Valuation of Bonds and Stocks, Study notes of Financial Economics

Download Valuation of Bonds and Stocks and more Study notes Financial Economics in PDF only on Docsity! 33 3. VALUATION OF BONDS AND STOCK Objectives: After reading this chapter, you should be able to: 1. Understand the role of stocks and bonds in the financial markets. 2. Calculate value of a bond and a share of stock using proper formulas. 3.1 Acquisition of Capital Corporations, big and small, need capital to do their business. The investors provide the capital to a corporation. A company may need a new factory to manufacture its products, or an airline a few more planes to expand into new territory. The firm acquires the money needed to build the factory or to buy the new planes from investors. The investors, of course, want a return on their investment. Therefore, we may visualize the relationship between the corporation and the investors as follows: Investors Capital   Return on investment Corporation Fig. 3.1: The relationship between the investors and a corporation. Capital comes in two forms: debt capital and equity capital. To raise debt capital the companies sell bonds to the public, and to raise equity capital the corporation sells the stock of the company. Both stock and bonds are financial instruments and they have a certain intrinsic value. Instead of selling directly to the public, a corporation usually sells its stock and bonds through an intermediary. An investment bank acts as an agent between the corporation and the public. Also known as underwriters, they raise the capital for a firm and charge a fee for their services. The underwriters may sell $100 million worth of bonds to the public, but deliver only $95 million to the issuing corporation. A corporation that is selling its bonds, or stock, for the first time may have to pay a higher percentage of the total value as underwriters' fees. Well-established companies with strong financial record can sell their stock or bonds with relative ease and so the underwriters' fees are lower. When a corporation issues its stock for the first time, it is known as an IPO, or an initial public offering. Later, the investors buy and sell the stock in the secondary markets, such as the New York Stock Exchange. 3.2 Valuation of Bonds Corporations sell bonds to borrow money from the investors. As a financial instrument, a bond represents a contractual agreement between the corporation and the bondholders. Eventually the corporation has to repay the principal to the investors and pay interest to them in the meantime. Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 34 Typically, a bond has the following features: 1. The face value, F. The face value of a bond, or its principal, is usually $1,000, which means that the investment in bonds is a multiple of $1,000. The total value of the bonds issued by a company at a certain time could be millions of dollars. 2. The market value, B. Although a bond may have a face value of $1000, it may not sell at $1000 in the bond market. If the issuing company is not doing well financially, its bonds may sell for less than $1000, perhaps at $950. If you look up their price on the Internet, or some financial newspaper, it is listed as 95. This means that the bond is selling at 95% of its face value, or $950. The bond is selling at a discount. If the market value of the bond is more than $1,000, and then it is selling at a premium. A bond with a market value less than $1,000 is selling at a discount, and a bond, which is priced at its face value, is selling at par. 3. The time to maturity, n. There is a definite date when a bond matures. At that time, the corporation must pay the face value of the bonds to the bondholders. This could be from as little as 5 years to as long as 100 years. The short-term bonds are also called notes. The companies that are starting out, do not want to carry a long-term debt burden and so they issue relatively short-term bonds. Well established companies prefer to use long-term debt in their capital, especially when the interest rates are low. 4. The coupon rate, c. This is the stated rate of interest of the bonds. For example, a bond may be paying 8% interest to the bondholders. The dollar amount of interest C, is the product of the face amount of the bond and the coupon rate. We may write this as C = cF The 8% bond is paying .08*1000 = $80 per year to the investors. The corporations generally pay the interest semiannually, so the 8% bond really pays $40 every six months. For example, a bond may pay interest on February 15 and August 15 in a calendar year. If an investor buys a bond between the interest payments dates, let us say on May 1, then he has to pay the accrued interest, the interest for the period February 16 to May 1, to the seller of the bond. The interest rate on a bond depends primarily on two factors. First, it depends on the general level of interest rates in the economy. At the time of this writing, the