CHAPTER 8 THE VALUATION AND CHARACTERISTICS OF STOCK FOCUS Like bonds, stocks are worth the present value of their expected future cash flows, but the process of estimating that value is far less precise than it is for bonds. We begin studying stock valuation with basic ideas comparing equity cash flows with those associated with bonds. We then turn to growth models of valuation beginning with the constant growth case and moving on to the more complex two-stage model. We conclude our treatment of common stock valuation by discussing pricing in the context of newly issued securities. To do that we explain investment banking and the IPO process including an analysis of the IPO pop phenomenon. Following that we consider some issues of corporate control along with the rights and privileges of stockholders. The point is made, however, that with the exception of activists, most equity investors are only in for the money, not for a voice in running the company. Next we move into preferred stock. Its straightforward valuation is followed by a discussion of preferred’s nature which makes it something of a cross between common stocks and bonds and its classification as a hybrid security. At this point we briefly outline the nature of securities analysis including a light treatment of the Efficient Market Hypothesis (EMH) and Behavioral Finance. The chapter concludes with a detailed treatment of options and warrants. The section opens with an introductory illustration of an option to buy real estate. This gets students used to the option concept before taking up a more quantitative treatment of stock options. We finish with a discussion of the problems created by stock options as executive compensation. PEDAGOGY Stock valuation models can be fairly complex as is the entire subject of options. A careful, motivated development of the ideas, always starting from scratch, gets the concept and method across. TEACHING OBJECTIVES After this chapter students should 1. Appreciate the difference between stock and bond valuation understanding that estimating the value of a stock is far more subjective. 2. Understand and be able to apply growth model valuation techniques including the relatively complex two stage model. 3. Gain an overall understanding of investment banking and the IPO process including the dynamics of pricing 4. Have a basic understanding of how corporations are run and the role (or lack of it) of stockholders. 5. Comprehend the nature of preferred stock and its valuation. 6. Appreciate the idea of securities analysis including the difference between fundamental and technical analysis and the message behind the EMH. Understand just a little about Behavioral Finance. 7. Understand the basics of stock options and warrants including executive stock options. OUTLINE I. COMMON STOCK A. The Return on an Investment in Common Stock Dividend and Capital Gains Yields B. The Nature of Cash Flows from Common Stock Ownership The imprecise nature of dividends and sale proceeds compared with a bond's cash flows. C. The Basis of Value Intrinsic value based on the present value of estimated future cash flows. II. GROWTH MODELS OF COMMON STOCK VALUATION The usefulness of a model based only on an assumption about growth. A. Developing Growth Based Models Switching to an infinite stream of dividends. B. The Constant Growth Model Developing and applying the Gordon Model. C. The Expected Return The expected return in the constant growth case. D. Two Stage Growth The model applied to situations in which constant growth is preceded by super normal growth. E. Practical Limitations of Pricing Models Our results are no better than our inputs, which are usually pretty rough. III VALUING NEW STOCKS – INVESTMENT BANKING AND THE IPO A. IPOs for Different Securities B. Investment Banking C. Promoting and Pricing the IPO D. Book Building and the Road Show E. Prices After the IPO IV. SOME INSTITUTIONAL CHARACTERISTICS OF COMMON STOCK A. Corporate Organization and Control The role of the Board of Directors B. Voting Rights and Issues Majority and cumulative voting C. Stockholders' Claims on Income and Assets - Being last in line can be good or bad. V. PREFERRED STOCK A. Valuation of Preferred Stock Valuation as a perpetuity B. Characteristics of Preferred Stock Why and how preferred is a hybrid between debt and common equity. Tax issues and risk. VI. SECURITIES ANALYSIS A. brief overview of fundamental analysis, technical analysis and the EMH. VII. OPTIONS AND WARRANTS A. Options in General An option on land provides an intuitive introduction to the concept. B. Stock Options – Call Options Terminology, intrinsic value, the writer and the buyer, why options have value, detailed explanation of leverage, a broad numerical example. C. Put Options Brief description. D. Warrants Distinguished from options. A primary market phenomenon. E. Employee stock options. DISCUSSION QUESTIONS 1. Discuss the nature of stock as an investment. Do most stockholders play large roles in the management of the firms in which they invest? Why or why not? Answer: The return on a stock investment comes from dividends and price appreciation. Although neither is guaranteed, both have the potential for growth in the future. This is in distinct contrast to investments in debt vehicles that guarantee future payments but offer little or no possibility of a return that's higher than promised. Although stock implies ownership, few equity investors expect to play a role in running the companies whose shares they buy. Such firms are widely held, and few stockholders have large enough blocks of stock to influence management decisions. In small business, of course, owners usually run their companies. 