Can someone help me understand this little formula here:
(1+r*)n(1-T*) + T* - (1-B)tcg
you are taking the after tax rate of return r* and compounding it then multiplying it again by the same effective tax rate, then adding the same tax rate and subtracting a portion of the original capital gains tax rate??.. 
help is appreciated!
r* is the return after accrual taxes, but not after capital gains taxes.
T* is the capital gains tax rate adjusted so that you can multiply it by the total gain and have it really tax only the untaxed gain at the statutory rate.
Adding T* removes the capital gains tax from the original investment, so that you’re taxing only the return.
Subtracting (1 − B)tcg taxes any untaxed portion of the original investment.
can you elaborate more on "subtracting (1 − B)tcg taxes any untaxed portion of the original investment."
I had issues with this formula as well, S2000magician nailed it!
I think the last part just takes into account the effect of cost basis on your capital gains, this is what magician meant about untaxed portion of the original investment i guess
isn’t the use of Tcg wrong over here? If market value was $100,000 and cost basis was $80,000, this would mean that there is $20,000 in gains after accrued taxes. These gains after accrued taxes should be taxed at T* instead of Tcg.
am i understanding it wrongly here? thanks in advance S2000magician.
I believe that you are.
You have $20,000 that was not taxed at all by the accrual taxes, as is appropriate: it’s a deferred capital gain, so it should be taxed at the rate appropriate for capital gains: TCG.
The problem I have with learning the formulae for r* and T* is that the text doesn’t explain the nature of those rates. When you look at T*, for example, it appears to be a tax rate; nothing more, nothing less. It isn’t. It’s a combination of a tax rate and a taxable fraction. For example, if T* is, say, 18%, it might be a combination of 60% of the gain being taxable at a tax rate of 30%. It might be easier to apply the 18% rate to the entire gain, but it obscures what’s really happening.
What’s really happening here is that the first part of the formula doesn’t tax the previously untaxed gain at all, so all of it is still taxable, at the capital gains tax rate.
but specifically for the example given, the portfolio had a beginning value of $100,000 and gained $8000 (before any taxes) in Year 1. The gain became $7020 after being taxed for interest, dividend and realised capital gain. There is $2000 in unrealised capital gains that has not been taxed.
$107,020 would be the beginning value of the portfolio in Year 2. If I were to use Year 2 as my starting point now, market value of my portfolio would be $107,020 and my cost basis should be $100,000. So there should be a gain of $7020 that has already been taxed by the accrual taxes. I can’t say that $7020 has not been taxed at all.
Tcg should apply to $2000, not $7020.
Going by the same logic, the $20,000 which I mentioned above should be treated the same as the $7020 gain and taxed at T*.
The $20,000 mentioned above should include interest income that has already been taxed, dividend income which has already been taxed and realised capital gains that has already been taxed. The balance of the gain is unrealised capital gain. I can’t see how Tcg can be applied to the entire $20,000, as if to say that the entire $20,000 is unrealised capital gains.
Of that $8,000 in the first year, how much is interest, how much is dividends, and how much is realized capital gains? What are the respective tax rates?
I want to answer your question accurately and fully, and to do so I need those numbers.
So, of the €8,000 gain:
That leaves a net return of €7,020 (= €8,000 − €140 − €300 − €540) of which €2,000 (= €8,000 − €400 − €2,000 − €3,600) has not been taxed, and €5,020 has been taxed.
No, because 71.5% of that €7,020 has already been taxed \left(\dfrac{€5,020}{€7,020}\ =\ 71.5\%\right), while none of the €20,000 has been taxed. The €20,000 is treated the same as the €2,000, but not the same as the €7,020.
if that’s the case, you must then make the assumption that no gains have been reinvested, unlike the Zahid Kharullah case. Is this correct?
I have no idea why you believe that.
No.
€7,020 of the €8,000 has been reinvested.
think I didn’t make myself clear there. i was referring to the example with $20,000 in gains where you said the entire $20,000 is unrealised capital gain and should be taxed at Tcg.
if I were to think of how the $20,000 came about, it would be similiar to how the $7020 came about - that is, interest + dividend + realised cap gains (all taxed) plus some unrealised cap gains (not taxed) in there.
for you to say that none of $20,000 have been taxed, it must be the case that all interest, dividend and realised cap gains made previously were not reinvested, making the entire $20,000 unrealised capital gains that is to be taxed at Tcg
The point is, it’s not.
When they say that the basis is €20,000 less than today’s value, they mean that that €20,000 has not been taxed. That’s the definition of basis: the €80,000 basis has been taxed (fully; you’ll never be taxed on it again) and the €20,000 has not been taxed (at all).
Does the definition of basis also imply that any gains are capital gains and nothing else? I.e. no interest income, dividend income etc.
It does, indeed.
that’s it! the whole problem solved with those 5 words. can’t understand how CFA expects its candidates to be experts in tax matters.
thanks a lot s2000magician!
My pleasure.