interest rates are at their historical lows due to the easy-credit policy of the Federal Reserve Board. This allows companies to borrow money at lower rates enabling them to expand their business easily. At other times, the interest rates may be quite high, partly because of Fed's tight money policy. This forces all companies to borrow at a higher rate of interest. Second, the company, which is issuing bonds, may not be in a strong financial condition. The sales are down, the cash flow is small, and the future prospects of the company are not too bright. It must borrow new money at a higher rate. On the other hand, well- Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 37 Normally, when an investor buys a bond he has to pay the accrued interest on the bond. This is the interest earned by the bond since the last interest payment date. Occasionally some bonds trade without the accrued interest and they are thus dealt in flat. Due to poor financial condition of the company, such bonds sell at a deep discount from their face value. An investor buys a bond for its future cash flows. To evaluate a bond, therefore, we have to find the present value of the cash flows. We use a very fundamental concept in finance: The present value of a bond is simply the present value of all future cash flows from the bond, discounted at the risk-adjusted discount rate. We may use this concept to find the value of any financial instrument, whether it is a stock, a bond, or a call option. For a bond, we need to find the present value of all the interest payments and the present value of the final payment, namely, the face amount of the bond. We may write it mathematically as B =  i=1 n C (1 + r) i + F (1 + r) n In the above equation, we define B = the present value, or the market value of the bond C = cash flow from the interest of the bond, and for semiannual interest payments, it should be one-half of the annual interest paid by the bond n = the number of semiannual payments received F = face amount of the bond r = risk-adjusted discount rate for the bond. For riskier bonds, the discount rate is higher. We can do the summation by using (2.5),  i=1 n C (1 + r) i = C [1 − (1 + r) −n ] r (2.5) Thus, we can find the value of a bond by Bond value, B = C [1 − (1 + r) −n ] r + F (1 + r) n (3.1) Consider a bond that is never going to mature, that is, it is a perpetual bond. An investor will buy such a bond and earn interest on it. The bond will pay a steady income forever. If he no longer needs an income, he can simply sell the bond to another investor. The bond represents a perpetual income stream and we can evaluate it by using (1.6), Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 38  i=1 ∞ C (1 + r) i = C r (1.6) For perpetual bonds, B = C r (3.2) It is also possible to get (3.2) by setting n =  in (3.1). Another type of a bond is a zero-coupon bond. Such a bond does not pay any interest but it does pay the principal at maturity. An investor who does not need a steady income, but requires $1000 at a future time, may buy such a bond. The value of a zero-coupon bond is found by letting C = 0 in (3.1). The result is For zero-coupon bonds, B = F (1 + r) n (3.3) Suppose you have the option of keeping your money in a savings account that pays interest at the rate of 6% per year, compounding it every year. You plan to keep this money for the next 10 years and then withdraw it. You would like to have $1000 after ten years. How much money should you deposit right now? The answer is, the present value of $1000 discounted at the rate of 6% per year. That is, 1000/1.06 10 = $558.48. Suppose a zero-coupon bond with face value $1000 is also available, which matures after 10 years. If you can buy this bond for $558.48, it will serve your purpose perfectly. It will also give you $1000 at maturity, after 10 years. Zero-coupon bonds are sold at a discount; occasionally well below their face value. Those investors who do not need steady income from bond investments will buy zero- coupon bonds. They are perhaps saving for retirement, or for children’s education. Those corporations that do not have enough money to pay the interest payments due to cash- flow problems may issue zero-coupon bonds. US Treasury bills are zero-coupon bonds. You buy them at a discount and when they mature, you get their face amount. The holder of a convertible bond is entitled to convert it into a fixed number of shares of the stock of the issuing corporation at any time before maturity. As the stock price rises, the value of the bond also rises. Occasionally, convertible bonds sell well above the par value. The convertible bonds are quite difficult to evaluate. An investor buys a bond for its yield, which is the annual return on the investment. We may define the current yield, y, of a bond as the annual interest C in dollars, divided by the market price of the bond B in dollars. In symbols, Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 39 y = C/B (3.4) This represents the return on investment provided one holds the bond for a short time. For instance, you buy a 5% coupon bond at 60. Then the annual interest received is $50, and the market price of the bond $600. Dividing one by the other, we get the current yield as y = 50 600 = 8.33% Suppose a bondholder wants to hold the bond all the way to its maturity. Then he may be interested to find its yield-to-maturity, Y. By definition, The yield-to-maturity of a bond is that particular value of r that will equate the market value of a bond to its calculated value by using (3.1) In practice, one can calculate the yield to maturity accurately by using Excel, WolframAlpha, or Maple. When you hold a bond to maturity, you receive money in the form of interest payments, plus there is a change in the value of the bond. If you have bought the bond at a discount, it will rise in value reaching its face value at maturity. On the other hand, the bond may drop in price if you have bought it at a premium. In any case, it should be selling for its face value at maturity. The total price change for the bond is (F − B) which may be positive or negative depending upon whether F is more or less than B. On the average, the price change per year is (F − B)/n. The average price of the bond for the holding period is (F + B)/2. We may calculate the yield to maturity of a bond, approximately, by dividing the average annual return by the average price. We write it as follows. Y ≈ annual interest received + annual price change average price of the bond for the entire holding period Or, Y ≈ C + (F − B)/n (F + B)/2 (3.5) Consider a bond with coupon rate 8% and 10 years to maturity. If the discount rate is 8%, then the bond is selling at par. Its value will remain $1000 with the passage of time. This is shown as the straight horizontal line in the middle of Fig. 3.3. If the discount rate is 6%, the bondholders’ required rate of return is 6%. Since the bond is providing 8% coupon, it is more than the required rate of return. This will make the market value of the bond more than its face value and the bond will be selling at a premium. Calculations indicate that it should sell for $1148.77. As the time passes, the time to maturity gets shorter, and the value of the bond slides along the top curve until it becomes $1000 at maturity. Note that the curve is not a straight line. Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 42 3.4. In 2001, a newspaper listed a bond as Slimline Corp 6s13 and showed its price as a two-digit number with a fraction. The bondholders had a required rate of return of 12% for these bonds. Find the (approximate) price of the bond as shown in the newspaper. The numbers 6s13 mean that the bond pays interest at the rate of 6% per year, and it will mature in the year 2013. In 2001, the bond still has 12 years before it matures. There are 24 semiannual periods, and the semiannual interest is $30. Using (3.1), B =  i=1 24 30 1.06 i + 1000 1.06 24 = 30(1 − 1.06 −24 ) .06 + 1000 1.06 24 = $623.49 The price of the bond is $623.49. The newspaper listed it as 62 3 /8. ♥ 3.5. The British Government issued perpetual bonds in 1821 with a coupon rate of 3% and face value of £100. Calculate the price of such a bond in 2008 when the riskless interest rate in London is 4.85%. With a 3% coupon, the £100 bond will pay £3 in interest annually forever. Put C = 3 and r = .0485 in (3.2) to get B = C/r = 3/.0485 = £61.86 ♥ The bond should be selling for £61.86. ♥ 3.6. In 2001, a newspaper lists a bond as AT&T 10s05 and its price as 105. Find the approximate yield to maturity for this bond. The bond will mature in 2005 and it has another 4 years before maturity. Its price is $1050 and its face value is $1000. Using (3.5), we have YTM ≈ annual interest received + annual price change average price of the bond for the entire holding period Or, YTM ≈ 100 + (1000 − 1050)/4 (1000 + 1050)/2 = 0.0854 ≈ 8.54% ♥ The reason for the yield to be less than 10% is that an investor has paid too much money for it, $1050, and he will get back only $1000 at maturity. 3.7. Berks Corp bonds pay interest semiannually and they will mature in 10 years. Currently a $1000 bond sells for $800 and the bondholders require annual return of 9%. Calculate the coupon rate of these bonds. The number of payments that investors will receive, n = 20. The face amount F = $1000 and the current price of the bond B = $800. The required rate of return r = 9% annually, or 4.5% semiannually. Suppose the coupon rate is c. The annual interest payment is Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 43 found by multiplying the coupon rate by the face amount of bond, or c(1000). The semiannual interest payment is half as much, or 500c. Substituting all this in (3.1), we get 800 =  i=1 20 500c 1.045 i + 1000 1.045 20 = 500c(1 − 1.045 −20 ) .045 + 1000 1.045 20 Moving things around, we get 800 − 1000 1.045 20 = 500c(1 − 1.045 −20 ) .045 Or,       800 − 1000 1.045 