The last term (+t cg) “is the tax of the untaxed cost also known as cost basis or basis associated with the initial investment.” In the blue box there is an example: = €100,000 × [(1 + 0.07)20(1 – 0.20) + 0.20] = €329,575.
Can someone please explain to me why we would be adding back the percentage of the tax? I can’t seem to understand why we add .20 because the tax rate is 20% and how that coincides with the explanation provided
(Institute 105)
Institute, CFA. 2015 CFA Level III Volume 2 Behavioral Finance, Individual Investors, and Institutional Investors. Wiley Global Finance, 2014-07-14. VitalBook file.
The citation provided is a guideline. Please check each citation for accuracy before use.
The first part of the formula – [(1 + r)^n](1 – tcg) – is what you would have left if the entire ending amount – principal plus interest – were taxed. However, the principal is not taxed, so that amount is too small by the tax on the principal (the principal in this case being 1); thus, you have to add back the tax on the principal.
If you want to go through the algebra, it’s:
FVIFcg = total future amount before taxes – taxes on the capital gain
By the way, I wouldn’t bother to remember the formula. If I saw this on the exam, I’d be happy to work it out just as I wrote it: figure out the total amount before taxes, figure the tax on the gain, subtract the latter from the former.