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Actuarily Equivalent Pension?
Old 07-03-2017, 10:34 AM   #1
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Actuarily Equivalent Pension?

I have a relative who will be turning 55 this fall. They are considering taking their private pension at 55 (early) versus waiting until “full retirement age” of 65. The pension plan website provides preliminary estimates of the benefit for various scenarios. The benefit increases every year that commencement is delayed up to Age 65. I was expecting (and explaining) that the values would be actuarily equivalent, but now I’m not so sure.

As the simplest example, under “single life annuity”, the value provided at Age 55 is $2870 per month for life. The value provide at Age 65 is $3680 per month for life.

I don’t want to embarrass myself by explaining all the math I’ve attempted to check this, but does this spread look reasonable?
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Old 07-03-2017, 11:15 AM   #2
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The answer depends on the date of death, doesn't it? Any calculation of NPV has to begin with an estimated "expiry date" for cash flows.
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Old 07-03-2017, 11:19 AM   #3
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Go to immediateannunities.com and input the ages and dollar amounts and see the values of the two annuities, compare and you will answer the question.
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Old 07-03-2017, 11:42 AM   #4
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"actuarially equivalent" means that the early retirement benefit is equal to the benefit payable at normal retirement date (65) using an interest rate and mortality assumption - so it's essentially a deferred annuity factor divided by an immediate annuity factor

the haircut in your example is only about 22% so that seems like a subsidized reduction to me
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Old 07-03-2017, 11:43 AM   #5
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Quote:
Originally Posted by Meadbh View Post
Any calculation of NPV has to begin with an estimated "expiry date" for cash flows.
not really, when I calculate present values I go out to the end of the mortality table, which could be 110 or 120

a present value is a mathematical expectation not an annuity certain to expected age at death
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Old 07-03-2017, 12:01 PM   #6
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not really, when I calculate present values I go out to the end of the mortality table, which could be 110 or 120

a present value is a mathematical expectation not an annuity certain to expected age at death
Actually for annuities you take the remaining life expectancy and use that to calculate the payouts. Annuities are a way for insurance companies to take the other side of the bet they make on life insurance. On life insurance the company bets you will live longer than the life expectancy and would win on that, on annuities the company bets you die before you life expectancy would suggest. In both cases if the insurance company wins the bet they are money ahead, conversely if you win the bet you or your beneficiary are money ahead.
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Old 07-03-2017, 12:19 PM   #7
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Thank you for the replies. When I go to Immediateannuiteis.com the age 55 option has a present value of $606K. The Age 65 option has a present value of $469K. That seems like a big difference to me and I can’t explain it. (Too big to be “we used a different mortality table”) I don’t know any reason they would be subsidizing the earlier option. So much for my "They will be actuality equivalent" advice!
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Old 07-03-2017, 12:40 PM   #8
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Quote:
Originally Posted by meierlde View Post
Actually for annuities you take the remaining life expectancy and use that to calculate the payouts. Annuities are a way for insurance companies to take the other side of the bet they make on life insurance. On life insurance the company bets you will live longer than the life expectancy and would win on that, on annuities the company bets you die before you life expectancy would suggest. In both cases if the insurance company wins the bet they are money ahead, conversely if you win the bet you or your beneficiary are money ahead.
none of these examples use a finite life expectancy

https://en.wikipedia.org/wiki/Actuarial_present_value
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Old 07-03-2017, 12:52 PM   #9
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Originally Posted by Big_Hitter View Post
none of these examples use a finite life expectancy

https://en.wikipedia.org/wiki/Actuarial_present_value

Quoting from your Wikipedia article:

"The probability of a future payment is based on assumptions about the person's future mortality which is typically estimated using a life table."
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Old 07-03-2017, 01:03 PM   #10
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Quoting from your Wikipedia article:

