"It's the cash value that the lottery starts with, and then it calculates the annuity based on prevailing interest rates."
I know how it works. That's why I commented about a cash value increase of about $7 million being reported as a $30 million increase in the advertised value. I think most of the other people here know it, too, but the advertised annuity value is what we see most from the lotteries, and I hear there's also a well know website that uses it more than the cash value, titling articles something like "$600 MILLION: Mega Millions jackpot soars after no winner Friday" for example. And the people around here, though virtually all of them would take the cash, also tend to discuss jackpots based on the advertised value. When the first post mentioned the chance of reaching a billion we all know it's a reference to the advertised jackpot, so that's what my reply was based on.
Of course we sometimes get newbies that aren't familiar with how it works.
"How do they figure this out? Why wouldn't always be the same?"
The lotteries start by selling tickets and collecting money from the players. In the case of (most) jackpot games they put most of that money into the "prize pool" for the jackpot and smaller amounts into the prize pools for the smaller prizes. Virtually everyone who wins a jackpot takes that cash as their prize, but for at least 40 years the lotteries have offered (and advertised) the jackpots as an annuity paid out over a period of years (in the past the annuity was the only choice, and was usually paid out in 20 annual installments).
On the rare occasions that a winner chooses the annuity the lotteries use the cash from the jackpot prize pool to buy an annuity. Because annuities are investments and interest rates vary, the size of the annuity that can be bought with a given amount of money varies with changes in interest rates. Even though most winners take the cash the lotteries advertise the (higher) annuity value.
"do you think record low mortgage rates and that like have a bearing on cash value?"
Of course Todd is correct that the lotteries actually start from the cash they have, so cash value depends strictly on ticket sales. The annuity value is based on what the invested cash would earn. Because people here usually discuss things based on the annuity value I usually work backwards from it, but that 73.7% figure I used in the first post is the inverse of the 1.357 rate that determines that the $442.4 million cash can buy an annuity that will pay a total of $600 million. The 1.357 isn't an interest rate. It's a conversion rate that's based on the interest rate and the payment schedule, so 442.4 cash * 1.357 annuity rate = 600.3368 total annuity payments.
Mortgages are an investment the banks make, and they're a lot like an annuity - they loan you money up front and you give them a payment every month for a fixed period, and the total of those monthly payments is more than the initial mortgage amount. There's a relationship between mortgage and annuity rates, but they're not directly connected. They're both low right now (along with car loan and CD rates) for the same general reasons.