What’s the difference between realized after tax return and accrual equivalent after tax returns? realized after tax return = r(1-t) accrual equivalent after tax returns = the “r” that makes the equation “FV = PV(1+r)^n” work, where FV is the terminal value of the taxable portfolio But when you think about it, shouldn’t they be the same? The return decreased for taxes should equal the rate that equates the PV with the after-tax FV. Here is a question on the topic that is stumping me: You compute that an investment with a current value and basis equal to $20,000 will have an annual return after realized taxes equal to 10% for the next 12 years until it is sold. The effective capital gains rate will be 15%. What will be the accrual equivalent after-tax return? A) 9.02%. B) 8.50%. C) 12.50%. Your answer: B was incorrect. The correct answer was A) 9.02%. The balance in the account after payment of all taxes in 12 years uses the future value interest factor after all taxes: Future value = $20,000 × [((1.1)12) × (1 - 0.15) + 0.15] = $56,353 The accrual equivalent after-tax return is then ($56,353 / $20,000)1/12 − 1 = 9.02%. [((1.1)12) × (1 − 0.15) + 0.15]
also in this q i dont see how they can put the after tax return into the equation when computing the future value, and then go ahead and tax it again with the 1-.015
20,000 * (1+.10)^12= 62,768.57 Your basis is 20,000, so your taxable gain is… 62,768.57-20,000 = 42,768.57 Capital Gains Taxes of 15% so… 42,768.57 * 0.15 = 6415.29 Your after tax gain is… 62,768.57 - 6415.29 = 56,353.28 Now you compute the Accrual Equivalent Return as follows: X(1+Rae)^n = Y 20000 (1+Rae)^12 = 56,353.28 Rae = 9.016%
thanks for the response, but all you did was rewrite their computation. i think the diff between after tax return and accrual equivalent after tax returns has something to do with tax drag and value of deferrals increasing as time goes on but i just dont see why accrual equivalent after tax returns is lower and approaches pretax return (as page 325 says) if it additionally incorporates deferred taxes.
I see. I didn’t get what you were asking. I’ll respond when I get home from work.
I think it’s just that “realized after tax return” refers to the annual after tax return during the time the investment is held, and “accrual equivalent return” refers to the after tax return _including_ the capital gain taxes paid by the time you sell the investment. Let’s say you hold some shares for 5 years and pay taxes on your dividends every year (these determine your “realized after tax return”). After 5 years you sell the shares and pay CG taxes on the gains realized all at the end. It is these latter ones that make the difference in the “accrual equivalent return”. Hope that helps.
naze, thanks for your help. i think youre right. the way i see it now, the accrual equivalent returns add in the deferred taxes from the capital gains taxes which occur at sale date. i suppose that this means that the accrual returns will always be smaller (because they include a tax for the deferred capital gains). also, as far as the example i posted up top, its a very simple question but what bugs me is that they say “annual return after realized taxes equal to 10%” and they stick that # into the formula. the “r” in that equation should be the pre-tax return, just like it is on pg 318, book 5. so it may (hopefully) be an error on schweser’s part. no way should u take the after tax return and then tax it again at the CG rate.
It seems to me that the 10% is used consistently. It’s the after tax return based on realized taxes, so it tells you how much your investment grows every year “after taxes”. 12 years @ 10% after tax equals a factor of 1.1^12. The Schweser formula you are referring to is purely for (unrealized) capital gains. It doesn’t take into account any realized gains before the investment is sold. So, if there are taxes on realized CG (or dividends, or interest), you have to account for those first. That gives you the “r”, which is “after tax” as far as DIV/Int/realCG is concerned, but “pre tax” when it comes to unrealized CG. Hope that helps.
so what youre saying is, in that schweser question on pg 318, they are calculating the unrealized CG tax only, kind of viewing it in isolation (neglecting all the realized returns and taxes paid over the life of holding the stock). in this question above, the “r” is the return AFTER yearly taxes but BEFORE unrealized cg. i assume that the reason that it is ok to use different deifinitions of “r” is because the questions are asking for diff things (only deffered cg in the book question, and realzied + unrealized in this one, since you need to find the r that equated pv with fv)…
Correct. Think of it this way: If r is the annual after tax return, then you don’t have to worry about the annual taxes anymore and you can use the formula from the book that deals with the taxes on (unrealized) capital gains exclusively.
great. i doubt this type of detail is necessary for the exam but i think i get it–thanks for your help with this.