Textbook Cases

spyderhp220

Chapter8.docx

Home >Business & Finance homework help >Accounting homework help >Textbook Cases

8 Stock Valuation

Learning Goals

After studying this chapter, you should be able to:

1. LG 1 Explain the role that a company’s future plays in the stock valuation process.

2. LG 2 Develop a forecast of a stock’s expected cash flow, starting with corporate sales and earnings, and then moving to expected dividends and share price.

3. LG 3 Discuss the concepts of intrinsic value and required rates of return, and note how they are used.

4. LG 4 Determine the underlying value of a stock using the zero-growth, constant-growth, and variable-growth dividend valuation models.

5. LG 5 Use other types of present value–based models to derive the value of a stock, as well as alternative price-relative procedures.

6. LG 6 Understand the procedures used to value different types of stocks, from traditional dividend-paying shares to more growth-oriented stocks.

What drives a stock’s value? Many factors come into play, including how much profit the company earns, how its new products fare in the marketplace, and the overall state of the economy. But what matters most is what investors believe about the company’s future.

Nothing illustrates this principle better than the stock of the oil driller, Helmerich & Payne (ticker symbol HP). The company announced its financial results for the first quarter of its fiscal year on January 29, 2015, reporting earnings per share of $1.85 with total revenue of $1.06 billion. Wall Street stock analysts had been expecting the company to earn just $1.55 per share with $977 million in total revenue, so the company’s performance was much better than expected. Even so, HP’s stock price slid nearly 5% in response to the earnings news. Why would investors drive down the stock price of a company that was outperforming expectations? The answer had to do with the company’s future rather than its past earnings. In its earnings report, HP warned investors that its earnings for the rest of 2015 would likely be hit by falling oil prices. Indeed, in early 2015 oil prices were lower than they had been in six years, and many analysts believed that the market had not yet hit bottom. Stock analysts who followed HP acknowledged that the company had experienced solid revenue growth and used a reasonable amount of debt. Nevertheless, these analysts advised investors who did not already own HP to stay away from the stock because of the company’s poor return on equity and lackluster growth in earnings per share.

How do investors determine a stock’s true value? This chapter explains how to determine a stock’s intrinsic value by using dividends, free cash flow, price/earnings, and other valuation models.

(Source: Richard Saintvilus, “Helmerich & Payne Stock Falls on Outlook Despite Earnings Beat,” http://www.thestreet.com/story/13027986/1/helmerich-payne-stock-falls-on-outlook-despite-earnings-beat.html , accessed on May 27, 2015.)

Valuation: Obtaining a Standard of Performance

1. LG 1

2. LG 2

3. LG 3

Obtaining an estimate of a stock’s intrinsic value that investors can use to judge the merits of a share of stock is the underlying purpose of stock valuation . Investors attempt to resolve the question of whether and to what extent a stock is under- or overvalued by comparing its current market price to its intrinsic value. At any given time, the price of a share of stock depends on investors’ expectations about the future performance of the company. When the outlook for the company improves, its stock price will probably go up. If investors’ expectations become less rosy, the price of the stock will probably go down.

Valuing a Company Based on Its Future Performance

Thus far we have examined several aspects of security analysis including macroeconomic factors, industry factors, and company-specific factors. But as we’ve said, for stock valuation the future matters more than the past. The primary reason for looking at past performance is to gain insight about the firm’s future direction. Although past performance provides no guarantees about what the future holds, it can give us a good idea of a company’s strengths and weaknesses. For example, history can tell us how well the company’s products have done in the marketplace, how the company’s fiscal health shapes up, and how management tends to respond to difficult situations. In short, the past can reveal how well the company is positioned to take advantage of the things that may occur in the future.

Because the value of a share of stock depends on the company’s future performance, an investor’s task is to use historical data to project key financial variables into the future. In this way, he or she can judge whether a stock’s market price aligns well with the company’s prospects.

An Advisor’s Perspective

Rod Holloway Equity Portfolio Manager, CFCI

“The best way to analyze a stock is to determine what you expect its sales numbers to be.”

MyFinanceLab

Forecasted Sales and Profits

The key to the forecast is, of course, the company’s future performance, and the most important aspects to consider in this regard are the outlook for sales and profits. One way to develop a sales forecast is to assume that the company will continue to perform as it has in the past and simply extend the historical trend. For example, if a firm’s sales have been growing at a rate of 10% per year, then investors might assume sales will continue at that rate. Of course, if there is some evidence about the economy, industry, or company that hints at a faster or slower rate of growth, investors would want to adjust the forecast accordingly. Often, this “naive” approach will be about as effective as more complex techniques.

Once they have produced a sales forecast, investors shift their attention to the net profit margin. We want to know what profit the firm will earn on the sales that it achieves. One of the best ways of doing that is to use what is known as a common-size income statement . Basically, a common-size statement takes every entry found on an ordinary income statement or balance sheet and converts it to a percentage. To create a common-size income statement, divide every item on the statement by sales—which, in effect, is the common denominator. An example of this appears in Table 8.1 , which shows the 2016 dollar-based and common-size income statements for Universal Office Furnishings. (This is the same income statement that we first saw in Table 7.4.)

Excel@Investing

Table 8.1 Comparative Dollar-Based and Common-Size Income Statement Universal Office Furnishings, Inc. 2016 Income Statement

	($ millions)	(Common-Size) *
* Common-size figures are found by using ‘Net Sales” as the common denominator, and then dividing all entries by net sales. For example, cost of goods sold= $1,128.5 ÷ $1,938.0=58.2%; EBIT=$235.2÷$1,938.0=12.1%cost of goods sold= $1,128.5 ÷ $1,938.0=58.2%; EBIT=$235.2÷ $1,938.0=12.1%.
Net Sales	$1,938.0	100.0%
Cost of goods sold	$1,128.5	58.2%
Gross operating Profit	$ 809.5	41.8%
Selling, general, & administrative expenses	$ 496.7	25.6%
Depreciation & amortization	$ 77.1	4.0%
Other expenses	$ 0.5	0.0%
Total operating expenses	$ 574.3	29.6%
Earnings before interest & taxes (EBIT)	$ 235.2	12.1%
Interest Expense	$ 13.4	0.7%
Income taxes	$ 82.1	4.2%
Net profit after taxes	$ 139.7	7.2%

Example

To understand how to construct these statements, let’s use the gross profit margin (41.8%) as an illustration. In this case, divide the gross operating profit of $809.5 million by sales of $1,938.0 million:

$809.5÷$1,938.0=0.4177=41.8%$809.5÷$1,938.0=0.4177=41.8%

Use the same procedure for every other entry on the income statement. Note that a common-size statement adds up, just like its dollar-based counterpart. For example, sales of 100.0% minus costs of goods sold of 58.2% equals a gross profit margin of 41.8%. (You can also work up common-size balance sheets, using total assets as the common denominator.)

Securities analysts and investors use common-size income statements to compare operating results from one year to the next. The common-size format helps investors identify changes in profit margins and highlights possible causes of those changes. For example, a common-size income statement can quickly reveal whether a decline in a firm’s net profit margin is caused by a reduction in the gross profit margin or a rise in other expenses. That information also helps analysts make projections of future profits. For example, analysts might use the most recent common-size statement (or perhaps an average of the statements that have prevailed for the past few years) combined with a sales forecast to create a forecasted income statement a year or two ahead. Analysts can make adjustments to specific line items to sharpen their projections. For example, if analysts know that a firm has accumulated an unusually large amount of inventory this year, it is likely that the firm will cut prices next year to reduce its inventory holdings, and that will put downward pressure on profit margins. Adjustments like these (hopefully) improve the accuracy of forecasts of profits.

Given a satisfactory sales forecast and estimate of the future net profit margin, we can combine these two pieces of information to arrive at future earnings (i.e., profits).

Future after-tax earnings in year t=Estimated sales in year t×Net profit margin expected in year tFuture after-tax earnings in year t=Estimated sales in year t×Net profit margin expected in year tEquation8.1

The year t notation in this equation simply denotes a future calendar or fiscal year. Suppose that in the year just completed, a company reported sales of $100 million. Based on the company’s past growth rate and on industry trends, you estimate that revenues will grow at an 8% annual rate, and you think that the net profit margin will be about 6%. Thus, the forecast for next year’s sales is $108 million (i.e., $100 million×1.08$100 million×1.08), and next year’s profits will be $6.5 million:

Future after-tax earnings next year =$108 million × 0.06 = $6.5 million––––––––––––––––––––––––––Future after-tax earnings next year =$108 million × 0.06 = $6.5 million__

Using this same process, investors could estimate sales and earnings for other years in the forecast period.

Forecasted Dividends and Prices

At this point the forecast provides some insights into the company’s future earnings. The next step is to evaluate how these results will influence the company’s stock price. Given a corporate earnings forecast, investors need three additional pieces of information:

· An estimate of future dividend payout ratios

· The number of common shares that will be outstanding over the forecast period

· A future price-to-earnings (P/E) ratio

For the first two pieces of information, lacking evidence to the contrary, investors can simply project the firm’s recent experience into the future. Except during economic downturns, payout ratios are usually fairly stable, so recent experience is a fairly good indicator of what the future will bring. Similarly, the number of shares outstanding does not usually change a great deal from one year to the next, so using the current number in a forecast will usually not lead to significant errors. Even when shares outstanding do change, companies usually announce their intentions to issue new shares or repurchase outstanding shares, so investors can incorporate this information into their forecasts.

Getting a Handle on the P/E Ratio

The most difficult issue in this process is coming up with an estimate of the future P/E ratio—a figure that has considerable bearing on the stock’s future price behavior. Generally speaking, the P/E ratio (also called the P/E multiple) is a function of several variables, including the following:

· The growth rate in earnings

· The general state of the market

· The amount of debt in a company’s capital structure

· The current and projected rate of inflation

· The level of dividends

An Advisor’s Perspective

Rod Holloway Equity Portfolio Manager, CFCI

“The P/E ratio by itself is a great gauge as to whether a stock is a good buy.”

