# Applications of the General Dividend Valuation Model - Financial Management

## The Generalized Dividend Valuation Model

The general dividend valuation model can be simplified if a firm’s dividend payments over time are expected to follow one of several different patterns, including zero growth, constant growth, and nonconstant growth.

Zero Growth Dividend Valuation Model

If a firm’s future dividend payments are expected to remain constant forever, then Dt in Equation, the general dividend valuation model, can be replaced by a constant value D to yield the following:

This equation represents the value of a perpetuity and is analogous to those used for valuing a perpetual bond and a preferred stock developed in the previous chapter. It can be simplified to obtain

P0 = D/ke

This model is valid only when a firm’s dividend payments are expected to remain constant forever. Although few common stocks strictly satisfy these conditions, the model can still be used to approximate the value of a stock for which dividend payments are expected to remain constant for a relatively long period into the future. To illustrate the zero growth dividend valuation model, assume that the Mountaineer Railroad common stock pays an annual dividend of $1.50 per share, which is expected to remain constant for the foreseeable future.What is the value of the stock to an investor who requires a 12 percent rate of return? Substituting$1.50 for D and 12 percent (0.12) for ke in Equation yields the following:

P0 = $1.50/0.12 =$12.50

Relationship Between Financial Decisions and Shareholder Wealth

Dividend Growth Patterns

Constant Growth Dividend Valuation Model

If a firm’s future dividend payments per share are expected to grow at a constant rate, g, per period forever, then the dividend at any future time period t can be forecast as follows:

Dt = D0(1 + g)t

where D0 is the dividend in the current period (t = 0). The expected dividend in period 1 is D1 = D0(1 + g)1, the expected dividend in period 2 is D2 = D0(1 + g)2, and so on. The constant-growth curve in Figure illustrates such a dividend pattern.

Substituting Equation for Dt in the general dividend valuation model (Equation ) yields the following:

Assuming that the required rate of return, ke, is greater than the dividend growth rate,17 g, Equation can be transformed algebraically to obtain the following simplified common stock valuation model:

P0 = D1/(ke-g)

Note that in the constant growth valuation model, the dividend value in the numerator is D1, that is, the dividend expected to be received one year from now. The model assumes that D0, the current dividend, has just been paid and does not enter the (forward -looking) valuation process.
The constant growth valuation model assumes that a firm’s earnings, dividends and stock price are expected to grow at a constant rate, g, into the future. Hence, to apply this model to a specific common stock, it is necessary to estimate the expected future growth rate, g. Considerable research evidence indicates that (1) the most accurate estimates of future growth are those provided by security analysts, and (2) consensus analyst forecasts of growth are an excellent proxy for growth expectations of investors. Sources of analyst growth rate forecasts include

1. Value Line Investment Survey. Value Line reports, even though they represent only one analyst’s forecast for each company, are readily available at most public and university libraries and have been shown to be reasonably accurate and closely related to investor expectations.
2. Zacks Earnings Estimates. It provides summaries of long-term (five years) and shortterm earnings growth expectations from more than 2,100 analysts covering more than 3,500 companies. Forecasts from Zacks are available through the Internet.
3. Thomson Financial/First Call. This service is similar to that of Zacks and can be accessed through the Internet.

The constant growth dividend valuation model can be used to illustrate the two forms of returns an investor can expect to receive from holding a common stock. Solving Equation for ke yields the following:

ke = (D1/P0)+g

The investor’s required rate of return is equal to the expected dividend yield, D1/P0, plus the price appreciation yield, g—the expected increase in dividends and, ultimately, in the price of the stock.

To illustrate the application of the constant growth valuation model, consider Eaton Corporation. Dividends for Eaton are expected to be $1.76 per share next year. According to estimates from Value Line and First Call, earnings and dividends are expected to grow at about 6.5 percent annually. To determine the value of a share of this stock to an investor who requires a 12 percent rate of return, substituting$1.76 for D1, 6.5 percent(0.065) for g, and 12 percent(0.12) for ke in Equation 8.12 yields the following value for a share of Eaton’s common stock:

P0 = $1.76/(0.12-0.065) =$32.00

Thus, the investor’s 12 percent required return consists of a 5.5 percent dividend yield (D1/P0 = $1.76/$32.00) plus a growth return of 6.5 percent annually.

Nonconstant Growth Dividend Valuation Model

Many firms experience growth rates in sales, earnings, and dividends that are not constant. Typically, many firms experience a period of above -normal growth as they exploit new technologies, new markets, or both; this generally occurs relatively early in a firm’s life cycle. Following this period of rapid growth, earnings and dividends tend to stabilize or grow at a more normal rate comparable to the overall average rate of growth in the economy. The reduction in the growth rate occurs as the firm reaches maturity and has fewer sizable growth opportunities. The upper curve in Figure illustrates a nonconstant growth pattern.

ENTREPRENEURIAL ISSUES

Valuation of Closely Held Firms

The ownership of many small firms is closely held. An active market for shares of closely held companies normally does not exist. As a result ,entrepreneurs occasionally need to have the value of their enterprises estimated by independent appraisers.The reasons for these valuations include mergers and acquisitions, divestitures and liquidations, initial public offerings, estate and gift tax returns, leveraged buyouts, recapitalizations, employee stock ownership plans, divorce settlements, estate valuation, and various other litigation matters.

The principles of valuation developed in this chapter and applied to large publicly traded firms also apply to the valuation of small firms. Small firm valuation poses several unique challenges.When valuing the shares of a closely held corporation, many factors are considered, including the nature and history of the business, the general economic outlook and the condition and outlook of the firm’s industry, earnings capacity, dividend paying capacity, the book value of the company, the company’s financial condition, whether the shares represent a majority or minority (less than 50 percent) interest, and whether the stock is voting or nonvoting.