2. Compare and contrast the nature of cash flows stemming from an investment in stock with those coming from bonds. Answer: The cash flows associated with both stocks and bonds consist of a stream of relatively small amounts followed by a final larger payment. The streams are dividends for stocks and interest payments for bonds, while the final payments are the selling price of stock and the return of a bond's principal. The similarity between the flows is rather superficial, and doesn't go far beyond the general shape just described. Both the interest and principal payments associated with a bond are contractually guaranteed, and tend to be very reliable. A stock's cash flows, on the other hand, are quite risky. Dividends can increase or decrease from their current levels or be omitted entirely at the discretion of the firm's board of directors. Similarly, the eventual selling price of a share is dependent on the company's performance and the state of the stock market at the time of sale. Both of these are subject to unpredictable changes. 3. Verbally rationalize the validity of a stock valuation model that doesn't contain a selling price as a source of cash flow to the investor. Give two independent arguments. Answer: Intuitively, a stock's value to an investor is best represented by the present value of the dividends paid while the share is held plus the present value of the price received upon sale. However, that final selling price can be replaced by a similar model of value in the mind of the investor who buys the share. Thus at the end of the first investor's holding period, another stream of dividends begins, followed by an eventual selling price. In effect the valuation model has been transformed into a longer stream of dividends and a selling price by the consideration of two sequential investors. This mental construct can be applied as many times as we like and the eventual selling price pushed indefinitely far into the future where its present value is zero. We're left with just the present value of an infinitely long series of dividends. Alternately, imagine the investing community acting as a single unit to value stock offered for sale by an issuing company. In other words, imagine that the financial world consists of the company and "the market" only. In that scenario, trades between investors inside the market are not observable or relevant. All that counts is the price the market as a whole puts on the stock. But the only basis for that price is the future payments to be made by the firm to the investing community. Those are just the dividends it pays to whoever in the community happens to own the stock. Hence the community acting as a whole can only base value on all future dividends and nothing else. 4. Why are growth rate models practical and convenient ways to look at stock valuation? Answer: Forecasting the future of a business and the price of its stock is a difficult and imprecise task especially for outsiders who don't have access to the company's detailed plans and records. However, an overall evaluation is often formed based on a variety of imprecise observations and feelings about the company. That subjective feeling can be nicely summed up in a projected growth rate. Growth rate models allow us to estimate stock prices based on this summary information which although incomplete is often all we have. 5. What is meant by normal growth? Contrast normal and super normal growth. How long can each last? Why? Answer: Normal growth implies a forecast dividend growth rate that is less than the return required on an investment in the stock. Super normal growth implies the reverse, a growth rate greater than the required return. Super normal growth exists, but is generally assumed to be temporary. It is usually modeled to last no more than a few years. Normal growth can last indefinitely. The implication of super normal growth that lasts indefinitely is an infinite value for the company and its stock, which doesn't make sense. (This is apparent from Equation (7-9) in which the numerators exceed the denominators by larger and larger amounts if g>k.) 6. Describe the approach to valuing a stock expected to grow at more than one rate in the future. Can there be more than two rates? What two things have to be true of the last rate? Answer: The two-stage growth model separates the future into two periods. The first is a finite number of years during which the growth rate can have any value but is usually assumed to be super normal. The second period is infinitely long and is characterized by normal growth. The procedure projects the firm's dividends from the present until just after normal growth begins. The Gordon