Financial math: Capital gains tax rates are going up 8.8% … So, how much will after-tax capital gains go down?

This is a relatively simple financial math question that most people I’ve asked have gotten wrong.

Answers have ranged from less than 8.8% – since only capital gains are being taxed (huh?) … 8.8% – because that’s how much the marginal rate is going up … to more than 8.8% – “otherwise you wouldn’t be asking the question”.

First, what’s magic about 8.8%?

Well, Obama did what he promised and jacked capital gains tax rates from 15% to 20% … and, don’t forget ObamaCare has a 3.8% non-payroll payroll tax on investment income starting in 2013.

So,  the effective capital gains tax rate is going from 15% to 23.8% … a delta of 8.8%.

That 8.8% increase will cut after-tax capital gains by 10.35% !

If you don’t believe me, here’s he math …

You can either watch the tutorial or ship down to the recap/

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Recap

Assume that you bought a stock for $750 and sold it for $1,000 … netting a $250 pre-tax gain.

If the capital gains tax is 15%, you pay $37.50 in taxes … netting you, after taxes, $212.50.

If the capital gains tax is 23.8%, you pay $59.50 in taxes … netting you, after taxes, $190.50.

The difference, is $22 ($212.50 less $190.50 … or simply, 8.8% times $250).

So the percentage drop in after-tax net gains is 10.35% ($22 divided by $212.50)

Note that that percentage stays constant at 10.35% regardless of the size of the gain – in absolute or relative to proportionate cost basis.

That’s not a coincidence, it’s math.

With a capital gains tax rate of 15%, the after tax gain is simply 1 minus the tax rate times the nominal gain … 1 minus 15% is 85%.

With a capital gains tax rate of 23.8%, the after tax gain is simply 1 minus that tax rate times the nominal gain … 1 minus 23.8% is 76.2%.

The difference is still 8.8%, but the denominator of the change ratio is is 85%, not 100% … and, 8.8% divided by 85% is 10.35%.

Again, that answer is generalizable … not specific to this example.

Q.E.D.

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