# Issues in Calculating EPS

Companies are required to disclose both basic EPS and diluted EPS. Basic EPS is the total earnings divided by the weighted average number of shares outstanding during the period. Diluted EPS reflects the effect of exercised stock options, warrants, and convertible bonds on EPS.  Diluted EPS is preferred over basic EPS when comparing companies.

Items that are expected not to recur in the future are removed from the earnings. This results in underlying earnings/persistent earnings/continuing earnings. Companies may disclose these adjusted earnings. However, this figure may not be comparable among companies because of the different bases of calculation. Analysts should therefore examine the calculation of this figure. The goal should be to compute persistent, continuing, and core earnings. The P/E used in valuation should be calculated consistently among all stocks under review. Identifying non-recurring earnings requires analysis of the income statement, footnotes, and management discussion and analysis section. Examples of nonrecurring items include:

• Changes in accounting estimates.
• Gains/losses from the sale of assets.
• Asset write-downs (impairments).
• Loss provisions.

#### Example: Calculating Trailing P/E Ratio Based on Underlying Earnings

Consider the following information:

$$\small{\begin{array}{l|r}\text{Reported EPS from the previous period} & 5.5 \\ \hline\text{Restructuring charges} & 0.15 \\ \hline\text{Amortization of intangibles} & 0.24 \\ \hline\text{Impairment charge} & 0.35 \\ \hline\text{Stock price} & 30\\ \end{array}}$$

\begin{align}\text{P⁄E based on reported earnings}&= \frac{30}{5.5}=5.45\\ \text{Rerported core earnings}&=5.5+0.15+0.24+0.35=6.24\\ \text{P⁄E based on reported core earnings}&=\frac{30}{6.24}=4.81\\ \text{Underlying earnings}&=5.5+0.35=5.85\\ \text{P⁄E based on underlying earnings}&= \frac{30}{5.85}=5.31\end{align}

Transitory earnings can come from business/industry cycle influences. These earnings are, however, expected to recur in subsequent cycles. P/Es for cyclical companies are often volatile. Analysts address this by normalizing EPS – estimating the level of EPS under mid-cycle conditions. There are two methods of normalizing EPS:

1. Historical average EPS: This is where normalized EPS is calculated as the average EPS over the most recent full cycle.
2. The average return on equity: This is where normalized EPS is calculated as the average return on equity (ROE) from the most recent full-cycle multiplied by the current book value per share.

Analysts should also adjust EPS for differences in accounting methods between companies such as LIFO or FIFO.

#### Example: Normalized Earnings

Consider the following information:

$$\small{\begin{array}{l|c|c|c|c}\textbf{Year} & \textbf{2017} & \textbf{2018} & \textbf{2019} & \textbf{2020}\\ \hline\text{EPS} & \5.80 & \5.51 & \7.61 & \6.53 \\ \hline\text{BVPS} & \25.00 & \26.00 & \26.00 & \40.60 \\ \hline\text{ROE} & 20\% & 20\% & 26\% & 15\% \\ \hline\text{Stock Price} & & & & \25\\ \end{array}}$$

Method of historical average EPS:

\begin{align*}\text{Average (normalized) EPS}&= \frac{(5.80+5.51+7.61+6.53)}{4}=\6.36\\ \text{P⁄E}&= \frac{\25}{\6.36}=3.93\end{align*}

Method of average ROE:

\begin{align*}\text{Average ROE}&= \frac{(20\%+20\%+26\%+15\%)}{4}=20.25\%\\ \\ \text{Average normalized EPS}&=\text{Average ROE} \times\text{Current equity book value per share}\\&=20.25\% ×\40.60=\8.22\\ \\ \text{P⁄E}&=\frac{\25}{\8.22}=3.04\end{align*}

## Question

Given the following information:

$$\small{\begin{array}{l|l|l|l|l}& \textbf{2018} & \textbf{2019} & \textbf{2020} & \textbf{2021}\\ \hline\text{ROE} & 22.5\% & 23\% & 23\% & 25\% \\ \hline\text{Book value per share} & 22.00 & 23.50 & 24.00 & 26.50 \\ \hline\text{Share price} & & & & 42.00\\ \end{array}}$$

The P/E ratio in 2021 is closest to:

1. 6.34.
2. 6.77.
3. 7.66.

#### Solution

\begin{align*}\text{Normalized EPS}&=\text{Average ROE} \\ & \times\text{Current equity book value per share}\\ \\ \text{Average ROE}&= \frac{(22.5\%+23\%+23\%+25\%)}{4}=23.38\%\\ \\ \text{Normalized EPS}&=23.38\%\times26.50=\6.20\\ \\ \text{P⁄E}&=\frac{\42.00}{\6.20}=6.77\end{align*}

Reading 25: Market-Based Valuation: Price and Enterprise Value Multiples

LOS 25 (e) Calculate and interpret underlying earnings, explain methods of normalizing earnings per share (EPS), and calculate normalized EPS.

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