Model is then used to determine the value of the stock at the beginning of the period of normal growth. The value of the stock today is the sum of the present values of the Gordon Model amount and all the calculated dividends up until that time. 7. Discuss the accuracy of stock valuation, and compare it with that of bond valuation. Answer: Stock valuation is considerably less precise than bond valuation for two reasons. First, there's a big difference in the predictability of the future cash flows associated with the two instruments. Bond payments are contractually specified and generally quite reliable. Dividends and the eventual selling price of stocks, on the other hand, are uncertain even for stable companies. Second, the appropriate discount rate for taking present values is an estimate based on perceived risk for stock, while it is a more readily known market return for bonds. 8. Do stocks that don't pay dividends have value? Why? Answer: Stocks that don't pay dividends have value because they are expected to pay dividends at some time in the future. This is true even if management states its intent never to pay out its earnings as dividends. The absence of dividends at some time during the firm's life implies that stockholders would never receive any value for their investments. 9. How is the IPO price of a stock determined? Is that price likely to be the stock’s intrinsic value. Answer: Company executives working with investment bankers estimate a range of prices for the stock to be issued. They then go on a road show making promotional presentations to potential investors. During the trip they ask investors, mostly institutional clients of the investment bank, to estimate the number of shares they will be willing to buy. This process is called “book” building. These estimates are not firm orders, but collectively represent likely investor demand for the stock. Based on the book the team decides on a price along with a volume number that will raise the amount of money the company is looking for. The IPO price may be a reasonable estimate of intrinsic value since it is developed by analyzing the firm’s business and estimates of demand from knowledgeable professionals. It may, however, be intentionally somewhat underpriced. 10. Is the IPO Pop experienced by most new stocks likely to be a reflection of market forces driving shares toward their intrinsic values. Answer: The pop isn’t likely to represent true value. It seems to be a result of irrational exuberance and the excitement associated with new things. The fact that pops rarely last is a signal that they were never real in the first place. 11. Preferred stock is said to be a hybrid of common stock and bonds. Explain fully. Describe the cash flows associated with preferred stock and their valuation. Answer: Preferred stock pays a constant dividend that is specified in amount but not guaranteed. However, the cumulative feature generally requires that preferred dividends be caught up before common dividends can be paid. The value of a preferred share is the present value of the perpetuity of its dividends. Preferred stock is legally equity but in some ways behaves more like debt. It is viewed as a hybrid because its characteristics are like those of common stock on some issues, like those of bonds on other issues, and lie somewhere in between on still others. The main issues are as follows. (1) Preferred dividends are constant, as are interest payments. They are unlike common stock dividends, which are usually expected to grow. (2) Bonds have maturity dates on which principal is returned. Preferred, like common stock, has no maturity, and never returns principal. (3) Interest must be paid, common dividends can be passed indefinitely. Preferred dividends are between in that they can be passed, but are subject to a cumulative feature. (4) In bankruptcy, the priority of preferred is between that of bonds and common stocks. (5) Like bondholders, preferred stockholders have no voting rights. (6) Interest is tax deductible to the paying company while dividends, common or preferred, are not. 12. Discuss the relative riskiness of investment in bonds, common stock, and preferred stock. Answer: The features of bonds, preferred, and common stocks create an ordering of risk. Bonds are the safest, because their payments are the most assured. Common is the most risky, because its payments are the least certain. Preferred is in the middle. The compensation for bearing the risk of common stock is that the return can be very high if the company does well. That possibility doesn't exist with bonds or preferred. 13. Compare fundamental analysis and technical analysis. Which makes more sense to you? Answer: Fundamental Analysis involves doing research to discover as much as possible about a company's business, and forecasting its future performance, including dividends and market price, based on that knowledge. Technical Analysis is based on the belief that market forces dictate prices and price movements, and that movement patterns repeat themselves. Therefore, technicians believe that recognizable patterns can predict stock price changes. Followers of the two schools of thought tend to be opposed to one another, although many people use both ideas. Academics are generally fundamentalists. Statistical studies have been unable to prove that either approach is right or wrong. 