The three measures we discuss in this section are probably the best known and most widely used of all financial ratios. In one form or another, they are intended to measure how efficiently a firm uses its assets and manages its operations. The focus in this group is on the bottom line, net income.

Page 65**Profit Margin** Companies pay a great deal of attention to their *profit margins:*

This tells us that Prufrock, in an accounting sense, generates a little less than 16 cents in profit for every dollar in sales.

All other things being equal, a relatively high profit margin is obviously desirable. This situation corresponds to low expense ratios relative to sales. However, we hasten to add that other things are often not equal.

For example, lowering our sales price will usually increase unit volume but will normally cause profit margins to shrink. Total profit (or, more important, operating cash flow) may go up or down; so the fact that margins are smaller isn’t necessarily bad. After all, isn’t it possible that, as the saying goes, “Our prices are so low that we lose money on everything we sell, but we make it up in volume”?7

**Return on Assets** *Return on assets* (ROA) is a measure of profit per dollar of assets. It can be defined several ways, but the most common is this:

**Return on Equity** *Return on equity* (ROE) is a measure of how the stockholders fared during the year. Because benefiting shareholders is our goal, ROE is, in an accounting sense, the true bottom-line measure of performance. ROE is usually measured as follows:

For every dollar in equity, therefore, Prufrock generated 14 cents in profit; but again this is correct only in accounting terms.

Because ROA and ROE are such commonly cited numbers, we stress that it is important to remember they are accounting rates of return. For this reason, these measures should properly be called *return on book assets* and *return on book equity*. In fact, ROE is sometimes called *return on net worth*. Whatever it’s called, it would be inappropriate to compare the result to, for example, an interest rate observed in the financial markets. We will have more to say about accounting rates of return in later chapters.

The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will examine the relationship between these two measures in more detail shortly.

**EXAMPLE 3.4 ROE and ROA**

Because ROE and ROA are usually intended to measure performance over a prior period, it makes a certain amount of sense to base them on average equity and average assets, respectively. For Prufrock, how would you calculate these?

Page 66We first need to calculate average assets and average equity:

With these averages, we can recalculate ROA and ROE as follows:

These are slightly higher than our previous calculations because assets and equity grew during the year, so the average values are below the ending values.

**MARKET VALUE MEASURES**

Our final group of measures is based, in part, on information not necessarily contained in financial statements—the market price per share of stock. Obviously, these measures can be calculated directly only for publicly traded companies.

We assume that Prufrock has 33 million shares outstanding and the stock sold for $88 per share at the end of the year. If we recall that Prufrock’s net income was $363 million, we can calculate its earnings per share:

**Price–Earnings Ratio** The first of our market value measures, the *price–earnings* (PE) *ratio* (or multiple), is defined here:

In the vernacular, we would say that Prufrock shares sell for eight times earnings, or we might say that Prufrock shares have or “carry” a PE multiple of 8.

PE ratios vary substantially across companies, but, in 2014, a typical large company in the United States had a PE in the 15–20 range. This is on the high side by historical standards, but not dramatically so. A low point for PEs was about 5 in 1974. PEs also vary across countries. For example, Japanese PEs have historically been much higher than those of their U.S. counterparts.

Because the PE ratio measures how much investors are willing to pay per dollar of current earnings, higher PEs are often taken to mean the firm has significant prospects for future growth. Of course, if a firm had no or almost no earnings, its PE would probably be quite large; so, as always, care is needed in interpreting this ratio.

Sometimes analysts divide PE ratios by expected future earnings growth rates (after multiplying the growth rate by 100). The result is the PEG ratio. Suppose Prufrock’s anticipated growth rate in EPS was 6 percent. Its PEG ratio would then be 8/6 5 1.33. The idea behind the PEG ratio is that whether a PE ratio is high or low depends on expected future growth. High PEG ratios suggest that the PE is too high relative to growth, and vice versa.

**Price–Sales Ratio** In some cases, companies will have negative earnings for extended periods, so their PE ratios are not very meaningful. A good example is a recent start-up. Such companies usually do have some revenues, so analysts will often look at the *price–sales ratio:*

Price–sales ratio = Price per share/Sales per share

Page 67In Prufrock’s case, sales were $2,311, so here is the price–sales ratio:

Price–sales ratio = $88/(**$2,311**/33) = $88/$70 = 1.26

As with PE ratios, whether a particular price–sales ratio is high or low depends on the industry involved.

**Market-to-Book Ratio** A third commonly quoted market value measure is the *market-to-book ratio:*

Notice that book value per share is total equity (not just common stock) divided by the number of shares outstanding.

Because book value per share is an accounting number, it reflects historical costs. In a loose sense, the market-to-book ratio therefore compares the market value of the firm’s investments to their cost. A value less than 1 could mean that the firm has not been successful overall in creating value for its stockholders.