MyFinanceLab

As a rule, higher P/E ratios are associated with higher rates of growth in earnings, an optimistic market outlook, and lower debt levels (less debt means less financial risk).

What Is a P/E Ratio?

The link between the inflation rate and P/E multiples, however, is a bit more complex. Generally speaking, as inflation rates rise, so do the interest rates offered by bonds. As returns on bonds increase, investors demand higher returns on stocks because they are riskier than bonds. Future returns on stocks can increase if companies earn higher profits and pay higher dividends, but if earnings and profits remain fixed, investors will only earn higher future returns if stock prices are lower today. Thus, inflation often puts downward pressure on stock prices and P/E multiples. On the other hand, declining inflation (and interest) rates normally have a positive effect on the economy, and that translates into higher P/E ratios and stock prices. Holding all other factors constant, a higher dividend payout ratio leads to a higher P/E ratio. In practice, however, most companies with high P/E ratios have low dividend payouts because firms that have the opportunity to grow rapidly tend to reinvest most of their earnings. In that case, the prospect of earnings growth drives up the P/E, more than offsetting the low dividend payout ratio.

A Relative Price-to-Earnings Multiple

A useful starting point for evaluating the P/E ratio is the average market multiple. This is simply the average P/E ratio of all the stocks in a given market index, like the S&P 500 or the DJIA. The average market multiple indicates the general state of the market. It gives us an idea of how aggressively the market, in general, is pricing stocks. Other things being equal, the higher the P/E ratio, the more optimistic the market, though there are exceptions to that general rule. Figure 8.1 plots the S&P 500 price-to-earnings multiple from 1901 to 2015. This figure calculates the market P/E ratio by dividing prices at the beginning of the year by earnings over the previous 12 months. The figure shows that market multiples move over a fairly wide range. For example, in 2009, the market P/E ratio was at an all-time high of more than 70, but just one year later the ratio had fallen to just under 21. It is worth noting that the extremely high P/E ratio in 2009 was not primarily the result of stock prices hitting all-time highs. Instead, the P/E ratio at the time was high because earnings over the preceding 12 months had been extraordinarily low due to a severe recession. This illustrates that you must be cautious when interpreting P/E ratios as a sign of the health of individual stocks or of the overall market.

Figure 8.1 Average P/E Ratio of S&P 500 Stocks

The average price-to-earnings ratio for stocks in the S&P 500 Index fluctuated around a mean of 13 from 1940 to 1990 before starting an upward climb. Increases in the P/E ratio do not necessarily indicate a bull market. The P/E ratio spiked in 2009 not because prices were high, but because earnings were very low due to the recession.

(Source: Data from http://www.multpl.com.)

Famous Failures IN Finance P/E Ratios Can Be Misleading

The most recent spike in the S&P 500 P/E ratio cannot be explained by a booming economy or a rising stock market. Recall that in 2008 stock prices fell dramatically, with the overall market declining by more than 30%. Yet, as 2009 began the average P/E ratio stood at an extraordinarily high level. The reason is that with the deep recession of 2008, corporate earnings declined even more sharply than stock prices did. So, in the market P/E ratio, the denominator (last year’s earnings) declined more rapidly than the numerator (prices), and the overall P/E ratio jumped. In fact, in mid-2009 the average S&P 500 P/E ratio reached an all-time high of 144!

Looking at Figure 8.1 , you can see that the market’s P/E ratio has increased in recent years. From 1900 to 1990, the market P/E averaged about 13, but since then its average value has been above 24 (or more than 22 if you exclude the peak in 2009). At least during the 1990s, that upward trend could easily be explained by the very favorable state of the economy. Business was booming and new technologies were emerging at a rapid pace. There were no recessions from 1991 to 2000. If investors believed that the good times would continue indefinitely, then it’s easy to understand why they might be willing to pay higher and higher P/E ratios over time.

With the market multiple as a benchmark, investors can evaluate a stock’s P/E performance relative to the market. That is, investors can calculate a relative P/E multiple by dividing a stock’s P/E by a market multiple. For example, if a stock currently has a P/E of 35 and the market multiple for the S&P 500 is, say, 25, the stock’s relative P/E is 35÷25=1.435÷25=1.4 Looking at the relative P/E, investors can quickly get a feel for how aggressively the stock has been priced in the market and what kind of relative P/E is normal for the stock.

Investor Facts

How to Spot an Undervalued (or Overvalued) Market Just as shares of common stock can become over- or undervalued, so can the market as a whole. How can you tell if the market is overvalued? One of the best ways is to examine the overall market P/E ratio relative to its long-term average. When the market’s P/E ratio is above its long-term average, that is a good sign that the market is overvalued and subsequent market returns will be lower than average. Conversely, when the market’s P/E ratio is unusually low, that is a sign that the market may be undervalued and future returns will be higher than average.

Other things being equal, a high relative P/E is desirable—up to a point, at least. For just as abnormally high P/Es can spell trouble (i.e., the stock may be overpriced and headed for a fall), so too can abnormally high relative P/Es. Given that caveat, it follows that the higher the relative P/E measure, the higher the stock will be priced in the market. But watch out for the downside: High relative P/E multiples can also mean lots of price volatility, which means that both large gains and large losses are possible. (Similarly, investors use average industry multiples to get a feel for the kind of P/E multiples that are standard for a given industry. They use that information, along with market multiples, to assess or project the P/E for a particular stock.)

The next step is to generate a forecast of the stock’s future P/E over the anticipated investment horizon (the period of time over which an investor expects to hold the stock). For example, with the existing P/E multiple as a base, an increase might be justified if investors believe the market multiple will increase (as the market becomes more bullish) even if they do not expect the relative P/E to change. Of course, if investors believe the stock’s relative P/E will increase as well, that would result in an even more bullish forecast.

Estimating Earnings per Share

So far we’ve been able to come up with an estimate for the dividend payout ratio, the number of shares outstanding, and the price-to-earnings multiple. Now we are ready to forecast the stock’s future earnings per share (EPS) as follows:

Estimated EPS in year t=Future after-tax earnings in year tNumber of shares of common stock outstanding in year tEstimated EPS in year t=Future after-tax earnings in year tNumber of shares of common stock outstanding in year tEquation8.2

Earnings per share is a critical part of the valuation process. Investors can combine an EPS forecast with (1) the dividend payout ratio to obtain (future) dividends per share and (2) the price-to-earnings multiple to project the (future) price of the stock.

Equation 8.2 simply converts total corporate earnings to a per-share basis by dividing forecasted company profits by the expected number of shares outstanding. Although this approach works quite effectively, some investors may want to analyze earnings per share from a slightly different perspective. One way to do this begins by measuring a firm’s ROE. For example, rather than using Equation 8.2 to calculate EPS, investors could use Equation 8.3 as follows:

EPS=After-tax earningsBook value of equity×Book value of equityShares outstanding= ROE × Book value per shareEPS=After-tax earningsBook value of equity×Book value of equityShares outstanding= ROE × Book value per shareEquation8.3

This formula will produce the same results as Equation 8.2 . The major advantage of this form of the equation is that it highlights how much a firm earns relative to the book value of its equity. As we’ve already seen, earnings divided by book equity is the firm’s ROE. Return on equity is a key financial measure because it captures the amount of success the firm is having in managing its assets, operations, and capital structure. And as we see here, ROE is not only important in defining overall corporate profitability, but it also plays a crucial role in defining a stock’s EPS.

To produce an estimated EPS using Equation 8.3 , investors would go directly to the two basic components of the formula and try to estimate how those components might change in the future. In particular, what kind of growth in the firm’s book value per share is reasonable to expect, and what’s likely to happen to the company’s ROE? In the vast majority of cases, ROE is really the driving force, so it’s important to produce a good estimate of that variable. Investors often do that by breaking ROE into its component parts— net profit margin, total asset turnover, and the equity multiplier (see Equation 7.15 ).

With a forecast of ROE and book value per share in place, investors can plug these figures into Equation 8.3 to produce estimated EPS. The bottom line is that, one way or another (using the approach reflected in Equation 8.2 or that in Equation 8.3 ), investors have to arrive at a forecasted EPS number that they are comfortable with. After that, it’s a simple matter to use the forecasted payout ratio to estimate dividends per share:

Estimated dividends per share in year t= Estimated EPS for year t× Estimated payout ratioEstimated dividends per share in year t = Estimated EPS for year t × Estimated payout ratioEquation8.4

Finally, estimate the future value of the stock by multiplying expected earnings times the expected P/E ratio:

Estimated share price at end of year t= Estimated EPS for year t× Estimated P/E ratioEstimated share price at end of year t = Estimated EPS for year t × Estimated P/E ratioEquation8.5

Pulling It All Together

Now, to see how all of these components fit together, let’s continue with the example we started above. Using the aggregate sales and earnings approach, if the company had two million shares of common stock outstanding and investors expected that to remain constant, then given the estimated earnings of $6.5 million obtained from Equation 8.1 , the firm should generate earnings per share next year of

Estimated EPS next year ×$6.5 million2 million = $3.25––––––––––––Estimated EPS next year ×$6.5 million2 million = $3.25__

An investor could obtain the same figure using forecasts of the firm’s ROE and its book value per share. For instance, suppose we estimate that the firm will have an ROE of 15% and a book value per share of $21.67. According to Equation 8.3 , those conditions would also produce an estimated EPS of $3.25 (i.e., 0.15×$21.670.15 ×$21.67). Using this EPS figure, along with an estimated payout ratio of 40%, dividends per share next year should equal

Estimated dividends per share next year = $3.25 × .40 = $1.30––––––––––––Estimated dividends per share next year = $3.25 × .40 = $1.30__

Keep in mind that firms don’t always adjust dividends in lockstep with earnings. A firm might pay the same dividend for many years if managers are not confident that an increase in earnings can be sustained over time. In a case like this, when a firm has a history of adjusting dividends slowly if at all, it may be that past dividends are a better guide to future dividends than projected earnings are. Finally, if it has been estimated that the stock should sell at 17.5 times earnings, then a share of stock in this company should be trading at $56.88 by the end of next year.

