Check my math/methodology for cFIREsim calc

[pigpen]

Hello,

Quick question that I feel stupid asking. I'm getting ready to run our retirement numbers in cFIREsim at the end of the year, and wanted to check my math/methodology on something.

The situation:

My wife has a defined benefit pension that she has the choice of starting at multiple points: 1. When she hits 60 years old in 2035 for the full benefit of $1,423/month (based on earnings history as of today), 2. When she hits 55 years old for a reduced benefit of $1,135/month, and 3. after 25 years of employment, which would be in 2022 at age 47, for a benefit of $692/month, which she would begin to draw immediately. These figures are in the dollars of the year she begins drawing the pension, at which point they will be adjusted for inflation each year after. In other words, if she begins drawing the pension at age 60, she will get exactly $1,423/month to start -- not $1,423 in today's dollars adjusted for inflation for the period from 2017-2035.

So, I pulled up one of those online compound interest calculators online to compare each of these scenarios for planning purposes.

Scenario 1:

Starting Amount: $0
Years to Save: 25 (based on an assumption of living to 85)
Rate of Return: 4% (but could be anything, I think, as long as I use the same value in each scenario)
Additional Contributions: $1,423/month, compounded annually
Result: $726,461

Scenario 3:

Starting Amount: $0
Years to Save: 38
Rate of Return: 4%
Additional Contributions: $692/month, compounded annually.
Result:$729,273

So, Scenario 3 seems like the winner over time, all else being equal, even though the monthly amount would be much lower. This also doesn't even account for the inflation adjustment of the $692/month each year once she starts drawing the pension. The downside to #3 is that she'd have to work 4 more years to get to 25 years.

Am I missing something?

Thanks.

Pigpen

[MDM]

Scenario 1:
Starting Amount: $0
Years to Save: 25 (based on an assumption of living to 85)
Rate of Return: 4% (but could be anything, I think, as long as I use the same value in each scenario)
Additional Contributions: $1,423/month, compounded monthly

Because the growth is occurring in a taxable account, the math changes a bit.  See rows 126-144 on the 'Misc. calcs' tab of the case study spreadsheet.

Growth in a taxable account
cgt = capital gain tax rate, %	15.0%
d = annual dividend rate, %	2.0%
g = annual growth excluding dividends, %	2.0%
n = years invested, yr	25
Compounding periods/yr	12
P = principal invested at start, $	$
Pmt = Recurring deposits, $	$1,423
1 = pmt at start, 0 = at end	0
t = tax rate on dividends, %	15.0%
nc = Number of compounding periods	300
dc = compounding dividend rate, %	0.167%
gc = compounding growth excl. div., %	0.167%
e = tax-adjusted growth, %	0.308%
ecgt = tax-adjusted cap. gain tax rate, %	8.108%
Basis	$552,703
F = Future, after tax, value	$678,507

Scenario 3:
Starting Amount: $0
Years to Save: 38
Rate of Return: 4%
Additional Contributions: $692/month, compounded monthly

Growth in a taxable account
cgt = capital gain tax rate, %	15.0%
d = annual dividend rate, %	2.0%
g = annual growth excluding dividends, %	2.0%
n = years invested, yr	38
Compounding periods/yr	12
P = principal invested at start, $	$
Pmt = Recurring deposits, $	$692
1 = pmt at start, 0 = at end	0
t = tax rate on dividends, %	15.0%
nc = Number of compounding periods	456
dc = compounding dividend rate, %	0.167%
gc = compounding growth excl. div., %	0.167%
e = tax-adjusted growth, %	0.308%
ecgt = tax-adjusted cap. gain tax rate, %	8.108%
Basis	$487,221
F = Future, after tax, value	$658,890

[secondcor521]

Well, I would approach the problem differently.

I would set up whatever you consider the default scenario (say, Scenario #1) in cFIREsim with all of your other data in there, save the data set, and then run the calculations and see what the result is.  Usually people focus on the success percent given a certain withdrawal rate.

Then I would reload that first dataset, change the pension to the next scenario, save that dataset with a different name, and then run the calculations and see what the result is.  If the success percentage goes up, then I'd consider making that my choice (considering any tradeoffs, like having your wife work longer or whatever).

My point is twofold:  (1) that cFIREsim can handle your situation without you have to do outside calculations and assumptions ahead of time as your OP implies, and (2) the most optimal scenario from a safe-withdrawal-rate-success point of view may be different than the scenario that compounds to the most money.  The reason this second point is important is that the magnitude and the timing of the payments could produce a different result than a compounding calculation, because a chunk of money early on may get you past a historically rough early period even if it doesn't add that much to a compounded pile of money.

[pigpen]

Great. Thanks a lot to both of you. I've never used the spreadsheet before, but I definitely will in the future.

[Monkey Uncle]

Well, I would approach the problem differently.

I would set up whatever you consider the default scenario (say, Scenario #1) in cFIREsim with all of your other data in there, save the data set, and then run the calculations and see what the result is.  Usually people focus on the success percent given a certain withdrawal rate.

Then I would reload that first dataset, change the pension to the next scenario, save that dataset with a different name, and then run the calculations and see what the result is.  If the success percentage goes up, then I'd consider making that my choice (considering any tradeoffs, like having your wife work longer or whatever).

My point is twofold:  (1) that cFIREsim can handle your situation without you have to do outside calculations and assumptions ahead of time as your OP implies, and (2) the most optimal scenario from a safe-withdrawal-rate-success point of view may be different than the scenario that compounds to the most money.  The reason this second point is important is that the magnitude and the timing of the payments could produce a different result than a compounding calculation, because a chunk of money early on may get you past a historically rough early period even if it doesn't add that much to a compounded pile of money.

Second this approach, with one caveat: cFiresim does everything in today's dollars, so pension payments that are valued in future dollars will need to be deflated by an appropriate annual CPI guesstimate to convert them to today's dollars.

[pigpen]

Thanks, MU. What would you use as an inflation rate? I've thought about this for a while too, and I'm not sure how to approach that part of it.

[Monkey Uncle]

Thanks, MU. What would you use as an inflation rate? I've thought about this for a while too, and I'm not sure how to approach that part of it.

I assumed 3%/yr when I did a similar calculation for my pension.  Although the actual CPI has been lower than that for years, I didn't want to be too optimistic.  Hopefully stagflation doesn't return.

[pigpen]

Great. Thanks. Gotta love the pension. We're not going to get a ton, but with both my wife and I getting one, we'll probably end up with maybe $20k total per year once we're both drawing ours. Possibly a little more.