Schweser Book 2.4 LOS 9.B According to Schweser, “B = cost basis / asset value at start of period n”. Why does it say “period n” instead of “period 1”? In the examples, it looks like B is being calculated based on period 1. “$1,000 is invested for 20 years at a pretax return of 10% . . . The cost basis is also $1,000 for B = 1.00.” If B were calculated at the start of period n, wouldn’t that mean that we have calculate the asset value at the beginning of the 20th year in order to calculate B?
Per Schweser (I am reading from the 2015 book) “Thus far we have assumed that the cost basis [in $] for computing taxes is the investment current value […] however the cost basis is often different from the investment current value”.
Cost Basis [in $] = original purchase price
Dipending on the situation (on the question), Investment Current Value may be = or to original purchase price.
If investment Current Value to original purchase price, then, in order to find the Future Value after Capital Gain Tax (FVcgt), one could perfiorm the following calculations:
step 1
Current Value * (1+r)^n * (1-cgt%)
which returns a certain FV < than FVcgt owing to the cg tax having been applied to the gain _ and _ to the cost basis.
step 2
The cost basis (which is not a gain) should not be taxed so one needs to add a term (in bold below) to negate the effect of the over taxation:
Current Value * [(1+r)^n * (1-cgt%)] + Cost Basis [in $] * cgt%= FVcgt
step 3
One could bring the term Cost Basis [in $] * cgt% within the square bracket and the formula would end up being:
Current Value * [(1+r)^n * (1-cgt%) + (Cost Basis/Current Value) * cgt%] = FVcgt
where (Cost Basis/Current Value) = B = cost basis / asset value at start of period n
Note: the ‘could’ means that, in reality, the formula in step 3 is what the the author believes is the most efficient way to perform the calculation; this said, that formula, is no better than thinking that, if one taxes the whole of the pre-tax future value (i.e. gain+cost basis) one should add back an amount = (cost basis*tax rate) in order to get to the after-cg tax FV (like in step 2).