Another Benefit of the Roth IRA or a Miscalculation

Dear Tax-haters,

So maybe you’ve read up on the Roth IRA like I suggested. But probably not. Money is interesting in that it’s a made-up idea yet it consumes so much of our thoughts. I'm beginning to understand that when you have a sufficient amount of money, any extra is just gravy. But a lot of gravy is nice. So skip to the next section to get to the Roth IRA stuff if you want to bypass an embarrassing story of my miscalculation.
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Back in high school I was captain of the science bowl team (go ahead and snicker), and our team made it all the way to nationals. Though I was proud, the qualifying regional was like playing in Conference USA; it wasn’t much of a challenge to get an automatic bid to the show. It was a several day affair in D.C. at a place that had dorms to sleep in and ballrooms in which to display our math and science prowess. I wonder how far it would set back American technology if something were to happen to that place during nationals; some of those kids were extremely bright yet extremely dull (myself included). Out of the 10 round robins, my team won a grand total of zilch. Needless to say, we didn’t advance.

Besides the main event of science bowl, there were side competitions like designing the best hydrogen fuel cell model car. The hydrogen fuel cell in my view at the time, was redundant. The reaction that powers the system is the combustion of hydrogen to make water and energy. Chemically, hydrogen + oxygen = water + energy. Though containers full of hydrogen is undoubtedly a very safe thing*, the way we got the hydrogen to fuel the model cars is via a hydrolysis reaction (water + energy = hydrogen + oxygen) powered by alkaline batteries. Then to power the car, they’d just let the reaction go in reverse; there wasn’t an internal combustion of hydrogen which was quite a disappointment.

A younger, more naïve g: ‘I think it’s stupid that we’re using a battery to power another battery. I don’t see the point in this experiment. I mean, if we were combusting the hydrogen, then I can kind of understand the idea somewhat.’

The thing I learned a little later is that a reaction produces the same maximal amount of energy, no matter the way in which it occurs. Therefore, the same amount of hydrogen and oxygen would produce the same maximum whether you lit the hydrogen and let it blow or stuck some wires to make a boring battery. In fact, the battery method is a much more efficient in harnessing the energy than the internal combustion of hydrogen, so it would be preferable to have the controlled reaction that you see in the developing hydrogen fuel cell cars. And there's the benefit that your car won't blow up, but that's a minor advantage.

As a sidenote, the controlled electric reaction of hydrogen and oxygen is still considered combustion since it is defined as the reaction of a fuel with oxygen. Are you still awake?

Thinking about the comment I made to my fellow competitors, I wonder how many of them thought I was a complete idiot. I totally missed the point: Making hydrogen requires energy, whether it be renewable or fossil fuel, but if we were to somehow make that process more efficient, we’d have a clean ‘burning’ fuel with only water as an emission. The internal combustion engine is a relatively inefficient (something like 33% gets converted to mechanical energy). To get the hydrogen in our particular exercise, we used batteries (redundant), but if it were a more efficient conversion of fossil fuels to get hydrogen like 45% instead of 33% at a hydrogen plant, then we’d possibly reduce emissions.

But money talks and so far, the money isn’t in hydrogen fuel cell cars. Earth, sucks to your ass-mar**.
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After reading some more stuff about investments (I want to retire when I’m 40 and become a decrepit degenerate), I thought about the tax advantages of a Roth vs traditional IRA.

The common consensus among investors is that the Roth is the preferable vehicle if you can contribute to it, which I wholeheartedly agree with for the many important reasons reported repeatedly across the internet. (if you don't believe me, google it yourselves)

But there was one more thing I thought about, which may turn out to be another miscalculation of mine. Even if it isn’t, this advantage is so minuscule that it really doesn’t matter unless you make frequent trades in your taxable account.

