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**DISCOUNTED DIVIDEND VALUATION**

CHP 2 DISCOUNTED DIVIDEND VALUATION

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1. INTRODUCTION This chapter provided an overview of Discounted Cash Flow (DCF) models of valuation, discussed the estimation of a stock’s required rate of return, and presented in detail the dividend discount model.

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2. PRESENT VALUE MODELS

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**EXAMPLE 2-1 Value as the Present Value of Future Cash Flows**

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**EXAMPLE 2-1 Value as the Present Value of Future Cash Flows Cont.**

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**EXAMPLE 2-1 Value as the Present Value of Future Cash Flows Cont.**

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**Streams of Expected Cash Flows**

Several alternative streams of expected cash ﬂows can be used to value equities, including dividends, free cash ﬂow, and residual income. A discounted dividend approach is most suitable for dividend-paying stocks, where the company has a discernible dividend policy that has an understandable relationship to the company’s proﬁtability, and the investor has a non-control (minority ownership) perspective.

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**Streams of Expected Cash Flows Cont.**

The free cash ﬂow approach (FCFF or FCFE) might be appropriate when the company does not pay dividends, dividends differ substantially from FCFE, free cash ﬂows align with proﬁtability, or the investor takes a control (majority ownership) perspective. The residual income approach can be useful when the company does not pay dividends (as an alternative to an FCF approach), or free cash ﬂow is negative.

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**EXAMPLE 2-2 Occidental Petroleum and Hormel Foods: Is the DDM an Appropriate Choice?**

As director of equity research at a brokerage, you have ﬁnal responsibility in the choice of valuation models. Two analysts have approached you on the use of a dividend discount model: an oil industry analyst examining Occidental Petroleum Corporation (NYSE: OXY) and a food industry analyst examining Hormel Foods (NYSE: HRL). Table 2-1 gives the most recent 10 years of data. (In the table, EPS is earnings per share, DPS is dividends per share, and payout ratio is DPS divided by EPS. ‘‘E$4.92’’ means that $4.92 is an estimated value.)

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**EXAMPLE 2-2 Occidental Petroleum and Hormel Foods: Is the DDM an Appropriate Choice? Cont.**

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**EXAMPLE 2-2 Occidental Petroleum and Hormel Foods: Is the DDM an Appropriate Choice? Cont.**

Answer the following questions based on the information in Table 2-1: 1. State whether a dividend discount model is an appropriate choice for valuing OXY. Explain your answer. 2. State whether a dividend discount model is an appropriate choice for valuing HRL. Explain your answer.

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**EXAMPLE 2-2 Occidental Petroleum and Hormel Foods: Is the DDM an Appropriate Choice? Cont.**

Solution to 1: DDM does not appear to be an appropriate choice for OXY. Although OXY is dividend-paying, OXY’s dividends do not bear an understandable and consistent relationship to earnings. Solution to 2: Because HRL is dividend paying and dividends bear an understandable and consistent relationship to earnings,using a DDM to value HRL is appropriate.

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**Discount Rate Determination**

In choosing a discount rate, we want it to reﬂect both the time value of money and the riskiness of the stock. The risk-free rate represents the time value of money. A risk premium represents compensation for risk, measured relative to the risk-free rate. The risk premium is an expected return in excess of the risk-free rate that is related to risk. When we decide on a discount rate that reﬂects both the time value of money and an asset’s risk, as we perceive it, we have determined our required rate of return. A required rate of return is the minimum rate of return required by an investor to invest in an asset, given the asset’s riskiness.

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**Discount Rate Determination Cont.**

The required rate of return on common stock is also known as the cost of equity. The two major approaches to determining the cost of equity are an equilibrium method (CAPM or APT) and the bond yield plus risk premium method. The equity risk premium for use in the CAPM approach can be based on historical return data or based explicitly on expectational data.

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**Discount Rate Determination Cont.**

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**Discount Rate Determination Cont.**

Market risk premium = expected return on the market - risk-free rate. In practice, we always estimate beta with respect to an equity market index when using the CAPM to estimate the cost of equity. So in practice, discussing equity, we are concerned speciﬁcally with the equity risk premium.

