Lump Sum vs Annuity

[hnzw_rui]

I agree. Below is a IRR analysis based on a quote for a 5.78% payout rate for a 55 year old male from immediate annuities.com. Note that the IRR converges towards the payout rate at older ages.

Stands to reason IRR convergence point is the same as payout rate as that's the rate at which you just make payouts from interest only never needing to touch the principal. Of course, it'll probably take a hundred years or so to reach anywhere near that point.

For fixed COLA, just add it to the initial payout rate (e.g. if COLA is 2%, convergence is at 7.78%).

By the way, IRR seems wrong for the first couple of years. How is it lower than -100%? Mind, Excel does have a built-in IRR function.

 

[pb4uski]

It can be lower than -100%. Remember,the definition of IRR is the discount rate that makes a series of cash flows equal to zero.

The proof is to calculate the PV using the IRR for the requisite periods (in this case months).

=PV(-348.329193618076%/12,12,-482)
=$100,000

So the PV of 12 payments of $482 at -348.32919361876% annually is $100,000 so the IRR is -348.32% or

		-348.3%
Month	Pmt	PV
1	482	679.14
2	482	956.90
3	482	1,348.27
4	482	1,899.70
5	482	2,676.67
6	482	3,771.41
7	482	5,313.90
8	482	7,487.26
9	482	10,549.51
10	482	14,864.21
11	482	20,943.60
12	482	29,509.43
		100,000.00

or alternatively create a list of cash flows of -$100,000 and $482 for 12 months, compute the IRR using Excel's IRR function and you'll get -29.03%, but then you need to multiply that by 12 to get an annual rate since the $482 are monthly payments.

	-348.33%
-100000	-29.03%
482
482
482
482
482
482
482
482
482
482
482
482

 

[hnzw_rui]

It can be lower than -100%. Remember,the definition of IRR is the discount rate that makes a series of cash flows equal to zero.

The proof is to calculate the PV using the IRR for the requisite periods (in this case months).

=PV(-348.329193618076%/12,12,-482)
=$100,000

So the PV of 12 payments of $482 at -348.32919361876% annually is $100,000 so the IRR is -348.32%

Think about it. If you have an IRR of -348%, that means future value isn't even 0, it's already in the negative. A -100% IRR means your lump sum drops from 100,000 to 0 without any withdrawals. If you have -348%, your lump sum drops from 100,000 to -248,000. Remember, the rate function is based on compounding for a specific number of periods. It's not a simple average.

By the way, if the rate was correct, PV on the first table in post #53 should all be -$100,000.

In this case, I think the better option in order to get the annual IRR would be to do the ff:

RATE(NPER_Years,PMT_Monthly*12,-PV)

Mind, doing the above matches IRR of yearly distributions of $5,784 ($482 * 12).

Years	Cash Flow	IRR
	-100000
1	5,784	-94.2160%
2	5,784	-72.8848%
3	5,784	-54.1246%
4	5,784	-40.5641%
5	5,784	-30.8815%
6	5,784	-23.8286%
7	5,784	-18.5614%
8	5,784	-14.5340%
9	5,784	-11.3894%
10	5,784	-8.8889%

 

[nun]

8.4% comes from a more detailed analysis I did. The pension actually pays a COLA on the first $13.5k and for the last few years its been 3%, but I've projected the increase on the COLA amount given historical data. I am not confusing payout rate with interest rate. This is a DB pension plan and not a commercial annuity. I would not buy a commercial annuity now, but given the chance to buy into a DB plan that returns 7.7% using current numbers and if I live an average lifespan, I'm not going to pass that up.

With any annuity with no COLA the IRR cannot ever be greater than the payout rate. The IRR will asymptotically approach the payout rate as you get older.

If you have a COLA the IRR can be larger than the initial payout rate. My payout rate is 7.4%, but with a simple 2% COLA and living to 82 the IRR is 7.7%

My main point in all this is that people need to know how to assess an annuity before they dismiss them out of hand. This is even more important if you are buying a deferred annuity. The difficulty is you have to assume lifespans and the return you might expect on your money if you kept it in the market.

 

[pb4uski]

After further review, I concede. I had a glitch in the compounding calc converting from monthly to annual. For one year, the IRR is -98.37% (sticking with monthly benefit payments).

n	n in years	Cash flow	PV factor	Cash flow
0	-	(100,000.00)	1.00	(100,000.00)
1	0.083	482.00	1.41	679.14
2	0.167	482.00	1.99	956.90
3	0.250	482.00	2.80	1,348.27
4	0.333	482.00	3.94	1,899.70
5	0.417	482.00	5.55	2,676.67
6	0.500	482.00	7.82	3,771.41
7	0.583	482.00	11.02	5,313.90
8	0.667	482.00	15.53	7,487.26
9	0.750	482.00	21.89	10,549.51
10	0.833	482.00	30.84	14,864.21
11	0.917	482.00	43.45	20,943.60
12	1.000	482.00	61.22	29,509.43
				(0.00)
IRR per period (month)	-29.03%
Coverted to annual rate		-98.37%

Though it is a bit academic as it is painfully obvious that if you buy an annuity and die soon thereafter that its a big time losing proposition.

