proof of the basic double-taxation cost

nickbragman

I wanted to give a little proof of the "think for a moment about why this formula is true," in case anyone had further issue:

Using the standard notations of y, Tc, Tp, let's say you invest some arbitrary amount x in a middleman, which invests the funds elsewhere (so you get double-taxed).

Then, assuming you actually obtain your required yield of y, the capital gain is x*y

Next, we get taxed at the corporate level: xyTc. These are funds that never even make it to our return.

Therefore, our personal gain net of the corporate tax is xy - xy*Tc (total gain - corporate tax). This is the amount of gain returned to us, and thus is the amount taxed personally.

Therefore, we are personally taxed (xy - xyTc)Tp

Thus, the total tax cost is the sum of the two (corporate tax + personal tax): xyTc+(xy - xyTc)Tp = xy[Tc+(1-Tc)*Tp], equivalent to the formula in the wiki (the wiki formula is tax rate, this would be total tax for any investment x).

Staff - AC

Yep, this is correct.