Can someone explain this equation in simple language? (reading 10 - taxes)

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sachin_patel

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FVIF = [(1+r*)(1-T*)] + T* - (1-B)tcg
I want to understand the point of the terms highlighted.
Thanks,
 
B=Proportion of your current portfolio (whose value is 1) that you started out with.
(1-B) therefore = the total amount of gain on the portfolio
(1-B)*Tcg = Capital Gains tax that you therefore paid.
 
The first part – [(1+r*)(1-T*)] (which should be [(1+r*)^n(1-T*)] I believe) – is the amount you would have left after taxes if the entire amount – principle plus gain – were taxed at the weighted-average rate T*.
The second part – + T* – adds back the weighted average tax on the principle, because only the gain is taxable.
The third part – −(1 − B)Tcg – subtracts the capital gains tax if the basis is less than the full principle.
 
You have to think that such formulas are for an initial portfolio value of 1 (to use them for real you will simply have to multiply them by your initial portfolio value). So it is like you have “1x” at the beginning of your formula, which makes no difference so you don’t show it.
The first part that you have not highlighted means that you have applied the tax rate T* to the total of your final portfolio value after it has grown. But you should not be taxed on the initial value of 1, but only on your various gains, interests and other income. So you put back the excess tax computed in the non-highlighted part, which is the initial value of your portfolio times the rate T*, or 1×T* or simply T*.
Now imagine that the tax authority says “i don’t care if you actually paid 1 to acquire this portfolio. I consider your cost basis is only 0.8 so when you reach 1 in value you already have to pay tax on 0.2” (for example, real estate investment with property initial value of 0.8, notary costs of 0.2, so you consider you start making capital gains when property value reaches 1, but tax authority in that jurisdiction says you can’t deduct notary fees and that you already made 0.2 capital gains when property value reaches 1). This cost basis of 0.8 is your B. When computing T* and r* according to the formula given by the CFAI you assumed your cost basis was 1. It actually happens to be B and it differs from 1 (otherwise, the formula still works, the last part of the formula gives you zero) so now you also have to pay capital gain tax on (1-B) (0.2 according to our example). This is the last part of your formula.
I hope this makes sense to you
 
S2000magician wrote:
The first part – [(1+r*)(1-T*)] (which should be [(1+r*)^n(1-T*)] I believe) – is the amount you would have left after taxes if the entire amount – principle plus gain – were taxed at the weighted-average rate T*.
The second part – + T* – adds back the weighted average tax on the principle, because only the gain is taxable.
The third part – −(1 − B)Tcg – subtracts the capital gains tax if the basis is less than the full principle.
Click to expand...
Perfect!!! Thank you!
 
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