HOT: If capital gains tax rates go up 8.8%, how much will after-tax capital gains go down?

Another HOT: Homa Online Tutorial

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 says he’ll jack capital gains tax  rates from 15% to 20% … and ObamaCare has a 3.8 non-payroll payroll tax on investment income starting in 2013.

So, if Obama is elected and he keeps his promise … the effective capital gains tax rate goes from 15% to 23.8% … a delta of 8.8%.

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

OK, let’s run thru the math.

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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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Advanced Financial Math Question

How much will after-tax ROI go down if capital gains tax rates are increased by 8.8%?

Hint: The math is more complicated than the above example, because the answer depends on the cost basis of the stock relative to its current market value.

I’ll give the answer is a later post.

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