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**EXAMPLE 2-3 Calculating the Cost of Equity Using the CAPM**

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**Discount Rate Determination Cont.**

For many markets, evidence suggests that multiple factors drive returns. At the cost of greater complexity and expense, the analyst can consider using an equilibrium model based on multiple factors. Such models are known as arbitrage pricing theory (APT) models. Whereas the CAPM adds a single risk premium to the risk-free rate, APT models add a set of risk premiums.

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**Discount Rate Determination Cont.**

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**EXAMPLE 2-4 Calculating the Cost of Equity Using an APT Model**

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**EXAMPLE 2-4 Calculating the Cost of Equity Using an APT Model Cont.**

One type of the APT model is the Burmeister, Roll, and Ross (1994) or BIRR model that is based on five macroeconomic factors that affect the average returns of U.S. stocks.

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**EXAMPLE 2-4 Calculating the Cost of Equity Using an APT Model Cont.**

The required rate of return for JNJ is r = 5.00% + (0.17 × 2.59%) − (0.74 × 0.66%) − (−0.15 × 4.32%) + (1.16 × 1.49%) + (0.72 × 3.61%) = 9.93%

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**Discount Rate Determination Cont.**

Having an alternative to the CAPM and APT is useful. For companies with publicly traded debt, the bond yield plus risk premium method (BYPRP) provides a quick estimate of the cost of equity. BYPRP cost of equity = YTM on the company’s long-term debt + Risk premium

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**EXAMPLE 2-5 The Cost of Equity of IBM from Two Perspectives**

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**EXAMPLE 2-5 The Cost of Equity of IBM from Two Perspectives Cont.**

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**EXAMPLE 2-5 The Cost of Equity of IBM from Two Perspectives Cont.**

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**EXAMPLE 2-5 The Cost of Equity of IBM from Two Perspectives Cont.**

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**3. THE DIVIDEND DISCOUNT MODEL (DDM)**

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**EXAMPLE 2-6 DDM Value with a Single Holding Period**

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**THE DIVIDEND DISCOUNT MODEL (DDM) Cont.**

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**EXAMPLE 2-7 The Expected Holding-Period Return on DaimlerChrysler Stock**

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**EXAMPLE 2-7 The Expected Holding-Period Return on DaimlerChrysler Stock Cont.**

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**The Expression for Multiple Holding Periods**

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**The Expression for Multiple Holding Periods Cont.**

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**EXAMPLE 2-8 Finding the Stock Price for a Five-Year Forecast Horizon**

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**The Expression for Multiple Holding Periods Cont.**

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**THE DIVIDEND DISCOUNT MODEL (DDM) Cont.**

We can forecast future dividends by assigning the stream of future dividends to one of several stylized growth patterns. The most commonly used patterns are constant growth forever (the Gordon growth model), two distinct stages of growth (the two-stage growth model and the H-model), and three distinct stages of growth (the three-stage growth model).

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**4. THE GORDON GROWTH MODEL**

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**EXAMPLE 2-9 Valuation Using the Gordon Growth Model (1)**

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**EXAMPLE 2-9 Valuation Using the Gordon Growth Model (1) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2)**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-10 Valuation Using the Gordon Growth Model (2) Cont.**

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**EXAMPLE 2-11 Valuation Using the Gordon Growth Model (3)**

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**EXAMPLE 2-11 Valuation Using the Gordon Growth Model (3) Cont.**

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Gordan Growth Model

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**EXAMPLE 2-13 Gordon Growth Model with Negative Growth**

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**EXAMPLE 2-14 The Growth Rate Implied by the Current Stock Price**

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**EXAMPLE 2-14 The Growth Rate Implied by the Current Stock Price Cont.**

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**Estimating the Expected Rate of Return with the Gordon Growth Model**

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**EXAMPLE 2-15 Finding the Expected Rate of Return with the Gordon Growth Model**

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**EXAMPLE 2-15 Finding the Expected Rate of Return with the Gordon Growth Model Cont.**

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**The Present Value of Growth Opportunities**

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**The Present Value of Growth Opportunities Cont.**

