# 2 tax formulas... Accrual equiv after tax return and Acc. Equiv Tax rate

seems so easy… wondering why im spending 2 hours figuring out what/how these formulas work and these quesitons… why???

You are falling victim to the “there-is-still-plenty-of-time” trap… 94.6% of CFA candidates (at any level) display it in varying degrees of seriousness.

It is not lethal and it rapidly disappears as (in the words of a fine tutor) '…one starts to smell the tulips…"

It’s pretty straightforward: you start with \$100,000, earn 7% per year for 30 years, pay a bunch of taxes (some annual, some deferred, whatever), and end up with \$600,000.

The accrual equivalent return is the annual compound return that gets you from \$100,000 to \$600,000:

\$100,000(1 + RAE)³º = \$600,000

RAE = 6.1545%

The accrual equivalent tax rate is the tax rate that gets you from 7% per year to 6.1545% per year:

6.1545% = 7%(1 − TAE)

TAE = 12.08%

My pleasure.

Magician, I believe whatever the CFAI does not clarify , you do. You make all of our lives easy and fun (at least on the CFA front). There is a collective thanks for that. I learn so much each time I see your post. Personally , I am overwhelmed.

Keep the wisdom flowing to us.

You’re quire welcome, ABAL.

I’ll do my best.

Thanks - starting to make sense after doing lots of practice questions. Def. a lot of ways they can ask them.

You’re welcome.

I would not say that any of this is making our lives fun but magician is definitely making our lives easier. Greatful as well! Thanks

Happy to be of help.

Quesitons like htis are the ways that are fustrating… seems like an easy questions.

And i do know the 3 tax formulas and the 2 accrual ones…

A stock is expected to increase in value form \$500 to \$1,000 over a five year peirod. The applicable cap gains tax rate is 28%. What is the expected after-tax value in five years.

Steps: 1) First find the pre-tax investment return.

1. Then use the return in the cap gains tax rate formula.

You have \$500 (= \$1,000 − \$500) in gain, taxed at 28%; that’s \$140 in taxes.

The value is \$860 (= \$1,000 − \$140).

Who needs a stupid formula?

Of course, they may have meant that there was an annual capital gains tax. Then we need the annual return:

\$500(1 + r)^5 = \$1,000

(1 + r)^5 = 2

1 + r = 2^(1/5) = 1.1487

r = 14.8698%

r(1 − t) = 14.8698%(1 − 0.28) = 10.7063%

\$500(1 + 10.7063%)^5 = \$831.44

Again, who needs a stupid formula?

I usually do this using TVM.

FV=1000 PV=-500, N =5 cpt I/Y

That’s how I’d do it on the exam.

But you still don’t need to memorize the tax formula.