# Tax or Inflation First? Why?

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:

Nominal Pre Tax Income: \$100 x 1.02 = \$102 then tax it: \$102 x (1-0.25) = \$76.50

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:

1. Apply tax to the nominal pre tax return
2. Deduct inflation

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:

1. Deduct inflation
2. Apply tax to the real pre tax return

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