Example:
Nominal pretax return of 9%
Tax rate of 25% and inflation of 2%
What is the real after tax return?
Which order do I do the calculation (i.e., first remove inflation, or first calculate after tax)?
Why should we do it in that order?
Greatly appreciate any help - these should be easy marks and I want to make sure I get them in the bag!
Thanks
add inflation, then apply tax. Otherwise you would be assuming any growth due to inflation is tax free.
I would say this question does not have any implications because of order:
Let’s say:
Real Pre Tax Income: $100
Taxed @ 25% Inflation being 2%.
Let’s calculate it both ways: First with inflation, then Tax. Second: tax it, then apply inflation:
Add Inflation first:
Nominal Pre Tax Income: $100 x 1.02 = $102 then tax it: $102 x (1-0.25) = $76.50
Add inflation after tax:
Real After Tax: $100 x (1-.025) = $75 and then to Nominal: $75 x 1.02 = $76.50
It’s one multiplication: $amount Real Pretax * inflation * (1-tax) = nominal after tax. But maybe I misread your question.
Thanks Goldmin.
For the example, it’s looking for the real after tax return.
First Approach:
Wouldn’t I be deducting too much?
I.e., 9%(0.75) - 2% = 4.75% real after tax return.
If I gross up the above to get the real pre tax value it’s 4.75%/0.75 it’s 6.33%
Second Approach - the reverse is to:
I.e., (9%-2%) * 0.75 = 5.25% real after tax return.
If I gross up the above to get the real pre tax value it’s 5.25%/0.75 it’s 7%.
Final comparison - if I take the given 9% (the nominal pre tax value) and get the real pre tax value , all I need to do is deduct 2% = 7%
Conclusion:
In this example, I need to use the second approach (take the nominal pre tax return, deduct inflation, and then apply tax) to get the real after tax return.
BUT! Schweser Mock AM Q 12 uses the first approach!
HELP!
so far, I’ve done 2014-2017 AM cfai exams and iirc none of them asked for pre-tax returns, only after-tax returns (either real or nominal)
expanding from this, it seems that cfai would assume return to keep up with inflation is taxable and therefore:
(real after tax + inflation)/(1-tax rate)
Thanks all -
@roebftb: What you wrote makes sense, but I can’t translate that into this example, because I don’t know the return values. Effectively your example shows X(1 + a)(1 + b) = X(1 + b)(1 + a).
@Edbert: Sorry for my thoughts being all over, but the question asked to go from nominal pre-tax to real after-tax return, which is consistent with your first statement. My comparison was just making an example of the 2 methods to get there.
For the formula you wrote: I guess I’m now just confused lol. Is the equation below correct too? If so, the first component equals the nominal pre-tax, hence my decision to subtract inflation first.
(real pre-tax + inflation) * (1-tax rate)
A more qualitative explanation:
A firm earns on products sold, which create income, which is taxed. If the income increase because of inflation, this component is also taxed.
Have I taught you people nothing?
Look at the account: is it taxable or not?
If so, inflation is taxed: multiply by (1 − tax rate), then subtract inflation.
If not, inflation is not taxed (as it will remain in the account): subtract inflation, then multiply by (1 − tax rate).
Sheesh!
Thanks - I think I’m just being thrown off by this corner case. I understand the logic from real pre-tax to nominal after-tax. I just going to remember the route to nominal after-tax and adjust from there. E.g., below:
Real pre-tax -> Nominal pre-tax -> Nominal after-tax: (real + inflation) * (1-tax rate)
Nominal pre-tax -> Nominal after-tax -> Real after-tax: [nominal * (1-tax rate)] - inflation
Appreciate you sticking with me as I go insane 