14. What does the efficient market hypothesis say? What is its implication for stock analysis? Answer: The efficient market hypothesis says that financial markets are efficient in that new information is disseminated very rapidly. This means that at any time, all available information is reflected in stock prices, and studying historical patterns of price movement can't consistently help an investor in earning above average returns. The EMH, therefore, contradicts the premise underlying technical analysis. It also implies that fundamental analysis won't help individual investors much, because professionals are doing it all the time. They discover and disseminate anything an individual can figure out long before he or she does. 15. Options are more exciting than investing in the underlying stocks because they offer leverage. Explain this statement. Answer: Leverage is any technique that amplifies return. Options amplify return because a given percentage change in a stock’s price drives a percentage option price change that can be many times larger. For example a 10% change in a stock price might result in a 200% change in the price of an option on that stock. That means large gains and losses are possible in options due to only small or moderate changes in stock prices. 16. Is investing in options really investing or is it more like gambling? Answer: It’s more like gambling. For the following reasons: 1. It’s a high-risk search for large short-term gains rather than long term growth with low or moderate risk. 2. There’s no economic benefit in that there’s no transfer of funds from savers to companies that will invest the money in productive assets. BUSINESS ANALYSIS 1. Your cousin Charlie came into a large inheritance last year and invested the entire amount in the common stock of IBD Inc., a large computer company. Subsequently he's been very interested in the company and watches it closely. Recently the newspaper carried a story about major strategic changes at IBD including massive layoffs and business realignments. Charlie was devastated. He doesn't understand how the firm could have made such changes without the knowledge and approval of its stockholders. Write a brief letter to Charlie explaining how things really work. Answer: Companies are run by managers, who are appointed by boards of directors. The directors in turn are elected by stockholders. Thus stockholders control companies only indirectly by electing their boards. Typically stockholders are not consulted on decisions relating to the running of the company. This is true even regarding major issues. Stockholders to vote on a few issues spelled out in the corporate bylaws. These typically include mergers. Where no individual or group owns a substantial portion of a company, the board can become entrenched and virtually run the firm as it pleases. Most stockholders view the firm strictly as an investment, and are unlikely to "revolt" unless financial performance becomes very bad. PROBLEMS Dividend and Capital Gain Yields, Page 348 1. Paul Dargis has analyzed five stocks and estimated the dividends they will pay next year as well as their prices at the end of the year. His projections are shown below. Stock Valuation Based on Projected Cash Flows: Concept Connection 8-1, Page 350 2. The stock of Sedly Inc. is expected to pay the following dividends: 3. Fred Tibbits has made a detailed study of the denim clothing industry. He's particularly interested in a company called Denhart Fashions that makes stylish denim apparel for children and teenagers. Fred has done a forecast of Denhart's earnings and looked at its dividend payment record. He's come to the conclusion that the firm will pay a dividend of $5.00 for the next two years followed by a year at $6.50. Fred's investment plan is to buy Denhart now, hold it for three years and then sell. He thinks the price will be about $75 when he sells. What is the most Fred should be willing to pay for a share of Denhart if he can earn 10% on investments of similar risk? Solution: Growth Rates: Concept Connection Example 8.2, Page 353 4. Mitech Corp’s stock has been growing at approximately 8% for several years and is now $30. Based on past growth rate performance, what would you expect the stock’s price to be in five years? Solution: Pn+1 = Pn (1+g) P5 = P0 (1.08)5 = P0(1.08) (1.08) (1.08) (1.08) (1.08) = $30.00(1.4693) = $44.08 The Constant Growth (Gordon) Model: Concept Connection Example 8.3, Page 355 5. The Spinnaker Company has paid an annual dividend of $2 per share for some time. Recently the board of directors voted to grow the dividend by 6% from now on. What is the most you would be willing to pay for a share of Spinnaker if you expect a 10% return on your stock investments? Solution: Apply the Gordon Model P0 = D0(1 + g) / (k – g) = $2(1.06) / (.10 .06) = $2.12 / .04 = $53.00 6. The Pancake Corporation recently paid a $3 dividend, and is expected to grow at 5% forever. Investors generally require an expected return of at least 9% before they'll buy stocks similar to Pancake. a. What is Pancake's intrinsic value? b. Is it a bargain if it's selling at $76 a share? Solution: b. That's not apparent. Although our calculated intrinsic price exceeds the market price, it only does so by about 4%. The modeling technique isn't accurate enough to identify 4% differences. Our result says that the stock has probably been priced about right by the market. 