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**Gordon Growth Model and the Price–Earnings Ratio**

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**Gordon Growth Model and the Price–Earnings Ratio Cont.**

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**EXAMPLE 2-16 The Expected P/E Found with the Gordon Growth Model**

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**EXAMPLE 2-16 The Expected P/E Found with the Gordon Growth Model Cont.**

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**EXAMPLE 2-16 The Expected P/E Found with the Gordon Growth Model Cont.**

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**EXAMPLE 2-16 The Expected P/E Found with the Gordon Growth Model Cont.**

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**Strengths and Weaknesses of the Gordon Growth Model**

The Gordon growth model is often useful for valuing stable-growth, dividend-paying companies. It is often useful for valuing broad-based equity indexes. The model features simplicity and clarity; it is useful for understanding the relationships among value and growth, required rate of return, and payout ratio. It provides an approach to estimating the expected rate of return given efﬁcient prices (for stable-growth, dividend-paying companies). As we show in the next section, the Gordon growth model can readily be used as a component of more-complex DDMs, particularly to model the ﬁnal stage of growth.

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**Strengths and Weaknesses of the Gordon Growth Model Cont.**

Calculated values are very sensitive to the assumed growth rate and required rate of return. The model is not applicable, in a practical sense, to non-dividend-paying stocks. The model is also inapplicable to unstable-growth, dividend-paying stocks.

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**5. MULTISTAGE DIVIDEND DISCOUNT MODELS**

For many companies, growth falls into phases. In the growth phase, a company enjoys an abnormally high growth rate in earnings per share, called supernormal growth. In the transition phase, earnings growth slows. In the mature phase, the company reaches an equilibrium in which factors such as earnings growth and the return on equity stabilize at levels that can be sustained long term. Analysts often apply multistage DCF models to value the stock of a ﬁrm with multistage growth prospects.

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**Two-Stage Dividend Discount Model**

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**EXAMPLE 2-17 Valuing a Stock Using the Two-Stage Dividend Discount Model**

General Mills (NYSE:GIS) is a large manufacturer and distributor of packaged consumer food products. Benoit Gagnon, a buy-side analyst covering General Mills, has studied the historical growth rates in sales, earnings, and dividends for GIS, and also has made projections of future growth rates. Gagnon expects the current dividend of $1.10 to grow at 11 percent for the next ﬁve years, and that the growth rate will decline to 8 percent and remain at that level thereafter. Gagnon feels that his estimate of GIS’s beta is unreliable, so he is using the bond yield plus risk premium method to estimate the required rate of return on the stock. The yield to maturity of GIS’s long-term bond (6.27s of 2019) is 6.67 percent. Adding a 4.0 percent risk premium to the yield-to-maturity gives a required return of percent, which Gagnon rounds to 10.7 percent.

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**EXAMPLE 2-17 Valuing a Stock Using the Two-Stage Dividend Discount Model Cont.**

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**EXAMPLE 2-17 Valuing a Stock Using the Two-Stage Dividend Discount Model Cont.**

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**EXAMPLE 2-17 Valuing a Stock Using the Two-Stage Dividend Discount Model Cont.**

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**EXAMPLE 2-18 Combining a DDM and P/E Model to Value a Stock**

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**EXAMPLE 2-18 Combining a DDM and P/E Model to Value a Stock Cont.**

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**EXAMPLE 2-19 Valuing a Non-Dividend-Paying Stock**

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**EXAMPLE 2-19 Valuing a Non-Dividend-Paying Stock Cont.**

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The H-Model

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The H-Model Cont.

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**EXAMPLE 2-20 Valuing a Stock with the H-Model**

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**EXAMPLE 2-20 Valuing a Stock with the H-Model Cont.**

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**EXAMPLE 2-20 Valuing a Stock with the H-Model Cont.**

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**Three-Stage Dividend Discount Models**

There are two popular versions of the three-stage DDM. In the ﬁrst version, the company is assumed to have a constant dividend growth rate in each of the three stages. For example, Stage 1 could assume 20 percent growth for three years, Stage 2 could have 10 percent growth for four years, and Stage 3 could have 5 percent growth thereafter. In the second version, in the middle (second) period, the growth rate is assumed to decline linearly.