Market-to-book ratios in recent years appear high relative to past values. For example, for the 30 blue-chip companies that make up the widely followed Dow Jones Industrial Average, the historical norm is about 1.7; however, the market-to-book ratio for this group has recently been twice this size.

Another ratio, called *Tobin’s Q ratio,* is much like the market-to-book ratio. Tobin’s Q is the market value of the firm’s assets divided by their replacement cost:

Notice that we used two equivalent numerators here: the market value of the firm’s assets and the market value of its debt and equity.

Conceptually, the Q ratio is superior to the market-to-book ratio because it focuses on what the firm is worth today relative to what it would cost to replace it today. Firms with high Q ratios tend to be those with attractive investment opportunities or significant competitive advantages (or both). In contrast, the market-to-book ratio focuses on historical costs, which are less relevant.

As a practical matter, however, Q ratios are difficult to calculate with accuracy because estimating the replacement cost of a firm’s assets is not an easy task. Also, market values for a firm’s debt are often unobservable. Book values can be used instead in such cases, but accuracy may suffer.

**Enterprise Value–EBITDA Ratio** A company’s enterprise value is an estimate of the mar ket value of the company’s operating assets. By operating assets, we mean all the assets of the firm except cash. Of course, it’s not practical to work with the individual assets of a firm because market values would usually not be available. Instead, we can use the right-hand side of the balance sheet and calculate the enterprise value as:

We use the book value for liabilities because we typically can’t get the market values, at least not for all of them. However, book value is usually a reasonable approximation for market value when it comes to liabilities, particularly short-term debts. Notice that the sum of the value of the market values of the stock and all liabilities equals the value of the firm’s assets from the balance sheet identity. Once we have this number, we subtract the cash to get the enterprise value.

Page 68**TABLE 3.8 Common Financial Ratios**

Enterprise value is frequently used to calculate the EBITDA ratio (or multiple):

This ratio is similar in spirit to the PE ratio, but it relates the value of all the operating assets (the enterprise value) to a measure of the operating cash flow generated by those assets (EBITDA).

**CONCLUSION**

This completes our definitions of some common ratios. We could tell you about more of them, but these are enough for now. We’ll go on to discuss some ways of using these ratios instead of just how to calculate them. Table 3.8 summarizes the ratios we’ve discussed.

Page 69

**Concept Questions**

**3.3a** What are the five groups of ratios? Give two or three examples of each kind.

**3.3b** Given the total debt ratio, what other two ratios can be computed? Explain how.

**3.3c** Turnover ratios all have one of two figures as the numerator. What are these two figures? What do these ratios measure? How do you interpret the results?

**3.3d** Profitability ratios all have the same figure in the numerator. What is it? What do these ratios measure? How do you interpret the results?

**3.4 The DuPont Identity**

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As we mentioned in discussing ROA and ROE, the difference between these two profitability measures is a reflection of the use of debt financing, or financial leverage. We illustrate the relationship between these measures in this section by investigating a famous way of decomposing ROE into its component parts.

**A CLOSER LOOK AT ROE**

To begin, let’s recall the definition of ROE:

If we were so inclined, we could multiply this ratio by Assets/Assets without changing anything:

Notice that we have expressed the ROE as the product of two other ratios—ROA and the equity multiplier:

ROE = ROA × Equity multiplier = ROA × (1 + Debt–equity ratio)

Looking back at Prufrock, for example, we see that the debt–equity ratio was .39 and ROA was 10.12 percent. Our work here implies that Prufrock’s ROE, as we previously calculated, is this:

ROE = 10.12% × 1.38 = 14.01%

The difference between ROE and ROA can be substantial, particularly for certain businesses. For example, in 2013, American Express had an ROA of 3.12 percent, which is fairly typical for financial institutions. However, financial institutions tend to borrow a lot of money and, as a result, have relatively large equity multipliers. For American Express, ROE was about 24.40 percent, implying an equity multiplier of 7.81 times.

We can further decompose ROE by multiplying the top and bottom by total sales:

If we rearrange things a bit, ROE looks like this:

Page 70What we have now done is to partition ROA into its two component parts, profit margin and total asset turnover. The last expression of the preceding equation is called the **DuPont identity**, after the DuPont Corporation, which popularized its use.

We can check this relationship for Prufrock by noting that the profit margin was 15.71 percent and the total asset turnover was .64:

This 14.01 percent ROE is exactly what we had before.

The DuPont identity tells us that ROE is affected by three things:

1. Operating efficiency (as measured by profit margin).

2. Asset use efficiency (as measured by total asset turnover).

3. Financial leverage (as measured by the equity multiplier).

Weakness in either operating or asset use efficiency (or both) will show up in a diminished return on assets, which will translate into a lower ROE.