7. Tyler Inc.'s most recent annual dividend was $3.55 a share. The firm has been growing at a consistent 4% rate for several years, but analysts generally believe that better times are ahead, and that future growth will be in the neighborhood of 5%. The stock is currently selling for $75. Stocks similar to Tyler earn returns ranging from 8% to 10%. a. Calculate values for a share of Tyler at interest rates of 8%, 9%, and 10%. b. Do you think Tyler is a good investment for the long run, that is, for someone planning to hold onto it for ten or more years? c. Do you think it's a good investment for the short term? That is, should you buy it with the expectation of selling in a relatively short period, say a year or less? d. Repeat the calculations of part a assuming that instead of rising, Tyler's growth rate (1) remains at 4% or (2) declines to 3%. e. Comment on the range of prices that you've calculated. Solution: b. Tyler would appear to be a good investment based on the figures in part a. The stock is priced at the low end of a range of reasonable values. This implies that, barring a major unforeseen problem, it should move generally upward over the next several years. c. Tyler's value isn't so clear in the short run, because we can't say how long it will take the market to recognize its intrinsic value and bid the price up. e. It's important to understand how sensitive the model results are to changes in the assumptions about return and growth rate. Whether the stock is a good buy at $75 boils down to how good we feel about those rates. Notice that the rates in all the calculations seem reasonable but result in a range of values from about $52 to $123, a wide spread indeed. 8. The Anderson Pipe Co. just paid an annual dividend of $3.75 and is expected to grow at 8% for the foreseeable future. Harley Bevins generally demands a return of 9% when he invests in companies similar to Anderson. a. What is the most Harley should be willing to pay for a share of Anderson? b. Is your answer reasonable? What’s going here? What should Harley do with this result? Solution: a. Apply the Gordon Model P0 = D0(1 + g) / (k – g) = $3.75(1.08) / (.09 .08) = $4.05 / .01 = $405.00 b. The answer probably isn’t reasonable. The valuation is too high because the denominator of the model is too small a number. That’s because the growth rate and the required rate of return are too close together. Harley probably isn’t demanding enough return to compensate him adequately for the level of risk in Anderson stock. He should rethink his return requirement or disregard the model’s result. 9. Cavanaugh Construction specializes in designing and building custom homes. Business has been excellent, and Cavanaugh projects a 10% growth rate for the foreseeable future. The company just paid a $3.75 dividend to its stockholders. Comparable stocks are returning 11%. a. What is the intrinsic value of Cavanaugh stock based on this information? b. Does this seem reasonable? Why or why not? c. If Cavanaugh’s growth rate is only 8.5% and comparable stocks are really returning 12%, what would the intrinsic value of Cavanaugh’s stock be? d. Do those relatively small changes in assumption justify the change in the intrinsic value of the stock? Why or why not? Solution: a. The Gordon Model yields [$3.75 (1.10)] / (.11 - .10) = $412.50 b. No, it does not seem reasonable. The problem is that the growth rate of 10% and the discount rate of 11% are too close together for the constant growth model to work effectively. c. [$3.75 (1.085)] / (.12 - .085) = $116.25 d. Probably not. The assumptions in part c. appear to be more reasonable than those in part a., in that they provide a sufficient spread in the growth and discount percentages for the constant growth model to work more effectively. The spread in the results is due to the fact that use of the model is inappropriate with part a inputs. Valuation Based on Two Stage Growth: Concept Connection Example 8.5, Page 357 10. The Miller Milk Company has just come up with a new lactose free dessert product for people who can’t eat or drink ordinary dairy products. Management expects the new product to fuel sales growth at 30% for about two years. After that competitors will copy the idea and produce similar products, and growth will return to about 3% which is normal for the dairy industry in the area. Miller recently paid an annual dividend of $2.60,which will grow with the company. The return on stocks like the Miller Company is typically around 10%. What is the most you would pay for a share of Miller? Solution: First draw a time line for the problem and enter the following data. Problems 11 through 13 refer to Softek Inc., a leader in the computer software field. Softek has two potentially big-selling products under development. Alpha, the first new product, seems very likely to catch on and is expected to drive the firm's growth rate to 25% for the next two years. However, software products have short lives, and growth can be expected to return to a more normal rate of 6% after that period if something new isn't launched immediately. Beta, the second product, is a logical follow-up, but management isn't as confident about its success as it is about Alpha's. Softek's most recent yearly dividend was $4.00, and firms in the industry typically return 14% on stockholder investments. 