###
The Lottery: Payments or Lump Sum?

I see that the Mega Millions Lottery is offering (a) $359 million
now or (b) $19.2 a year for 26 years. The gross value of the payment
stream is of course 19.2x26=$499.2 million. Hey, do the math and you'll
see that $499.2 tops $359 so take the deferred payments,
right?

Well, I gather that's that what the grownups want us to think. Don't take it now or you'll blow it. Take the payments, you'll do better in the long run.

But of course it's not right. Time is money and the present value
of the payment stream is the nominal value discounted at the
appropriate interest rate.

Anyway, try this. Assume you get your first payment today
and subsequent payments at the beginning of each of 25 more years. So
if you take the payments you are "paying" $339.8 ($359-$19.2) million.
What is the implied discount rate (internal
rate of return)? Excel says 2.85* percent per year.

So, what is *your* discount rate? If your rate is *lower* than 2.85percent, then the implied present value of the payment stream is
*higher* than 339.8. If lower, higher. Such is the conventional wisdom.

And is *this* right? Well, there's taxes. Not really my department, though I *think* you have to pay tax on the lump sum payment at the front end, but on the payments only as they come in, which seems to tilt the advantage towards payments. And I suppose with this kind of money, you may be able to get some Mitt Romney action.

Oh, wait--the "I" word, "inflation." I gather that discount rate is based on the long-term treasury rate. The rate is supposed to "impound" inflation. But it looks to me like the inflation rate is *already running *close to 3 percent--low by historical standards but still high enough to eat up all of the implied discount rate. And what are the chances that inflation in the future will stay that low, huh? Huh?

Short answer: take the money and run. What say you?

[h/t: Buce's friend Bruce.]
*See comments.
## 2 comments:

Hi, your Excel calculation fails to take into account compounding. The effective interest rate is less than 1.5%, not 2.6%.

Use a "future value of $1" accounting table, and you'll see that if $389,800,000 on-hand now is to grow to $540,000,000 after 25 years of compound interest, then the implied annual interest rate necessary is between 1% and 1.5%.

But your conclusion is correct: cash value option is better than the annuity payments because interest rates (and thus inflation) is unlikely to remain at the current historic lows.

Actually, there was a computational error in the original: the correct number is 2.85, not 2.6 (I must have used the wrong number of periods). But the formula does account for compounding. It's the Excel internal rate of return. To double check, discount each of the payments as PT(1.0285)^t, and sum. You'll get $339.80. Not sure what $389.8 has to do with it, nor $540.

If you ask: what is the implied rate of return when $339.8 grows to $499.2 over 25 years, the answer is 1.55 percent ((FV/PV)^(1/25)-1], but that is an entirely different question from the one I was undertaking to answer. I.e., I wasn't asking for the 25-year value, only for the DPV of payments from the time at which they were paid.

43889

Post a Comment