Ease Prcouens 1-5 7-2) (DPS Calculation 7-2) consone Gowen Waltuarion (73) Constant Growth Yaluarion (7-4) Woluarion (7-5) Nonconstant Growth Valuation rocoare Promens 6-16 (7-6) Constant Growth Rate, g q-7) Constant Growth Valuation (7-8) Preferted Stock Rate of Rerun (7-9) Dedining Growth ‘Stock Waluarion (7-10) Rates of Rerum and Equilibaum Chapter 7: Stocks, Stock Valuation, and Stock Market Equilibrium 297 ‘Thress Industries just paid a dividend of $1.50 a share (i.e., Dy = $1.50). The divi- dend is expected to grow 5% a year for the next 3 years and then 10% a year there- after. What is the expected dividend per share for each of the next 5 years? Boehm Incorporated is expected to pay a $1.50 per share dividend at the end of this year (Le., Dy = $1.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, ra, is 15%. What is the value per share of Bochm’s stock? Woidrke Manufacturing’s stock currently sells for $20 a share, The stock just paid a dividend of $1,00 a share (e,, Dp = $1.00), and the dividend is expected to grow for- ever at a constant rate of 10% a year, What stock price is expected | year from now? ‘Whar is the required rate of return on Woideke’s stock? Nick's Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred sells for $50 a share. What is the stack’s required rate of retum? ‘A company currently pays a dividend of $2 per share (Dp = $2). It is estimated that the company’s dividend will grow at a rate of 20% per year for the next 2 years, then at a constant rate of 7% thereafter. The company’s stock has a beta of 1.2, the risk- free rate is 7.5%, and the market risk premium is 4%. What is your estimate of the stock’s current price? A stock is trading at $80 per share. The stock is expected to have a year-end dividend of $4 per share (D = $4), and it is expected to grow at some constant rate g through- out time. The stock's required rate of return is 14%. If markets are efficient, what is your forecast of g? You are considering an investment in Crisp Cookware's common stock. The stock is expected to pay a dividend of $2 a share at the end of this year (D1 = $2.00); its beta is 0.9; the risk-free rate is 5.6%; and the market risk premium is 6%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $25 a share. Assuming the market is in equilibrium, whag does the market believe will be the stock's price at the end of 3 years fi.e., what is P,)? What is the nominal rate of return on a preferred stock with a $100 par value, a stated dividend of 8% of par, and a current market price of (a) $60, (b) $80, (©) $100, and (d) $140? Brushy Mountain Mining Company’s ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising, As a result, the company’s earings and dividends are declining at the constant rate of 4% per year. If Dy = $5 and r, = 15%, what is the value of Brushy Mountain's stock? ‘The beta coefficient for Stock C is be = 0.4 and that for Stock D is bp = -0.5. (Stock D's beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative-beta stocks, although collection agency and gold mining stocks are sometimes cited as examples.)298 Part 3: Stocks and Options (7-44) jonconstant Growth Stock Valuation (7-12) Nonconstant Growth ‘Steck Valuation (7-13) Prefered Stock ‘Valuation (7-14) Rerun on Common ‘Stock (7-45) Constant Growth Stock Valuation (7-16) Equilibrium Stock Price a. If the risk-free rate is 9% and the expected rate of return on an average stock is 13%, what are the required rates of return on Stocks C and D? 1b, For Stock C, suppose the current price, Po, is $25; the next expected dividend, Dy, is $1.50; and the stock's expected constant growth rate is 4%, Is the stock in equilibrium? Explain, and describe what would happen if the stock were not in equilibrium, Assume that the average firm in your company’s industry is expected to grow at 4 constant rate of 6% and that its dividend yield is 7%, Your company is about as risky as the average firm in the industry, but it has just successfully completed some R&D work that leads you to expect that its earnings and dividends will grow ata rate of 50% [D, = Do(1 + g) = Do(.50)] this year and 25% the following year, after which growth should return to the 6% industry average. If the last dividend paid (Dg) was $1, what is the value per share of your firm’s stock? Simpkins Corporation is expanding rapidly, and it does not pay any dividends be- cause it currently needs to retain all of its earnings. However, investors expect Simp= kins to begin paying dividends, with the first dividend of $1.00 coming 3 years from today. The dividend should grow rapidly—at a rate of 50% per year—during Years 4 and 5. After Year 5, the company should grow at a constant rate of 8% per year. If the required return on the stock is 15%, what is the value of the stock today? Several years ago, Rolen Riders issued preferred stock with a stated annual dividend of 10% of its $100 par value, Preferred stock of this type currently yields 9%. As- sume dividends are paid annually. a. What is the value of Rolen's preferred stock? 1b, Suppose interest rate levels have risen to the point where the preferred stock now yields 12%, What would be the new value of Rolen’s preferred stock? You buy a share of The Ludwig Corporation stock for $21.40. You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in Years 1, 2, and 3, respectively, and you expect to sell itat a price of $26.22 at the end of 3 years. a. Calculate the growth rate in dividends b, Calculate the expected dividend yield. cc. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return, What is this stock’s expected total rate of return? Investors require a 15% rate of return on Brooks Sisters’s stock (r, = 15%), a. What would the vale of Brooks's stock be if the previous dividend was Do = $2 and if investors expect dividends to grow at a constant annual rate of (I) -5%, (2) 0%, (3) 5%, and (4) 10%? b. Using data from part a, what is the Gordon (constant growth) model’s value for Brooks Sisters’s stock if the required rate of return is 15% and the expected growth rate is (1) 15% or (2) 20%? Are these reasonable results? Explain cc. Is it reasonable to expect that a constant growth stock would have g > 1? The risk-free rate of return, rer is 11%; the required rate of return on the market, ry is 14%; and Schuler Company's stock has a beta coefficient of 1.5.Cuauoncs Proaus 17-19 (7-47) Constant Growth Stock falvation (7-18) Nonconstant Growth Sock Waluation ‘Chapter 7: Stocks, Stock Valuation, and Stock Market Equilibrium 299 a. If the dividend expected during the coming year, Dj, is $2.25, and if g is a con- stant 5%, then at what price should Schuler’s stock sell? b. Now suppose that the Federal Reserve Board increases the money supply, caus ing a fall in the risk-free rate to 9% and in ryq to 12%. How would this affect the price of the stock? c. In addition to the change in part b, suppose investors’ risk aversion declines; this fact, combined with the decline in rap, causes ty to fall to 11%, At what price would Schuler’s stock now sell? d, Suppose Schuler has a change in management, The new group institutes policies that increase the expected constant growth rate to 6%, Also, the new management stabilizes sales and profits and thus causes the beta coefficient to decline from 1.5 to 1.3. Assume that trp and ry are equal to the values in part ¢. After all these changes, what is Schuler’s new equilibrium price? (Note: Dy goes to $2.27.) Suppose a firm’s common stock paid a dividend of $2 yesterday. You expect the divi- dend to grow at the rate of 5% per year for the next 3 years; if you buy the stock, you plan to hold it for 3 years and then sell it. a. Find the expected dividend for each of the next 3 years; in other words, calculate Dj, Dg, and Dy. Note that Do = $2. b. Given that the appropriate discount rate is 12% and that the first of these divi- dend payments will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PV of D;, Dz, and Dy, and then sum these PVs. ¢. You expect the price of the stock 3 years from now to be $34.73 (ie., you expect #5= $34.73). Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $34.73. d. If you plan to buy the stock, hold it for 3 years, and then sell it for $34.73, what is the most you should pay for it? e, Use Equation 7-2 to calculate the present value of this stock. Assume that g = 5% and is constant. f, Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned holding period were 2 years or $ years rather than 3 years, would this affect the value of the stock today, Pj? Explain your answer, Reizenstein Technologies (RTT) has just developed a solar panel capable of generating 200% more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 15% annual growth rate for the next 5 years, By the end of 5 years, other firms will have developed comparable technology, and RTs growth rate will slow to 5% per year indefinitely. Stockholders require a return of 12% on RT's stock. ‘The most recent annual dividend (Dy), which was paid yesterday, was $1.75 per share. a, Calculate RT's expected dividends for t= 1, t= 2, t= 3,t=4, and t= 5, b, Calculate the intrinsic value of the stock today, Po. Proceed by finding the pres- ent value of the dividends expected at t= 1, ¢= 2, t= 3,t=4,and p= 5 plus the present value of the stock price that should exist at t = 5, B;. The Ps stack price can be found by using the constant growth equation. Note that to find Ps you use the dividend expected at t= 6, which is 5% greater than the t = 5 dividend.300) Part 3: Stocks and Options c. Calculate the expected dividend yield (DyB,), the capital gains yield expected during the first year, and the expected total regen (dividend yield plus capital gains yield) during the first year. (Assume that Pos Po, and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Also calculate these same three yields for t = 5 (e.g., De/Ps). d. If your calculated intrinsic value differed substantially from the current market price, and if your views are consistent with those of most investors (the marginal investor), what would happen in the markerplace? What would happen if your views were or consistent with those of the marginal investor and you turned out to be correct? (7-19) — Taussig Technologies Corporation (TTC) has been growing at a rate of 20% peli Supemormal Grawh year in recent years. This same supernormal growth rate is expected to last for ang Stock Valuation — other 2 years (g, = g: = 20%). a. If Do = $1.60, r, = 10%, and g, = 6%, then what is TTC’s stock worth today? Whar is its expected dividend yield and its capital gains yield at this time? b. Now assume that TTC’s period of supernormal growth is to last another 5 years rather than 2 years (gi = g2 = gs = g4 = gs = 20%). How would this affect its price, dividend yield, and capital gains yield? Answer in words only. c. What will TTC’s dividend yield and capital gains yield be once its period of su- pernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth, and the calculations are very easy:) d. Of what interest to investors is the relationship over time between dividend yield and capital gains yield?