 

[Big_Hitter]

yes but it would be a stress free death

 

[hnzw_rui]

After further review, I concede. I had a glitch in the compounding calc converting from monthly to annual. For one year, the IRR is -98.37% (sticking with monthly benefit payments).

n	n in years	Cash flow	PV factor	Cash flow
0	-	(100,000.00)	1.00	(100,000.00)
1	0.083	482.00	1.41	679.14
2	0.167	482.00	1.99	956.90
3	0.250	482.00	2.80	1,348.27
4	0.333	482.00	3.94	1,899.70
5	0.417	482.00	5.55	2,676.67
6	0.500	482.00	7.82	3,771.41
7	0.583	482.00	11.02	5,313.90
8	0.667	482.00	15.53	7,487.26
9	0.750	482.00	21.89	10,549.51
10	0.833	482.00	30.84	14,864.21
11	0.917	482.00	43.45	20,943.60
12	1.000	482.00	61.22	29,509.43
				(0.00)
IRR per period (month)	-29.03%
Coverted to annual rate		-98.37%

Though it is a bit academic as it is painfully obvious that if you buy an annuity and die soon thereafter that its a big time losing proposition.

There still seems to be something wrong in those calcs. If you were able to get one full year's worth of payments (5,784), IRR for the first year would be (100,000 - 5,784) / 100,000 or 100% minus payout rate which is -94.216%.

But yes, dying immediately after you buy an annuity sucks for the retiree. Very profitable for the insurance company, though. If I were buying, life with 20-year period certain is what I'll probably get (~0-1% IRR at 20 years). However, given the effects of inflation, I'd be more inclined to create an I-bonds ladder sufficient to supplement SS to cover necessities.

 

[hnzw_rui]

yes but it would be a stress free death

Lol, that's certainly true as long as you don't plan on leaving anything to your heirs.

 

[nun]

To worry about dying soon after you buy an annuity for money reasons seems to miss the point that you are dead. If you are worried about heirs then you should not be planning on spending down your retirement money and should stop using the 4% rule. Also I forgot to mention that my DB plan has a contingent beneficiary so they get a lump sum payment if I die early.

 

[hnzw_rui]

To worry about dying soon after you buy an annuity for money reasons seems to miss the point that you are dead.

Alas, just because you're dead doesn't mean some obligations disappear. One of my grandmothers lived to 89 years and 361 days and outlived 4 out of her 7 children. The other is 92 and still okay physically although she has dementia now. Should I predecease my parents, I'm hoping to leave them well provided for with a steady income stream.

 

[nun]

Alas, just because you're dead doesn't mean some obligations disappear. One of my grandmothers lived to 89 years and 361 days and outlived 4 out of her 7 children. The other is 92 and still okay physically although she has dementia now. Should I predecease my parents, I'm hoping to leave them well provided for with a steady income stream.

I'm planning on leaving my grand nieces enough money to be comfortable. So I'm not doing the 4% SWR thing at all. I'm using 18% of my portfolio to buy into my DB pension and I'll keep reinvesting dividends on the rest. My plan is to be in the accumulation phase until I die.

My opinion is that people don't go into retirement with enough diversification. They carry very similar AAs into retirement as they had while they were working; having just stock and bond funds isn't enough for me. Of course the alternatives are pretty poor today as the traditional DB pension is rare and annuities are very expensive in this low interest rate environment. I think it was pretty unanimous the the OP should take the pension being offered rather than the lump sum so obviously the pension/annuity route is a good one when the circumstances and offer are right. I-bonds, a stable value fund or rental real estate might be good additions to many retirement portfolios when a DB pension or good value annuity isn't an option. Of course there is SS, but for the early retiree that isn't available and I think they take on a lot of risk by relying on a market based total return approach if they retire around 55.

 

[pb4uski]

There still seems to be something wrong in those calcs. If you were able to get one full year's worth of payments (5,784), IRR for the first year would be (100,000 - 5,784) / 100,000 or 100% minus payout rate which is -94.216%. ....

Did you follow the math in the table?