11. You are an investment analyst for a brokerage firm, and have been asked to develop a recommendation about Softek for the firm's clients. You've studied the fundamentals of the industry and the firm, and are now ready to determine what the stock should sell for based on the present value of future cash flows. a. Calculate a value for Softek's stock assuming product Alpha is successful but Beta isn't. In other words, assume two years of growth at 25% followed by 6% growth lasting indefinitely. b. Calculate a price, assuming Beta is also successful and holds Softek's growth rate at 25% for two additional years. Solution: 12. Calculate a price for Softek assuming that Alpha is successful and Beta is successful, but doesn't do quite as well as Alpha. Assume that Softek grows at 25% for two years and then at 18% for two more. After that it continues to grow at 6%. (Hint: Don't be confused by the fact there are now three growth periods. Just calculate successive dividends multiplying by one plus the growth rate in effect until you get the first dividend into the period of normal growth. Then apply the Gordon model. A time line is a must for this problem.) Solution: 13. How would you advise clients on the stock as an investment under the following conditions? a. Softek is currently selling at a price very near that calculated in part a of problem 11. b. It is selling near the price calculated in problem 12. c. It is selling at a price slightly above that calculated in part b of problem 11. Solution: a. This could be a good buy because the calculated price is counting on only the success of Alpha, which is fairly certain. Any success from Beta will raise its value further. b. This a risky but not unreasonable investment, because moderate success from Beta is factored into the price. It's a middle of the road opportunity in that actual performance could be better or worse than what is capitalized into the market price. c. This probably isn't a wise investment. Although the firm has good prospects in projects Alpha and Beta, their success is already factored into the market price. Since they aren't likely to do better than the performance included in the model, and could do worse, there's nowhere for value to go but down. This is an important general point with respect to investing. Students tend to confuse good business prospects with a good investment. A firm with a good future isn't a particularly good investment if its current price already reflects those optimistic expectations. 14. Garrett Corp. has been going through a difficult financial period. Over the past three years, its stock price has dropped from $50.00 to $18.00 per share. Throughout this downturn, Garrett has managed to pay a $1.00 dividend each year. Management feels the worst is over, but intends to maintain the $1.00 dividend for three more years, after which they plan to increase it by 6% per year indefinitely. Comparable stocks are returning 11%. If these projections are accurate, is Garrett stock a good buy at $18.00? How do you think the market feels about Garrett’s management? Solution: b. At 11%, the PV of the cash flows is $17.94. This is very close to the current market price of the stock, so apparently the market has some confidence that Garrett will be able to deliver on its earnings and dividend projections. Garrett stock is not a bargain, but appears to be priced just about right. 15. General Machine Works Inc. (GMW) has been losing money for some time but has managed to maintain an annual dividend of $1.. The company’s strategy is to restructure by getting smaller while working on labor and product line problems at the same time. Once that’s done management feels the firm will return to profitability and begin a long period of growth at about 3% per year. GMW’s stock price has been declining steadily for some time and is now the neighborhood of $20 per share. You’re an analyst for Barnstead and Heath, a small brokerage firm that employs a number of financial consultants who advise clients on stock investments. Some of the consultants feel that GMW’s strategy will work as planned and have asked you if they should tell their clients that this is a good time to buy GMW stock. How would you advise them? Assume clients demand a return of about 10% and that dividends will shrink by 10% per year for 3 years. Solution: We’ll approach this problem by modeling GMW management’s assumptions using the two stage growth model assuming a negative 10% growth rate for three years followed by an indefinite period of normal growth at 3%. Our goal will be to see if the model gives us an intrinsic