# ROE calculation

In the ROE calculation should the Equity be a) the average of Beg and End or b) the Ending. value at someplaces its a) at others its b). How do you decide?

The choice may depend on the context of the analysis being performed. Within the context of the CFA curriculum, the formula for ROE seems to be based on average shareholders’ equity (see the DuPont framework diagrom on p. 608 of Volume 3 of the 2008 Level I text). It actually says “average shareholders’ equity” in the diagram. Depending on the exercise at the end of the readings, we may actually be asked to use the ending balance of shareholders’ equity. Hopefully, the acutal test questions we get will let us know which to use, as both measures, in practice, are used and are vaild.

If they give you two balance sheets, you should probably take the average. If there’s only one bs, then there’s no question there. I don’t think that the answer will hinge on that though, I’m sure it’s not going to be ambiguous.

for purposes of this exam, I’m confident CFAI won’t force you to decide between the two. However, I think the averages of balance sheet accounts should be used when calculating mixed ratios (i.e. ratios involving the balance sheet and another financial statement, like the income statement). Why? Well, the income statement and cash flow statement show activity over a period of time (like a fiscal year or quarter), whereas a balance sheet is a snapshot of a company at a single point in time. For example, which of these two ratios is a better indicator of asset turnover *during* a year? 1) Sales / Assets FYE 2) Sales / Average Assets (average over the period in which sales are measured) I think the second calculation is most representative of asset turnover over a period of time. Similarly, I think this is why EPS using average shares outstanding (basic or diluted) is better than using shares outstanding at a company’s FYE. So, returning to the basic DuPont equation, it seems to me that ROE for a fiscal year should be ROE = (NI FYE / Sales FYE) * (Sales FYE / Avg. Assets) * (Avg. Assets / Avg. Equity) and by extension ROA = (NI FYE / Sales FYE) * (Sales FYE / Avg. Assets) Using averages also disincentives companies to engage in year-end shenanigans to improve various financial ratios. So imagine if CSO FYE was used for EPS rather than weighted-average CSO. A company could buy back a bunch of shares just before FYE to juice up EPS. Anyway, just my \$0.02, if others disagree, it wouldn’t be my first mistake in the forums

Good stuff. Wouldn’t it even be better to use time-weighted average for assets? For example, U.S. GAAP could require comapnies to keep a monthly figure for assets (and other items) to be used for calculating ratios! That would surely be more accurate. A daily figure would even be better! Under the current method a company which is about to buy some huge assets around end of year, could decide to do it on Jan 1st to keep TA for current year low. Have you also thought about how market indices, and portfolio returns in general, are based on Jan 1- Dec 31 time frames? If some wild event drives prices low on Dec 31, next year return will look much better than it really should! Dreary