# Pre-tax return computation: Contradictory CFAI Examples

There is an extremely disturbing discrepancy in the way CFAI calculates Pre-tax nominal return between an example in their reading and a question in their 2009 morning session exam.

The Susan Fairfax example in the CFAI Text, Page 190 of Book 2, Chapter 10 (Managing Individual Investor Portfolios) implies to take after-tax return (3% in example), add inflation (4%), then divide by (1 - T) [here (1-T) = 0.65] to get the pre-tax nominal return requirement of 10.8%.

In the CFAI 2009 morning section, the after-tax return would be 45,000 / 1,000,000 = 4.5%. Following the same methodology as Fairfax, adding the 4% inflation = 8.5%, then dividing by (1 - 0.20) = 10.625%. But the answer key doesn’t follow the same methodology as Fairfax. Instead, it first divides the 4.5% by (1 - 0.20) to get 5.625%, then adds inflation of 4% to get 9.625%.

Which methodology should be used? This is making me so nervous because I don’t know which way their answer key will do it!

I have seen other posts on this forum about the Fairfax example, and others about the surrounding question I have here, but none of them addresses this discrepancy.

Thank you in advance. Hopefully this post helps out more than one person here.

Stick to the current curriculum, not a 5-year old exam.

In the 2009 exam, they were explicit about taxes only being on withdrawals from the account. I think the default assumption is that all gains from the account are taxed though (so thus inflation would also need to be grossed up for taxes).

I don’t have the current CFA Institute text, but in the 2009 morning session, question 1, it is explicit that only the withdrawals from the Tracys’ account are taxable ; thus, the inflation component that will remain in the account is not taxed.

I’ve written this time and again: read the vignette. It will tell you whether inflation is taxed or not. You needn’t guess about which approach to take.