Earlier this year the Mega Millions lottery jackpot prize pool was advertised as $1.602 billion. The winner had a choice of 2 payout options:

Growing Annuity. The winner can choose to take his or her prize over 30 graduated payments, with the first paid immediately and the rest paid annually over the next 29 years. Each payment is 5% larger than the previous one. Currently, for every $100 million in the prize pool, the first payment is $1,505,144 and eventually grows to $6,195,375 by the last payout.

Lump Sum Today. The winner can choose to receive a smaller cash amount all upfront in a lump sum. The lump sum amount is calculated based on what the lottery program would need to invest in U.S. government securities in order to fund the annual payouts under the annuity option. For this jackpot, lottery winners would be offered $48.9 million lump sum per $100 million in the jackpot prize pool.

a) Compute the NPV of the 2 payout options for a $1.602 billion prize pool, with a discount rate of 6.00%.

b) At what discount rate would these 2 options be equivalent? (hint: one method is to use Goal Seek or Solver in Excel)