EV and Other Aspects

Dividend Yield

The dividend yield (D/P) is the ratio of the common dividend to the market price. It is most often used for valuing indexes. Advantages of the dividend yield approach include:

• Dividend yield contributes to total investment return.
• Dividends are not as risky as the capital appreciation component of total return.

Disadvantages of the dividend yield approach include:

• The focus on dividend yield is incomplete because it ignores capital appreciation.
• The dividend displacement of earnings concept argues that dividends paid now displace future earnings, which implies a trade off between current and future cash flows.

Total return on an investment has two components: dividend yield and capital appreciation. Dividend yield (D/P) is the ratio of trailing or leading dividend divided by current market price per share:

The supposed lower risk of dividends relative to capital appreciation assumes that the market is biased in its risk assessment of the components of return.

Underlying Earnings

Calculating the P/E ratio is easy, and estimating the market price is usually straightforward. However, estimating the appropriate earnings measure is crucial to successfully using the P/E ratio in market based valuation. The key focus of an analyst is estimating underlying earnings (a.k.a.

persistent, continuing, or core earnings), which are earnings that exclude nonrecurring components, such as gains and losses from asset sales, asset write downs, provisions for future losses, and changes in accounting estimates.

For comparative purposes, analysts generally use diluted EPS, so that the effect of any dilutive securities is taken into account.

Normalized Earnings

Analysts adjust P/Es for cyclicality by estimating normalized (or normal) earnings per share, which is an estimate of EPS in the middle of the business cycle. The following two methods are used to normalize earnings:

1. Under the method of historical average EPS, the normalized EPS is estimated as the average EPS over some recent period, usually the most recent business cycle.
2. Under the method of average return on equity, normalized EPS is estimated as the average return on equity (ROE) multiplied by the current book value per share (BVPS). Once again, average ROE is often measured over the most recent business cycle. The reliance on BVPS reflects the effect of firm size changes more accurately than does the method of historical average EPS.

The method of historical average EPS ignores size effects, so the method of average ROE is preferred.

Negative earnings render P/E ratios meaningless. In such cases, it is common to use normalized EPS and/or restate the ratio as the earnings yield (E/P) because price is never negative. A high E/P suggests a cheap security, and a low E/P suggests an expensive security, so securities can be ranked from cheap to expensive based on E/P ratios.

Justified P/E Multiple

As we said earlier, the justified P/E price multiple is a P/E ratio with the “P” in the numerator equal to the fundamental value derived from a valuation model. The best way to analyze the fundamental factors that affect the P/E ratio is to use the single- stage Gordon growth model:

If we express $D^0$ as the product of current earnings per share ($E^0$) and the payout ratio ($D^0$ / $E^0$) and express the retention rate as b, the previous formula becomes trailing P/E:

Recognizing that $E^1$ = $E^0$ (1 + g) and $D^1$ = $D^0$ (1 + g), the leading P/E is calculated as:

By examining the formulas for justified (leading and trailing) P/E, we can conclude that the fundamental factors that affect P/E are expected growth rate and required return (which is related to risk). The justified P/E ratio is:

• Positively related to the growth rate of expected cash flows, whether defined as dividends or free cash flows, all else equal.
• Inversely related to the stock’s required rate of return, all else equal.
• While not directly apparent, P/E ratio is positively related to inflation pass through rate. If two similar companies operate in the same inflationary environment, the firm with the higher inflation pass through rate (i.e., ability to pass some portion of higher costs on to customers) should have the higher P/E ratio.

Justified P/B Multiple

Using the sustainable growth relation of g = ROE × b and observing that $E^1$ = $B^0$ × ROE, we can also derive the justified P/B from the Gordon growth model as:

We can draw two useful conclusions from this formula concerning the fundamentals that influence the P/B ratio:

• P/B increases as ROE increases, all else equal.
• The larger the spread between ROE and r, all else equal, the higher the P/B ratio. This makes sense if you remember that ROE is the return on the firm’s investment projects and r is the required return. The larger the spread, all else equal, the more value the firm is creating through its investment activities and the higher its market value as represented by $V^0$.

We can then use fundamental forecasts of ROE, r, and g to find a value for this ratio.

Justified P/S Multiple

Since net profit margin ($P{M}^0$) is equal to $E^0$/$S^0$, we can also restate the Gordon growth model as:

Net profit margin ($E^0$/$S^0$) thus influences P/S directly as well as indirectly through its effect on the sustainable growth rate, g:

Sometimes, analysts want to calculate the price to sales ratio using forecasted sales ($P_0$/$S_1$). In such a case,

This means that the P/S ratio will increase, all else equal, if:

• Profit margin increases.
• Earnings growth rate increases.