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**EXAMPLE 2-21 The Three-Stage DDM with Three Distinct Stages**

IBM currently pays a dividend of $0.55 per year. We estimate the current required rate of return at 12 percent. Assume we believe that dividends will grow at 7.5 percent for the next two years, 13.5 percent for the following four years, and percent into perpetuity. What is the current estimated value of IBM using a three-stage approach? We show our calculations in Table 2-9.

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**EXAMPLE 2-21 The Three-Stage DDM with Three Distinct Stages Cont.**

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**EXAMPLE 2-21 The Three-Stage DDM with Three Distinct Stages Cont.**

Given these assumptions, the three-stage model indicates that a fair price should be $ Nevertheless, an analyst might well question whether an percent long-term growth rate is plausible.

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**EXAMPLE 2-22 The Three-Stage DDM with Declining Growth Rates in Stage 2**

Elaine Bouvier is evaluating HRL (addressed earlier in Example 2-2). She wishes to value HRL using the three-stage dividend growth model with a linearly declining dividend growth rate in Stage 2. After considerable study, Bouvier has decided to use the following information in her valuation (as of the beginning of 2003): The current dividend is $0.39. Bouvier estimates the required rate of return on HRL stock at 8.72 percent. In Stage 1, the dividend will grow at 11.3 percent annually for the next ﬁve years. In Stage 2, which will last 10 years, the dividend growth rate will decline linearly, starting at the Stage 1 rate and ending at the Stage 3 rate. The equilibrium long-term dividend growth rate (in Stage 3) will be 5.7 percent.

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**EXAMPLE 2-22 The Three-Stage DDM with Declining Growth Rates in Stage 2 Cont.**

Bouvier values HRL by computing the ﬁve dividends in Stage 1 and ﬁnding the present values at 8.72 percent. The dividends in Stages 2 and 3 can be valued with the H-model, which estimates their value at the beginning of Stage 2. This value is then discounted back to ﬁnd the dividends’ present value at t = 0.

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**EXAMPLE 2-22 The Three-Stage DDM with Declining Growth Rates in Stage 2 Cont.**

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**EXAMPLE 2-22 The Three-Stage DDM with Declining Growth Rates in Stage 2 Cont.**

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**EXAMPLE 2-22 The Three-Stage DDM with Declining Growth Rates in Stage 2 Cont.**

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Spreadsheet Modeling DDMs such as the Gordon growth model and the multistage models presented earlier assume stylized patterns of dividend growth. With the computational power of personal computers, calculators, and personal digital assistants, however, any assumed dividend pattern is easily valued.

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**EXAMPLE 2-23 Finding the Value of a Stock Using a Spreadsheet Model**

Yang Co. is expected to pay a $21.00 dividend next year. The dividend will decline by 10 percent annually for the following three years. In Year 5, Yang will sell off assets worth $100 per share. The Year 5 dividend, which includes a distribution of some of the proceeds of the asset sale, is expected to be $60. In Year 6, we expect the dividend to decrease to $40. We expect that this dividend will be maintained at $40 for one additional year. It is then expected to grow by 5 percent annually thereafter. If the required rate of return is 12 percent, what is the value of one share of Yang? The value is shown in Table Each dividend, its present value discounted at 12 percent, and an explanation are included in the table. The ﬁnal row treats the dividends from t = 8 forward as a Gordon growth model because after Year 7, the dividend grows at a constant 5 percent annually. V7 is the value of these dividends at t = 7.

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**EXAMPLE 2-23 Finding the Value of a Stock Using a Spreadsheet Model**

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**Finding Rates of Return for Any DDM**

In addition to valuing equities, DDMs are used to ﬁnd expected rates of return. For simpler models (like the one-period model, the Gordon growth model, and the H-model), well-known formulas may be used to calculate these rates of return. For many dividend streams, however, the rate of return must be found by trial and error, producing a discount rate that equates the present value of the forecasted dividend stream to the current market price. Adjustments to the expected return estimates may be needed to reﬂect the convergence of price to value.

