# pre tax vs after tax return

Is it {1+[after tax return/(1-tax rate)]} x (1+inflation rate) or [(1+after tax return) x (1 + inflation rate)]/(1-tax rate)

the first one

Neither, second one is close though. In CFAI Book #2 page 113 it says the following: “[Note: Strictly speaking, the inflation rate should be adjusted upward by the portfolio’s average tax rate…]” Inflation affects how much things cost over time (cars, TV’s, etc.). You pretty much always buy these things with your after-tax dollars. Because inflation refers to prices and how much they change from year to year it is already in an after-tax form. Thus a pretax return would include a higher inflation rate (adjusted for the tax rate). I’m almost 100% the equation should be the following: Pretax Rate: ((1+r)*(1+i) - 1) /(1-t) r - real return i - inflation t - tax rate

nominal after tax (NAT) = CF needs / portfolio value real after tax (RAT) = [(1+NAT)(1+i) - 1] real pre tax = RAT / (1-t)

So generally for the exam we: Calculate the nominal return Multiply by inflation divide by (1-tax rate)

Hold up. A nominal rate INCLUDES inflation. Slouisclar’s post with respect to the real after tax (RAT) is incorrect, it’s double counting inflation. It should read as follows: RAT = [(1+NAT) / (1-i)] - 1 You basically geometrically ‘subtract out’ the inflation to get the real after tax (RAT)

slouiscar : Shouldn’t Nominal returns be higher than real returns ? Or am i just confused in between the 2 of them. Thanks

From wikipedia. The “real interest rate” is approximately the nominal interest rate minus the inflation rate So wouldn’t it be the real rate * inflation all divided by (1-tax rate) ?

Arithmetic: r + i = n Geometric: (1+r)*(1+i) = (1+n) r - real rate i - inflation n - nominal rate As long as inflation is greater than 0% the nominal rate will be larger than the real rate.

you got it hh ! You just have to be careful with the adding/subtracting of 1 when you are using the different ways to calculate it, thus: { [(1 + REAL_RATE) * (1 + INFLATION)] - 1 } / (1 - TAX_RATE)

Wow, sorry. I flipped the terms real and nominal. My brain is mush apparently. I think what I meant was this: The real required return after taxes is = CF needs / portfolio value …adjust for inflation to determine the nominal after-tax RR = (1+real-after-tax RR)(1+i) - 1 …adjust for taxes to determine the nominal pre-tax RR = (nominal-after-tax RR) / (1-t)

There ya go !

man, i got backwards on that too. thats one of those things that I do correctly in my head but when I see it written out I short circuit for some reason.

I try to remember a simple rule…do before-tax calculation at the very end, after everything else is accounted for. Then you should be safe.