20      .045 500(1 − 1.045 −20 ) = c This gives c = .0592495  5.925% ♥ The following instruction gets the answer on WolframAlpha as c = .0592495. WRA 800=Sum[500*c/1.045^i,{i,1,20}]+1000/1.045^20 To do the problem on an Excel sheet, proceed as follows. The calculation assumes that the bonds pay interest semiannually. The answer in cell B5 is .05925, or 5.925%. A B 1 Face value, $ 1000 2 Time to maturity, years 10 3 Market price, $ 800 4 Required rate of return .09 5 Unknown coupon rate, c =B4*(B3-(1+B4+1/4*B4^2)^(-B2)*B1)/B1/(1-4^B2*(1/(2+B4)^2)^B2) 3.8. In 2001, Milhous Co 12s09 bonds are listed as 97, and they pay interest semiannually. If your required rate of return is 13%, how much should you pay for one of these bonds? Would you buy them at the market price? The term “12s09” means that the coupon rate of the bonds is 12% and that they will mature in the year 2009. If the bond is listed as 97, it is selling at 97% of its face value. A $1000 bond is selling for $970. The bonds will mature after 8 years, meaning there are 16 semiannual periods. The interest per period is $60, and the required rate of return is 6.5% per period. The intrinsic value B of the bond is B =  i=1 16 60 1.065 i + 1000 1.065 16 = 60(1 − 1.06 −16 ) .065 + 1000 1.065 16 = $951.16 The intrinsic value of the bonds is $951.16 each and, therefore, one should not buy the bond at the market price of $970. ♥ Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 44 3.9. You have bought a zero-coupon bond for $300. It will mature in 6 years and pay the face value of $1,000. Assuming annual compounding, what is the implied rate of return for the bond? A zero-coupon bond pays no interest. However, one can buy the bond at a deep discount from its face value. When the bond matures, the holder is entitled to receive the face amount of the bond, which is generally $1,000. The present value of the bond is $300, and its future value $1000. This is a single payment problem, thus 1000 = 300(1 + r) 6 Or, 1 + r = (1000/300) 1/6 = 1.2222 Or, r = 22.22% ♥ 3.10. Albert Company bonds, with current yield 12%, will mature after 10 years. The coupon rate of these bonds is 10%. Calculate their market price and the yield to maturity. By definition, the current yield of the bond is equal to the annual interest payment from the bond, divided by the market value of the bond. Write it as Current yield = Annual interest payment from the bond Market price of the bond With 10% coupon, the annual interest from the bond is $100. Putting numbers, .12 = 100 B Or, B = 100/.12 = $833.33 ♥ To find their yield to maturity, we use (3.5), which gives Y = 100 + (1000 − 833.33)/10 ½(1000 + 833.33) = 12.73% ♥ Problems 3.11. The WSJ lists a bond as Acme 9s13 and the price as 89.875. If your required rate of return is 10%, would you buy one of these bonds in 2001? B = $931.00, yes. ♥ 3.12. Bakersfield Company 8.5s26 bonds pay interest semiannually, and they are quoted in the WSJ as 90. If your required rate of return is 10%, would you buy these bonds in 2011? B = $884.71, no. ♥ Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 47 3.36. A bond pays interest semiannually and it will mature after six years. The required rate of return by the bondholders is 14% per year, and the face amount of the bond is $1000. If the market price of the bond is $920.60, find its coupon rate. 12% ♥ 3.37. Bennett Company bonds will mature after 5 years and they are selling at 80.175% of their face value. The bonds pay interest annually. The required rate of return by the bondholders is 12%. Find the coupon rate of these bonds. 6.5% ♥ 3.38. Cleveland Company bonds have current yield 8% and yield to maturity 9%. They are selling at $725.50 per $1000 bond. Find the time to maturity for these bonds. 14 years ♥ 3.39. You are planning to buy Ford 6¼s10 bonds in 2001 with the price at 79. The bonds pay interest semiannually. If your required rate of return is 11%, would you buy these bonds? B = $732.91, no. ♥ 3.40. Checking The Wall Street Journal, you find that the Burns Co. 7s21 bonds are quoted as 66. The bonds pay interest semiannually. If in 2001 your required rate of return for such bonds is 12%, would you buy Burns bonds? B = $623.84, no. ♥ 3.3 Valuation of Stock Myron J. Gordon, 1920-2010 There are two types of investors, the stockholders, and the bondholders, who provide the financial capital of a company. The stockholders are the real owners of the corporation. They have an equity stake in the business. The bondholders merely lend the money to the company. They receive a set rate of return determined by the coupon rate on the bonds. The stockholders receive dividends. However, the company does not guarantee dividends, and some companies do not pay any dividends at all. The bondholders receive regular, guaranteed interest payments. If the bondholders do not receive the interest payments on time, they have a right to sue the company and seize the assets of the firm. The bondholders also receive the face value of the bonds at maturity. The stockholders are taking on more risk because their dividends are dependent on uncertain cash flows. To conserve cash a company may resort to eliminating cash dividends. The bondholders' position is much safer. The company must pay the interest before it pays the income tax or dividends. The stockholders participate in the growth of the company. They also bear the losses when the times are tough. The bondholders cannot participate in the growth of the company. At the most, they can receive the interest payments and the face value of the bonds. Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 48 The stockholders have the right to elect the board of directors of the corporation. The board is responsible for the implementation of major decisions at the company, such as the appointment of the president. In this way, the stockholders can participate in the management of the firm. The bondholders cannot participate in the running of the company. The cash flows for a stock are quite random. The firm faces economic uncertainties. There is the possibility of labor strife, or shortage of raw materials, or unexpected action by the competitors. Each turn of events can make the earnings of the company unpredictable. The sudden changes in the stock price are essentially due to the changes in the financial condition of a firm. A look at the stock pages in a newspaper, with up and down movements of the stock prices, makes this idea quite clear. The stockholders are sharing this risk of the company. The valuation of the equity of a firm is a much more difficult process due to the inherent uncertainty of the cash flows. Equation (3.6) gives a general formula for the stock valuation. However, we derive this formula under severe restrictions: (1) The growth of the company is uniform from year to year, that is, the growth rate g is constant. This is not true for actual firms. The company may grow by 10% and it may drop in value by 5% the following year. (2) The growth will continue forever. This assumption is also unrealistic, because the companies go through a supernormal growth period for a while. Then the competition gets in and slows the growth. Mature companies show little growth, and they may even shrink in value. (3) The dividends paid out by the firms will also grow at the same rate as the overall growth of the company. In real life, the companies set their dividend policy based on their investment needs, their cash flow projections, and their capital structure. (4) The required rate of return of the stockholders is greater than the growth rate of the company. This is strictly a mathematical requirement to make sure that the formula will work properly. Since no firm can meet all these conditions, the formula is only approximately true. To develop the formula, let us suppose that the dividend paid during the current year has been D0. If the dividends are growing uniformly, the dividend next year is (1 + g) times the dividend this year, that is, D1 = D0(1 + g) The dividend available two years from now will be D2 = D1(1 + g) Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 49 and so on. The dividend available after three years should be D3 = D2(1 + g) = D1(1 + g) 2 When we buy the stock we expect to receive dividends D1, D2, D3, ... after one, two, three, ... years. The sum of the future dividends, properly discounted, is just equal to the current price of the stock. Thus P0 = D1 1 + R + D1(1 + g) (1 + R) 2 + D1(1 + g) 2 (1 + R) 3 + ... ∞ We can find the summation using WolframAlpha. WRA P0=Sum[D1*(1+g)^(i-1)/(1+R)^i,{i,1,infinity}] This is an infinite geometric series with first term a = D1 1 + R , and ratio between the terms, x = 1 + g 1 + R . Using (3.2) for the summation of such series, we get P0 = D1 1 + R 1 − 1 + g 1 + R After some simplification, we get the final result as P0 = D1 R − g (3.6) In the above equation, R is the risk-adjusted discount rate. The stocks are much riskier and thus we must use a much higher discount rate. This discount rate is the required rate of return, required by the investor who is putting his money at risk. Usually called Gordon’s growth model, after Myron J. Gordon who initially developed the above equation in 1959 at University of Toronto. Besides common stock, a firm may also issue preferred shares of stock. The preferred stock lies somewhere between the common stock and the bonds of a company in terms of priority of claims on the assets of the firm. The preferred stockholders get constant dividends and they are not entitled to participate in the growth of the company. Thus substituting g = 0 in (3.5), we get the value of a preferred share as P0 = D R (3.7) Comparing (3.7) and (3.2), we may think of preferred stock to be like a perpetual bond with dividends D annually, and discount rate R. Sometimes the preferred stock is Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 52 E(D1) = 0.3(4.50) + 0.7(5.00) = $4.85. Using