We can also do a little algebra and solve for P/S as a function of trailing P/E, which might be an easier formula to remember:

Justified P/CF Multiple

The justified price to cash flow based on fundamentals can be calculated by finding the value of the stock using a DCF model and dividing the result by the chosen measure of cash flow. For example, equity value using the single stage FCFE model is:

P/CF will increase, all else equal, if:

• Required return decreases.
• Growth rate increases.

Justified EV/EBITDA Multiple

The justified EV/EBITDA based on fundamentals is simply the enterprise value based on a forecast of fundamentals divided by EBITDA forecast based on fundamentals. The ratio is:

• Positively related to the growth rate in FCFF and EBITDA.
• Negatively related to the firm’s overall risk level and weighted average cost of capital (WACC).

Justified Dividend Yield

The dividend yield relative to fundamentals may be expressed in terms of the Gordon growth model as:

Dividend yield is:

• Positively related to the required rate of return.
• Negatively related to the forecasted growth rate in dividends. This implies that choosing high dividend yield stocks reflects a value rather than a growth investment strategy.

regression methodology.

Cross sectional regression refers to a regression in which the explained and explanatory variables are all based on the same point in time.

A predicted P/E can be estimated from linear regression of historical P/Es on its fundamental variables, including expected growth and risk. While such empirical analysis can provide an analyst with useful insight, there are three main limitations:

• The predictive power of the estimated P/E regression for a different time period and/or sample of stocks is uncertain.
• The relationships between P/E and the fundamental variables examined may change over time.
• Multicollinearity is often a problem in these time series regressions, which makes it difficult to interpret individual regression coefficients.

The basic idea of the method of comparables is to compare a stock’s price multiple to that of a benchmark portfolio. Firms with multiples below the benchmark are undervalued, and firms with multiples above the benchmark are overvalued. However, the fundamentals of the stock should be similar to the fundamentals of the benchmark before we can make direct comparisons and draw any conclusions about whether the stock is overvalued or undervalued.

In other words, we have to ensure that we’re comparing apples to apples. That’s why the fundamental variables (i.e., the fundamentals) that affect each multiple are important in applying the method of comparables.

Let’s use the P/E ratio as an example. Remember that justified P/E is positively related to growth rates and negatively related to required rate of return and risk. Suppose we determine that the P/E of our stock is less than the benchmark.

There are (at least) three possible explanations for this:

• The stock is undervalued.
• The stock is properly valued, but the stock has a lower expected growth rate than the benchmark, which leads to a lower P/E.
• The stock is properly valued, but it has a higher required rate of return (higher risk) than the benchmark, which leads to a lower P/E.

In order to conclude that the stock is truly undervalued, we have to make sure that the stock is comparable to the benchmark; it should have similar expected growth and similar risk.

The Fed and Yardeni Models

The Fed model considers the overall market to be overvalued (undervalued) when the earnings yield (i.e., the E/P ratio) on the S&P 500 Index is lower (higher) than the yield on 10 year U.S. Treasury bonds.

The Yardeni model includes expected earnings growth rate in the analysis:

Taking reciprocals of the Yardeni model (and ignoring the error term), we get:

This shows that the P/E ratio is negatively related to interest rates and positively related to growth.

The relationship between earnings growth and P/E is captured by the P/E to growth (PEG) ratio:

The PEG is interpreted as P/E per unit of expected growth. Remember that the growth rate is one of the fundamental factors that affect P/E (P/E is directly related to the growth rate). The PEG ratio, in effect, “standardizes” the P/E ratio for stocks with different expected growth rates.

The implied valuation rule is that stocks with lower PEGs are more attractive than stocks with higher PEGs, assuming that risk is similar.

A terminal value that is projected as of the end of the investment horizon should reflect the earnings growth that a firm can sustain over the long run, beyond that point in time. Analysts often use terminal price multiples like P/E, P/B, P/S, and P/CF to estimate terminal value. No matter which ratio is used, terminal value is calculated as the product of the price multiple (e.g., P/E ratio) and the fundamental variable (e.g., EPS).

There are two methods of estimating the price multiple: based on fundamentals and based on comparables. The terminal price multiple based on fundamentals is the product of the justified price multiple and an estimate of the fundamental value. For example, the terminal value based on a justified P/E ratio is:

The terminal price multiple based on comparables is calculated as the benchmark price multiple and an estimate of the fundamental value. For example, the terminal value based on a benchmark P/E is:

The strength of the comparables approach is that it uses market data exclusively. In contrast, the fundamentals approach requires estimates of the growth rate, required rate of return, and payout ratio. One weakness of the comparables approach is that a benchmark marred by mispricing will transfer that error to the estimated terminal value.

There are at least four definitions of cash flow available for use in calculating the P/CF ratio: (1) earnings plus noncash charges (CF); (2) adjusted cash flow (adjusted CFO); (3) free cash flow to equity (FCFE); and (4) earnings before interest, taxes, depreciation, and amortization (EBITDA). Expect to see any one of them on the exam.

