Recently I completed my first post on the topic of taxation. This is an area I have previously avoided – faced with over 2,600 pages of the tax code I felt much like Will Durant at the start of his epic The Lessons Of History – “only a fool would try to compress a hundred centuries into a hundred pages of hazardous conclusions. We proceed.”
So I chose to look at a very small section of the code and in part 1 I gave a very natural extension to Michael Kitces’s work on capital gains “Bump Zones”. If you’re not familiar with these then I suggest you start with part 1 or the original Kitces article as a primer and then proceed here.
I was pretty pleased with the first post, but this area gets more interesting…
Bump Zones are combinations of income and capital gains that produce unexpectedly high marginal income tax rates. Since the taxation of capital gains takes place after income Michael Kitces observed that an additional dollar of income can “crowd out” the lower marginal rates and force capital gains into higher brackets.
For example in the chart below you can see that a taxable income of $60,000 and long term capital gains of $20,000 can result in marginal income tax rates of 27% (married filing jointly). Bear in mind that this is occurs when the marginal income tax rate alone without LTCG is only 12%. So it’s really a significant bump!
Effective Tax Rates
Marginal rates are useful, but they are like derivatives in calculus in that they tell you about the instantaneous change. Sometimes it’s more useful to look at the underlying function. In the case of tax rates this is the effective rate. The effective tax rate is the single equivalent tax rate that would apply to all the taxable income.
Note that I’m working here with taxable income and taking my effective rate as a percentage of the taxable income. You could take an effective rate as a percentage of gross income. I’m not sure what’s more typical. Also I’m only considering Federal taxes – but my blog, my rules…
If you plot out the effective tax rates for taxable income with no long-term capital gains you get the following (married filing jointly).
The weird kinks at $19,400 and $78,950 occurs where your income is high enough to enter the 12% and 22% marginal income tax brackets respectively. At these points your effective rate accelerates.
In this article – Optimizing Taxes will mean reducing your effective tax rate
We not only have a tax system where the rich pay more, but we have a progressive tax system where the rich pay proportionally more. This means that the above chart of effective rates increases with income. It’s then pretty trivial to reduce, or optimize, your effective tax rate. Simply reduce your income and your effective rate will decrease. Preferably to zero!
So that’s clearly not very helpful. But stick with it, as things will get interesting when we add capital gains…
In the above chart I’ve noted that if you are earning above $78,950 and can reduce your income then you get quite a lot of bang for your buck in terms of optimizing your taxes until you hit the lower marginal rate at which point reducing your income has a bit of a meh impact.
Note that if you have regular paid employment then I completely appreciate that you might have no flexibility to reduce your income, but when taking an income from savings (either pre or post tax) then you might have considerable freedom. In other words pre-retirement you may have little to no flexibility, but post-retirement you can have considerably more flexibility.
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Optimizing Taxes With Capital Gains
Let’s now look at the effective rates for a couple with $30,000 long term capital gains. I’ve plotted the effective rate below along with the chart we saw above.
The situation has changed quite considerably. The threshold, or kink, is no longer at $78,950 but has moved lower. This impacts the curvature of the effective rate and so for incomes above $78k optimizing is a bit meh, but the curvature increases below $78k making it more and more valuable to reduce your income if you are interested in tax optimization.
I know what you’re thinking – that’s pretty cool right? But these are two isolated examples, let’s see the whole glorious picture.
I’m ahead of you…
Effective Tax Rates for Income and LTCG
The chart below shows combinations of taxable income up to $130k and LTCG up to $100k. You can see that effective rates range from 0% to 15.1% for these income levels. A 0% effective rate is achievable by using solely capital gains to fill the marginal 0% bracket up to $78,750 for married filing jointly.
If we look at the bump zone for an income level of $40k we see that the edge of the bump zone is a LTCG of $40k.
If you keep income constant at $40k and reduce capital gains you move down the highlighted column in the chart above. This moves through the bump zone with a high marginal rate of 27%. In this zone LTCG attracts a 15% marginal rate so reducing it will optimize your effective rate. The optimal point is when you emerge from the bump zone at $40k and LTCG attract a 0% marginal rate.
As you continue to reduce LTCG below $40k you now enter a strange dynamic. You are peeling off LTCG where you are currently paying 0% marginal rate. So reducing your LTCG at this point will not reduce your tax bill. You therefore end up paying the same dollars of tax on a reducing total income. Thus increasing your effective rate.
The following summary should help (watch out for the reversed x-axis!). Here we keep taxable income constant at $40k and play with the level of LTCG to find the minimum effective tax rate.
We’re not quite done yet. There is a neat geometrical way to visualize this (and I bet you were just thinking “this is great, but I just wish there was a neat geometrical way to visualize this…”). The effective tax rates are like heights on a map where equal effective rates are contour lines. You can see this below where I’ve provided a 3D plot.
The kink running along the surface corresponds to the optimal LTCG for a given income level. In terms of optimizing your tax the goal is to move down the slope – i.e. reduce your effective rate. The kink is bit like a river running down the hill and if you were to pour water on the surface it would first move into the river and then down the hill. The path that water would take down the hill is the path you should take for your optimal tax strategy. Get it?
Author Bio: I started actuary on FIRE as I did not see any actuaries taking a prominent role in the personal finance area and wanted to remedy a shortage of actuary jokes and write for those that appreciate rigor with fancy charts. In my day job I advise corporate America on investment and retirement strategies. I am a qualified actuary, a registered investment adviser and have a PhD in mathematics and I reserve the right to include the occasional math post.