tax

In comparing tax deferred accounts versus tax free accounts which of the following statements is most accurate? A) Assuming equivalent rates of return between the tax free and tax deferred investments, the tax free investment will always result in a greater accumulated future value. B) If the current tax rate is less than future tax rate then you are better off investing in a tax deferred account. C) If the investment returns and tax rates are equal for both the tax deferred and tax free accounts the future accumulated value will be the same. is this a crappy question, or am I missing something?

C

I like C as well

C is correct. make sense to me now.

An investor deposited $54,000 in a zero coupon bond position 10 years ago. It consisted of 100 zero coupon bonds each with a face value of $1,000 and 10 years to maturity. Over the years he has sold portions of the position to pay income taxes on the position. The investor’s average marginal tax rate is currently 20%. At maturity, the value of the position is $92,000. Compute the accrual equivalent tax rate.

A is correct as well. If the rates of return are the same, Tax Free grows to be I((1+r)n)) Tax Deferred is the same value times (1-t). This only doesn’t work if you assume they started with two different amounts of money or there was a tax at the beginning they didn’t mention. So therefore I say crappy question.

1morelevel Wrote: ------------------------------------------------------- > A is correct as well. > > If the rates of return are the same, > > Tax Free grows to be I((1+r)n)) > > Tax Deferred is the same value times (1-t). > > This only doesn’t work if you assume they started > with two different amounts of money or there was a > tax at the beginning they didn’t mention. > > So therefore I say crappy question. I disagree. A assumes “equivalent rates of return” not equal rates of return between the tax free and tax deferred investments, therefore, tax free and tax deferred investments should generate the same accumulated future value.

tax free = tax-exempt ? CFAI use “tax-exempt”

happyking - Is it 13.9%?

Oh, gotcha. Still poor question IMO. “Equivalent” should not be that vague.

mp2438 Wrote: ------------------------------------------------------- > happyking - Is it 13.9%? Correct, 13.99%

hmm, I got 13.89%. Close enough.

Ok, here is the difference between the two accounts (tax-free v. tax-deferred): FV(tax-free) = 1,000*(1-To)*(1+r)^n FV(tax-deferred) = 1,000*(1+r)^n*(1-Tn) The only difference here is To (Tax rate today) and Tn (Tax rate in year n) … if To > Tn, then the tax-free account will have a lower future accumulated value. And vice-versa…

what’s the calc here? not getting the exact answer.

happyking02: could you show the calculation for your questions? Thanks

“An investor deposited $54,000 in a zero coupon bond position 10 years ago. It consisted of 100 zero coupon bonds each with a face value of $1,000 and 10 years to maturity. Over the years he has sold portions of the position to pay income taxes on the position. The investor’s average marginal tax rate is currently 20%. At maturity, the value of the position is $92,000. Compute the accrual equivalent tax rate.” Return without tax = [(100*1000)/54,000]^(1/10) -1 =6.36% Accrual equivalent return = (92,000/54,000)^(1/10) =5.47% Acrual equivalent tax rate = 1- (5.47%/6.36%) =13.99%

i’m an idiot - had my pre tax return switched with my accrual equivalent after tax return. f me

I left it in excel form to get 13.89%. Amazing that simple rounding leads to a .1% increase. 0.054725405 0.063556642 as opposed to 0.0547 0.0636

Thanks Happyking02. My difficulty with this question was how do we know that final pre-tax amount was 100,000. The questions says - “Over the years he has sold portions of the position to pay income taxes on the position.” Any thoughts…

Thanks Happyking02. My difficulty with this question was how do we know that final pre-tax amount was 100,000. The questions says - “Over the years he has sold portions of the position to pay income taxes on the position.” Any thoughts…