Just by comparing the returns between deferred capital gains and cost basis, how is it that for the cost basis the returns are lower. (Example 3 and Example 4). If I purchase an asset for a lower cost basis, should my returns not be higher? The formula for cost basis includes the tax liability for a lower cost basis but not the capital gains. Appreciate any help:)

If an asset of 1$ today earns r% return for n years -> total value at the end of n year = (1+r)^n

how much tax would you pay on the asset? T*((1+r)^n - 1)

What are you left with at the end? (1+r)^n - (T*((1+r)^n - 1)) = (1+R)^n*(1-T) + T --> which is your formula.

Now instead of 1$ if the original asset had been worth only 0.10$ - and you had bought it at 1$ (This is what the cost basis means), how much tax would you have paid?

T * (1+r)^n - B) --> which would be a higher amountâ€¦

So you end up paying MORE TAXES - so your deferred capital gains FVIF is lower.