Specifically, however, in valuing a company that sells products and services, earnings capacity is usually the most important factor to be considered. Typically, the company as a whole is valued by determining a normal earnings level and multiplying that figure by an appropriate price —earnings multiple.This approach is known as the “capitalization of earnings” approach and results in a “going concern value.” If the shares represent a minority interest in the corporation, a discount is taken for the lack of marketability of these shares.

Determination of Normal Earnings

The determination of an average, or “normal,” earnings figure usually involves either a simple average or some type of weighted average of roughly the last five years of operations. For example, if the earnings of the company have been growing, some type of weighted average figure that places greater emphasis on more recent results is often used.

In some cases, the reported earnings of the company may not be an appropriate figure for valuation purposes. For example, suppose a portion of the salary paid to the president (and principal stockholder) really constitutes dividends paid as salary to avoid the payment of income taxes. In this situation, it is appropriate to adjust the reported earnings to account for these dividends.

Determination of an Appropriate Price–Earnings Multiple

The next step in the valuation process is to determine an appropriate rate at which to capitalize the normal earnings level.This is equivalent to multiplying the earnings by a price –earnings multiple. Had there been recent armslength transactions in the stock, the price –earnings multiple would be known and observable in the financial marketplace. However, this situation rarely exists for closely held corporations.As a consequence, the analyst must examine the price–earnings multiple for widely held companies in the same industry as the firm being valued in an attempt to find firms that are similar to the firm of interest.The price –earnings multiple for these comparable firms is used to capitalize the normal earnings level.

Minority Interest Discount

The owner of a minority interest in a closely held corporation has an investment that lacks control and often marketability.There is usually either no market for the shares or the only buyer is either the other owners or the corporation itself. In addition, the owner of minority interest shares generally receives little, if any, dividends. The minority interest shareholder lacks control and is not able to change his or her inferior position.As a result of these problems, it is a widely practiced and accepted principle of valuation that the value of minority interest shares should be discounted.

The usual procedure in valuing minority interest shares is to value the corporation as a whole. Next, this value is divided by the number of shares outstanding to obtain a per-share value. Finally, a discount is applied to this per-share value to obtain the minority interest share value.These discounts have ranged from a low of 6 percent to more than 50 percent.

In conclusion, the basic valuation concepts are the same for small and large firms. However, the lack of marketability of shares for many small firms and the problem of minority interest positions pose special problems for the analyst.

Nonconstant growth models can also be applied to the valuation of firms that are experiencing temporary periods of poor performance, after which a normal pattern of growth is expected to emerge. (The lower nonconstant growth line in Figure illustrates this type of pattern.) For example, during 1992 IBM paid a dividend of $1.21 per share. This dividend was cut to$0.40 in 1993 and $0.25 in 1994. As IBM’s restructuring efforts progressed, earnings and dividend growth resumed. Dividends in 2000 grew to$0.51. Value Line projects year 2004 dividends of $0.70 per share and$1.25 per share by 2007. An investor attempting to value IBM’s stock at the beginning of 1993 should have reflected the declining, then increasing pattern of dividend growth for the firm.

There is no single model or equation that can be applied when nonconstant growth is anticipated. In general the value of a stock that is expected to experience a nonconstant growth rate pattern of dividends is equal to the present value of expected yearly dividends during the period of nonconstant growth plus the present value of the expected stock price at the end of the nonconstant growth period, or: Present value of expected Present value of the expected

P0= dividends during period + stock price at the end of the of nonconstant growth nonconstant growth period

The stock price at the end of a nonconstant growth rate period can be estimated in a number of ways:

1. Security analysts such as Value Line provide an estimated (five -year) future price range for the stocks they follow.
2. Value Line, Zacks, and Thomson Financial/First Call all provide earnings growth rate estimates for five years into the future. These growth rate estimates can be used to derive earnings per share (EPS) forecasts for five years in the future. The EPS forecasts can be multiplied by the expected price -to-earnings (P/E) multiple, estimated by looking at current P/E multiples for similar firms, to get an expected price in five years.
3. At the end of the period of nonconstant growth, an estimate of the value of the stock can be derived by applying the constant growth rate valuation model. For example, consider a firm expected to experience dividend growth at a nonconstant rate for m periods. Beginning in period m + 1, dividends are expected to grow at rate g2 forever. The value of the stock, Pm, at the end of period m is equal to
Pm = (Dm + 1)/(ke – g2)

To demonstrate how this model works, suppose an investor expects the earnings and common stock dividends of HILO Electronics to grow at a rate of 12 percent per annum for the next five years. Following the period of above -normal growth, dividends are expected to grow at the slower rate of 6 percent for the foreseeable future. The firm currently pays a dividend, D0, of $2 per share.What is the value of HILO common stock to an investor who requires a 15 percent rate of return? Value of HILO Electronics Common Stock Table illustrates the step -by -step solution to this problem. First, compute the sum of the present values of the dividends received during the nonconstant growth period (years 1 through 5 in this problem). This equals$9.25. Second, use the constant growth model to determine the value of HILO common stock at the end of year 5; P5 equals $41.56. Next, determine the present value of P5, which is$20.66. Finally, add the present value of the dividends received during the first five years ($9.25) to the present value of P5 ($20.66) to obtain the total value of the common stock of \$29.91 per share. A timeline showing the expected cash flows from the purchase of HILO common stock is given in Figure.