Using Analyst Forecasts to Estimate the Expected Dividend Growth Rate To
compute the riskadjusted discount rate for equity from this equation, only g, the expected rate of growth of the firm's dividends, and div 1/So, the firm's dividend yield,
need to be estimated. Analysts' forecasts of the growth rate of a firm's earnings
13A historical average of the ratio of dividend per share to prior year stock price per share, sometimes over a period of five years, can be used if the coming year's dividend payout is expected to be unusual.
provide one estimate for g. Under the assumption that a firm pays a fixed percentage of its earnings as dividends, the expected growth rate in dividends equals the forecasted growth rate in earnings. This growth rate can then be added to the existing dividend yield to derive the expected return on the firm's stock.14
For example, suppose that Value Line, an investment advisory service, forecasts a 12.9 percent rate of growth for IBM's earnings. Adding this to the firm's 0.5 percent dividend yield (as of early 2001) implies an expected rate of return on IBM stock of 13.4 percent. To obtain a cost of capital for an IBMlike project, it is necessary to adjust this 13.4 percent rate of return for debt in IBM's capital structure. For example, in the riskfree debt no taxes case of Section 11.2, one can obtain rA by multiplying rE by E/(D + E).
Using the Plowback Ratio Formula to Estimate the Expected Dividend Growth Rate. An alternative method for estimating g, the growth rate in dividends, employs accounting data. This method estimates the growth rate as g = b X ROE (11.6)
where b = the plowback ratio, the fraction of earnings retained in the firm
ROE = book return on equity, that is, earnings divided by last year's (midyear) book equity15
The intuition for the plowback ratio formula, given in equation (11.6), is that the book return on equity (ROE) represents the rate of growth of capital invested in the firm. When a firm has an ROE of 10 percent, every $1 invested in the firm returns $1.00 of equity capital and $0.10 of earnings next year, or $1.10. If this $1.10 is entirely reinvested, it will grow another 10 percent to $1.21 one year later. However, if 75 percent of the earnings are paid out in the form of dividends, implying a plowback ratio of .25, the capital will only grow at a rate of (1  .75)($.10)—that is, at 25 percent of the 10 percent growth rate, or 2.5 percent. In this case, at the end of the first year, 75 percent of $0.10 would be paid out in dividends, implying that only $1.025 [= $1.10  .75($.10)] is left in the firm for reinvestment. This would grow to $1.025(1.1), but if 75 percent of the amount over $1.025 (the earnings) is paid out as a dividend, the amount to be reinvested is just $1.025(1.1)  .75($1.025)(.1) = $1.0252. Thus, paying out a fixed proportion of a company's earnings as dividends slows the growth rate of the funds available for reinvestment. Moreover, since earnings and dividends are a constant proportion of the reinvestment amount, their growth rates will be the same as the growth rate of the funds available for investment in the firm.
Assumptions and Pitfalls of the Dividend Discount Model. The plowback ratio formula, equation (11.6), uses the book return on equity in lieu of the return on new investment, the return that theoretically should be used but which is more difficult to measure accurately. If old assets and new assets have different returns, ROE in the plowback ratio formula should be the book return of equity for new asset investment. If the project is a positive NPV project, the appropriate book return of equity will exceed the project's cost of capital.
14Note that using the current dividend yield in equation (11.5b) gives the wrong answer. The formula requires next year's expected dividend in the numerator. Multiplying the current dividend per share by 1 + g and dividing by the current stock price gives the appropriate dividend yield estimate.
15Alternatively, it is possible to use forecasts of next year's earnings divided by this year's (midyear) book equity.
390 Part III Valuing Real Assets
The implicit assumptions of the dividend discount model's estimate of the cost of capital are that:
• The earnings growth forecasts, whether from analysts or equation (11.6), are unbiased; that is, they do not tend to systematically underestimate or overestimate the earnings growth rate.
• The earnings growth forecasts are based on the same information that investors use to value the firm's stock.
• The firm's earnings and dividends grow at the same constant rate, forever.
To the extent that these assumptions are valid, the dividend discount model may provide a better estimate of the expected rate of return on a firm's stock or project than either the CAPM or the APT because it does not require estimates of beta or estimates of the expected return of the market portfolio or of factor portfolios. However, these assumptions, particularly that of a constant growth rate, are stringent and may not apply to many of the firms or projects that an analyst wants to value.
What If No Pure Comparison Firm Exists?
Many firms are large diversified entities that have many lines of business. In this instance, the equity returns of potential comparison firms are distorted by other lines of business and cannot easily be used as comparison firms for projects that represent only a single line of business. Unfortunately, in many situations, there is no appropriate comparison firm with a single line of business. A financial manager in this situation still may be able to obtain an appropriate comparison by forming portfolios of firms that generate a "pure" line of business. The mathematics behind the approach taken in Example 11.3, which illustrates how to create comparison investments in a pure line of business when none initially exists, is similar in spirit to the formation of pure factor portfolios in Chapter 6.
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