Question

In our class example, I simplified the “annuity” prize option by assuming level, equal annual payments. Actually, this annuity prize option us now on an annuitized prize payment schedule with 26 beginning of year payments that start at a lower amount with each successive payment being 5% higher than the previous annual payment. The sum of these 26 annuitized payments equal the announced estimated jackpot amount with a lower one-time lump-sum payment also being available as the Cash Option. A recent Mega Millions estimated jackpot amount is $227 million which is the undiscounted sum of the 30 annuity option payments with a Cash Option of $134 million. The first payment under the Annuity Option which would occur immediately is $8,730,769 with 25 additional annual payments with each payment being 5% larger than the previous one. Using this information and assuming you demand a 4.5% annual return, would you prefer the Annuity Option or the Cash Option if you have the winning ticket? Please include the following to support your decision: 1. A complete schedule of all 26 annual payments under the Annuity Option. 2. A comparison of the present value of all the payments under the Annuity Option and the present value of the Cash Option. 3. Your decision.

Answer 1

Answer 1:

Given:

First annual payment (occurs immediately) = $8,730,769

Each subsequent annual payment is higher by 5%

Number of total payments made (at the beginning of each year) = 26

Expected annual return = 4.5%

Let us assume cash option = $285 million

Let us calculate the schedule of 26 annual payments, PV factor for each year at 4.5% and PV.

Year 1 annual payment = $8,730,769, since it is paid immediately at the start of year PV = $8,730,769

Year 2 annual payment = $8,730,769 * (1 + 5%).

As the amount is paid at the beginning of 2nd year, which is as good as end of year 1, the PV factor = 1 / (1+4.5%) and

PV will be = $8,730,769 * (1 + 5%). * {1 / (1+4.5%)}

Similarly PV of Year 3 annual payment = $8,730,769 * (1 + 5%)² * {1 / (1+4.5%)²}

This way we calculate below Annual payment schedule, PV factor and PV for all 26 years.

Answer 2:

We find that Jackpot amount is $446,259,758 and PV of all 26 annual payments = $241,110,829

As the cash option gives the amount immediately, the PV of cash option will be same as cash option given. If the cash option is $285 million, PV of cash option will be same = $285 million.

On comparison, we find PV of cash option higher than PV of annual payment under annuity options.

Answer 3:

As the PV of cash option is higher than the PV of annual payment under annuity option, I shall prefer cash option. If I get cash option of any amount higher than $241,110,829, I shall prefer cash option.