Question on Taxes

So I’m going through the section on taxes and I came across a question that has me confused and was wondering if someone may be able to help.

The question is as follows:

John Kaplan and Anna Forest both have €100,000 each split evenly between a tax deferred account and a taxable account. Kaplan chooses to put stock with an expected return of 7 percent in the tax-deferred account and bonds yield- ing 4 percent in the taxable account. Forest chooses the reverse, putting stock in the taxable account and bonds in the tax deferred account. When held in taxable account, equity returns will be taxed entirely as deferred capital gains at a 20 percent rate, while interest income is taxed annually at 40 percent. The tax rate applicable to withdrawals from the tax deferred account will be 40 percent. Cost basis is equal to market value on asset held in taxable account.

  1. What is Kaplan’s after-tax accumulation after 20 years? A €196,438. B €220,521. C €230,521.

  2. In the previous question, what is Forest’s after-tax accumulation after 20 years? A €196,438. B €220,521. C €230,521.

In question 14 I am having difficulty understanding the answer’s formula used for tax deffered account (stocks)

FVTDA =€50,000(1+r)n(1−Tn)

Why is there no cost basis added back? I thought for tax deferred capital gains we need to add back the cost basis?

In question 15 the answer for the taxable account (stocks) does include the cost basis -> why does this one include adding back the cost basis but above it does not?

FV =€50,000⎡(1+r)n(1−t ) + t ⎤

If I recall this question correctly, has to do with one of the investments being bonds w/o a basis. Bonds in a TDA allow you to defer the interest income. S2000 may have more insight for ya

I believe that the answers are, respectively, A and C.

Because in the tax-deferred account the tax is on withdrawals, not on gains: the entire amount withdrawn is taxable.

Because in the taxable account the tax is paid on returns (gains), not on the total value.

I strongly encourage my candidates not to try to memorize the formulae and then pick the appropriate one for a given problem. I encourage them to work through each problem and _ follow the money. _

For Kaplan’s stock in the tax-deferred account, it grows for 20 years at 7%, then 40% _ of the total _ is paid in taxes; the net amount is €116,091.

For Kaplan’s bonds in the taxable account, they grow for 20 years at 4% × (1 – 0.4) = 2.4%; the net amount is €80,347.

For Forest’s bonds in the tax-deferred account, they grow for 20 years at 4%, then 40% _ of the total _ is paid in taxes; the net amount is €65,734.

For Forest’s stock in the taxable account, it grows for 20 years at 7%, then 20% _ of the gain _ is paid in taxes; the net amount is €164,787.

Thanks for your thoughts andytrader and thanks for the very detailed explanation s2000magician. Your answer cleared up any doubts I had about this question. Many many thanks!

My pleasure.

here i m all alone on a friday, reading threads in AF…and i dunno what the qn is talking about…the exam is 3 months back only…im screwed…

thank you for the very detailed explanation s2000magician.

Still only one question on the Forest stock :

“Forest’s stock in the taxable account, it grows for 20 years at 7%, then 20% _ of the gain _ is paid in taxes; the net amount is €164,787”

If gain is 7% and 20% of that gain is taken away in taxes - Forest is left with 0.07 (1 - 0.20) = 5.6%

5.6% accumulated over 20 years = 2.97 x 50,000 = 148,679

You’re treating it as if 20% of the gain is taxed each year. That’s not what’s happening. None of the gain is taxed each year; the total gain is taxed at the end.

The reason that they’re different is that by not taxing it until the end, you have a higher amount each year earning a higher rate of return each year: you get a compounding bonus when you don’t tax it until the end.

for taxed account so why is bond treated as if it is taxed each year and stock is treated differently by adding back the basis?

I guess my question is why is bond taxed annually buy stock is deferred capital gain?

Technically that’s specific to the country. But generally that’s just out the tax code developers assigned stocks and bonds. But I guess you might find a country somewhere unknown that allows stocks to be taxed annually and bonds to be deferred.

Because that’s what the author of the question said to do.

Because that’s what the author of the question wanted.

You don’t need to know any tax law. They’ll be super diligent on exam to give you any inputs or information you’ll need. Just do what they say.

Why do you use pre-tax dollars when calculating FVIF for the taxable account? Wouldn’t that provide a tax advantage?

Do you have an example of this? Perhaps the page number from the curriculum?