Generally, your math is correct. And generally, you're making an apples-to-apples comparison. There is some quibbling to be had about your assumptions (such as whether 2% salary growth is too low, whether 5% investment growth is too low, whether a 5% safe withdrawal rate is too high, whether a 20% marginal tax on the FERS pension payments is correct, and whether a retirement age at 60 would be realistic when two more years in the service would bump your annuity calculation from 1.0 percent to 1.1 percent for each year of service).
However, given the assumptions you have, I independently came to the same result: the "breakeven point" for the number of years of work needed for the defined-benefit pension of a FERS-FRAE participant to roughly equal withdrawals from a Roth IRA in an alternate world where you could put your FERS contributions toward a Roth IRA is at around 13 years of federal service. Higher assumed salary growth, lower safe-withdrawal-rates from the IRA, and lower assumed taxes on the pension pull that point forward, while higher assumed investment returns push it out.
There are at least three other considerations you need to think about when doing this comparison, though: COLAs, risk, and retiring at 62.
FERS annuities are subject to a COLA each year. The current COLA formula for FERS increases benefits annually by inflation as measured by Q3/Q3 growth in CPI-W. The COLA adjustment equals inflation if inflation is at or below 2%, equals 2% if inflation is between 2% and 3%, and equals inflation minus 1.0 percent point if inflation is above 3%. Thus, in a world where your safe withdrawal rate is equal to your annual investment earnings, your monthly FERS benefit might equal your Roth IRA withdrawals at age 60, but by age 70, your FERS benefit will be about 20% higher. This would push the "breakeven" point a little forward.
Your calculations do not include any kind of risk premium, either. FERS benefits are guaranteed*. If you are receiving a defined-benefit pension, you will get the amounts specified for the rest of your life. With a Roth IRA, however, you run the risk of running out of money before your time is up. In terms of my own financial security, $635 per month at age 60 guaranteed for forever is worth more than $635 per month at age 60 not guaranteed. In my view, the greater certainty under FERS also pushes the breakeven point forward.
Finally, the FERS benefit factor for annuity computations is usually 1.0%, and it would be 1.0% under the assumptions you have. However, that annuity computation factor bumps up to 1.1% for each year of service if you retire at age 62 with 20 or more years of service. Thus, the "pension" line would be quite a bit steeper for years after 20 if you took your delayed annuity at age 62, instead of at age 60. If you chose 60 to avoid this bump up, then this analysis doesn't properly take into account the FERS annuity supplement, which would increase your income for two years while you wait to receive your Social Security benefits.
For commenters, why does that Roth line look like that?
The graph shows the future value of contributions up through the current years' worth of contributions. The value of a contribution of $2,640 in 2019 will be worth $13,900 in 34 years given the assumptions stated (and assuming compounding does not start until the end of 2019). Then, in 2020, after salary growth of 2%, the contribution of $2,693 made that year would be worth $13,500 after 33 years. In 2053, the contribution of $5,075 that you would make that year would be worth $5,330 at the end of 2054, the year of retirement. Each additional year's worth of work adds less to the final retirement amount because that year's worth of work has less time to grow. As a result, on a future-value basis, each addition year's worth of work is worth less than the previous years'. The graph reflects that.
What about those assumptions?
Assumptions are always up for discussion, but you asked what you might have missed, so I figured I might add a little bit of meat to the discussion of assumptions that you picked.
Salary increases: Federal pay adjustments under FEPCA have averaged around 2.7% per year, after including the 0% adjustments in 2011, 2012, 2013, the 1.0% in 2014, 2015, the 1.3% in 2016, the 2.1% in 2017, and the 1.9% in 2018 and 2019. That amount, however, ignores within-grade step increases and grade increases. Unless you plan on doing the same exact job for 35 years (and $60,000 represents the 10th step in grade), 2.7% is also a low assumption.
Investment returns: The average annual growth rate of the S&P 500 has averaged nearly 10% over the past 50 years. Past performance is not necessarily indicative of future returns, but it's better than just picking a number from thin air. Of course, you probably don't want to keep your Roth IRA entirely in stock indexes the year before you retire. If you're investing sensibly, your true return over the next 35 years would be lower than that 10%.
Safe withdrawal rate: The oft-cited SWR rate is 4% (and, as the article notes, sometimes 3%).
Pension taxes: Not all of your FERS pension is taxable. Completing Worksheet A using the assumptions of your question indicates that maybe about 87% of your pension would be taxable. Accordingly, you wouldn't reach a level of 80% taxation on your pension until every dollar of your FERS pension were taxed at a marginal rate of about 24%. If you're in a state with no income taxes, that means each dollar of your pension would have to be on top of $84,200 in other taxable income in today's dollars (assuming tax rates don't change from their current levels, expiring tax provisions be damned).
So if I leave the federal service before 13 years, I should cash out?
No. Your contributions to FERS do not grow over time. Therefore, your lump sum payout at year 13 would be less than if you had been contributing 4.4% of your base pay to a Roth IRA over the past 13 years. Additionally, you would have to find a way to get lump sum contributions into a Roth IRA in one year, which may not be possible given Roth IRA contribution limits.
*Benefits are guaranteed to the extent that lawmakers do not change the program. Since the 80s, there have been three major reforms to civilian federal employee retirement programs: the 1984 reforms which created FERS (and closed CSRS), the Middle Class Tax Relief and Job Creation Act of 2012 which created FERS-RAE, and the Bipartisan Budget Act of 2013 which created FERS-FRAE. There are consistent proposals to further restrict FERS benefits, along with some to increase benefits. Whether those changed are enacted (or whether they would apply to current employees and not just newly-hired employees as have all previous reforms) could further change this analysis.
