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# NAU FIN 331 - Common Stock Valuation

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Finance 331, Common Stock Valuation (Chapter 13)Symbols and Definitions:V = intrinsic value of a share of stockP = market price of a shareD = dividend per shareE = earnings per sharek = required return on the stockb = retention rate, or “plowback” (percentage of earnings added to retained earnings)1-b = dividend payout (percentage of earnings paid as dividends)g = growth rate of E &/or DPVGO = present value of growth opportunitiesROE = return on equityNumerical subscripts refer to time.Some basic relationships:Retained earnings per share = b X ED = (1-b) X EApproaches to Valuing EquityThere are three general approaches to valuing equity:Dividend based techniquesValuation multiplesCash flow based techniquesWe will consider only the first two approaches in this course. Our purpose is to emphasize the relationships between firm characteristics and firm value. As a result, the method of stock valuation we use is not critical.Required Return (CAPM)One of the first steps in the valuation process is to determine the required return on the firm’s stock. To use CAPM for this, we need the risk-free rate, the market risk premium, and the stock’s beta.To look up the yield on T-bills, we go to www.bloomberg.com or www.yahoo.com. 6-month T-bill yield = _______1According to p. 126 of our text, historically the average annual return on large cap stocks is 8.4 percent above the T-bill rate. We will use that as the historical market risk premium. The only other thing we need to look up is the beta on our stock, which we can get from Value Line, Yahoo, moneycentral.msn, or other sources. We will use Value Line to find the beta for Target.Beta for TGT = ______k = rf +  ( MRP) = _____ + _____ ( _____ ) = _____While at Value Line, go to “Look up Industry” and click on “Industry Commentary” for Retail Store.Dividend-Based Stock Valuation Techniques: 1. Constant Growth (Gordon) Dividend Discount ModelV0 = D1 / (k - g) (1)where:V0 = value per share at t = 0D1 = expected dividend in year 1 k = required return on the stockg = expected growth rate for dividendsSolving eqn (1) provides the present value of expected future dividends.Necessary conditions: 1. firm must pay dividends2. g must be constant indefinitely3. k > gOne way to estimate the growth rate of earnings (E) and dividends (D) is as follows:g = ROE X bwhere b is the retention rate. For example, if ROE equals 10%, the relationship between b and g is shown below: b g 1.0 10%0.5 50.0 0Relationship Between Firm Growth and Stock Value.2Are growth stocks worth more than stock in firms whose earnings are not growing? Let’s look at a couple of examples.Example #1: The following applies to Delta, Inc.:Book value of equity is \$100ROE on existing assets and planned investments is 8%K = .10Dividend payout = (1-b) = 100%a. Calculate earnings per share in the next year: E1 = (BV)x(ROE) b. Calculate D1.c. Calculate the growth rate.d. Calculate the stock value (V0).The value we have solved in (d) is the no-growth value for Delta. If a firm has 100% dividend payout, D1 = E1 and g = 0. In that case:V0 = E1 / k (no-growth value)Now. let’s consider what happens if Delta changes its dividend policy. If Delta lowers its dividend payout to 25%:a. Calculate D1.b. Calculate the growth rate.c. Calculate the stock value.3The \$50 value calculated in (c) is the stock value with 6% annual growth in earnings and dividends. However, it is lower than the no-growth value of \$80.Conventional wisdom is that a higher growth rate for earnings and dividends should result in a higher stock price.The difference between the \$25 value with growth and the \$40 value of Deltawithout growth is the present value of growth opportunities (PVGO):PVGO = Value with growth – Value without growthWhere:Value with growth = D1 / (k-g) = \$50Value without growth = E / k = \$80PVGO = 50 – 80 = -\$30 Example #2: As a counter example, consider Elron, Inc.:Book value is \$80 per shareROE is 12.5%. Required return on equity (k) is 10%. Initial dividend payout is 100% a. Calculate earnings per share (E1), D1 and g.b. Calculate the stock value (V0)The value calculated in (b) is the no-growth value.If Elron reduces its dividend payout to 50%:a. Calculate D1.b. Calculate g.4c. Calculate V0. d. Calculate the PVGO for Elron.Growth increases the value of Elron stock because it is investing in projects with positive NPV (ROE > k). The difference between the \$133.33 value with growth and the \$100 value of Elron without growth is the present value of growth opportunities (PVGO):The relationship between ROE, k and V are shown below:Relationship between Impact of g > 0 ROE and k on stock value (V) (PVGO) ROE > k positive ROE = k zero ROE < k negativeNote that the relevant ROE is the expected ROE on new investments, not theROE on existing assets. Example #3.The risk-free rate is 2% and the market risk premium is 8%. Bogle, Inc. has a beta of 1.25, ROE on existing assets and on planned investments equals 16%. In the fiscal year just ended, earnings per share were \$4 and the dividend was \$2. It has a market price of \$54 per share.(a) Calculate the required return on equity (k).(b) Calculate dividend payout.(c) Calculate the growth rate.5(d) Calculate the value per share (V0).(e) Calculate the value in one year (V1).(f) If you bought the stock today for \$54, kept it one year and sold it for \$58.32, what is your percentage return?(g) Calculate the leading P/E (P0/E1) and trailing P/E (P0/E0) for Bogle.(h) Calculate what Bogle’s stock value would be if it had 100% dividend payout (the no-growth value).(i) Calculate the PVGO for Bogle.(i) What would happen to Bogle’s stock price and P/E if it reduced dividend payout to 25%? 62. Nonconstant (Two-stage) Growth Model. If any of the conditions to use the constant growth DDM are not met, we mustuse another approach. A common situation is one in which a high growth rate is expected for a period of time, followed by a lower (normal) growth rate that is expected to last forever. We must estimate how long we expect the high growth rate to last. Assume the high growth rate is expected to last n periods. We first calculate dividends for the next n+1 periods. Then we calculate the projected stock price at the end of period n:Vn = Dn+1 / (k - gc) (2)The growth rate that is used in this equation for “gc” is the normal growth rate expected to exist after the end of period n. We often use a rate from 6 to8 percent for the

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