Question

In our class example, I simplified the “annuity” prize option by assuming level, equal annual payments. Actually, this annuity prize option is now on an annuitized prize payment schedule with 30 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 30 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 $200 million which is the undiscounted sum of the 30 annuity option payments with a Cash Option of $138 million. The first payment under the Annuity Option which would occur immediately is $3,010,300 with 29 additional annual payments with each payment being 5% larger than the previous one. Using this information and assuming you demand a 3.5% 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 30 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

Present value of each payment = payment / (1 + required return)^year

The total of the present values of the annuity payments is $112,125,302

The cash option present value is the cash amount itself, as it is received immediately. The cash amount is $138 million

As the present value of cash option is higher, the cash option should be chosen