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I tried looking at the chegg answers for this question (same question with different numbers), but each of them used different ways to solve it,

I tried looking at the chegg answers for this question (same question with different numbers), but each of them used different ways to solve it, so I'm confused about which one's the right one.

If any excel formula is used, please show that! Please briefly explain the working. Thank you so much!!!

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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.

At the end of July, someone in Illinois won the Mega Millions estimated jackpot of $1,337 million ($1.337 billion) which is the undiscounted sum of the 30 annuity option payments with a Cash Option of $780.5 million. The first payment under the Annuity Option which would occur immediately is $20,123,769 with 29 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 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. 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.
  5. Finally, imagine you elect the cash option and buy a 30-year annuity-due that has equal annual payments with a 4.5% rate of return. What would be your annual annuity payment?

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