60% of the prize amount at the time of winning, the prize amount should be advertised as $217.8 mn instead. In the annuity scheme, the advertised amount of $363 mn is the amount receivable after 25 years.

+ Question 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 4%?


Larry could start investing the annuities that he receives at the risk free market rate. This would increase the value he receives after 25 years!

+ Question 5

Why do most winners select the cash option plan when given a choice?


Since the amounts receivable through both the plans are almost equal (approx. $124 mn), the winners go with the cash option.


+ Question 6

If Michigan would like to give the annuity option an equal chance of being selected, how would it have to structure its payments?


Since the future value received through annuities depends more on the amount of each annuity than the number of annuities, the state could increase the annuity amount and decrease the number of years.


Thank You!!!Any doubts or queries are welcome


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