Estimated share price at the end of next year = $3.25 × 17.5 = $56.88––––––––––––––Estimated share price at the end of next year = $3.25 × 17.5 = $56.88__

Actually, an investor would be most interested in the price of the stock at the end of the anticipated investment horizon. Thus, the $56.88 figure would be appropriate for an investor who had a one-year horizon. However, for an investor with a three-year holding period, extending the EPS figure for two more years and repeating these calculations with the new data would be a better approach. The bottom line is that the estimated share price is important because it has embedded in it the capital gains portion of the stock’s total return.

Investor Facts

Target Prices A target price is the price an analyst expects a stock to reach within a certain period of time (usually a year). Target prices are normally based on an analyst’s forecast of a company’s sales, earnings, and other criteria, some of which are highly subjective. One common practice is to assume that a stock should trade at a certain price-to-earnings multiple—say, on par with the average P/E multiples of similar stocks—and arrive at a target price by multiplying that P/E ratio by an estimate of what the EPS will be one year from now. Use target prices with care, however, because analysts will often raise their targets simply because a stock has reached the targeted price much sooner than expected.

Developing a Forecast of Universal’s Financial Performance

Using information obtained from Universal Office Furnishings (UVRS), we can illustrate the forecasting procedures we discussed above. Recall that our earlier assessment of the economy and the office equipment industry was positive and that the company’s operating results and financial condition looked strong, both historically and relative to industry standards. Because everything looks favorable for Universal, we decide to take a look at the future prospects of the company and its stock.

Let’s assume that an investor considering Universal common stock has a three-year investment horizon. Perhaps the investor believes (based on earlier studies of economic and industry factors) that the economy and the market for office equipment stocks will start running out of steam near the end of 2019 or early 2020. Or perhaps the investor plans to sell any Universal common stock purchased today to finance a major expenditure in three years. Regardless of the reason behind the investor’s three-year horizon, we will focus on estimating Universal’s performance for 2017, 2018, and 2019.

Table 8.2 Selected Historical Financial Data, Universal Office Furnishings

	2012	2013	2014	2015	2016
* To find the annual rate of growth in sales divide sales in one year by sales in the previous year and then subtract one. For example, the annual rate of growth in sales for 2016 = ($1,938.00−$1,766.20)÷$1,766.20−1 = 9.73%2016 = ($1,938.00−$1,766.20)÷$1,766.20−1 = 9.73%.
Total assets (millions)	$554.20	$ 694.90	$ 755.60	$ 761.50	$ 941.20
Total asset turnover	1.72	1.85	1.98	2.32	2.06
Sales revenue (millions)	$953.20	$1,283.90	$1,495.90	$1,766.20	$1,938.00
Annual rate of growth in sales *	−1.07%	34.69%	16.51%	18.07%	9.73%
Net profit margin	4.20%	6.60%	7.50%	8.00%	7.20%
Payout ratio	6.80%	5.20%	5.50%	6.00%	6.60%
Price/earnings ratio	13.5	16.2	13.9	15.8	18.4
Number of common shares outstanding (millions)	77.7	78.0	72.8	65.3	61.8

Table 8.2 provides selected historical financial data for the company, covering a five-year period (ending with the latest fiscal year) and provides the basis for much of our forecast. The data reveal that, with one or two exceptions, the company has performed at a fairly steady pace and has been able to maintain a very attractive rate of growth. Our previous economic analysis suggested that the economy is about to pick up, and our research indicated that the industry and company are well situated to take advantage of the upswing. Therefore, we conclude that the rate of growth in sales should pick up from the 9.7% rate in 2016, attaining a growth rate of over 20% in 2017—a little higher than the firm’s five-year average. After a modest amount of pent-up demand is worked off, the rate of growth in sales should drop to about 19% in 2018 and to 15% in 2019.

The essential elements of the financial forecast for 2017 through 2019 appear in Table 8.3 . Highlights of the key assumptions and the reasoning behind them are as follows:

· Net profit margin . Various published industry and company reports suggest a comfortable improvement in earnings, so we decide to use a profit margin of 8.0% in 2017 (up a bit from the latest margin of 7.2% recorded in 2016). We’re projecting even better profit margins (8.5%) in 2018 and 2019, as Universal implements some cost improvements.

· Common shares outstanding . We believe the company will continue to pursue its share buyback program, but at a substantially slower pace than in the 2013–2016 period. From a current level of 61.8 million shares, we project that the number of shares outstanding will drop to 61.5 million in 2017, to 60.5 million in 2018, and to 59.0 million in 2019.

· Payout ratio . We assume that the dividend payout ratio will hold at a steady 6% of earnings.

· P/E ratio . Primarily on the basis of expectations for improved growth in revenues and earnings, we are projecting a P/E multiple that will rise from its present level of 18.4 times earnings to roughly 20 times earnings in 2017. Although this is a fairly conservative increase in the P/E, when it is coupled with the hefty growth in EPS, the net effect will be a big jump in the projected price of Universal stock.

Table 8.3 Summary Forecast Statistics, Universal Office Furnishings

	Latest Actual Figure (Fiscal 2016)	Weighted Average in Recent Years (2012–2016)	Forecasted Figures **
			2017	2018	2019
* N/A: Not applicable.
** Forecasted sales figures: Sales from preceding year × (1 + growth rate in sales) = forecasted salesSales from preceding year × (1 + growth rate in sales) = forecasted sales.
For example, for 2017: $1,938.0 × (1 + 0.22) = $2,364.4$1,938.0 × (1 + 0.22) = $2,364.4.
Annual rate of growth in sales	9.7%	15.0%	22.0%	19.0%	15.0%
Net sales (millions)	$1,938.0	N/A *	$2,364.4	$2,813.6	$3,235.6
× Net profit margin	7.2%	5.6%	8.0%	8.5%	8.5%
= Net after-tax earnings (millions)	$ 139.7	N/A	$ 189.1	$ 239.2	$ 275.0
÷ Common shares outstanding (millions)	61.8	71.1	61.5	60.5	59.0
= Earnings per share	$ 2.26	N/A	$ 3.08	$ 3.95	$ 4.66
× Payout ratio	6.6%	6.2%	6.0%	6.0%	6.0%
= Dividends per share	$ 0.15	$0.08	$ 0.18	$ 0.24	$ 0.28
Earnings per share	$ 2.26	N/A	$ 3.08	$ 3.95	$ 4.66
× P/E ratio	18.4	16.8	20.0	20.0	20.0
= Share price at year end	$ 41.58	N/A	$ 61.51	$ 79.06	$ 93.23

Excel@Investing

Table 8.3 also shows the sequence involved in arriving at forecasted dividends and share price behavior; that is:

1. The company dimensions of the forecast are handled first. These include sales and revenue estimates, net profit margins, net earnings, and the number of shares of common stock outstanding.

2. Next we estimate earnings per share by dividing expected earnings by shares outstanding.

3. The bottom line of the forecast is, of course, the returns in the form of dividends and capital gains expected from a share of Universal stock, given that the assumptions about sales, profit margins, earnings per share, and so forth hold up. We see in Table 8.3 that dividends should go up to 28 cents per share, which is a big jump from where they are now (15 cents per share). Even with a big dividend increase, it’s clear that dividends still won’t account for much of the stock’s return. In fact, our projections indicate that the dividend yield in 2019 will fall to just 0.3% (divide the expected $0.28 dividend by the anticipated $93.23 price to get a yield of just 0.3%). Clearly, our forecast implies that the returns from this stock are going to come from capital gains, not dividends. That’s obvious when we look at year-end share prices, which we expect to more than double over the next three years. That is, if our projections are valid, the price of a share of stock should rise from around $41.50 to more than $93.00 by year-end 2019.

We now have an idea of what the future cash flows of the investment are likely to be. We can now use that information to establish an intrinsic value for Universal Office Furnishings stock.

The Valuation Process

Valuation is a process by which an investor determines the worth of a security keeping in mind the tradeoff between risk and return. This process can be applied to any asset that produces a stream of cash—a share of stock, a bond, a piece of real estate, or an oil well. To establish the value of an asset, the investor must determine certain key inputs, including the amount of future cash flows, the timing of these cash flows, and the rate of return required on the investment.

In terms of common stock, the essence of valuation is to determine what the stock ought to be worth, given estimated cash flows to stockholders (future dividends and capital gains) and the amount of risk. Toward that end we employ various types of stock valuation models, the end product of which represents the elusive intrinsic value we have been seeking. That is, the stock valuation models determine either an expected rate of return or the intrinsic worth of a share of stock, which in effect represents the stock’s “justified price.” In this way, we obtain a standard of performance, based on forecasted stock behavior, which we can use to judge the investment merits of a particular security.

Either of two conditions would make us consider a stock a worthwhile investment candidate: (1) the expected rate of return equals or exceeds the return we feel is warranted given the stock’s risk, or (2) the justified price (intrinsic worth) is equal to or greater than the current market price. In other words, a security is a good investment if its expected return is at least as high as the return that an investor demands based on the security’s risk or if its intrinsic value equals or exceeds the current market price of the security. There is nothing irrational about purchasing a security in those circumstances. In either case, the security meets our minimum standards to the extent that it is giving investors the rate of return they wanted.

Remember this, however, about the valuation process: Even though valuation plays an important part in the investment process, there is absolutely no assurance that the actual outcome will be even remotely similar to the projections. The stock is still subject to economic, industry, company, and market risks, any one of which could negate all of the assumptions about the future. Security analysis and stock valuation models are used not to guarantee success but to help investors better understand the return and risk dimensions of a potential transaction.