Let's start with a truism: If the current tax rate and your retirement tax rate were the same, then the Roth and traditional IRA would have the exact same return, assuming the same annual rates of return, investment amount, and length of investment. Some website had a pretty graph, but I'll prove it to you mathematically:

Roth -
principal x (1 - present tax rate) = investment amount
investment amount x (1 + annual rate of return)^length of investment = net value at retirement
P x (1 - tax%) = I
I x (1 + ARR)^n = net value
therefore, P x (1 - tax%) x (1 + ARR)^n = net value

Traditional -
principal = investment amount
investment amount x (1 + annual rate of return)^length of investment = pretax value at retirement
pretax value x (1 - retirement tax rate) = net value
therefore, P x (1 + ARR)^n x (1 - tax%) = net value

So Roth would win if the retirement tax rate were higher than the present tax rate, which given the state of our national debt, is likely. Traditional IRA proponents argue that you'd be making less money when you retire than at present, so you would be in a lower tax bracket. I wouldn't count on that--40 years is a long time from now.

There's a lot of advantages/disadvantages I'm ignoring, and financial websites do them justice. I'm purely focusing on the numbers.

Finally getting to my point. Let’s assume some numbers:
Bank account/income for last quarter = $10,000
Roth/Traditional contribution limit = $5,000
Marginal tax rate = 25%

Average annual return in stock market mutual fund = 7% (that’s a nice, round lucky number)
Returns are based on dividends/interest and growth. Dividends and interest get taxed yearly, but growth isn’t taxed until it is realized via capital gains. So let’s assume that 2% is attributed to dividends/interest and 5% is attributed to growth, and you invest your taxable account in a buy-and-hold strategy.

Qualified dividend/capital gains rate = 20%
Length of investment = 35 years
No further investments in future years
Invest remainder of bank account in a taxable investment
Taxable investment return = 5% + 2% x (1 - 0.2) = 6.6% return (accounting for the tax on interest & dividends)

Roth IRA
Contribute $5,000. Pay marginal tax of 25% on $10,000 which is $2,500.
Ending balance = $2,500 in bank account and $5,000 in Roth

Traditional IRA
Contribute $5,000. Pay 25% on $5,000, which is $1,250.
Ending balance = $3,750 in bank account and $5,000 in traditional IRA

In the Roth:
IRA: $5,000 x (1 + 0.07)^35 years = $53,382 tax free
taxable acct: $2,500 x (1 + 0.066)^35 years = $23,412
after capital gains tax = $23,412 x (1 - 0.20) = $18,730
NET = $72,112

In the Traditional:
IRA: $5,000 x (1 + 0.07)^35 years = $53,382, taxed at 25% marginal rate
after tax = $40,037
taxable acct: $3,750 x (1 + 0.066)^35 years = $35,118
after 20% capital gains tax = $28,095
NET = $68,132

Difference of $3,980. Small change considering inflation and what-not 35 years from now. The difference is attributed to the fact that you're putting 'more money' into the Roth, since those dollars have the tax rolled into it. With the traditional, the investment dollars haven't been taxed yet and those would be 'worth less' than the Roth dollars. To get the same IRA return from the traditional IRA, you'd have to invest $6,666 initially:

IRA = $6,666 x (1 + 0.07)^35 = $71,170
after 25% tax = $53,378
taxable acct: $3334 x (1 + 0.066)^35 = $31,223
after 20% capital gains tax = $24,978
NET = $78,356

So in this hypothetical scenario (the contribution limit for both IRAs is a meager $5,000), you'd be up $6,244 over the Roth.

Long, long, convoluted story short: With the Roth, you're investing a higher initial amount. But in reality, that little extra amount may not mean much if you're disciplined in you manage your taxes in your taxable accounts. You also aren't tempted to spend that cash you have lying around in your bank account.

In my opinion, the true advantage of the Roth IRA is that you're locking in your tax rate now. And although your tax bill may have seemed heavy, it's nothing compared to the 70s which had top marginal tax rates of 70%.

Why did I go through this whole ordeal to prove (possibly) a minor point, which probably isn't worth mentioning? Because it's good practice. And it doesn't even require calculus.

A quote from Warren Buffett: Investment must be rational; if you don't understand it, don't do it. From what I hear, he does pretty well for himself.

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*come on, Hindenburg was a fluke!
**Lord of the Flies