One commonly used proxy for cash flow is earnings plus noncash charges (CF):

The limitation of this definition, as we mentioned previously, is that it ignores some items that affect cash flow, such as noncash revenue and changes in net working capital.

Another proxy for cash flow is cash flow from operations (CFO) from the cash flow statement. CFO is often adjusted for nonrecurring cash flows. US GAAP requires interest paid, interest received, and dividends received to be classified as operating cash flows.

IFRS, however, is more flexible: interest paid may be classified as either an operating or financing cash flow, while interest and dividends received can be classified as either operating or investing cash flows. Thus, care should be taken when comparing firms reporting under different standards.

Analysts also often use free cash flow to equity (FCFE) and earnings before interest, taxes, depreciation, and amortization (EBITDA) as proxies for cash flow. As we mentioned previously, theory suggests that FCFE is the preferred way to define cash flow, but it is more volatile than straight cash flow.

EBITDA is a pretax, pre interest measure that represents a flow to both equity and debt. Thus, it is better suited as an indicator of total company value than just equity value. More on this point is provided in our discussion of the enterprise value to EBITDA ratio.

Analysts typically use trailing price to cash flow ratio, which relies on the most recent four quarters of cash flow per share. Given one of the four definitions of cash flow, the P/CF ratio is calculated as:

Because EBITDA is a flow to both equity and debt, it should be related to a numerator that measures total company value. Enterprise value (EV) is total company value:

The rationale for subtracting cash and investments is that an acquirer’s net price paid for an acquisition target would be lowered by the amount of the target’s liquid assets. Thus, enterprise value indicates the value of the overall company, not equity.

EV/EBITDA is the ratio of enterprise value to EBITDA:

EV/EBITDA is useful in a number of situations:

• The ratio may be more useful than P/E when comparing firms with different degrees of financial leverage.
• EBITDA is useful for valuing capital intensive businesses with high levels of depreciation and amortization.
• EBITDA is usually positive even when EPS is not.

EV/EBITDA has a number of drawbacks, however:

• If working capital is growing, EBITDA will overstate CFO. Further, the measure ignores how different revenue recognition policies affect CFO.
• Because FCFF captures the amount of capital expenditures, it is more strongly linked with valuation theory than EBITDA. EBITDA will be an adequate measure if capital expenses equal depreciation expenses.

Using relative valuation methods that require the use of comparable firms is challenging in an international context due to differences in accounting methods, cultures, risk, and growth opportunities. Further, benchmarking is difficult because P/Es for individual firms in the same industry vary widely internationally and country market P/Es can vary significantly. Common differences in international accounting treatment fall into several categories: goodwill, deferred income taxes, foreign exchange adjustments, R&D, pension expense, and tangible asset revaluations.

The usefulness of all price multiples is affected to some degree by differences in international accounting standards. The least affected is P/FCFE, while P/B, P/E, P/EBITDA, and EV/EBITDA will be more seriously affected because they are more influenced by management’s choice of accounting methods and estimates.

Momentum indicators relate either the market price or a fundamental variable (such as EPS) to the time series of historical or expected value. Common momentum indicators include earnings surprise, standardized unexpected earnings, and relative strength.

Unexpected earnings or earnings surprise is the difference between reported earnings and expected earnings:

This is usually scaled by a measure that expresses the variability of analysts’ EPS forecasts. The economic rationale for examining earnings surprises is that positive surprises may lead to persistent positive abnormal returns.

Similarly, the standardized unexpected earnings (SUE) measure is defined as:

A given size forecast error is more meaningful the smaller the size of the historical forecast errors.

Relative strength indicators compare a stock’s price or return performance during a given time period with its own historical performance or with some group of peer stocks. The economic rationale is that patterns of persistence or reversal may exist in stock returns. These are thought to possibly depend on the length of an investor’s time horizon.

The price to earnings multiple for a stock index is not equal to the mean or weighted mean of the P/Es of the portfolio stocks. Consider two stocks: one priced at $10 with earnings of $1 per share (P/E = 10) and one priced at $16 with earnings of $2 (P/E = 8). For a portfolio with one share of each stock, earnings per share are 1 + 2 = 3 and the “price” of a portfolio share is 10 + 16 = 26. The portfolio price to earnings is 26 / 3 = 8.67.

We will demonstrate that the portfolio or index P/E (as well as other relative value ratios based on price) is best calculated as the weighted harmonic mean P/E. With the P/Es denoted by X and the weights as w, we have:

Consider the following alternative measures of the mean P/E for the portfolio:

An analyst must be aware of how portfolio P/Es are calculated to understand them. Note that when there are extreme (high or low) outliers, the arithmetic mean will be the most affected. Analysts should be aware that the harmonic mean puts more weight on smaller values.

In this case, the median or weighted harmonic mean with the outliers excluded may be the most appropriate measures of the P/E for a portfolio or index. For an equal weighted portfolio or index, the harmonic mean and weighted harmonic mean will be equal.