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**EXAMPLE 2-24 Finding the Expected Rate of Return for Varying Expected Dividends**

An analyst expects JNJ’s (Johnson & Johnson, from Example 2-4) current dividend of $0.70 to grow by 14.5 percent for six years and then grow by 8 percent into perpetuity. JNJ’s current price is $ What is the expected return on an investment in JNJ’s stock?

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**EXAMPLE 2-24 Finding the Expected Rate of Return for Varying Expected Dividends Cont.**

In performing trial and error with the two-stage model to estimate the expected rate of return, it is important to have a good initial guess. We can use the expected rate of return formula from the Gordon growth model and JNJ’s long-term growth rate to ﬁnd a ﬁrst approximation: r = ($0.70 × 1.08)/$ = 9.42%. Because we know that the growth rate in the ﬁrst six years is more than 8 percent, the estimated rate of return must be above 9.42 percent. Using 9.42 percent and 10.0 percent, we calculate the implied price in Table 2-12:

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**EXAMPLE 2-24 Finding the Expected Rate of Return for Varying Expected Dividends Cont.**

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**EXAMPLE 2-24 Finding the Expected Rate of Return for Varying Expected Dividends Cont.**

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**Strengths and Weaknesses of Multistage DDMs**

The multistage DDMs can accommodate a variety of patterns of future streams of expected dividends. Even though the multistage DDMs may use stylized assumptions about growth, they can provide useful approximations. In addition to valuing dividend streams with a DDM, the expected rates of return can be imputed by ﬁnding the discount rate that equates the present value of the dividend stream to the current stock price. These expected return values can be adjusted to reﬂect the expected market correction of mispricing.

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**Strengths and Weaknesses of Multistage DDMs Cont.**

Because of the variety of DDMs available, the analyst is both enabled and compelled to carefully evaluate the assumptions about the stock under examination. The valuation model should ﬁt the assumptions (because the analyst is not forced to accept a set of assumptions that ﬁt a speciﬁc model). Spreadsheets are widely available, allowing the analyst to construct and examine an almost limitless number of models. Using a model forces the analyst to specify assumptions, rather than simply using subjective assessments. Analysts can thus use common assumptions, understand the reasons for differing valuations when they occur, and react to changing market conditions in a systematic manner.

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**Strengths and Weaknesses of Multistage DDMs Cont.**

Garbage in, garbage out. If the inputs are not economically meaningful and appropriate for the company being valued, the outputs from the model will not be useful. Analysts sometimes employ models that they do not understand fully. For example, the H-model is an approximation model. An analyst may think it is exact and misuse it. As a sensitivity analysis usually shows, valuations are very sensitive to the models’ inputs. Programming and data errors in spreadsheet models are very common. Spreadsheet models should be checked thoroughly.

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**THE FINANCIAL DETERMINANTS OF GROWTH RATES**

Sustainable Growth Rate: is rate of dividend (and earnings) growth that can be sustained for a given level of return on equity, keeping the capital structure constant over time and without issuing additional common stock.

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**EXAMPLE 2-25 Example Showing g = b× ROE**

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**Dividend Growth Rate, Retention Rate, and ROE Analysis**

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**Dividend Growth Rate, Retention Rate, and ROE Analysis Cont.**

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**EXAMPLE 2-26 ROA, Financial Policies, and the Dividend Growth Rate**

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**EXAMPLE 2-27 Forecasting Growth with the PRAT Formula**

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**EXAMPLE 2-27 Forecasting Growth with the PRAT Formula Cont.**

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**EXAMPLE 2-27 Forecasting Growth with the PRAT Formula Cont.**

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**EXAMPLE 2-27 Forecasting Growth with the PRAT Formula Cont.**

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**EXAMPLE 2-27 Forecasting Growth with the PRAT Formula Cont.**

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**EXAMPLE 2-28 A Spreadsheet Model for Forecasting Dividends**

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**EXAMPLE 2-28 A Spreadsheet Model for Forecasting Dividends Cont.**

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**EXAMPLE 2-28 A Spreadsheet Model for Forecasting Dividends Cont.**

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**EXAMPLE 2-28 A Spreadsheet Model for Forecasting Dividends Cont.**

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