# Blended Taxation - rationale behind the formula?

Hello guys,

First of all, my apologies if that is an already well discussed topic here. I went up to page 3 and couldnt find anything about it and [noob] couldnt find no Search bar as well [/noob].

Apologies asked, here is my question:

Im trying to find some sense behind the equations that deal with blended taxation, I can understand what weighted average realized tax rate (wartr) and r* (which equals r(1-wartr)), but when it comes to T* (as defined below), I just cant find any good train of thought that can explain why the formula is defined as it is.

Schweser defines those concepts as:

weighted average realized tax rate (wartr) = p_i * t_i + p_d * t_d + p_cg * t_cg

r* = r * (1 - wartr)

T* = [( 1 - (p_i + p_d + p_cg)) / (1 - wartr)] * t_cg = [p_def_cg / (1 - wartr)] * t_cg

here is my assessment of this expression:

since r* overstates after tax returns (since it dont take into account tax liabilities due to unrealized capital gains), we must adjust the tax rate to be used to calculate the final value of invested factor after taxes, that is when T* comes to the scene. We must then see T* as the average tax rate that must be applied to the total pretax gains to account for every aspect of the return (both realized and unrealized capital gain, as well as interest and dividends gains).

If my assessment is correct, can someone help me link it to the algebra of T*?

Finally, does anyone found a meaning for the term between brackets below?

FVIF_at = (1 + r*) * (1 - T*) + [T* - (1 - B) * t_cg]

Thanks in advance guys! Wish you all the best during our journey to the final bout

Hi Imancedo.

Sorry for the delay in responding.

The effective capital gain tax rate formula was hard to understand to me too but you can find excellent explanations in the following.

http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91318635

1recho gave a very good explanation to the formula and carthurj baked it up with a practical, easy to understand example.

Also, I happened to notice a typo in your formula. The first term should be as follows.

FVIF_at = (1 + r*)^n * (1 - T*) + [T* - (1 - B) * t_cg]

Thanks.

>> Finally, does anyone found a meaning for the term between brackets below?

>> FVIF_at = (1 + r*) * (1 - T*) + [T* - (1 - B) * t_cg]

(1-B)t_cg is the tax charged on value that is above the cost basis