*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.

*click for the Homa Online Tutorial*

** * * * **

**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.

* * * * *

**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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This entry was posted on October 15, 2012 at 2:30 pm and is filed under Capital gains - taxes, Financial math, HOT - Homa Online Tutorial, Taxes. You can follow any responses to this entry through the RSS 2.0 feed.
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