lottery case study

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+ Lottery Winnings

Looks Can Be Deceptive!

Financial ManagementSankar Akshay Goyal Jitesh Agarwal Srikanth Erraballi

+ Case Description

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.

A RUPEE IN HAND IS BETTER THAN TWO IN THE FUTURE!

+ 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?