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 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 $300 million which is the undiscounted sum of the 26 annuity option payments with a Cash Option of $207 million. The first payment under the Annuity Option which would occur immediately is $4,515,432 with 29 additional annual payments with each payment being 5% larger than the previous one. Using this information and assuming you demand a 4% 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. (Please use excel)

2. A comparison of the present value of all the payments under the Annuity Option and the present value of the Cash Option.

3. Use the Excel IRR function to find the interest rate that equates the PV of the annual payments with the cash option. This is the rate of return that the annuity option pays. Hint: you will have to deduct the first annual payment from the cash option amount for the initial (time zero) cash flow to calculate this rate.

4. Your decision.

Answer 1

Part (1)

The complete schedule

Payment no.	Cash flows
1	4,515,432.00
2	4,741,203.60
3	4,978,263.78
4	5,227,176.97
5	5,488,535.82
6	5,762,962.61
7	6,051,110.74
8	6,353,666.28
9	6,671,349.59
10	7,004,917.07
11	7,355,162.92
12	7,722,921.07
13	8,109,067.12
14	8,514,520.48
15	8,940,246.50
16	9,387,258.83
17	9,856,621.77
18	10,349,452.86
19	10,866,925.50
20	11,410,271.77
21	11,980,785.36
22	12,579,824.63
23	13,208,815.86
24	13,869,256.66
25	14,562,719.49
26	15,290,855.46
27	16,055,398.24
28	16,858,168.15
29	17,701,076.56
30	18,586,130.38

Part (2)

Please see the table below. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

PV of cash option = $ 207 mn = $ 207,000,000

Part (3)

Part (4)

My decision: Since PV of the cash option > PV of the annuities, my decision will be to choose the cash option