Alonso’s advisor proposes a 100,000 U.S. dollar (USD) investment in a portfolio of dividend-paying equities in the taxable account. All dividend income and realized capital gains would be taxed at 20% and reinvested. The advisor suggests a strategy of realizing no more than half of the available capital gains annually. He estimates the 3-year and 15-year accrual equivalent returns on the proposed portfolio to be 5.8% and 6.3%, respectively.
B. Explain why the estimated accrual equivalent returns differ for the two time periods? Ans - The estimated accrual equivalent return is higher for the 15-year period than that of the 3-year period as a result of deferring taxes on realized gains over time. In the case of this portfolio, the difference occurs because only a maximum of half of the capital gains are realized and taxed each year, allowing for compound earnings on the reinvested balances. I DIDN’T GET THE ANSWER. CAN SOMEONE SIMPLIFY IT?
if you are deferring taxes for a longer period - lower amount of taxes are paid each period. So the (net after taxes) amount is higher - grows higher - as the period of time you hold the instrument.
so at the end of 3 years - you would have a lower accumulated amount when compared to at the end of 15 years.
so since (Et/E0)^(1/t) = Accrual Equivalent Return … the conclusion above
Sorry but I couldn’t quite understand the so called reinvested balance. do you mean that the realized capital gain after tax is reinvested the portfolio and grow in compound rate?
My understanding is that only maximum of half on capital gain is realized and taxed. The unrealized capital gain shall remain in the portfolio and grow on a compound basis. So 15 years will have greater return than 3 years. the lesser realized capital gain, the lesser return subject to the tax and hence the higher return.
Sorry, can I reopen this topic? Why isn’t the dividend income mentioned in the answer, wherein the re-investment of the portion would contrbutute to higher accural equivalent return as well?
Sorry, I guess I have mis-interpreted. Since all capital gains need to be taxed eventually, by deferring the taxation of these capital gains over a period of time (in which the longer the better), the RAE will be higher. Nothing to do with the dividends.