# After tax real return -> Before tax nomial return, how to calculate?

I don’t have the book in front of me, but if I remember it correctly, we should do it this way:

after tax real return + expected inflation rate = after tax nomial return ( or shall I use compounding??)

after tax nominal return / (1-tax rate) = before tax nominal return

But if you look at Schweser Book 2 P228 Q6 answer, they firstly calculate before tax real return and then add inflation rate.

Which way is correct?

I don’t use schweser, but I think they are correct. After Tax Real Return / (1 - Tax) = Before Tax Real Return. Then you can add inflation (or more precisely you do (1+r)*(1+Inflation)). It shouldnt make much difference usually …

The mistake you’re making is you are essentially taxing inflation

The order in which you do things depends on whether the account in which you have your portfolio is taxable or not.

If it is taxable – so that you are taxed on 100% of your returns, including the return to cover inflation – then you add inflation to your after-tax real return to get an after-tax nominal return, then divide by (1 – tax rate) to get the before-tax nominal return.

If it is nontaxable – so you are taxed only on the withdrawals from the account to cover your expenses, but not the return to cover inflation that stays in the account – then you divide your after-tax real return by (1 – tax rate) to get the before-tax real return, then add inflation to get the before-tax nominal return.

Generally the vignette will tell you whether the account is taxable or not. CFA Institute’s default position used to be that it is nontaxable (I’m told), but they’ve changed that to a default position of taxable (I’m told). Should the vignette be silent on this point, I’d go with taxable, but I’d state that explicitly: I’m assuming that I pay taxes on all returns, including those to cover inflation.

Don’t think about compounding the return and inflation; you get full marks for simply adding them, so compounding is more work for no reward.

That’s very very helpful! Thank you.

You’re welcome.

Really struggling on calculating the required return for CFAI EOC Qsn 13 - I just don’t see how the required rate of return is after tax is 4.427% - can anyone help explain ? The return calc.I get (after tax) is 26,000/1,235,000 which is 2.11%.

Thanks a lot.

I struggled with this too. I calculated an income need of 2.11% (26,000/1,235,000). There’s also a growth need of 2.71%, which represents the compound average annual return needed to turn 1,235,000 into 2,000,000 in 18 years (2,000,000/1,235,000)^(1/18) = 2.71%.

Income need = 2.11%, Growth need = 2.71%. Total Required Annual Return is 4.82%, and I don’t see how that’s wrong but the book says it’s 4.427%. As long as you show your work, it should be good.

PV=1235(Inflow) , FV=-2000(outflow), PMT=-26 (outflow), N=18

CPT I/Y = 4.427%

Thank you both ! It was driving me crazy - I did the FV/PV calculation but put N=18 x 2 …