## Tuesday, August 25, 2009

### Annuity math

As I noted earlier I plan to start receiving a pension from my former employer in November after I turn 55. For obscure reasons I have options to take portions as a lump sum instead of a single life annuity. In one case the lump sum is about 90 times the monthly annuity and in the other case it is about 133. The information packet I received suggested these options are bad deals and that a fair conversion ratio would be about 188.5. This is roughly consistent with annuity quotes I found on the web which had ratios which varied from 164 to 206.

According to the information packet a life expectancy (for males) at 55 of 26 years and a discount rate of 4.3% was used to compare the value of the annuity and lump sum options. And indeed assuming I will live exactly 26 additional years (receiving 312 monthly payments) and applying a discount rate of 4.3% does produce a similar ratio, 189.3. The discount rate needed to produce a ratio of 133 seems to be over 8%. Since I don't think my expected investment returns are over 8% and I don't have any reason to believe my life expectancy is significantly less than average it looks like I will decline the lump sum options.

1. i believe that annuity income are the very good investment for us.

2. Out of curiosity, what timing went into your result of 189.3? Depending on a period of compounding and on whether the annuity payments start before, at same time, or after the optional lumpsum payment is received (in months steps), I am getting ratios of close to 189, but never specifically 189.3.
I wish you long long life after the additional 23 so that you maximize your benefit of this decision!

3. The NPV comparison seems useful as a starting point, but how about
1)the fact, if true, that the (life) annuity will automatically scale itself to your uncertain lifespan, while the principal portion of the lump sum option won't
2) the fact that the lump sum gives you more flexibility if you need a lot of cash early on

My gut feel is that 2 outweighs 1 (which is mitgated in any case by the ability to borrow, possibly insurance, etc.) So on net these extra factors seemed to only bolster your decision, but then I thought of

3) Is the annuity somehow inflation-indexed? If not I suppose this must count against it relative to lump sum, whose no-risk interest rate would increase w/ inflation.

On balance I'd probably still go w/ the annuity, but I wouldn't be real confident as I'm fuzzy on the value of 3 vs 1-2. Then again maybe some of these factors are illusory (it wouldn't be the first time:-)

4. Oops, in my previous comment I meant "1 outweighs 2," not "2 outweighs 1."

5. The reason you aren't getting 189.3 is probably because I made a small computational error. The correct (hopefully) result is 190.0.

6. Unfortunately the annuity is not inflation indexed.

Regarding comparing the values, if the lump was valued higher but you wanted an annuity you could take the lump sum and use it to buy a bigger annuity. This would clearly be better than taking the annuity (ignoring taxes and possible credit risk).

On the other hand if the annuity was valued higher but you needed a lump sum in theory you could sell the annuity stream and obtain a bigger lump sum. But since there isn't as much demand in this direction there would probably be practical difficulties in obtaining a fair price. Fortunately I am not in immediate need of cash and so can go for the greater value over time.

Taxes are another reason for taking the annuity. If I took the lump sum it appears I would need to roll it into an IRA type account or pay a penalty. And once in the IRA I would have to wait to age 59.5 to take money out without penalty. So the lump sum is not as flexible as might first appear.

7. So I guess a rough summary would be that you think that the higher NPV plus the tax advantage of the annuity outweigh its higher inflation risk. Sounds plausible to me.

I would be even more comfortable w/ a fully quantitative analysis. Then again, quantifying inflation risk seems tough to do w/ any degree of confidence.