After tax return

CFA Level III
#1

After-tax future value for

Investment income tax: [1+R(1-T)]^n

Wealth-based tax: [(1-T)+R(1-T)]^n

There should be the reason Curriculum/Kaplan use {(1+R)(1-T)]^n approach. Any idea?

#2

your formula is absolutely WRONG Mr Frank.

It is [(1+r)(1-T)]^n

1 $ become 1 + R at the end of year.

the entire (1+R) gets taxed @ T so (1+r)(1-T) is what 1 $ becomes at the end of 1 year.

at the end of N years => [(1+r)(1-T)]^n

#3

Wealth tax is applied on both return and principal.

Investment tax is only applied on return.

Think of this as 1st year. Then compound n years.

#4

I think Frank is right

(1+r)(1-T)= 1-T+r-rT=1-T+r(1-T)

but the curriculum’s is more intuitive

#5

that works ONLY for 1 period. It is not the same when that is raised to N years.

the formula - when I commented on Frank’s original post - missed the bracketing.

think about what would be easier to do

(1.1 * 0.98)^20

or

[(1-T)+R(1-T)]^n

(0.98 + 0.1 * 0.98)^20

#6

I just compared what’s relevant. Of course for multiple periods you raise the bracket to the power of n

#7

May I know why my formua is wrong?

From intuition, it shows tax deducts the principle directly. [(1-T)+r(1-T)]^n

From math, [(1+r)(1-T)]^n= [1-T+r-rT]^n=[1-T+r(1-T)]^n

#8

i missed the brackets. Your formula is ok. However it is a long way of going about it.

would you do for a 10% return, 2% tax…

(1.1 * 0.98)^20

or

[(1-T)+R(1-T)]^n

(0.98 + 0.1 * 0.98)^20

#9

Thanks. Yes, the curriculum one is quicker for calculation. But I think [(1-T)+r(1-T)]^n is more intuitive, no?

#10

not sure what you are fighting the intuition for.

1 $ grows to (1+r) due to r% return.

and then tax is applied to the entire amount.

so what is left = (1+r)(1-t)

and this continues on for n years

so [(1+r)(1-t)]^n

#11

Thanks cpk. Both become intuitive now!

#12

Just curious,

Frank, what’s your background? mine is STEM

#13

Physics

#14

Slaying a new beast. That’s commendable

#15

Not yet… smiley Hope will not be killed by a new beast…