Long Lottery Vertical Call Expected Value

At a $1.80 billion headline (annuity) jackpot, what is the expected value of a Powerball (offered in USA) lottery ticket?

About $0.01 when adjusted for federal taxes.

Assumptions:

* The jackpot is not split among multiple winners
* Discount rate is \~2.72% over 29 years (based on lump sum listed at Powerball.com)
* Assumes federal tax rate of 37% on entire winnings and no state taxes
* Ignores potential discounts to the EV as a function of "y" parameter in a CRRA utility function (i.e. results are risk-neutral and apply no discount for risk aversion / diminishing utility value of money)

How large must the jackpot be for each ticket to have an EV of $0.00 (i.e. ticket value = purchase price) with the same assumptions?

About $1.79 billion.

Play responsibly.

Edit: corrected double counting of ticket price and not adjusting the non-jackpot prizes for taxes. Updated image below. Credit to u/Strawberrybadger for catching the errors; thank you.

https://preview.redd.it/3khzn75gulnf1.png?width=1272&format=png&auto=webp&s=1da28b5c14333a82b5639bac654b1faca73f8597