value that exceeds $20 per share. If it does, now might be a good time to buy the stock. If our result is below that price, however, the implication is that our investors should stay away from GMW at this time. First draw a time line out four years and walk the dividends forward until one period after the assumed growth rate changes. Start with D0 = $1.00 and multiply successively in the first three periods by (1+g1) which is .9 in this case since g1 is -10%. Then multiply by 1.03 for D4 16. Sudsy Inc. recently paid an annual dividend of $1.00 per share. Analysts expect that amount to be paid for three years after which dividends will grow at a constant 5% per year indefinitely. The stock is currently trading at $20, and investors require a 15% return on similar issues. Has the stock market properly priced Sudsy’s stock? Solution: We’ll solve this problem using a variant on the two stage growth model with a 0% first stage growth rate. The stock’s value today will be the sum of the present value of three $1 dividends plus the present value of all dividends to be paid after 5% growth starts in year 4. Use the present value of an annuity formula to calculate the present value of the first three dividends. PVA =PMT [PVFAk,n] = $1.00[PVFA15,3] = $1.00[2.2832] = $2.28 Then apply the Gordon Model at the end of year three to get the present value of the growing stream of future dividends at that time. This figure is the projected price of the stock at the end of year three. P3 = D4/(k-g) = $1.00(1+.05) / (.15-.05) = $10.50 This sum is discounted back three years as an amount for a current present value. PV = PV [PVFAk,n] = $10.50 [PVF15,3] = $10.50[.6575] = $6.90 The stock’s price today is the sum of these present values. P0 = $2.28 + $6.90 = $9.18 which is substantially less than $20. Hence the stock is significantly overvalued. Pricing Preferred Stock: Concept Connection Example 8.6, Page 370 17. Blackstone Corporation's $7 preferred was issued five years ago. The risk-appropriate interest rate for the issue is currently 11%. What is this preferred stock selling for today? Solution: 18. Fox Woodworking Inc. issued preferred shares at a face value of $50 to yield 9% 10 years ago. The shares are currently selling at $60. What return are they earning for investors who buy them today? Solution: 19. The following preferred stocks are returning 8.5% to their owners: Solution: Current return = $ Dividend / Current price and $ Dividend = (Dividend %) (Issue price) Substituting Current return = [(Dividend %) (issue price)] / Current price Solving for Issue price yields Issue price = (current return) (current price) / dividend % Stock A: Issue price = .085($14.71) / .05 = $25.00 Stock B: Issue price = .085($41.18) / .07 = $50.00 Stock C: Issue price = .085($129.41) / .11 = $100.00 20. Koski and Hass (K&H) just paid a $2 dividend which is expected to grow at 5% indefinitely. The return on comparable stocks is 9%. What percent of the intrinsic value of K&H stock is derived from dividends paid more than 20 years into the future? Solution: Use the Gordon Model to estimate the stock’s intrinsic value: P0 = D0(1+g) / (k-g) = $2.00 (1.05)/(.09 - .05) = $52.50 The PV of all of the dividends after the first 20 is found by estimating the value of the stock after 20 years of growth at 5%, and discounting it back to the present at 9%. Stock price in 20 years = $52.50 (1.05)20 = $139.30 The present value of that amount is $139.30/(1.09)20 = $24.86 Therefore, $24.86/$52.50 or about 47.4% of the intrinsic value of the stock comes from dividends more than 20 years into the future. Stock Options: Concept Connection Example 8.7, Page 380 21. Seth Harris is an avid investor who likes to speculate on stock price changes. Lately he’s become bored with the slow movement of most stock prices and thinks options might be more exciting. He’s been following the stock of Chelsea Club Inc., a women’s apparel manufacturer. Chelsea’s stock price has been stable for more than a year, but Seth is convinced it will increase in the near future but probably not rapidly. Amanda Johnson owns 1,000 shares of Chelsea Club purchased a year ago at $37. She thinks the stock’s price will continue in the upper $30s indefinitely and may even fall a little. Her broker has recommended writing options as a source of income on stagnant stocks. Chelsea is selling for $38, and six month call options at a $36 strike price sell for $4. This morning Amanda wrote call options on her 1,000 shares which Seth bought through an options exchange. At the time of that transaction: a. What was the intrinsic value of an option? b. What was the option’s time premium? c. Was the call in or out of the money? d. How much has Amanda invested? e. What is the most Seth can make or lose? f. What is the most Amanda can make or lose? It’s almost six months later, Chelsea is selling for $44, Amanda’s options are about to expire, and Seth exercises. g. What is Seth’s profit or loss? h. What is Amanda’s profit or loss? i. Does Amanda incur an “opportunity loss?” If so how much is it? j. What would Amanda’s profit or loss have been if her call had been written naked. Solution: c. The call option was in the money