So would anyone turn down a single life annuity with a 7% internal rate of return given a 3% COLA?
I'd take it, but not for my full portfolio. (up to 1/3rd or so).
So would anyone turn down a single life annuity with a 7% internal rate of return given a 3% COLA?
Exactly. Even with a COLA the underlying interest rate to support the annual inflation adjustment can be calculated, it's just an increasing annuity. So as my employer's pension has a COLA it bumps up the internal interest rate to 7% assuming a 3% annual COLA which is what it was last year. If I was to use 1970s inflation numbers like 10% for the COLA the interest rate would have to be 15%.
So would anyone turn down a single life annuity with a 7% internal rate of return given a 3% COLA?
You have won a $400 million lottery prize, consisting of 20 annual payments of $20 million each. How small would the lump sum option have to be in order for you to opt for $20 million per year over 20 years instead of the lump sum?
$300 million lump sum
$200 million lump sum
$100 million lump sum
$50 million lump sum
$25 million lump sum
$10 million lump sum
$5 million lump sum
$1 million lump sum
less than $1 million lump sum
I'd take it, but not for my full portfolio. (up to 1/3rd or so).
longinvest I would assume is referring to 'SPIAs realistically available'.
Since a main function of a SPIA is to offer protection against longevity risk a non-COLA one loses much of its appeal: By the time the longevity materializes cumulative inflation could have gone virtually anywhere.
I voted for 6%, I am 55 so my life expectancy is 25 years......
You should look at the latest life expectancy tables.....you have at least 3 years longer to live.
Really I used social securities Actuarial table. Is there a better source?
The few inflation adjusted annuities I looked at years ago seemed very expensive.
Yes they are...which is why I'm amazed that I get the chance to use $263k of my state retirement DC money to buy back into my state's DB pension and get $19.6k/year (70% of which gets a COLA) starting at 55. It seems that many people would like to have an inflation adjusted annuity in their portfolio if they were better value for money.
If I used the annuity PV calculator from your link correctly, a standard market quote (Immediate Annuities website) would yield this.
Immediate Annuity for 55yo male, not COLAd, produces:
Initial payment of $263k = ~$14.4k/year (not COLAd)
Discount rate ~ 3.5%
Compared to this, your DB purchase is a great deal. It's a shame all of us can't find such a deal.
Your 1.655% looked kind of low given current interest rates. So I did my own math.Ok, I have definitely learned something new today. I had been vaguely aware that lottery jackpot winners are given a lump sum option that tends to be roughly half the annuity option, and that the winners, without any exceptions that I have ever heard of, always prefer the lump sum. I now believe I know why.
Let's take the Powerball rules as an example. Using the following link, I see that Wednesday's Powerball drawing is expected to be $80 million, payable to the winner in 30 installments. But the installments aren't equal. The first one is $1,426,408 and the others seem to be the same $1,426,408, except that each year the amount is credited with 4% compounded growth. So the second payment is $1,483,464 and the 30th is $4,448,469 - more than three times the first payment, but you have to wait 29 years to get it. Ouch! Adding up all 30 payments, you get $80,000,000.
In contrast, the lump sum is $49,700,000. If you invested this amount, getting a 1.655% return per year, after 29 years you would have the same $80 million as you get from the 30 installment payments.
https://www.usamega.com/powerball-jackpot.asp
No doubt taking taxes into consideration would alter this calculation some. But there is no doubt in my mind that even financially unsophisticated winners have an intuitive sense that they aren't getting enough extra money to make it anywhere near the 29 year wait to collect all 30 installments.
Your 1.655% looked kind of low given current interest rates. So I did my own math.
Suppose I took the $49.7 million today, put it into some investments that earn x%, and withdrew $1,426,408 immediately, then $1,483,464 the next year, and so on until I withdraw $4,448,469 at the beginning of the 30th year.
What x is just enough that the last payment cleans out my account? My answer is 2.96%. Today's 5, 10, 20, and 30 year treasury yields are 1.63%, 2.36%, 2.80%, and 3.07%. The the 2.96% IRR on the lottery payout seems "reasonable" given those yields.
Of course, most people feel they can beat treasury yields.
I also had second thoughts about my calculations after I posted my results, and I think your calculations are a much fairer way of comparing options. My 1.655% answer ignores the fact that most of the installment payments are available before year 29 and can be invested in whatever the prize winner wants. If I take the installments as they are paid and invest them with an assumed 2.96% growth, the money will grow to $115,793,491.87 after 29 years. This compares to a lump sum of $49.7 million that will grow to $115,809,416.04 at the same 2.96% compounded growth. So your calculation is correct to within the three significant figures that you performed the math.Your 1.655% looked kind of low given current interest rates. So I did my own math.
Suppose I took the $49.7 million today, put it into some investments that earn x%, and withdrew $1,426,408 immediately, then $1,483,464 the next year, and so on until I withdraw $4,448,469 at the beginning of the 30th year.
What x is just enough that the last payment cleans out my account? My answer is 2.96%. Today's 5, 10, 20, and 30 year treasury yields are 1.63%, 2.36%, 2.80%, and 3.07%. The the 2.96% IRR on the lottery payout seems "reasonable" given those yields.
Of course, most people feel they can beat treasury yields.
That makes it much less financially ridiculous to choose annuitizing the payments, but I still can see why no one picks this option. Not only would almost everybody think they can invest their money and get more than 2.96% return, but the fact that the installment payments are heavily backloaded to the tail end of the 29 year period would make almost anyone wonder if they would live long enough to enjoy the full amount of their winnings.
I used online calculators for the present value of an increasing annuity and compound interest using the same interest rate for both calculations and adjusted the rate until the income match my pension income. I used the IRS life expectancy tables to come up with the number of periods. I then checked it with excel.
Present Value of a Growing Annuity
This way you can back out the interest rate as distinct from the payout rate, which is simply the ratio of the principal to the annual income you get....for a COLAed annuity/pension the payout rate changes....on my DB pension that starts at 7% at 55 and increases to 12% when I'm in my 80s.
I said 6%.
Alternative rates - You'd also have to consider what other interest rate options are. If the annuity 'yield' is only 3%, and I can get 3% on a 10 year CD, I'm going with the CD. If I happened to find an annuity that paid reasonably higher than other rates I could find, I'd look very closely at it....but, the odds of such an annuity existing outside of a sweetheart pension clause in some small municipality's pension set-up are probably slim.
Don't believe that I will ever have a need for an annuity, no matter what the rate offered. No place to vote.
Not even if you got one with a 7% interest rate for an actuarial mortality and used it in place of other fixed income in your portfolio, al a Wade Pfau?