# Before Tax Required Return Calculation

How does the CFAI wants a specific calculation laid out as to how to calculate the before tax return? An example is an expense base is being met… eg 200k/yr and the person retires, so you need to calculate before tax return, which need to take into account inflation. 2 ways to go about this, taking a simple example: 1) ([EXP/AssetBase -1] + Inflation)/(1-t) 2) (EXP/1-t)/Assetbase -1) + Inflation Obviously you get two different #'s (the first being higher than the 2nd) as your are grossing up a larger # so there will be a greater effect. The reason I ask is because there seems to be some discrepancy in this issue. EG from a 2003 exam (in an end of reading question in Monitoring and rebalancing in the CFAI (reading 42 Q4), the CFAI use this method in the question body. Schweser also outlines this method in the Asset Allocation summary. The CFAI and Schweser both use the former method in the past exams, I’ve seen and in the Schweser Exam book, Exam 2, Morning session, Q6). This is a big contradiction to me.

I think the most recent exam papers have been using option 1.

Option 1 also makes more sense. Option 2 suggests that extra returns to cover inflation are not taxable. BTW, I don’t think you should -1 in either formula.

I agree, that make sense.

i think #1. think of it this way: your expenses grow at 5%/year inflation = 3% you need an 8% return after tax =8%/(1-t)

I think it is 2. Say your expenses are \$10,000, tax 30%, your need \$10,000/0.7 to meet expense requirement. And suppose you have \$1,000,000 portfolio, the required real before-tax return is (\$10,000/0.7)/\$1,000,000. On the top of that, you add inflation to get your required before tax return.

There are two portions of inflation, i.e. inflation to cancel out the effect on living expense and inflation to protect the real purchasing power of the portfolio. The previous portion is taxable while the latter portion is not taxable. I think 2 is a precise way to calculate the required return. But 1 has its merit because it provides a safety margin (it usually results in a higher return).

Option 1 results in a higher return not because of a safety margin but because the extra portion of the return is also taxable at 30% rate. If you’re thinking that unrealized gains on portfolio value are not taxable, don’t because all CFAI examples all say that the tax applies on all income and appreciation.

bump, yep just did that 2003 question. Got all correct except for return. i am sticking to ([EXP/AssetBase -1] + Inflation)/(1-t), where EXP expected return in the year to come (current * (1+inflation))

I agree, they actually use this method in 2000 as well. Do we have to assume that asset returns given are Before tax if it’s not mentioned anywhere ?

it was mentioned in this example that returns are before tax, but yes, i would assume so