"The probability of a future payment is based on assumptions about the person's future mortality which is typically estimated using a life table."
correct, but if you look at the last formula under annuities, tpx is the probability that a life aged x is alive x+t years from now. v^t is the that cash flow discounted

no where do any of the formulae use a finite life expectancy, just probabilities of death at each age from now until there is a 100% chance of death - the summations go to infinity but in practice most tables stop at age 110 or 120
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Old 07-03-2017, 01:08 PM   #11
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Originally Posted by Louis2 View Post
Thank you for the replies. When I go to Immediateannuiteis.com the age 55 option has a present value of $606K. The Age 65 option has a present value of $469K. That seems like a big difference to me and I can’t explain it. (Too big to be “we used a different mortality table”) I don’t know any reason they would be subsidizing the earlier option. So much for my "They will be actuarially equivalent" advice!
Yeah, that surprises me. The quotes probably come from two different companies so yes, they probably aren't using the same mortality table although I can't explain that kind of a difference just by mortality tables. They probably have different interest rate assumptions, which would have a bigger effect. (If the company thinks it can make a bigger return on investing your premium over the years it will give you a lower price.)

Did the site ask for more specific details such as smoking habits, whether you have a history of cancer or cardiac problems, etc.? That could explain some of the differences, too. Two companies may price those factors differently, Unlike life insurance, they give you a lower premium for an annuity if they think you'll die faster than average!
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Old 07-03-2017, 01:26 PM   #12
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The Immediateannuiteis.com data just backs up my offline calculations.

This person is better off taking the pension at 55 almost regardless of assumptions. Even assuming 0% return on any invested dollars, the break even point for (Age 55—$2870) versus (Age 65-- $3680) seems to be 45 years or 100 years old! If you assume some conservative rate of return, the break even point pushes out even farther.

This is a company pension, so the only factors being assumed are gender and age, I believe.

Again, thanks for everyone’s input.
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Old 07-03-2017, 01:39 PM   #13
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Quote:
Originally Posted by Louis2 View Post
I have a relative who will be turning 55 this fall. They are considering taking their private pension at 55 (early) versus waiting until “full retirement age” of 65. The pension plan website provides preliminary estimates of the benefit for various scenarios. The benefit increases every year that commencement is delayed up to Age 65. I was expecting (and explaining) that the values would be actuarily equivalent, but now I’m not so sure.

As the simplest example, under “single life annuity”, the value provided at Age 55 is $2870 per month for life. The value provide at Age 65 is $3680 per month for life.

I don’t want to embarrass myself by explaining all the math I’ve attempted to check this, but does this spread look reasonable?
This does not look reasonable to me using these numbers. Here is my math. YMMV
2870(x+120) = 3680x where x is in months
2870x + 344400 = 3680x
2870x - 2870x + 344400 = 3680x - 2870x
344400 = 810x
344400/810 = 810x/810
425 = x
x is 425 months = 35.4 years from age 65
x+120 = 545 months = 45.4 years from age 55
Your friend would need to live to 55 + 45.4 = 100.4 years of age to "break even" before considering investment returns squandered by waiting.

ETA: Louis beat me to it.
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Old 07-03-2017, 02:10 PM   #14
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Quote:
Originally Posted by Louis2 View Post
I have a relative who will be turning 55 this fall. They are considering taking their private pension at 55 (early) versus waiting until “full retirement age” of 65. The pension plan website provides preliminary estimates of the benefit for various scenarios. The benefit increases every year that commencement is delayed up to Age 65. I was expecting (and explaining) that the values would be actuarily equivalent, but now I’m not so sure.

As the simplest example, under “single life annuity”, the value provided at Age 55 is $2870 per month for life. The value provide at Age 65 is $3680 per month for life.

I don’t want to embarrass myself by explaining all the math I’ve attempted to check this, but does this spread look reasonable?
I just went to immediateannuities.com. A $622k premium for a 55 yo male in FL would provide a benefit of $2,870/month beginning in 1 month. If the same $622k is paid at age 55 but payments are deferred to 10 years to begin at age 65, then the monthly pension benefit would be $4,874/month.

However, your relative may want to check for each year... (55, 56, etc).... my pension had generous benefit increases from 55 to 60 but much less so from 60 to 65... so I waited and started my pension at 60.
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Old 07-03-2017, 02:22 PM   #15
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Annuity threads are guaranteed to demonstrate that internet forums are helpful, but sometimes all over the map with regard to quality of information.

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