Deferred Capital Gains vs Cost Basis

[Needsomemotivation]

Sorry if this is an obvious one.
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

 

[cpk123]

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

 

[Needsomemotivation]

hi cpk123,
thanks for your reply.
in the formulas given, or in your example where is the 0.90$ capital gains incorporated? Is it included in the r?

 

[cpk123]

0.90 is the difference between the end value and the 0.1 and on that you pay the tax.