© 2000 John Petroff
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© 2000 John Petroff |
Return on equity ROE is a version of ROI. In the previous subsection, we allowed an ever more restrictive definition of the funds that constitute investment, ending with only permanent funds. The logical next step is to eliminate debt altogether, and define investment as equity. ROI then becomes ROE. One must be careful to take the amount of equity from the balance sheet that corresponds to the amount of net profit after tax that is available to equity owners. One may have to include in equity all stock, common and preferred, as well as all classes, A and B, if there are classes. But, normally, only common stock equity CS is included (because it is relevant and important to common shareholders). This implies that preferred shares, as well as minority interests must not be present in equity. This also means that preferred stock dividends DPS and the minority interests' share of income MI must have been deducted from profit after tax. The return on equity ROE is given by
ROE = (PAT-DPS-MI) / CS
This ratio gives the rate of return earned by equity owners in the current year. It is one of the most commonly used ratios. In this format it is correctly linking the net after tax earnings which will accrue to owners in the form of dividends or retained earnings. One will recall from the previous section that averaging of the denominator is recommended, but it is not always done in order not to lose historical information.
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Once again, we use Lucent Technologies for this calculation. And once again, from Table T-6.7, Lucent Technology Income Statement, we take the 1999 profit after tax of $ 4,766 millions, and from Table T-6.8, Lucent Technology Balance Sheets, we take equity of $ 13,584 millions. The resulting return on equity is ROE = 4,766 / 13,584 = 0.3508 or 35% which can be found in Table T-5.19, Lucent Technology Ratios. This is quite a nice return, but we remember that there is a large extraordinary item that distorts profits after tax in 1999. If we exclude the cumulative effect of accounting change of $ 1,308 millions, return on equity becomes ROE = 3,458 / 13,584 = 0.2546 or 25% If we look at the historical pattern of return on equity, we observe that it was only 13% in 1998, 10% in 1997 and negative the year before. In other words, Lucent Technologies experienced a major turn around. |
There are a few more modifications that can be found in certain circumstances. One is to exclude from equity, intangible assets which were previously mentioned as no longer (or not yet) contributing to profit generation. The investment concept used is then net worth (i.e. total assets minus all debt, which naturally equals equity), and the deduction of intangibles leaves tangible net worth TNW in the denominator. The ratio is return on tangible net worth ROTNW
ROTNW = PAT / TNW
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Now it is Merck's turn. We take net profit after tax of $ 5,248 millions for 1998 from Table T-6.3, Merck & Co., Inc. Income Statements, and equity of $ 12,802 millions and goodwill of $ 8,287 millions from Table T-6.4, Merck & Co., Inc Balance Sheets 1997-98. This gives a return on net worth of ROTNW = 5,248 / (12,801 - 8,287) = 5,248 / 4,515 = 1.1623 or 116% The value is so high that it is difficult to understand its meaning. As before, we keep in mind the very large gain from joint operation termination. It seems that the deduction for the large goodwill is actually a distortion rather than an improvement of ROE. The large amount of goodwill may be the result of a relatively recent (1993) acquisition of a very large company (Medco). |
Robert Morris Associates prefer to use profit before tax for the reason indicated earlier (i.e. avoid distortions from differences in tax exposure) and offer their ROTNW as before tax return on net worth
ROTNWb = PBT / TNW
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Lucent Technologies is used for this demonstration. We take from Table T-6.7, Lucent Technology Income Statements, the 1999 profit before tax of $ 5,443 millions, and from Table T-6.8, Lucent Technology Balance Sheets, we take equity of $ 13,584 millions. Intangible assets are included in other assets which amount to $ 3,352 millions. As part of note #1 to financial statements, a list of acquisitions in the past two years shows amounts of goodwill (to be amortized over three to ten years). It is not possible to calculate the exact amount, but only an approximate unamortized goodwill of $ 801 millions in 1999. Furthermore, the balance sheet shows capitalized software development costs of $ 470 millions, Note #2 indicates that these capitalized software development costs will be amortized when products are released: this suggests that this is also an intangible asset (since it has no market value until the software is released).The resulting before tax return on net worth is ROTNWb = 5,443 / (13,584 -801 - 470) = 5,443 / 12313 = 0.4420 or 44% This return on net worth value of 44% is different from the value of profit before tax / equity of 40% found in Table T-5.19, Lucent Technology Ratios, because the adjustment for intangibles conducted above could not be conveniently incorporated into a spreadsheet calculation. With a similar adjustment for goodwill in 1998, the return on net worth for 1998 is 39% (i.e. 2638/6683). By ordinary standards, a return of 44% is superb. Comparing it to the telephone communication industry, ROTNWb is higher than the average of 25.1%, and higher than the median of 30.8% for the largest firms. But it is lower than the upper quartile of 68% for the largest firms, and lower than the upper quartile of 60% for the entire industry. This shows that Lucent Technology did well in 1999, but a large proportion of competitors did