This isn't homework, but I'm hoping there may be some savvy investors hiding in the JSP community. I'm sure Paul at least has plenty of money to invest by now.

I want to find how much extra money you would need to make on a stock (by day trading it, etc) to offset paying a yearly capital gains tax on it. This amount would be expressed as a percentage of the basic investment. Assume capital gains tax is 15% and ignore the (more damaging) difference between short term capital gains tax and long term, always assuming a short term tax at 15%. Also ignore brokerage fees.

For example: I invest $1000 in company Z at the beginning of the financial year. It goes up 10% over the first year and I sell it at $1100. I owe gains tax on $100, and I'm left with $1085. I reinvest my $1085 in Z and it goes up another 10% over the next year. I sell it for $1193.50. I owe gains tax on $108.50 (the difference between $1193.50 and $1085), and I'm left with $92.225 profit for this year. My net profit for both years is thus $1085 + $92.225 - $1000 = $177.225

By buddy Greg on the other hand invests $1000 in company Z and holds it for 2 years before selling. This is easily modeled by the compound interest equation: Z = P(1 + r/n)^nt
where,
n = number of times compounded per year = 1
Z = total
P = principle
r = interest rate
t = number of years

Z = 1000(1 + .1/1)^1x2
Z = 1210
Greg owes gains tax on his earnings of $210, leaving him with a net profit of $178.50. As you can see, I lost $1.275 by paying the tax yearly. This equates to .1275% of my principle investment. Extending this example out yields around .41% of my principle lost at 3 years and .86% lost at 4 years.

I can't write an equation for the investment taxed yearly so I can't solve for the amount required to compensate for yearly taxation. Any useful insight would be appreciated and rewarded!

how did you calculate the profit of 92.225?

edit: I'm European, I guess it's a comma for me and not 92k. Trying to get the formula now.

This post was edited by D2FreakIt on Dec 20 2013 05:40am

if you sell it within a year, its a short term gain. we would need to know what earnings tax brackets you both are in.

also, another issue is that you say you only reinvest 1085 after the first year. are you going to be removing taxes from your reinvestment or are you just going to reinvest total amount right away?


basically, it should be this:
The long-term capital gains tax rate is 15% (0% for taxpayers in the 10% and 15% tax brackets, and 20% for taxpayers in the 39.6 bracket
Long term rate --- earnings tax rate
0% -----------------10%-15%
15% ------------------25%-35%
20% ------------------39.6%

so depending on your tax bracket, you will need to earn : (Income tax rate)-(long term rate) more

or something like that. sorry, its early and i gotta head to work soon
/e oh and then there is brokerage fees

This post was edited by cialda on Dec 20 2013 07:23am

Assuming g is always positive, you can just do a recurrence relation in excel

Edit if not just add in tax credit each year and use a solver to optimize your tax strategy

This post was edited by madeinchinars on Dec 20 2013 01:09pm

Stop worrying about different capital gains taxes and just use the example given.

$92.225 is what's left after the second profit of $108.5 is taxed at 15%.

As for reinvesting the $1085: yes, we're assuming we immediately reinvest the full post-tax amount. It's not entirely realistic as you will have some period of time where you haven't paid taxes - but this assumes the most conservative.


Finding the amount you need to make to offset constant yearly taxation would help you make calculations for more complicated and dynamic trading situations. Again, do not worry about different tax rates, brokerage fees, reinvesting more or less money, etc.



Then by all means, please set one up for the example given. What exactly is "g"?

so you just want something that gives the % as you did in OP ?



/e for long term amount, it assumes you sold out that year. the short term, assumes you sell every year and post tax amount reinvested

Also, what information from this are you looking to gain?

This post was edited by cialda on Dec 20 2013 05:47pm

That looks good - can you post the equations you used for excel or the spreadsheet itself? I also want to be able to vary the stock yield from just 10%.

I hope to use this to predict what one's gains need to be to offset yearly taxation under variable circumstances.

Thanks for helping!

Short term

Pre tax = post tax of previous year *1.1
Post tax = Pre tax - (Pre tax - post tax of previous year)*.15

If this doesn't help, I'll type it out when I get back onto my computer

For any "Pre tax" / "post tax" to the right of equals, use cell code to link

This post was edited by cialda on Dec 20 2013 08:08pm

get the tutorial for the program stella and learn it. I just did a model related to investing with it this semester.

Google Stella from iSEE