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Originally Posted by JohnEyles
Now I AM confused. I'm not sure exactly what IRR is doing. But if I change
MY spreadsheet so that there's $250K left in the hypothetical account after the
37 payments (that began at $11465 and increased at 3% per year), then the
rate would have to be about 6.85%. In other words, that's what Vanguard,
(or whoever) would have to earn on my premium to make those payments to
me and return my $250K. (But of course they're NOT returning the $250K).
Fascinatingly, that's less than a point more than the 6.2% the premium would
have to earn to make the graded payments but return nothing after 37yrs ! So
returning the principal doesn't represent that much add'l effective ROR, oddly.
The point is well-taken that the effective ROR is a lot less if I only live to 78yo
or 81yo or whatever. But, as I said, it makes sense for me to design the plan
to the most problematic reasonable scenario, the one where I live to the 90%
percentile of life expectancy (which is about 37 add'l years for a 53yo, according
to the table in Greaney's "How much can you safely withdraw" paper).
John
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IRR basically tells you, if you give it a series of cash flows, what is the interest rate one would have to earn in order to match that series of cash flows. So if you put in a $1,000 deposit in year 1 and a $1,100 year withdrawal in year two, the IRR would be 10%, because that is what you would have to earn in that case. (Alternatively, you can look at it as borrowing $1,000 in year 1 and paying back $1,100 a year later...you'd be paying 10% interest). Excel or a basic finance course can fill in more details.
The reason it doesn't make that much of a difference is that what you are in effect calculating is the rate of return Vanguard would have to earn if they took your $250K, made all those 37 payments to you at $11K and change, then paid you a bonus payment of $250K in year 37 or year 38 and
still ended up with $250K in their pocket. The reason it's not that much different is that the extra 60-odd basis points of interest (I get 6.6291% versus 6.0017% if the bonus payment is in year 38) difference over 37 or 38 years on $250K actually adds up to that $250K extra. Compound interest -- the 8th wonder of the world. This is why all those little old ladies are moving their jumbo CD's around for a 1/4% interest rate change -- it makes a big difference over the long haul.
You are right in saying that your plan makes sense
as long as you don't care that you don't get that extra $250K back. You're right in that you don't care, because you're dead, but do you have any heirs to worry about or provide for? Another way to look at this is that you could either take the $250K and buy the annuity or put it into a 30-year treasury bond and pull out the annuity payments you would have otherwise received. 30 years later, if you're still alive, you would be in the same spot with respect to your cash receipts, but in one hand you'd have an annuity that was now worth much less than $250K (based on your inflated payments and your reduced life expectancy as an 83 year old of only about 8-9 years). But it's an illiquid asset -- the only way to get your money out would be to sell your annuity stream, and you could get as little as $150K -- maybe, depending on your health and what rate of return the investor wants. In the other hand, you'd have $250K in cash.
I was going to attach my spreadsheet for you but it won't let me upload xls files. Here's the data, anyway. First column is the description, second column is if you got paid the bonus $250K, third column is without the $250K, and fourth column is the annuity that you might get at 83 years old:
Initial Amount $(250,000.00) $(250,000.00)
First payment $11,465.00 $11,465.00
3% increase $11,808.95 $11,808.95
… etc … $12,163.22 $12,163.22
Payment 4 $12,528.12 $12,528.12
5 $12,903.96 $12,903.96
6 $13,291.08 $13,291.08
7 $13,689.81 $13,689.81
8 $14,100.50 $14,100.50
9 $14,523.52 $14,523.52
10 $14,959.22 $14,959.22
11 $15,408.00 $15,408.00
12 $15,870.24 $15,870.24
13 $16,346.35 $16,346.35
14 $16,836.74 $16,836.74
15 $17,341.84 $17,341.84
16 $17,862.10 $17,862.10
17 $18,397.96 $18,397.96
18 $18,949.90 $18,949.90
19 $19,518.40 $19,518.40
20 $20,103.95 $20,103.95
21 $20,707.07 $20,707.07
22 $21,328.28 $21,328.28
23 $21,968.13 $21,968.13
24 $22,627.17 $22,627.17
25 $23,305.98 $23,305.98
26 $24,005.16 $24,005.16
27 $24,725.32 $24,725.32
28 $25,467.08 $25,467.08
29 $26,231.09 $26,231.09
30 $27,018.02 $27,018.02
31 $27,828.56 $27,828.56 $27,828.56
32 $28,663.42 $28,663.42 $28,663.42
33 $29,523.32 $29,523.32 $29,523.32
34 $30,409.02 $30,409.02 $30,409.02
35 $31,321.29 $31,321.29 $31,321.29
36 $32,260.93 $32,260.93 $32,260.93
37 $33,228.76 $33,228.76 $33,228.76
38 $250,000.00 $- $34,225.62
$35,252.39
6.6291% 6.0017% $145,891.72
2Cor521