A common question that plagues many Level III candidates is how to treat inflation when calculating a **nominal**, before-tax required rate of return for an individual investor: do you add inflation to the real after-tax return, then compute the before-tax return, or do you start with the real after-tax return, compute the before-tax return, then add inflation? (If you’re asked to calculate a * real*, before-tax required rate of return, you do not add inflation, so the question doesn’t arise.)

Obviously, the two approaches will give you very different before-tax required rates of return. For example, suppose that you have calculated that the real after-tax required rate of return is 5%, you anticipate 2% inflation, and your client’s marginal tax rate is 40%.

If you add inflation before accounting for taxes, you get:

\[Before–tax\ return\ =\ \frac{5\%\ +\ 2\%}{1\ -\ 40\%}\ =\ \frac{7\%}{0.6}\ =\ 11.67\%.\]

If you account for taxes before you add inflation, you get:

\[Before–tax\ return\ =\ \frac{5\%}{1\ -\ 40\%}\ +\ 2\%\ =\ \frac{5\%}{0.6}\ +\ 2\%\ =\ 10.33\%.\]

You cannot afford to write 11.67% when the correct answer is 10.33% – or vice versa – nor can you afford to write that it might be one and it might be the other; you’re guaranteed to lose marks.

The question of which approach is appropriate can be solved easily, by appealing to – where else? – the vignette: it should tell you whether the account in which the portfolio is held is a taxable account or a nontaxable account. (If the vignette is not explicit whether the account is taxable or not, it appears that CFA Institute has historically taken the default position that it is nontaxable, but I have heard recently that they have changed that default position to assuming a taxable account. I would suggest that you follow this guideline (*after you’ve made absolutely certain that the vignette doesn’t mention whether the account is taxable or not*), but state explicitly in your answer that you assumed that the account was taxable, so that all returns – whether they are withdrawn from the account or remain in the account – were subject to taxes. However, I honestly believe that

*, and I have a preponderance of evidence to substantiate that belief. See below.)*

**you will not have to rely on a default position**Taxable Account

If the account is taxable, then the entire return that the account earns – to cover the investor’s annual expenditures as well as to cover the increase required to keep pace with inflation – is taxed. In that case, you use the first calculation of 11.67%: the account has to earn 7% after taxes to cover spending and inflation, and that entire return (yielding 7% after taxes) is taxable.

Nontaxable Account

If the account in nontaxable, then the only portion of the return that will be taxed is the amount that the investor removes from the account to cover expenditures; the return to cover inflation remains in the account, so that portion isn’t taxed. In that case, you use the second calculation of 10.33%: the account has to earn 5% after taxes which will be withdrawn and taxed, and an extra 2% which won’t be withdrawn and, thus, won’t be taxed.

Examples from CFA Institute Morning Exams

*2004*

*“. . . all capital gains and investment income are taxed at 40 percent . . . .”*

Here, all returns, whether for living expenses or for inflation, are taxable. Add inflation, then increase the sum for taxes.

*2005*

*“Calculate the after-tax nominal rate of return that is required to achieve this objective for her first year of retirement.”*

Here, the calculations are all done after taxes; the problem doesn’t exist.

*2006*

*“Calculate the after-tax nominal rate of return that is required during his first year of retirement.”*

Here, the calculations are all done after taxes; the problem doesn’t exist.

*2007*

Here, all return requirements were given pretax, so the problem doesn’t exist.

*2008*

*“. . . dividends and interest are taxed at 20 percent, and capital gains at 15 percent.”*

Here, all returns, whether for living expenses or for inflation, are taxable. Add inflation, then increase the sum for taxes.

*2009*

*“. . . a tax rate of 20% [applies] to the . . . withdrawals from the investment account.”*

Here, only the withdrawals are taxable; the inflation component will remain in the account, untaxed. Increase the return for taxes, then add inflation.

*2010*

*“Income and gains grow tax-deferred and portfolio reallocations are not subject to tax. Income taxes are paid on full amount of withdrawals.”*

Here, only the withdrawals are taxable; the inflation component will remain in the account, untaxed. Increase the return for taxes, then add inflation.

*2011*

*“Income, realized capital gains, and estate assets (at death) are all taxed at a flat 20% rate.”*

Here, all returns, whether for living expenses or for inflation, are taxable. Add inflation, then increase the sum for taxes.

*2012*

*“[The] income tax rate is 30%. Other than a small cash reserve, [the investor] holds all of his investment assets in a tax-exempt account . . . . Contributions to this account are made after tax. Withdrawals are entirely tax-free, without penalty.”*

Here, the account is not taxable, nor are withdrawals; the problem doesn’t exist

*2013*

*“The tax rate on ordinary income and all investment returns is 30%.”*

*2014*

*“Calculate the investment portfolio’s percentage return after taxes.”*

Here, the calculations are all done after taxes; the problem doesn’t exist.

*2015*

No question on this topic appeared on the 2015 morning session of the Level III CFA exam.

*2016*

No question on this topic appeared on the 2016 morning session of the Level III CFA exam.

*2017*

*“Determine Patel’s nominal after-tax required rate of return.”*

Here, the calculations are all done after taxes; the problem doesn’t exist.

*2018*

*“. . . investment returns are . . . taxed at 25%.”*