Required Rate of Return

One of the key ingredients in the stock valuation process is the required rate of return . Generally speaking, the return that an investor requires should be related to the investment’s risk. In essence, the required return establishes a level of compensation compatible with the amount of risk involved. Such a standard helps determine whether the expected return on a stock (or any other security) is satisfactory. Because investors don’t know for sure what the cash flow of an investment will be, they should expect to earn a rate of return that reflects this uncertainty. Thus, the greater the perceived risk, the more investors should expect to earn. This is basically the notion behind the capital asset pricing model (CAPM).

Recall that using the CAPM, we can define a stock’s required return as

Required rate of return = Risk-free rate + [Stock's beta × (Market return−Risk-free rate)]Required rate of return = Risk-free rate + [Stock's beta × (Market return−Risk-free rate)]Equation8.6

Two of the required inputs for this equation are readily available. You can obtain a stock’s beta from many online sites or print sources. The risk-free rate is the current return provided by a risk-free investment such as a Treasury bill or a Treasury bond. Estimating the expected return on the overall stock market is not as straightforward. A simple way to calculate the market’s expected return is to use a long-run average return on the stock market. This average return may, of course, have to be adjusted up or down a bit based on what investors expect the market to do over the next year or so.

An Advisor’s Perspective

Rod Holloway Equity Portfolio Manager, CFCI

“The higher the beta, the more that stock will move up if the market is going up.”

MyFinanceLab

In the CAPM, the risk of a stock is captured by its beta. For that reason, the required return on a stock increases (or decreases) with increases (or decreases) in its beta. As an illustration of the CAPM at work, consider Universal’s stock, which we’ll assume has a beta of 1.30. If the risk-free rate is 3.5% and the expected market return is 10%, according to the CAPM model, this stock would have a required return of

Required return=3.5%+[1.30×(10.0%−3.5%)] = 11.95%––––––––––––––––Required return=3.5%+[1.30×(10.0%−3.5%)] = 11.95%__

This return—let’s round it to 12%—can now be used in a stock valuation model to assess the investment merits of a share of stock. To accept a lower return means you’ll fail to be fully compensated for the risk you must assume.

Concepts In Review

Answers available at http://www.pearsonhighered.com/smart

1. 8.1 What is the purpose of stock valuation? What role does intrinsic value play in the stock valuation process?

2. 8.2 Are the expected future earnings of the firm important in determining a stock’s investment suitability? Discuss how these and other future estimates fit into the stock valuation framework.

3. 8.3 Can the growth prospects of a company affect its price-to-earnings multiple? Explain. How about the amount of debt a firm uses? Are there any other variables that affect the level of a firm’s P/E ratio?

4. 8.4 What is the market multiple and how can it help in evaluating a stock’s P/E ratio? Is a stock’s relative P/E the same thing as the market multiple? Explain.

5. 8.5 In the stock valuation framework, how can you tell whether a particular security is a worthwhile investment candidate? What roles does the required rate of return play in this process? Would you invest in a stock if all you could earn was a rate of return that just equaled your required return? Explain.

Stock Valuation Models

1. LG 4

2. LG 5

3. LG 6

Investors employ several stock valuation models. Although they are usually aimed at a security’s future cash flows, their approaches to valuation are nonetheless considerably different. Some models, for example, focus heavily on the dividends that a stock will pay over time. Other models emphasize the cash flow that a firm generates, focusing less attention on whether the company pays that cash out as dividends, uses it to repurchase shares, or simply holds it in reserve.

There are still other stock valuation models in use—models that employ such variables as dividend yield, abnormally low P/E multiples, relative price performance over time, and even company size or market cap as key elements in the decision-making process. For purposes of our discussion, we’ll focus on several stock valuation models that derive value from the fundamental performance of the company. We’ll look first at stocks that pay dividends and at a procedure known as the dividend valuation model. From there, we’ll look at several valuation procedures that can be used with companies that pay little or nothing in dividends. Finally, we’ll move on to procedures that set the price of a stock based on how it behaves relative to earnings, cash flow, sales, or book value. The stock valuation procedures that we’ll examine in this chapter are the same as those used by many professional security analysts and are, in fact, found throughout the “Equity Investments” portion of the CFA exam, especially at Level-I. And, of course, an understanding of these valuation models will enable you to better evaluate analysts’ recommendations.

An Advisor’s Perspective

Rod Holloway Equity Portfolio Manager, CFCI

“The stock valuation model that I prefer depends on the type of stock that I’m looking for.”

MyFinanceLab

The Dividend Valuation Model

In the valuation process, the intrinsic value of any investment equals the present value of its expected cash benefits. For common stock, this amounts to the cash dividends received each year plus the future sale price of the stock. One way to view the cash flow benefits from common stock is to assume that the dividends will be received over an infinite time horizon—an assumption that is appropriate as long as the firm is considered a “going concern.” Seen from this perspective, the value of a share of stock is equal to the present value of all the future dividends it is expected to provide over an infinite time horizon.

When an investor sells a stock, from a strictly theoretical point of view, what he or she is really selling is the right to all future dividends. Thus, just as the current value of a share of stock is a function of future dividends, the future price of the stock is also a function of future dividends. In this framework, the future price of the stock will rise or fall as the outlook for dividends (and the required rate of return) changes. This approach, which holds that the value of a share of stock is a function of its future dividends, is known as dividend valuation model (DVM) .

There are three versions of the dividend valuation model, each based on different assumptions about the future rate of growth in dividends:

1. The zero-growth model assumes that dividends will not grow over time.

2. The constant-growth model assumes that dividends will grow by a constant rate over time.

3. The variable-growth model assumes that the rate of growth in dividends will vary over time.

In one form or another, the DVM is widely used in practice to solve many kinds of valuation problems.

Zero Growth

The simplest way to picture the dividend valuation model is to assume the stock has a fixed stream of dividends. In other words, dividends stay the same year in and year out, and they’re expected to do so in the future. Under such conditions, the value of a zero-growth stock is simply the present value of its annual dividends. To find the present value, just divide annual dividends by the required rate of return:

Value of a share of stock = Annual dividendsRequired rate of returnValue of a share of stock = Annual dividendsRequired rate of returnEquation8.7

Famous Failures in Finance Ethical Conflicts Faced by Stock Analysts: Don’t Always Believe the Hype

Buy, sell, or hold? Unfortunately, many investors have learned the hard way not to trust analysts’ recommendations.

Consider the late 1990s stock market bubble. As the market began to fall in 2000, 95% of publicly traded stocks were free of sell recommendations, according to investment research firm Zacks, and 5% of stocks that did have a sell rating had exactly that: one sell rating from a single analyst. When the market began its climb back up, analysts missed the boat again. From 2000 to 2004, stocks that analysts told investors to sell rose 19% per annum on average, while their “buys” and “holds” rose just 7%.

Why were the all-star analysts wrong so often? Conflict of interest is one explanation. Analysts often work for investment banks who have business relationships with the companies that analysts follow. Analysts may feel pressure to make positive comments to please current or prospective investment banking clients. Also, analysts’ buy recommendations may induce investors to trade, and those trades generate commissions for the analysts’ employers.

Analyst hype is a real problem for both Wall Street and Main Street, and the securities industry has taken steps to correct it. The SEC’s Regulation Fair Disclosure requires that all company information be released to the public rather than quietly disseminated to analysts. Some brokerages ban analysts from owning stocks they cover. In 2003 the SEC ruled that compensation for analyst research must be separated from investment banking fees, so that the analyst’s job is to research stock rather than solicit clients.

Most important, investors must learn how to read between the lines of analysts’ reports. In early 2014 there were nearly eight times as many “buy” recommendations for stocks in the S&P 500 as there were “sell” recommendations. If analysts were really unbiased, it seems very unlikely that their recommendations would be so heavily tilted toward the buy side. What should investors do? To start, they should probably lower analysts’ ratings by one notch. A strong buy could be interpreted as a buy or a buy as a hold, and a hold or neutral as a sell. Also, investors should give more weight to negative ratings than to positive ones. A recent study found that sell recommendations were followed by an immediate drop of 3% in the price of downgraded stocks, whereas buy recommendations had either a more muted effect or no effect at all. Downgrades and those rare sell recommendations may signal future problems. Investors should also pay attention to forecasts in which a ratings change is accompanied by an earnings forecast revision in the same direction. That is, if an analyst moves a stock from sell to buy and simultaneously raises the earnings forecast for the stock, that is more credible than a report that simply changes the rating to “buy.” Finally, when in doubt, investors should do their own homework, using the techniques taught in this text.

Critical Thinking Question

Why do you think sell ratings tend to cause stock prices to fall, while buy ratings do not lead to stock price increases?

(Sources: Jack Hough, “How to Make Money off Analysts’ Stock Recommendations,” Smart Money, January 19, 2012, http://www.smartmoney.com/invest/stocks/how-to-make- money-off-analysts-stock-recommendations-1326759491635/ ; Rich Smith, “Analysts Running Scared,” The Motley Fool, April 5, 2006, http://www.fool.com .)

Example

Suppose a stock pays a dividend of $3 per share each year, and you don’t expect that dividend to change. If you want a 10% return on your investment, how much should you be willing to pay for the stock?

Value of stock=$3÷0.10=$30Value of stock=$3÷0.10=$30

If you paid a higher price, you would earn a rate of return less than 10%, and likewise if you could acquire the stock for less, your rate of return would exceed 10%.

As you can see, the only cash flow variable that’s used in this model is the fixed annual dividend. Given that the annual dividend on this stock never changes, does that mean the price of the stock never changes? Absolutely not! For as the required rate of return (capitalization rate) changes, so will the price of the stock. Thus, if the required rate of return goes up to 15%, the price of the stock will fall to $20($3÷0.15)$20 ($3÷0.15). Although this may be a very simplified view of the valuation model, it’s actually not as far-fetched as it may appear, for this is basically the procedure used to price preferred stocks in the marketplace.