 

[hnzw_rui]

After further review, I concede. I had a glitch in the compounding calc converting from monthly to annual. For one year, the IRR is -98.37% (sticking with monthly benefit payments).

n	n in years	Cash flow	PV factor	Cash flow
0	-	(100,000.00)	1.00	(100,000.00)
1	0.083	482.00	1.41	679.14
2	0.167	482.00	1.99	956.90
3	0.250	482.00	2.80	1,348.27
4	0.333	482.00	3.94	1,899.70
5	0.417	482.00	5.55	2,676.67
6	0.500	482.00	7.82	3,771.41
7	0.583	482.00	11.02	5,313.90
8	0.667	482.00	15.53	7,487.26
9	0.750	482.00	21.89	10,549.51
10	0.833	482.00	30.84	14,864.21
11	0.917	482.00	43.45	20,943.60
12	1.000	482.00	61.22	29,509.43
				(0.00)
IRR per period (month)	-29.03%
Coverted to annual rate		-98.37%

Did you follow the math in the table?

I was kinda sleepy when I looked at first looked at it. After a second review, you've got your cash flow on the far right column inverted. Yes, -98.37% is compounded rate [(1 - 0.2903)^12 - 1] but doing it this way disregards your cash flow.

I'm thinking we're probably going to need some complicated ln formula or something to convert the monthly rate at month 12 to the annual rate.

Consider the ff:

PV(-29.03%, 12, 482) = -100,000.00

PV(-98.37%/12, 12, 482) = -10,530.03

PV(-98.37%, 1, 482*12) = -354,113.19

n in Months	Initial Balance	Gain/Loss	Distribution	Total Cash Flow	Ending Balance
1	100,000.00	-29,027.43	-482.00	-29,509.43	70,490.57
2	70,490.57	-20,461.60	-482.00	-20,943.60	49,546.97
3	49,546.97	-14,382.21	-482.00	-14,864.21	34,682.75
4	34,682.75	-10,067.51	-482.00	-10,549.51	24,133.24
5	24,133.24	-7,005.26	-482.00	-7,487.26	16,645.98
6	16,645.98	-4,831.90	-482.00	-5,313.90	11,332.08
7	11,332.08	-3,289.41	-482.00	-3,771.41	7,560.67
8	7,560.67	-2,194.67	-482.00	-2,676.67	4,884.00
9	4,884.00	-1,417.70	-482.00	-1,899.70	2,984.30
10	2,984.30	-866.27	-482.00	-1,348.27	1,636.06
11	1,636.03	-474.90	-482.00	-956.90	679.14
12	679.14	-197.14	-482.00	-679.14	0
Monthly Rate	-29.02743%

 

[pb4uski]

....After a second review, you've got your cash flow on the far right column inverted. ....[/TABLE]

Sorry... far right column was mislabled... it is not cash flow... it is PV of cash flow which is the cash flow (in the third column) multiplied by the PV factor in the 4th column. The PV factor is 1/(1+i)^n where i is the -.983... and n is in years or fractions thereof.

As an example, the PV factor for the 11th month is 1/(1+-0.983666239766709)^(11/12)= 43.45

The -98.37% can be derived as =((1+-0.2903)^12)-1 which is odd but thankfully I don't very often work with negative interest rates/

 

[tcaron20]

I have been looking at annuities in place of my pension to see if I can do better and preserve the annuity payment for heirs.
Anyone found a great deal on an income indexed annuity?

Tom C.


Sent from my iPad using Early Retirement Forum

 

[ETFs_Rule]

I have been looking at annuities in place of my pension to see if I can do better and preserve the annuity payment for heirs.
Anyone found a great deal on an income indexed annuity?

Tom C.


Sent from my iPad using Early Retirement Forum

Bad move. Have fun earning 2 - 5%.
The Ugly Truth about Equity Index Annuities

Also there's no such thing as a "great deal" with insurance products. They are all variations of the same thing. None are playing Santa Claus.

 

[nun]

I have been looking at annuities in place of my pension to see if I can do better and preserve the annuity payment for heirs.
Anyone found a great deal on an income indexed annuity?

Tom C.


Sent from my iPad using Early Retirement Forum

Company pensions are usually better value than an annuity that you can buy. I would never buy an index annuity because you'll be crippled by fees and/or fine print. An index annuity that has some component that you can pass on to heirs will be even worse value.

What are the specifics of your pension?

 

[nun]

Also there's no such thing as a "great deal" with insurance products. They are all variations of the same thing. None are playing Santa Claus.

True for most commercially available annuities, but in the employer pension area the lump sum payout vs lifetime income decision often comes down on the side of the annuitized payments.

As an example through an admittedly rare and lucky set of circumstances I can buy into my employer's pension plan for $183k and receive $20k a year with a current 2% COLA starting at age 55 (I'm a 54 year old male now).