Please help to figure this out… Q13 in the CFA reading 15: Calculate the pre-tax rate of return that is required to achieve the objectives: 1) Annual after-tax outflow of 26,000 2) 2,000,000 in 18 years We have: 1) 1,235,000 today 2) tax rate on income and capital gain of 40% 3) Inflation effect on outflow of 26,000 is covered (need not to be considered) The CFA answer to this Q is 4.427% after-tax, 7.38% pretax I know how they got 4.427%: PMT = 26,000, PV = 1,235,000, FV = 2,000,000, N = 18, CPT I/Y => 4.427% My question is: Is it OK to assume that they are going to pay taxes on capital gain every year? I mean, the answer of pretax return of 7.38% assumes that every year (N=18) they will pay taxes on capital gains and income. What if they invest today in non-dividend stocks and hold them for 18 years? I may be wrong, just need your opinion on this

then how can they get $26.000 after-tax for a living?

You are overthinking it.

Agree with ws, answer the question with the information given. Also, there has to be a negative sign in front of either PV or FV or you will get an error.

Also, remember that it’s a cash inflow to the person so its a Positive PMT if the person was putting 26,000 intot he fund each year it would be Negative PMT. So in other words, you should enter: N=18, PV = -1,235,000; PMT = 26,000; FV = 2,000,000; compute i. If you accidentially put PMT as -26,000 you would get 4.14% instead of 4.427%! Tricky

Thanks for the replies! I forget to put “-”, I calculated it with “-” … Maybe I was overthinking, but if you assume that: 1) The Annual pretax outflow is 43,333 (26,000/0.6) 2) They do not change portfolio a lot in the next 18 years (don’t pay taxes on capital gains, use dividends/coupon to cover 43,333, or even sell some stock to cover it) You will get the pre-tax rate of return of 5.59% PMT = 43,333, PV = -1,235,000, FV = 2,000,000, N = 18, CPT I/Y => 5.59% I know that the answer is based on my assumption 2), but how in the world I will know what assumptions are correct when solving this problem? They did not state that the portfolio gains/losses would be realized annually and they did not say that they will hold to it for 18 years either…

The portfolio MV is After Taxes. IF you use your method you would have to get the Beg MV and the End MV as Before Taxes, so N = 18, PV = -2,058,333; Pmt = 43,333; FV = 3,333,333, solve for i and you get 4.427%. Since the MVs given for a portfolio are 99.99% of the time AFter taxes, you have to calculate the return after taxes FIRST then take the return and Gross it up by the Taxes to get the Before Tax return. Does that makes sense?

I should also note, that if this was a tax-exempt plan then AFter tax = before tax.

Bigwilly, THANKS A LOT!!! I guess now I get it… It’s kind of confusing - I was sure that the phrase “Maclins have accumulated the following assets (current market value): … 220,000 in Barnett common stock.” means they did not pay any taxes yet and this amount is just = #shares*market value So should I always think that the $ amount of assets the family has in stocks/… is after-tax? I don’t want to make this kind of silly mistake during the exam

Bigwilly, why there is positive PMT (26 000) in the calculations ? I thought it is on the analogy of coupon payment for bond calculations. And because here we routinely withdraw from portfolio $26 000 we should use negative PMT. I know my logic is wrong because Return with negative PMT< Rerurn with Positive PMT. That means calculator consider positive PMT as outflow for portfolio. But I don’t understand why

A positive PMT is an outflow from teh fund or an inflow to the investor…an negative payment is an inflow to the fund or an outflow from the investor…

peter19, it doesn’t matter…swith the sign for every variable (except N), you will still get the same answer. As long as your PV has different sign from FV and PMT.

i actually have to side with rbaranov here. I made the same mistake and was shocked to see CFAI actually comupitng after tax return in this manner. Portfolio value IS NOT AFTER Taxes. When you MTM, you dont apply taxes, come on, look at GIPS it is not MTM with after taxes. After tax it is a liquidation value of the portfolio

so it means that when investor receives 26 000 that amount should be included in return for investor despite the fact the amount’ll not participate in future inv.process. How do you think why then bond’s coupons that are reinvested at YTM are set into calculator also like 26K in our case (just like Positive PMT)? so in both cases we have positive periodic payments for investor but : 1. in case of the bond these amounts are reinvested 2. in case of our portfolio these amounts are withdrawed from portfolio…but calculations are the same