Constant Growth

The zero-growth model is a good beginning, but it does not take into account a growing stream of dividends. The standard and more widely recognized version of the dividend valuation model assumes that dividends will grow over time at a specified rate. In this version, the value of a share of stock is still considered to be a function of its future dividends, but such dividends are expected to grow forever at a constant rate of growth, g. Accordingly, we can find the value of a share of stock as follows:

Value of a share of stock = Next year's dividendsRequired rate of return−Dividend growth rateValue of a share of stock = Next year's dividendsRequired rate of return−Dividend growth rateEquation8.8

V=D1r−gV= D1r−gEquation8.8a

where

D1 = annual dividend expected next year (the first year in the forecast period)r = the required rate of return on the stockg = the annual rate of growth in dividends, which must be less than rD1 = annual dividend expected next year (the first year in the forecast period)r = the required rate of return on the stockg = the annual rate of growth in dividends, which must be less than r

Even though this version of the model assumes that dividends will grow at a constant rate forever, it is important to understand that doesn’t mean we assume the investor will hold the stock forever. Indeed, the dividend valuation model makes no assumptions about how long the investor will hold the stock, for the simple reason that the investment horizon has no bearing on the computed value of a stock. Thus, with the constant-growth DVM, it is irrelevant whether the investor has a one-year, five-year, or ten-year expected holding period. The computed value of the stock will be the same under all circumstances. So long as the input assumptions (r, g, and D1) are the same, the value of the stock will be the same regardless of the intended holding period.

Investor Facts

Steady Stream of Dividends The Canadian company Power Financial Corp. paid a $0.35 dividend for 27 consecutive quarters from December 2008 to December 2014. After receiving the same dividend for so long, did investors value Power Financial based on the assumption that it would pay $1.40 per year ($0.35 per quarter 4 times per year) forever? If we assume that investors required an 8% return on the stock, then under the assumption of constant dividends, the stock would sell for $17.50 per share (i.e., 1.40÷0.081.40÷0.08). In fact, the stock traded in the $30 range in December 2014. Therefore, we can surmise that investors either required a return that was lower than 8% or they expected dividends to rise. In fact, the company did announce a dividend increase a few months later in March 2015.

Note that this model succinctly captures the essence of stock valuation. Increase the cash flow (through D or g) or decrease the required rate of return (r), and the stock value will increase. We know that, in practice, there are potentially two components that make up the total return to a stockholder: dividends and capital gains. This model captures both components. If you solve Equation 8.8a for r, you will find that r=D1/V+gr=D1/V+g. The first term in this sum, D1/V, represents the dividend expected next year relative to the stock’s current price. In other words, D1/V is the stock’s expected dividend yield. The second term, g, is the expected dividend growth rate. But if dividends grow at rate g, the stock price will grow at that rate too, so g also represents the capital gain component of the stock’s total return. Therefore, the stock’s total return is the sum of its dividend yield and its capital gain.

The constant-growth model should not be used with just any stock. Rather, it is best suited to the valuation of mature, dividend-paying companies that have a long track record of increasing dividends. These are probably large-cap (or perhaps even some mature mid-cap) companies that have demonstrated an ability to generate steady—although perhaps not spectacular—rates of growth year in and year out. The growth rates may not be identical from year to year, but they tend to move within a relatively narrow range. These are companies that have established dividend policies and fairly predictable growth rates in earnings and dividends.

Example

In the 25 years between 1990 and 2015, the food company General Mills increased its dividend payments by about 7% per year. The food industry is not one where we would expect explosive growth. Food consumption is closely tied to population growth, so profits in this business should grow relatively slowly over time. In April 2015 General Mills was paying an annual dividend of $1.76 per share, so for 2016 investors were expecting a modest increase in General Mills dividends over the coming year to $1.88 per share (7% more than the 2015 dividend). If the required return on General Mills stock is 10%, then investors should have been willing to pay $62.67 for the stock ($1.88÷(0.10−0.07))($1.88÷(0.10−0.07)) in 2015. In fact, General Mills stock was trading in a range between $55 and $57 at the time, so our application of the constant growth model suggests that General Mills was slightly undervalued. That is, its intrinsic value ($62.67) was a little higher than the stock’s market price. Of course, our estimate of intrinsic value might be too high if the required return on General Mills shares is higher than 10% or if the long-run growth rate in dividends in less than 7%. Indeed, one drawback to the constant growth model is that the estimate of value that it produces is very sensitive to the assumptions one makes about the required return and the dividend growth rate. For example, if we assumed that the required return on General Mills stock was 11% rather than 10%, our estimate of intrinsic value would fall from $62.67 to $47!

Analysts sometimes use the constant-growth DVM to estimate the required return on a stock based on the assumption that the stock’s market price is equal to its intrinsic value. In other words, analysts plug the stock’s market price and an estimate of the dividend growth rate into Equation 8.8a and solve for r rather than solving for V. For General Mills, if the stock’s market price is $56, the next dividend is $1.88, and the dividend growth rate is 7%, we can estimate the required return on General Mills’ stock as follows:

$56=$1.88÷(r−0.07)$56=$1.88÷(r−0.07)

Solving this equation for r, we find that the required return on General Mills’ stock is about 10.36%.

Estimating the Dividend Growth Rate

Use of the constant-growth DVM requires some basic information about the stock’s required rate of return, its current level of dividends, and the expected rate of growth in dividends. A fairly simple, albeit naïve, way to find the dividend growth rate, g, is to look at the historical behavior of dividends. If they are growing at a relatively constant rate, you can assume they will continue to grow at (or near) that average rate in the future. You can get historical dividend data in a company’s annual report or from various online sources

With the help of a calculator or spreadsheet, we can use basic present value arithmetic to find the growth rate embedded in a stream of dividends. For example, compare the dividend that a company is paying today to the dividend it paid several years ago. If dividends have been growing steadily, dividends today will be higher than they were in the past. Next, use your calculator to find the discount rate that equates the present value of today’s dividend to the dividend paid several years earlier. When you find that rate, you’ve found the dividend growth rate. In this case, the discount rate is the average rate of growth in dividends. (See Chapter 4 for a detailed discussion of how to calculate growth rates.)

Example

In 2015 General Mills paid an annual dividend of $1.76 per share. The company had been increasing dividends steadily since 1990, when the annual dividend was just $0.32 per share. The table below shows the present value of the 2015 dividend, discounted back 25 years at various interest rates. You can see that when the discount rate is 7%, the present value of the 2015 dividend is approximately equal to the dividend paid in 1990, so 7% is the growth rate in dividends from 1990 to 2015.

Discount rate	PV of 2015 dividend ($1.76)
5%	$0.52
6%	$0.41
7%	$0.32 (matches actual 1990 dividend)
8%	$0.26

Growth Rate Calculator

Once you’ve determined the dividend growth rate, you can find next year’s dividend, D1, as D0×(1 + g)D0×(1 + g), where D0 equals the current dividend. In 2015 General Mills was paying dividends at an annual rate of $1.76 per share. If you expect those dividends to grow at the rate of 7% a year, you can find the expected 2016 dividend as follows: D1=D0(1 + g) = $1.76(1+0.07)=$1.88D1=D0(1 + g) = $1.76(1+0.07)=$1.88. The only other information you need is the required rate of return (capitalization rate), r. (Note that r must be greater than g for the constant-growth model to be mathematically operative.) As we have already seen, if we assume that the required return on General Mills stock is 10%, that assumption, combined with an expected dividend next year of $1.88 and a projected dividend growth rate of 7%, produces an estimate of General Mills’ stock value of $62.67.

Stock-Price Behavior over Time

The constant-growth model implies that a stock’s price will grow over time at the same rate that dividends grow, g, and that the growth rate plus the dividend yield equals the required return. To see how this works, consider the following example.

Suppose that today’s date is January 2, 2016, and a stock just paid (on January 1) its annual dividend of $2.00 per share. Suppose too that investors expect this dividend to grow at 5% per year, so they believe that next year’s dividend (which will be paid on January 1, 2017) will be $2.10, which is 5% more than the previous year’s dividend. Finally, assume that investors require a 9% return on the stock. Based on those assumptions, we can estimate the price of the stock on January 2, 2016, as follows:

Price on January 2, 2016=Dividend on January 1,2017÷(r−g)Price=$2.10÷(0.09−0.05)=$52.50.Price on January 2, 2016=Dividend on January 1, 2017 ÷(r−g)Price=$2.10÷(0.09−0.05)=$52.50.

Imagine that an investor purchases this stock for $52.50 on January 2 and holds it for one year. The investor receives the next dividend on January 1, 2017, and then sells the stock a day later on January 2, 2017. To estimate the expected return on this purchase, we must calculate the expected stock price that the investor will receive when she sells the stock on January 2, 2017.

Price on January 2, 2017=Dividend on January1, 2018÷(r−g)Price=$2.10(1+0.05)÷(0.09−0.05)Price=$2.205÷(0.09−0.05)=$55.125Price on January 2, 2017=Dividend on January1, 2018÷(r−g)Price=$2.10(1+0.05)÷(0.09−0.05)Price=$2.205÷(0.09−0.05)=$55.125

Now let’s look at the investor’s expected return during the calendar year 2016. She purchases the stock for $52.50 at the beginning of the year. One year later on January 1, 2017, she receives a dividend of $2.10 per share, and then she sells the stock for $55.125. Her total return equals the dividend plus the capital gain, divided by the original purchase price.

Total return=(dividend+capital gain)÷purchase priceTotal return=($2.10+$55.125−$52.50)÷$52.50=0.09=9.0%Total return=(dividend+capital gain)÷purchase priceTotal return=($2.10+$55.125−$52.50)÷$52.50=0.09=9.0%

The investor expects to earn 9% over the year, which is exactly the required return on the stock. Notice that during the year the stock price increased by 5% from $52.50 to $55.125. So the stock price increased at the same rate that the dividend payment did. Furthermore, the dividend yield that the investor earned was 4% ($2.10 /$52.50). Therefore the 9% total return consists of a 5% capital gain and a 4% dividend yield.