Considering the DuPont identity, it appears that the ROE could be leveraged up by increasing the amount of debt in the firm. However, notice that increasing debt also increases interest expense, which reduces profit margins, which acts to reduce ROE. So, ROE could go up or down, depending. More important, the use of debt financing has a number of other effects, and as we discuss at some length in Part 6, the amount of leverage a firm uses is governed by its capital structure policy.

The decomposition of ROE we’ve discussed in this section is a convenient way of systematically approaching financial statement analysis. If ROE is unsatisfactory by some measure, then the DuPont identity tells you where to start looking for the reasons.

General Motors provides a good example of how DuPont analysis can be very useful and also illustrates why care must be taken in interpreting ROE values. In 1989, GM had an ROE of 12.1 percent. By 1993, its ROE had improved to 44.1 percent, a dramatic improvement. On closer inspection, however, we find that over the same period GM’s profit margin had declined from 3.4 to 1.8 percent, and ROA had declined from 2.4 to 1.3 percent. The decline in ROA was moderated only slightly by an increase in total asset turnover from .71 to .73 over the period.

Given this information, how is it possible for GM’s ROE to have climbed so sharply? From our understanding of the DuPont identity, it must be the case that GM’s equity multiplier increased substantially. In fact, what happened was that GM’s book equity value was almost wiped out overnight in 1992 by changes in the accounting treatment of pension liabilities. If a company’s equity value declines sharply, its equity multiplier rises. In GM’s case, the multiplier went from 4.95 in 1989 to 33.62 in 1993. In sum, the dramatic “improvement” in GM’s ROE was almost entirely due to an accounting change that affected the equity multiplier and didn’t really represent an improvement in financial performance at all.

DuPont analysis (and ratio analysis in general) can be used to compare two companies as well. Yahoo! and Google are among the most important Internet companies in the world. We will use them to illustrate how DuPont analysis can be useful in helping to ask the right questions about a firm’s financial performance. The DuPont breakdowns for Yahoo! and Google are summarized in Table 3.9.

As shown, in 2013, Yahoo! had an ROE of 10.4 percent, up from its ROE in 2012 of 8.0 percent. In contrast, in 2013, Google had an ROE of 14.8 percent, about the same as its ROE in 2012 of 15.0 percent. Given this information, how is it possible that Google’s ROE could be so much higher during this period of time, and what accounts for the increase in Yahoo!’s ROE?

**DuPont identity** Popular expression breaking ROE into three parts: operating efficiency, asset use efficiency, and financial leverage.

Page 71**TABLE 3.9**

On closer inspection of the DuPont breakdown, we see that Yahoo!’s profit margin in 2013 was 29.2 percent. Meanwhile, Google’s profit margin was 21.6 percent. Further, Yahoo! and Google have similar financial leverage. What can account for Google’s advantage over Yahoo! in ROE? We see that in this case, it is clear that the difference between the two firms comes down to asset utilization.

**AN EXPANDED DUPONT ANALYSIS**

So far, we’ve seen how the DuPont equation lets us break down ROE into its basic three components: profit margin, total asset turnover, and financial leverage. We now extend this analysis to take a closer look at how key parts of a firm’s operations feed into ROE. To get going, we went to finance.yahoo.com and found financial statements for science and technology giant DuPont. What we found is summarized in Table 3.10.

Using the information in Table 3.10, Figure 3.1 shows how we can construct an expanded DuPont analysis for DuPont and present that analysis in chart form. The advantage of the extended DuPont chart is that it lets us examine several ratios at once, thereby getting a better overall picture of a company’s performance and also allowing us to determine possible items to improve.

**TABLE 3.10**

Page 72**FIGURE 3.1 Extended DuPont Chart for DuPont**

Looking at the left side of our DuPont chart in Figure 3.1, we see items related to profitability. As always, profit margin is calculated as net income divided by sales. But as our chart emphasizes, net income depends on sales and a variety of costs, such as cost of goods sold (CoGS) and selling, general, and administrative expenses (SG&A expense). DuPont can increase its ROE by increasing sales and also by reducing one or more of these costs. In other words, if we want to improve profitability, our chart clearly shows us the areas on which we should focus.

Turning to the right side of Figure 3.1, we have an analysis of the key factors underlying total asset turnover. Thus, for example, we see that reducing inventory holdings through more efficient management reduces current assets, which reduces total assets, which then improves total asset turnover.

Page 73

**Concept Questions**

**3.4a** Return on assets, or ROA, can be expressed as the product of two ratios. Which two?

**3.4b** Return on equity, or ROE, can be expressed as the product of three ratios. Which three?

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**3.5 Using Financial Statement Information**

Our last task in this chapter is to discuss in more detail some practical aspects of financial statement analysis. In particular, we will look at reasons for analyzing financial statements, how to get benchmark information, and some problems that come up in the process.

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