Was just reviewing an exam and had been asked to calculate the pre tax required return. I had calculated the pre tax amount required by the investor and then calculated the return and added in the inflation. The answer calculates the return off the after tax required amount, adds in the inflation and then grosses up that entire amount by (1 -t). Do you always calculate the return using the latter method? Also, is the reason why this is done in order to preserve the portfolio on an after tax basis?
outq13 Wrote: ------------------------------------------------------- > Was just reviewing an exam and had been asked to > calculate the pre tax required return. > > I had calculated the pre tax amount required by > the investor and then calculated the return and > added in the inflation. Portfolio gains are going to be taxed so this method won’t work for a taxable investor. > > The answer calculates the return off the after tax > required amount, adds in the inflation and then > grosses up that entire amount by (1 -t). > > Do you always calculate the return using the > latter method? Also, is the reason why this is > done in order to preserve the portfolio on an > after tax basis? I would go with this method. This method give you the before tax return necessary to keep the value of the portfolio intact on the real basis.
If you’re doing geometrical compounding, both should return the same results. There are only multiplications and divisions, so regardless of the order thu which you go thru these, you should get the same result. If you’re doing arithmetical compounding, well you know that you would only get an approximation anyway…
You don’t get the same result - in the first calculation you are not gross up the inflation component for taxes and in the 2nd result you are. That is the difference between the two.
You are taxed on inflation so you have to do it the second way (at least you are in the US, it has been called the phantom tax).
outq13 Wrote: ------------------------------------------------------- > You don’t get the same result - in the first > calculation you are not gross up the inflation > component for taxes and in the 2nd result you are. > That is the difference between the two. Ok, so you are adding inflation rather than multipling by 1+inflation. Same caveat as geometrical/arithmetrical. I stand to what I said, if you only do multiplications and divisions, it doesn’t matter in which order they were performed.
mwvt9 Wrote: ------------------------------------------------------- > You are taxed on inflation so you have to do it > the second way (at least you are in the US, it has > been called the phantom tax). Yes, I agree. You either do it the second way or you multiply by 1+inflation.
olivier Wrote: ------------------------------------------------------- > outq13 Wrote: > -------------------------------------------------- > ----- > > You don’t get the same result - in the first > > calculation you are not gross up the inflation > > component for taxes and in the 2nd result you > are. > > That is the difference between the two. > > > Ok, so you are adding inflation rather than > multipling by 1+inflation. Same caveat as > geometrical/arithmetrical. > > I stand to what I said, if you only do > multiplications and divisions, it doesn’t matter > in which order they were performed. This seems off to me oliver. Can you show me where I am wrong? Pre-tax expenses needed from portfolio are 50k Taxes are at 20% Therefore, After Tax expenses needed are 40 Asset base in 5,000k inflation is 4% 40k/500k=8% real after tax 1.08*1.04=12.32% geometric nominal after tax 8%+4%=12% arithmetic nominal after tax 12.32%/(1-.2)=15.4% geometric before tax nominal 12/(1-.2)=15% arithmetic before tax nominal 50k/500k=10% real before tax 1.10*1.04=14.4% geometric nominal before tax 10%+4%=14% arithmetic nominal before tax
olivier Wrote: ------------------------------------------------------- > > Yes, I agree. You either do it the second way or > you multiply by 1+inflation. You mean the tax rate?
Which exam are you reviewing? Spoiler for the 2003 CFAI Exam. In the 2003 individual IPS question they ask for pre-tax return. They calculate the return based on after tax needs and they simply add the expected inflation to that amount. They do not include inflation before accounting for taxes.