Accrual equivalent and capital gains tax rate

CFA Level III Portfolio Management
#1

I am trying to explain why as the cost basis decreases and approaches zero, the accrual equivalent tax rate surpasses the capital gains tax rate.

If the cost basis decreases, “B” will be lower and future value will be lower. Therefore, the accrual equivalent after tax return will be lower (Rae = (FV/PV)-1), which is probably due to the higher capital gain tax rate. I can understand the logic but miss the mathematical relationship.

Could somebody show analytically in a mathematical statement, how accrual equivalent tax rate and capital gain tax rate interrelate?

#2

capital gains tax rate up-> ending after tax amt lower.

(ending amt / beginning amt )^(1/n) - 1 = Accrual equivalent tax rate.

if cost basis is lower additionally - the amount on which you pay the tax is [final total amount - cost basis] which will be higher - so you pay a higher tax.

so the total after tax amount will be lower then as well.