I need help trying to figure this out!
The question is:


Several years ago tobacco companies agreed to pay states for health-care costs related to smoking. One of the states was awarded a settlement equal to 25 years of payments totaling $5.6 billion. Rather than wait 25 years to receive the money the state sold the receivable to an investment company for an immediate one time payment of $1.26 billion. Why was the state willing to accept $1.26 billion rather than the payments totaling $5.6 billion? Do you agree with the state’s decision to accept the one time cash settlement? Why?

Im thinking that the state accepted the money because maybe they will receive more from investing the money rather than waiting 25 years to receive small payments that will probably be getting taxed.
Im not sure.

You're on the right track, although the state isn't going to pay itself tax. Think of it this way - if a person agreed to give you $1.00 today or $1.00 a year now, clearly you would prefer to take the $1.00 now. How much would you be willing to accept a year from now in order to choose that instead? If you assume an interest rate of 5%, receiving $1.00 today is the same as receiving $1.05 in a year. Or to put it another way - if someone agreed to pay you $1.05 a year from now, you might decide to trade that $1.05 for $1.00 that you could get today. If interest rates are higher than 5%, you'd be willing to acept even less than $1.00 today. So the question for the state was this - is it better to take $1.26B today or $5.6B spread out over 25 years? If you assume an interest rate of I, the present value of the 25 payments of $224 million/year is:

$224M * [1 + 1/(1+i) + 1/(1+i)^2 + 1/(1+i)^3 +... + 1/(1+i)^24]

You can make a quick spreadsheet to do the math. I think you'll find that whoever made this deal with the state is getting an equivalent interest rate of about 15%, so it was a great deal for them, not so good for the taxpayers.