Repeating this process allows you to estimate the stock price on January 2 of any succeeding year. As the table below shows, each and every year the stock price increases by 5%, and the stock’s dividend yield is 4%. Therefore, an investor in this stock earns exactly the 9% required return year after year.

Year	Dividend paid on January 1	Stock price on January 2 *
* As determined by the dividend valuation mode, given g=0.05g=0.05 and r=0.09r=0.09.
2016	$2.000	$52.50
2017	$2.100	$55.125
2018	$2.205	$57.881
2019	$2.315	$60.775

Variable Growth

Although the constant-growth dividend valuation model is an improvement over the zero-growth model, it still has some shortcomings. The most obvious deficiency is that the model does not allow for changes in expected growth rates. To overcome this problem, we can use a form of the DVM that allows for variable rates of growth over time. Essentially, the variable-growth dividend valuation model calculates a stock price in two stages. In the first stage, dividends grow rapidly but not necessarily at a single rate. The dividend growth rate can rise or fall during this initial stage. In the second stage, the company matures and dividend growth settles down to some long-run, sustainable rate. At that point, it is possible to value the stock using the constant-growth version of the DVM. The variable-growth version of the model finds the value of a share of stock as follows:

Value of a share of stock = Present value of future dividends during the initial variable-growth period + Present value of the price of the stock at the end of the variable-growth periodValue of a share of stock = Present value of future dividends during the initial variable-growth period + Present value of the price of the stock at the end of the variable-growth periodEquation8.9

V=D1(1+r)1+D2(1+r)2+…Dv(1+r)v+Dv(1+g)(r−g)(1+r)vV=D1(1+r)1+D2(1+r)2+…Dv(1+r)v+Dv(1+g)(r−g)(1+r)vEquation8.9a

where

D1, D2, etc.=future annual dividendsv=number of years in the initial variable-growth periodD1, D2, etc.=future annual dividendsv=number of years in the initial variable-growth period

Note that the last element in this equation is the standard constant-growth dividend valuation model, which is used to find the price of the stock at the end of the initial variable-growth period, discounted back v periods.

This form of the DVM is appropriate for companies that are expected to experience rapid or variable rates of growth for a period of time—perhaps for the first three to five years—and then settle down to a more stable growth rate thereafter. This, in fact, is the growth pattern of many companies, so the model has considerable application in practice. It also overcomes one of the operational shortcomings of the constant-growth DVM in that r does not have to be greater than g during the initial stage. That is, during the variable-growth period, the rate of growth, g, can be greater than the required rate of return, r, and the model will still be fully operational.

Finding the value of a stock using Equation 8.9 is actually a lot easier than it looks. To do so, follow these steps:

1. Estimate annual dividends during the initial variable-growth period and then specify the constant rate, g, at which dividends will grow after the initial period.

2. Find the present value of the dividends expected during the initial variable-growth period.

3. Using the constant-growth DVM, find the price of the stock at the end of the initial growth period.

4. Find the present value of the price of the stock (as determined in step 3). Note that the price of the stock is discounted for the same length of time as the last dividend payment in the initial growth period because the stock is being priced (per step 3) at the end of this initial period.

5. Add the two present value components (from steps 2 and 4) to find the value of a stock.

Applying the Variable-Growth DVM

To see how this works, let’s apply the variable-growth model to Sweatmore Industries (SI). Let’s assume that dividends will grow at a variable rate for the first three years (2016, 2017, and 2018). After that, the annual dividend growth rate will settle down to 3% and stay there indefinitely. Starting with the latest (2015) annual dividend of $2.21 a share, we estimate that Sweatmore’s dividends should grow by 20% next year (in 2016), by 16% in 2017, and then by 13% in 2018 before dropping to a 3% rate. Finally, suppose that SI’s investors require an 11% rate of return.

Using these growth rates, we project that dividends in 2016 will be $2.65 a share ($2.21×1.20)($2.21×1.20) and will rise to $3.08($2.65×1.16)$3.08($2.65×1.16) in 2017 and to $3.48($3.08×1.13)$3.48 ($3.08×1.13) in 2018. Dividing 2019’s $3.58 dividend by 8% (r−g)(r−g) gives us the present value in 2018 of all dividends paid in 2019 and beyond. We now have all the inputs we need to put a value on Sweatmore Industries. Table 8.4 shows the variable-growth DVM in action. The value of Sweatmore stock, according to the variable-growth DVM, is $40.19 a share. In essence, that’s the maximum price an investor should be willing to pay for the stock to earn an 11% rate of return.

Defining the Expected Growth Rate

Mechanically, application of the DVM is really quite simple. It relies on just three key pieces of information: future dividends, future

Excel@Investing

Table 8.4 Using the Variable-Growth DVM to Value Sweatmore Stock

Step

1. Projected annual dividends:

Most recent dividend	2015	$2.21
Future dividends	2016	$2.65
	2017	$3.08
	2018	$3.48

2. Estimated annual rate of growth in dividends, g, for 2019 and beyond: 3%

3. Present value of dividends, using a required rate of return, r, of 11%, during the initial variable-growth period:

Year	Dividends	Present Value
2016	$2.65	$2.39
2017	$3.08	$2.50
2018	$3.48	$2.54
	Total	$7.43 (to step 5)

4. Price of the stock at the end of the initial growth period:

P2018=D2019r−g−D2018×(1−g)r−g=$3.48×(1.03)0.11−0.03=$3.580.08=$44.81––––––––––––––P2018=D2019r−g−D2018×(1−g)r−g=$3.48×(1.03)0.11−0.03=$3.580.08=$44.81__

5. Discount the price of the stock (as computed above) back to its present value, at r, of 11%:

$44.81÷(1.11)3 = $32.76 (to step 5)$44.81÷(1.11)3 = $32.76 (to step 5)

6. Add the present value of the initial dividend stream (step 2) to the present value of the price of the stock at the end of the initial growth period (step 4):

Value of Sweatmore stock: 7.43 + $32.76 = $40.19–––––––Value of Sweatmore stock: 7.43 + $32.76 = $40.19_

growth in dividends, and a required rate of return. But this model is not without its difficulties. One of the most difficult (and most important) aspects of the DVM is specifying the appropriate growth rate, g, over an extended period of time. Whether you are using the constant-growth or the variable-growth version of the dividend valuation model, the growth rate, g, has an enormous impact on the value derived from the model. As a result, in practice analysts spend a good deal of time trying to come up with a good way to estimate a company’s dividend growth rate.

As we saw earlier, we can estimate the growth rate by looking at a company’s historical dividend growth. While that approach might work in some cases, it does have some serious shortcomings. What’s needed is a procedure that looks at the key forces that actually drive the growth rate. Fortunately, there is such an approach that is widely used in practice. This approach assumes that future dividend growth depends on the rate of return that a firm earns and the fraction of earnings that managers reinvest in the company. Equation 8.10 illustrates this idea:

g=ROE×The firm's retention rate, rrg=ROE×The firm's retention rate, rrEquation8.10

where

rr = 1−Dividend payout ratiorr = 1−Dividend payout ratioEquation8.10a

Both variables in Equation 8.10 (ROE and rr) are directly related to the firm’s future growth rate. The retention rate represents the percentage of its profits that the firm plows back into the company. Thus, if the firm pays out 35% of its earnings in dividends (i.e., it has a dividend payout ratio of 35%), then it has a retention rate of 65%: rr=1−0.35 = 0.65rr=1−0.35 = 0.65 The retention rate indicates the amount of capital that is flowing back into the company to finance growth. Other things being equal, the more money managers reinvest in the company, the higher the growth rate.

The other component of Equation 8.10 is the familiar return on equity (ROE). Clearly, the more the company can earn on its retained capital, the higher the growth rate. Remember that ROE is the product of three things: the net profit margin, total asset turnover, and the equity multiplier (see Equation 7.13 ).

Example

Consider a situation where a company retains, on average, about 80% of its earnings and generates an ROE of around 18%. (Driving the firm’s ROE is a net profit margin of 7.5%, a total asset turnover of 1.20, and an equity multiplier of 2.0.) Under these circumstances, we would expect the firm to have a growth rate of 14.4%:

g=ROE×rr=0.18×0.80=14.4%g=ROE×rr=0.18×0.80=14.4%

This firm might even achieve faster growth if it raises more capital through a stock offering or borrows more money and thereby increases its equity multiplier. If the firm chooses not to do any of those things, Equation 8.10 gives you a good idea of what growth the company might be able to achieve. To further refine your estimate of a company’s growth rate, consider the two key components of the formula (ROE and rr) to see whether they’re likely to undergo major changes in the future. If so, then what impact is the change in ROE or rr likely to have on the growth rate? The idea is to take the time to study the forces (ROE and rr) that drive the growth rate because the DVM itself is so sensitive to the rate of growth being used. Employ a growth rate that’s too high and you’ll end up with an intrinsic value that’s way too high also. The downside, of course, is that you may end up buying a stock that you really shouldn’t.

Other Approaches to Stock Valuation

In addition to the DVM, the market has developed other ways of valuing stock. One motivation for using these approaches is to find techniques that allow investors to estimate the values of non-dividend-paying stocks. In addition, for a variety of reasons, some investors prefer to use procedures that don’t rely on corporate earnings as the basis of valuation. For these investors, it’s not earnings that matter, but instead things like cash flow, sales, or book value.

One approach that many investors use is the free cash flow to equity method (or simply the flow to equity method), which estimates the cash flow that a firm generates for common stockholders, whether it pays those out as dividends or not. Another is the P/E approach, which builds the stock valuation process around the stock’s price-to-earnings ratio. One of the major advantages of these procedures is that they don’t rely on dividends as the primary input. Accordingly, investors can use these methods to value stocks that are more growth-oriented and that pay little or nothing in dividends. Let’s take a closer look at both of these approaches, as well as a technique that arrives at the expected return on the stock (in percentage terms) rather than a (dollar-based) “justified price.”

