Is the math wrong on these future value and draw-down calculations?

Question

Let's say I plan on retiring in 10 years, have some IRAs (401(k) rollovers), a conservatively invested taxable account and plan on contributing 15% to my 401(k) until I retire.

I'm using round numbers just to keep it simple.

4.25% is what is 5% after 15% taxes, because it's 50% bonds.

                    Compound
         Current    Growth     Future
Fund     Value      Rate       Value
----     -------    --------   ------
IRA      $300,000   6%         $537,254
Taxable  $100,000   4.25%      $151,621

According to Libre Office, the FV of $9,000 annual 401(k) contribs (which is 15% of my fictitious salary) for 10 years at 6% = $118,627.

Thus, the sum of my assets would be $537,254 + $151,621 + $118,627 = $807,503 (with some rounding errors).

I then move that money to conservative portfolios earning 4%, and decide to withdraw $5,000/month * 12 months = $60,000 all at the beginning of the year (because that simplifies the math).

Thus, after 15 years, there would still be a tad under $205,000 in my accounts.

    Beginning   After       After
Year    Value   Withdrawal  4% growth
 1    807,503   747,503     777,403
 2    777,403   717,403     746,099
 3    746,099   686,099     713,543
 4    713,543   653,543     679,685
 5    679,685   619,685     644,472
 6    644,472   584,472     607,851
 7    607,851   547,851     569,765
 8    569,765   509,765     530,156
 9    530,156   470,156     488,962
10    488,962   428,962     446,120
11    446,120   386,120     401,565
12    401,565   341,565     355,228
13    355,228   295,228     307,037
14    307,037   247,037     256,919
15    256,919   196,919     204,795

Even if the math is right -- and acknowledging that I've #1 simplified things for SE (including ignoring taxes), and #2 understand that markets go up and down so I actually might be living in my daughter's basement while working at McDonald's -- am I missing anything obvious?

Answer 1

1. You've stopped the drawdown projection after 15 years, but you could easily live longer than that, and in just a few more years you'd run out of money. Your initial withdrawal rate of >7% is very high.

2. You haven't considered the need to grow your withdrawals with inflation.

3. As a result of the above, most people cannot rely purely on "conservative portfolios" in retirement and need to take some more risk to generate enough return even after retiring.

4. You haven't explicitly noted that withdrawals from (traditional) IRAs and 401(k)s are taxable, so your spendable income would be $60k minus taxes.

Answer 2

You're not missing anything obvious, but I would reduce the amount that you need to live somewhat.

Your fictitious income is 60k (15% of 60k is 9k). You're contributing $9k to a 401k. You're calculating the money you need based on that 60k income to be 60k as if you were continuing the contributions after retirement. You should either include those 9k in the final (after growth) value, or you should remove it from the money you need to withdraw.