because the stock’s market price was above the options strike price. d. Amanda committed the shares she had previously purchased for $37 offset by the receipt of the option price of $4. On a per share basis her investment was Investment = PS – POp = $37 - $4 = $33 On 1,000 shares her investment was $33,000. e. Seth can’t lose any more than the option price of $4, $4,000 in total. In theory, there’s no limit to what he can make. f. The most Amanda can make is the option price of $4 or $4,000. This happens if Seth doesn’t exercise the options. If he does, she’ll have to sell him shares for $36 that she bought at $37. Hence her per share gain will be reduced by $1 to $3, for a total of $3,000. That’s the worst she can do on paper. In fact, she’ll have an “opportunity loss” of the difference between $36 and the share price at the time of exercise, reduced by the option price. COMPUTER PROBLEMS 22. The Rollins Metal Company is engaged in a long-term planning process and is trying to choose among several strategic options, which imply different future growth rates for the company. Management feels that the main benefit of higher growth is that it enhances the firm's current stock price. However, high growth strategies have a cost in that they generally involve considerable risk. Higher risk means that investors demand higher returns which tends to depress current stock price. Management is having a hard time evaluating this cost-benefit trade-off because growth and risk are conceptual abstractions. In other words, it's hard to visualize how growth and risk interact with each other as well as with other things to produce stock prices. Management can, however, intuitively associate each strategy option with a growth rate and a required rate of return implied by risk. You are a financial consultant who's been hired to help make some sense out of the situation. You feel your best approach is to develop a systematic relationship between return, growth and stock price that you can show to management visually. Use the STCKVAL program to develop the following chart assuming the strategic options result in different constant growth rates that start immediately. The firm's last dividend was $2.35 per share. The stock price is relatively constant along diagonal lines within the matrix where (k-g) is also constant. That implies the main driver of value in the model is the difference between the growth rate and the return (the denominator). If that reflects reality, it makes little sense to go after the high growth-high return situations in the lower right, as they imply a high risk of failure. According to the model, prices nearly as high can be achieved at lower risk levels where required returns are similarly low. This interpretation strains the model's credibility. 23. Suppose the strategic options available to the Rollins Company in the last problem result in temporarily enhanced growth. Each option can be associated with a super normal growth rate that lasts for some period after which growth returns to the firm's normal 5%. Further suppose the duration of the super normal growth is a variable that can also be affected by strategic policy. Use the STCKVAL program for two-stage growth to develop the following chart assuming a required return of 10%. The benefit of extending the duration of the super normal growth is substantial. For the figures shown it is in the same order of magnitude as raising the rate of super normal growth. Hence, it's a viable policy option. DEVELOPING SOFTWARE 24. Program your own two-stage growth model for two years of super normal growth (g1) followed by normal growth (g2) lasting forever. Treat both growth rates, the last dividend (D0), and the required rate of return (k) as inputs. Here's how to do it. Answer: 1. Lay out four cells horizontally in your spreadsheet (to represent a time line starting with time zero). 2. Put D0 in the first cell. 3. Form the next two cells by multiplying the one before by (1+g1). 4. Form the fourth cell by multiplying the third by (1+g2). 5. Calculate P2 in another cell using the Gordon Model with the fourth cell in the numerator and (k- g2) in the denominator. 6. Form P0 as the sum of the present values of the middle two cells in the time line and the present value of the cell carrying P2. 25. Program a model for three years of super normal growth. Answer: To model three years of "super normal growth" in a financial or business context, you'd typically use a supernormal growth model that assumes a high growth rate for the first few years, followed by a stable or constant growth rate afterward. Here's the formula for valuing a company with supernormal growth: 1. Supernormal growth phase (Year 1 to Year 3): Where FCF0 is the current free cash flow, and g1, g2, g3 are the high growth rates for years 1, 2, and 3. 2. Terminal value after Year 3 (assuming a constant growth rate g4 3. Present Value of Free Cash Flows: You need to substitute the specific values for FCF0, growth rates, and discount rate to calculate the final present value of the business. Solution Manual for Practical Financial Management William R. Lasher 9781305637542
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