Free Cash Flow to Equity

As we saw earlier, the value of a share of stock is a function of the amount and timing of future cash flows that stockholders receive and the risk associated with those cash flows. The free cash flow to equity method estimates the cash flow that a company generates over time for its shareholders and discounts that to the present to determine the company’s total equity value. The model does not consider whether a firm distributes free cash flow by paying dividends or repurchasing shares or whether it merely retains free cash flow. Instead, the model simply accounts for the cash that “flows to equity,” meaning that it is the residual cash flow produced by the firm that is not needed to pay bills or fund new investments. The model begins by estimating the free cash flow that a company is expected to generate over time.

Free cash flow to equity is the cash flow that remains after a firm pays all of its expenses and makes necessary investments in working capital and fixed assets. It includes a company’s after-tax earnings, plus any noncash expenses like depreciation, minus new investments in working capital and fixed assets. Using the flow-to-equity method requires forecasts of the cash flow going to equity far out into the future, just as the dividend valuation model requires long-term dividend forecasts. With cash flow forecasts in hand, analysts calculate the stock’s intrinsic value by taking the present value of free cash flow going to equity and dividing by the number of shares outstanding. We can summarize the flow-to-equity model with the following equations:

Value of a share of stock=present value of future free cash flows going to equityshares outstandingFree cash flow=after-tax earnings+depreciation−investments in working capital−investments in fixed assetsValue of a share of stock=present value of future free cash flows going to equityshares outstandingFree cash flow=after-tax earnings+depreciation− investments in working capital−investments in fixed assetsEquation8.11

V=FCF1(1+r)1+FCF2(1+r)2+…NV=FCF1(1+r)1+FCF2(1+r)2+…NEquation8.11a

where

FCFt=free cash flow in year tN=number of common shares outstandingFCFt=free cash flow in year tN=number of common shares outstanding

Note that there are similarities here to the dividend-growth model. Equation 8.11a is a present-value calculation, except that we are discounting future free cash flows rather than future dividends. As in the dividend-growth model, we may assume that free cash flows remain constant over time, grow at a constant rate, or grow at a rate that varies over time.

Zero Growth in Free Cash Flow

Victor’s Secret Sauce is a specialty retail company that sells a variety of bottled sauces for home cooks. Last year (2015) the company generated $2.2 million in after-tax earnings. Victor’s took depreciation charges against its fixed assets equal to $250,000, and it invested $50,000 in new working capital and $40,000 in new fixed assets. Thus, the company’s free cash flow last year was:

Victor's Secret Sauce free cash flow (2015)=$2,200,000+$250,000−$50,000−$40,000=$2,360,000Victor's Secret Sauce free cash flow (2015)=$2,200,000+$250,000−$50,000−$40,000=$2,360,000

Victor’s had four million common shares outstanding, and the firm’s shareholders expected a 9% rate of return on their investment. Suppose you believe that Victor’s would continue to generate $2.36 million in free cash flow indefinitely, without additional growth. In other words, you would treat Victor’s free cash flow like a perpetuity, so the present value of all of the company’s future cash flows would equal:

PV of future cash flows=$2,360,000÷0.09=$26,222,222PV of future cash flows=$2,360,000÷0.09=$26,222,222

Given that the company has four million outstanding shares, the intrinsic value of the company’s stock would be:

Value of Victor's common shares=$26,222,222÷4,000,000 shares=$6.56 per shareValue of Victor's common shares=$26,222,222÷4,000,000 shares=$6.56 per share

Our calculation here is analogous to the approach we took in dividend valuation model when dividends were not expected to grow. In this case, however, we are discounting free cash flow rather than dividends, and we take no stand on whether the firm will actually pay this cash out as a dividend in the current year or not.

Constant Growth in Free Cash Flow

Now suppose that you expect Victor’s free cash flow to grow over time at a constant rate of 2%. This implies that the company will generate cash flow next year (in 2016) that is 2% higher than last year’s cash flow. Clearly, with a growing cash flow, Victor’s shares should be more valuable than in the no-growth case, and indeed, that is what we find.

PV (in 2015) of future cash flows=Cash flow (in 2016) ÷ (r − g)PV of future cash flows=$2,360,000(1+ 0.02) ÷ (0.09 − 0.02)=$34,388,571Value of common shares=$34,388,571 ÷ 4,000,000 = $8.60 per sharePV (in 2015) of future cash flows=Cash flow (in 2016) ÷ (r − g)PV of future cash flows=$2,360,000(1+ 0.02) ÷ (0.09 - 0.02)=$34,388,571Value of common shares=$34,388,571 ÷ 4,000,000 = $8.60 per share

Notice that we obtained the present value of Victor’s future cash flows in the same way that we did in the constant-growth version of the dividend valuation model. We divided the cash flow expected next year, which is 2% greater than the previous year’s free cash flow, by the difference between the required return on the stock and the expected growth rate in cash flow.

Variable Growth in Free Cash Flow

Finally, suppose that you expected Victor’s Secret Sauce to experience rapid growth in free cash flow for the next couple of years. To be specific, suppose that Victor’s cash flow grows 20% next year, 10% the year after that, and then 2% per year for all subsequent years. To value the company’s stock, we follow the same method that we used when valuing a company whose dividends grew at a variable rate.

First, calculate the expected free cash flow for 2016 and 2017. If last year’s cash flow was $2.36 million, then next year’s cash flow will be 20% higher, or $2,832,000 (i.e., $2,360,000 × 1.20$2,360,000 × 1.20). The year after, Victor’s cash flow rises another 10% to $3,115,200 (i.e., $2,832,000×1.10$2,832,000×1.10). Using the required return of 9%, we can calculate the present value of the cash flow generated in the next two years.

Year	Cash Flow	Present Value
2016	$2,832,000	$2,832,000÷1.09=$2,598,165$2,832,000÷1.09=$2,598,165
2017	$3,115,200	$3,115,200÷1.092=$2,622,002$3,115,200÷1.092=$2,622,002

Next, calculate the present value as of 2017 of all the cash flows that Victor’s will generate in years 2018 in beyond. In 2018, the company will generate 2% more in cash flow than it did the prior year, and from that point forward, cash flows grow at the constant 2% rate. We can calculate the present value (as of 2017) of all cash flows generated in years 2018 and beyond as follows:

PV2017=FCF2018÷(r−g)=FCF2017(1+g)÷(r−g)PV2017=$3,115,200(1+0.02)÷(0.09−0.02)=$45,392,914PV2017=FCF2018÷(r−g)=FCF2017(1+g)÷(r−g)PV2017=$3,115,200(1+0.02)÷(0.09−0.02)=$45,392,914

As of 2017, the present value of all free cash flow that Victor’s generates in 2018 and beyond is almost $45.4 million. As an additional step, we need to discount this figure two more years, so we have the present value as of 2015.

PV2015=$45,392,914÷1.092=$38,206,308PV2015=$45,392,914÷1.092=$38,206,308

Now we are ready to calculate the present value of all future free cash flows generated by the company, including the cash flows produced during the rapid growth stage (2016 and 2017) and the cash flows earned during the constant-growth phase (2018 and beyond). Dividing that total by 4,000,000 shares outstanding gives us an estimate of Victor’s intrinsic value.

PV of all future cash flows=$2,598,165+$2,622,002+$38,206,308= $43,426,474Value of common shares=$43,426,474÷4,000,000=$10.86 per sharePV of all future cash flows=$2,598,165+$2,622,002+$38,206,308= $43,426,474Value of common shares=$43,426,474÷4,000,000=$10.86 per share

To summarize, our estimate of the value of Victor’s is $6.56 when we expect no growth in cash flow, $8.60 when we expect steady 2% growth, and $10.86 when we expect rapid growth for two years followed by constant 2% growth. Because the free cash flow to equity method does not focus on the timing and amount of dividends that a company pays, but instead emphasizes the cash flow that the firm generates for its stockholders, it is well suited for valuing younger companies that have not yet established a dividend-paying history.

Using IRR to Solve for the Expected Return

Sometimes investors find it more convenient to think about what a stock’s expected return will be, given its current market price, rather than try to estimate the stock’s intrinsic value. This is no problem, nor is it necessary to sacrifice the present value dimension of the stock valuation model to achieve such an end. You can find the expected return by using a trial-and-error approach to find the discount rate that equates the present value of a company’s future free cash flows going to equity (or its future dividends if the firm pays dividends) to the current market value of the firm’s common stock. Having estimated the stock’s expected return, an investor would then decide whether that return is sufficient to justify buying the stock given its risk.

To see how to estimate a stock’s expected return, look once again at the variable growth scenario for Victor’s Secret Sauce. Recall that as of the end of 2015, we had the following projections for Victor’s free cash flow going to equity:

2016	$2,832,000
2017	$3,115,200

Remember that cash flow in 2018 is 2% higher than in 2017 and that cash flow will continue to grow at 2% indefinitely starting in 2018. This means that as of 2017, the present value of all cash flow that Victor’s will generate for stockholders from 2018 and beyond can be calculated as:

PV2017=3,115,200 (1.02)(r−0.02)=3,177,504(r−0.02)PV2017=3,115,200 (1.02)(r−0.02)=3,177,504(r−0.02)

Therefore, if we wanted to calculate the present value in 2015 of Victor’s cash flow going to equity, we could use this equation:

PV=2,832,000(1+r)+3,115,200(1+r)2+3,177,504÷(r−0.02)(1+r)2PV=2,832,000(1+r)+3,115,200(1+r)2+3,177,504÷(r−0.02)(1+r)2

Suppose we know that in 2015 the price of Victor’s common stock is $12 per share. With four million common shares outstanding, the total value of Victor’s common equity is $48 million. What does that value imply about the expected return on Victor’s shares? Just plug $48 million into the equation above as the present value of Victor’s free cash flow going to equity, and then use a trial and error method to solve for r. If you do this, you will find that the value of r that solves the equation is roughly 8.34%. Again, this means that given the cash flow forecast for Victor’s and given the company’s current stock price, its expected return is 8.34%. An investor who believed that Victor’s stock ought to pay a 9% return based on its risk would not see Victor’s as an attractive stock at its current $12 per share market price.

