Accrual Equivalent Return

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patso

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“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.”
Explain why the estimated accrual equivalent returns differ for the two time periods. Note: No calculations are required.
CAN SOMEBODY HELP WITH EXPLATIO????
 
as T increases and approaches the investment time period - Accrual Equivalent Return increases.
 
Realized capital gains are taxed before they’re reinvested, but unrealized capital gains aren’t taxed, so there will be more money to reinvest each year if the gains aren’t realized. The longer you can reinvest the additional money, the higher the overall return, so the higher the accrual equivalent return.
 
Thanks Gents but i still dont get “WHY” a 3 year AER would be lower than a 15 year AER. I understand AER is I/Y on the calculator but im still not clear if the above answers the question, maybe im gettig lost on the concept of AER.
 
AER approaches the actual return as the time period increases
 
Suppose that you earn 5% per year. If it’s capital gains, it’s taxed at 20%. If not, it’s taxed when it’s withdrawn at 30%. What are your final balance and AER after 3 years and 12 years if you start with $1,000?
Capital gains: you’re taxed 20% of 5% each year, so each year you net 4%.
  • After 3 years you have $1,000(1.04)³ = $1,124.86. Your AER is 4%.
  • After 12 years you have $1,000(1.04)¹² = $1,601.03. Your AER is 4%.
Not capital gains: you’re taxed 30% on the total gain when you withdraw the money.
  • After 3 years you have $1,000(1.05³ − 0.3(1.05³ − 1)) = $1,110.34. You’re AER is 3.5504%.
  • After 12 years you have $1,000(1.05¹² − 0.3(1.05¹² − 1)) = $1,557.10. You’re AER is 3.7591%.
The reason that the AER increases for longer investment periods is that you have a higher percentage return (because it’s as yet untaxed) that is allowed to compound for a longer period of time.
 
Hi Magician, sorry to bother you with something that i thought i had nailed. Could you please explain why this statement is correct (this is from a prep provider material):
“The accrual equivalent after-tax return moves closer to the pre-tax return as the time horizon increases because the value of the tax deferral increases with time.”
My take from your explanation above is that the increase in AER over time horizon is due to compounding effect. Though the value of tax deferral increases with time, the real reason for increase in AER is as you explain above.
 
look at magician’s 2nd example. it is evident there. and I had stated the same 2 posts up as well.
3.75 is closer to 5 than 3.55 is. and that change is because you are deferring the taxes - which means the portfolio that has to grow is bigger. as a result there is more compounding effect.
 
cpk123 wrote:
look at magician’s 2nd example. it is evident there. and I had stated the same 2 posts up as well.
3.75 is closer to 5 than 3.55 is. and that change is because you are deferring the taxes - which means the portfolio that has to grow is bigger. as a result there is more compounding effect.
Click to expand...
Thanks CPK. Silly me. Now makes sense!. Thanks once again.
 
Think of it this way: if you deferred the taxes forever, you’d never pay the 30% tax, so you’d earn 5% AER.
 
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