# A question about required pre-tax returns

An investor has a required, post tax return of 3% to cover his spending and also wants to preserve the real value of the portfolio.

His tax rate is 25% and inflation is 2%.

What is his required, pre-tax return?

I have it as: (3 + 2) / 0.75 = 6.66% or ((1.03)(1.02) - 1) / 0.75 = 6.75%

The Schweser book has it as: 3 / 0.75 + 2 = 6% (book 2, asset allocation self test, page 252.)

But the return to cover inflation is going to be taxed as well, so why shouldn’t it be grossed up as it is in my calculation?

Is this an error in the book? or an error in my thinking?

Thanks,

Chris

Yeah, im confused, too, because volume 2 (CFAI) page 193, the guy wants a 3 % REAL after-tax return, which means a gross return of 10.8%

3 % + 4% inflation = 7% after-tax nominal return

pretax = 7% / (1-.35 tax rate = 10.8%

Schweser is wrong?

In my books

"Carlson’s spending rate is estimated to be 3%. With an inflation rate of 2%, Carlson’s after-tax return requirement is equal to [(1.03 × 1.02) – 1] = 5.06%. Given a tax rate of 25%, Carlson’s before-tax return requirement is equal to [5.06% / (1 – 0.25)] = 6.75%. "

perhaps a difference between the pdf and hardcopy!

the thing is, in one of schweser’s practice exams, they do it the “wrong” way, too!

Schweser is wrong.

Thanks for the comments guys. I am going to assume Schweser is wrong here (unless anyone can explain otherwise). Its the only thing that makes sense.

Thank you for this post, I was literally just thinking about this and couldn’t find my notes. I remember that one always came first, inflation, or taxes, and couldnt remember which. TBH I still don’t really understand the logic but I’m just gonna remember “IT”

In schweser class, I was told that adding the inflation at last. IPS’s return is just an approximation – yes, you aren’t taxed on inflation, but you’re taxed on any realized gains. OP’s first post is a valid solution. My vague memory tells me that CFAI answers to this kind of questions are not always the same, either. All answers from old IPS questions, EOC and schweser’s are acceptable.

hopefully “all” , not “none” !