The Price-to-Earnings (P/E) Approach

One of the problems with the stock valuation procedures we’ve looked at so far is that they require long-term forecasts of either dividends or free cash flows. They involve a good deal of “number crunching,” and naturally the valuations that these models produce are only as good as the forecasts that go into them. Fortunately, there is a simpler approach. That alternative is the price-to-earnings (P/E) approach to stock valuation.

The P/E approach is a favorite of professional security analysts and is widely used in practice. It’s relatively simple to use. It’s based on the standard P/E formula first introduced previously. We showed that a stock’s P/E ratio is equal to its market price divided by the stock’s EPS. Using this equation and solving for the market price of the stock, we have

Stock price=EPS×P/E ratioStock price=EPS×P/E ratioEquation8.12

Equation 8.12 basically captures the P/E approach to stock valuation. That is, given an estimated EPS figure, you decide on a P/E ratio that you feel is appropriate for the stock. Then you use it in Equation 8.12 to see what kind of price you come up with and how that compares to the stock’s current price.

Actually, this approach is no different from what’s used in the market every day. Look at the stock quotes in the Wall Street Journal or online at Yahoo! Finance. They include the stock’s P/E ratio and show what investors are willing to pay for each dollar of earnings. Essentially, this ratio relates the company’s earnings per share for the last 12 months (known as trailing earnings) to the latest price of the stock. In practice, however, investors buy stocks not for their past earnings but for their expected future earnings. Thus, in Equation 8.12 , it’s customary to use forecasted EPS for next year—that is, to use projected earnings one year out.

The first thing you have to do to implement the P/E approach is to come up with an expected EPS figure for next year. In the early part of this chapter, we saw how this might be done (see, for instance, Equations 8.2 and 8.3 on pages 302 and 303 ). Given the forecasted EPS, the next step is to evaluate the variables that drive the P/E ratio. Most of that assessment is intuitive. For example, you might look at the stock’s expected rate of growth in earnings, any potential major changes in the firm’s capital structure or dividends, and any other factors such as relative market or industry P/E multiples that might affect the stock’s multiple. You could use such inputs to come up with a base P/E ratio. Then adjust that base, as necessary, to account for the perceived state of the market and/or anticipated changes in the rate of inflation.

Along with estimated EPS, we now have the P/E ratio we need to compute (via Equation 8.12 ) the price at which the stock should be trading. Take, for example, a stock that’s currently trading at $37.80. One year from now, it’s estimated that this stock should have an EPS of $2.25 a share. If you feel that the stock should be trading at a P/E ratio of 20 times projected earnings, then it should be valued at $45 a share (i.e., $2.25×20$2.25×20). By comparing this targeted price to the current market price of the stock, you can decide whether the stock is a good buy. In this case, you would consider the stock undervalued and therefore a good buy, since the computed price of the stock of $45 is more than its market price of $37.80.

Other Price-Relative Procedures

As we saw with the P/E approach, price-relative procedures base their valuations on the assumptions that the value of a share of stock should be directly linked to a given performance characteristic of the firm, such as earnings per share. These procedures involve a good deal of judgment and intuition, and they rely heavily on the market expertise of the analysts. Besides the P/E approach, there are several other price-relative procedures that are used by investors who, for one reason or another, want to use some measure other than earnings to value stocks. They include:

· The price-to-cash-flow (P/CF) ratio

· The price-to-sales (P/S) ratio

· The price-to-book-value (P/BV) ratio

Like the P/E multiple, these procedures determine the value of a stock by relating share price to cash flow, sales, or book value. Let’s look at each of these in turn to see how they’re used in stock valuation.

A Price-to-Cash-Flow (P/CF) Procedure

This measure has long been popular with investors who believe that cash flow provides a more accurate picture of a company’s true value than do net earnings. When used in stock valuation, the procedure is almost identical to the P/E approach. That is, analysts use a P/CF ratio along with projected cash flow per share to estimate the stock’s value.

Although it is quite straightforward, this procedure nonetheless has one problem—defining the appropriate cash flow measure. While some investors use cash flow from operating activities, as obtained from the statement of cash flows, others use free cash flow. The one measure that seems to be the most popular with professional analysts is EBITDA (earnings before interest, taxes, depreciation, and amortization), which we’ll use here. EBITDA represents “pretax cash earnings” to the extent that the major noncash expenditures (depreciation and amortization) are added back to operating earnings (EBIT).

The price-to-cash-flow ratio is computed as follows:

P/CF ratio=Market price of common stockCash flow per shareP/CF ratio=Market price of common stockCash flow per shareEquation8.13

where cash flow per share = EBITDA ÷ number of common shares outstanding.

Before you can use the P/CF procedure to assess the current market price of a stock, you first have to come up with a forecasted cash flow per share one year out and then define an appropriate P/CF multiple to use. For most firms, it is very likely that the cash flow (EBITDA) figure will be larger than net earnings available to stockholders. As a result, the cash flow multiple will probably be lower than the P/E multiple. In any event, once you determine an appropriate P/CF multiple (subjectively and with the help of any historical market information), simply multiply it by the expected cash flow per share one year from now to find the price at which the stock should be trading. That is, the computed price of a share of stock = cash flow per share × P/CF ratio.

Example

Assume a company currently is generating an EBITDA of $325 million, which is expected to increase by some 12% to around $364 million (i.e., $325 million×1.12$325 million×1.12) over the course of the next 12 months. Suppose the company has 56 million shares of stock outstanding. The company’s projected cash flow per share is $6.50. If we feel this stock should be trading at about eight times its projected cash flow per share, then it should be valued at around $52 a share. Thus, if it is currently trading in the market at $45.50 (or at seven times its projected cash flow per share), we can conclude, once again, that the stock is undervalued and, therefore, should be considered a viable investment candidate.

Price-to-Sales (P/S) and Price-to-Book-Value (P/BV) Ratios

Some companies, like high-tech startups, have little, if any, earnings. Or if they do have earnings, they tend to be quite volatile and therefore highly unpredictable. In these cases, valuation procedures based on earnings (and even cash flows) aren’t much help. So investors turn to other procedures—those based on sales or book value, for example. While companies may not have much in the way of profits, they almost always have sales and, ideally, some book value.

Investors use the P/S and P/BV ratios exactly like the P/E and P/CF procedures. Recall that we defined the P/BV ratio in Equation 7.21 (on page 282 ) as follows:

P/BV ratio=Market price of common stockBook value per shareP/BV ratio=Market price of common stockBook value per share

We can define the P/S ratio in a similar fashion:

P/S ratio=Market price of common stockSales per shareP/S ratio=Market price of common stockSales per shareEquation8.14

where sales per share equals net annual sales (or revenues) divided by the number of common shares outstanding.

Investor Facts

Crafty Investors Spot Problem with Etsy’s IPO In April 2015, Etsy, Inc., the online marketplace for hand-crafted goods, became a public company by issuing shares to the public in an IPO. Initially priced at $16 per share, Etsy’s common stock doubled on its first trading day. That runup put Etsy’s price-to-sales ratio into double digits, several times higher than the P/S of the S&P 500, and even higher than some of the most rapidly growing tech stocks. Etsy’s inflated P/S ratio was a sign of trouble to come, as the stock lost more than 40% of its value in its first two months of trading.

Many bargain-hunting investors look for stocks with P/S ratios of 2.0 or less. They believe that these securities offer the most potential for future price appreciation. Especially attractive to these investors are very low P/S multiples of 1.0 or less. Think about it: With a P/S ratio of, say, 0.9, you can buy $1 in sales for only 90 cents! As long as the company can convert some of the sales into cash flow and earnings for shareholders, such low P/S multiples may well be worth pursuing.

Keep in mind that while the emphasis may be on low multiples, high P/S ratios aren’t necessarily bad. To determine if a high multiple—more than 3.0 or 4.0, for example—is justified, look at the company’s net profit margin. Companies that can consistently generate high net profit margins often have high P/S ratios. Here’s a valuation rule to remember: High profit margins should go hand-in-hand with high P/S multiples. That makes sense because a company with a high profit margin brings more of its sales down to the bottom line in the form of profits.

Watch Your Behavior

Short-Lived Growth So-called value stocks are stocks that have low price-to-book ratios, and growth stocks are stocks that have relatively high price-to-book ratios. Many studies demonstrate that value stocks outperform growth stocks, perhaps because investors overestimate the odds that a firm that has grown rapidly in the past will continue to do so.

You would also expect the price-to-book-value measure to be low, but probably not as low as the P/S ratio. Indeed, unless the market becomes grossly overvalued (think about what happened in 1999 and 2000), most stocks are likely to trade at multiples of less than three to five times their book values. And in this case, unlike with the P/S multiple, there’s usually little justification for abnormally high price-to-book-value ratios—except perhaps for firms that have abnormally low levels of equity in their capital structures. Other than that, high P/BV multiples are almost always caused by “excess exuberance.” As a rule, when stocks start trading at seven or eight times their book values, or more, they are becoming overvalued.

Concepts In Review

Answers available at http://www.pearsonhighered.com/smart

1. 8.6 Briefly describe the dividend valuation model and the three versions of this model. Explain how CAPM fits into the DVM.

2. 8.7 What is the difference between the variable-growth dividend valuation model and the free cash flow to equity approach to stock valuation? Which procedure would work better if you were trying to value a growth stock that pays little or no dividends? Explain.

3. 8.8 How would you go about finding the expected return on a stock? Note how such information would be used in the stock selection process.

4. 8.9 Briefly describe the P/E approach to stock valuation and note how this approach differs from the variable-growth DVM. Describe the P/CF approach and note how it is used in the stock valuation process. Compare the P/CF approach to the P/E approach, noting the relative strengths and weaknesses of each.

5. 8.10 Briefly describe the price-to-sales ratio and explain how it is used to value stocks. Why not just use the P/E multiple? How does the P/S ratio differ from the P/BV measure?