even better. If we compare Lucent Technologies's performance to the communication services industry, we find that Lucent Technologies ROTNWb 44% is also higher than the median of 22.9%, but it is again lower than the upper quartile of 72.8%, and this time by a wide margin. We note, however, that the communications services firms tend to be much more leveraged with average debt to worth of 4.4 and proportion of equity of 18%, whereas Lucent Technologies's debt to equity is 1.7 and the proportion of equity is 35%. It is always better to compare a company's performance with that of its direct competitors. It is only appropriate to use more aggregate comparative statistics when there is a specific purpose. For instance, we may want to find what ought to be Lucent Technologies's cost of capital. One way of doing that is to see in what rating group Lucent Technologies would qualify. On the basis of its return on net worth of 44%, Lucent Technologies would qualify for a AAA Moody's rating since the highest value is 26% in Table T-3.2, Median Key Financial Ratios of Industrial Companies by Moody's Rating Category 1987-1989. |
Another (more common) modification of ROE is to define investment as market value of equity (i.e. total market capitalization), calculated as current common stock price P multiplied by the number of shares outstanding N. The stock price P is the closing price on the day of the end of the fiscal year of the company. The number of shares outstanding N is given in the financial statements or can be calculated by subtracting the number of shares held as treasury stock from the number of shares authorized and issued. The return on market capitalization ROMC is given by
ROMC = PAT / (P * N)
Once again, it is appropriate to average the total market capitalization to reflect the changing equity funds entitled to share in the profits. The averaging is based on the number of days a given number of shares is outstanding (as already indicated in the case of earnings per share). Each given number of shares is multiplied by the average price over the period. Although, mathematically desirable, this modification is rarely done, except when the equity has changed drastically such as in the case of large new stock flotation and information of outstanding common stock is present in the annual report.
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This time we choose The Dow Chemical Company to conduct the analysis. From Table T-6.13, The Dow Chemical Company Income Statements, we take 1998 profit after tax of $ 1,327 millions. As before, we must exclude from profit after tax, payments to others than common shareholders. In the annual report, we read that preferred stock dividends amounted to $ 6 millions in 1998, and minorities interests are entitled to $ 17 millions. Thus the amount of profit after tax available to common shareholders is PAT - DPS - MI = 1,327 - 6 - 17 = 1,304 We take the closing price of $ 90.94 on December 31, 1998. The number of shares outstanding is calculated by taking the number of shares authorized and issued of 327,125,854, and subtracting the number of shares held as treasury stock of 106,749,081 at the end of 1998: N = 327,125,854 - 106,749,081 = 220,037,677 We calculate Dow's total market capitalization as the product of Dow's share price by the number of shares outstanding: P x N = 90.94 x 220,037,677 = 20,007,000,000 Now, we can calculate Dow's return on total market capitalization, which is ROMC = 1,304 / 20,007 = 0.06518 or 7% Now we calculate the same return on market capitalization using the weighted average number of shares 223,500,000 which is given as an explanation of EPS calculation. The return on market capitalization becomes ROMC = 1,304,000,000/(90.94x223,500,000) = 1,304/20,325 = 0.0641 |
One can easily recognize that if numerator and denominator are divided by the number of shares N,
ROMC = (PAT/N) / (P * N/N)
what is left is
ROMC = EPS / P
This ratio is current rate of return on common stock ROCS
ROCS = EPS / P
Note that this current rate of return on common stock does not account for price appreciation in the stock market which is captured in a stock's market rate of return (see holding period return in Chapter 2).
Actually, the current rate of return on common stock is more often used in its inverted form as the very familiar earnings multiple or price to earnings ratio P/E
P/E = P / EPS
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Dow's price to earnings ratio is P/E = 90.94 / 5.83 = 15.60 This value is naturally identical to the inverse of the current return on market price 1/ROCS = 1 / 0.0641 = 15.60 |
One last version of ROI which investors concerned with regular income use to compare stocks on the basis of how much dividends different stocks pay, is the dividend yield
Dividend yield = D / P
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We conclude with The Dow Chemical Company for this example. The annual report indicates that common stock dividends declared in 1998 were $ 3.48. With Dow's stock price of $ 90.94, we calculate the dividend yield as Dividend yield = 3.48 / 90.94 = 0.03828 or 3.8% Compared to historical returns on various securities in Table T-2.1, Annual Returns for Five Classes of US Securities, 1926-1988, Dow's dividend yield of 3.8% is only slightly better than the return on government issues. Naturally, dividend yield is only a small part of what investors expect in owning stocks: appreciation is usually more important. In fact, Dow's dividend yield is higher than that of most corporations in the United States. For instance, the average dividend yield on Forbes 500 (i.e. the best 500 American companies) was only 2.5% in 1999, as indicated in "Forbes 500s, Earnings and Dividends", Forbes, April 17, 2000, page 361. |
See review questions Q-13B4.1 through Q-13B.10.
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