P0 = D1 R − g (3.6) we get, P0 = 4.85 .12 − .08 = $121.25 ♥ 3.45. Wilson Corp preferred stock pays annual dividend of $4. The preferred stockholders have a required rate of return of 11%. Find the price of a Wilson preferred share. The preferred stock does not participate in the growth opportunities of a company. Its dividend remains fixed. We can evaluate a preferred stock by using (3.7) with the understanding that g = 0. Further, R = .11, and D = 4. Thus P0 = 4/0.11 = $36.36 ♥ 3.46. You bought a stock at $45 last year. After one year, you received a dividend of $2.50, and then sold the stock for $49.00. Calculate the rate of return on your investment. The total return of a stock is, by definition Total return on a stock = dividend received + capital gain purchase price Thus R = 2.50 + 4 45 = .1444 = 14.44% ♥ 3.47. Rudolph Co stock has just paid its annual dividend of $2.25. The expected growth rate of Rudolph is 7% in the long run. If your required rate of return is 16%, how much should you pay for a share of Rudolph stock? P0 = D1 R − g = D0(1 + g) R − g = 2.25(1.07) 0.16 − 0.07 = $26.75 ♥ Problems 3.48. Invercargill Company stock has paid a $6.00 annual dividend in 2003 and a $6.50 dividend in 2004. This growth in dividends will continue in the future. The stockholders of Invercargill require a 17% return on their investment. Calculate the price of one share of Invercargill stock in 2005. $88.02 ♥ 3.49. Boston Corporation stock currently pays $6 annual dividend and sells at $62 per share. The company expects to show continued growth at the rate of 4% per year. Find the required rate of return by the stockholders. 14.06% ♥ Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 53 3.50. A stock sells at $54 a share. Its current dividend is $2.00 a share, and the stockholders require a return of 16% on their investment. Find the expected growth rate of the dividends of this stock. 11.86% ♥ 3.51. Cape Town Company stock paid a dividend of $4.00 in 1999 and $3.75 in 1998. These dividends reflect the long-term growth rate of the company. If your required rate of return is 16% for Cape Town stock, how much should you pay for a share in 1999? $45.71 ♥ 3.52. Adams Company stock paid a dividend of $3.00 last year, and $3.25 this year. The increase in the dividend is similar to the long-term growth of the company. Considering the risk, your required rate of return from this stock is 14%. Find the price of the stock. $62.13 ♥ 3.53. The expected dividend of Arnold Co for next year has the following probability distribution: 20% $2.00, 30% $2.25, 40% $2.50, and 10% $2.75. The growth rate of Arnold is almost zero. If your required rate of return is 12%, find the price of an Arnold share in your estimation. $19.58 ♥ 3.54. You feel that Exxon has a long-term growth rate of 5%. Its dividend next year has the following probability distribution: 30% $4.50, 30% $4.75, and 40% $5.00. What should you pay for Exxon stock if your required rate of return is 12%? $68.21 ♥ 3.55. The current price of Ford stock is $50 a share and it has paid a dividend of $4 this year. The required rate of return for Ford shareholders is 16%. What is the expected growth rate of Ford? 7.407% ♥ 3.56. Bradford Corp preferred stock pays a quarterly dividend of $1.25 and the stockholders have a required rate of return of 12% annually on their investments. Assuming quarterly compounding, find the price of a Bradford preferred share. $41.67 ♥ 3.57. The estimates of long-term growth for Glenn Co are: 5% (probability 50%), 6% (probability 30%), or 7% (probability 20%). Its current dividend is $2 and the investors' required rate of return is 12%. Find the price of one share of Glenn stock. $34.16 ♥ 3.58. Ekberg Mining Co is winding down its business in 1997. It will pay dividend of $7 per share in 1998, $6 in 2000, $5 in 2001, $15 in 2003, and then it will go out of business. Suppose you pay 28% tax on dividend income and your after-tax required rate of return is 11%, how much should you pay for a share of Ekberg? Also, assume that the loss of the stock cannot offset your other income. $15.84 ♥ 3.59. Reno Corporation stock has just paid its annual dividend of $2.00. This dividend will become $2.10 next year, in line with the long-term growth record of the company. Considering the risk of the company, the stockholders have a 15% required rate of return. Find the price of one share of Reno stock. $21.00 ♥ Introduction to Finance 3. Valuation of Bonds and Stock _____________________________________________________________________________ 54 3.60. The long-term growth rate of Jackson Corp is 6%. The stockholders have a required rate of return of 13%. The dividend of Jackson this year was $4.40. Find the price of a share of Jackson. $66.63 ♥ 3.61. Moscow Company has paid a constant dividend of $3 per share every year, and it expects to do so in the future. If your required rate of return for this investment is 17%, what should you pay for a share of Moscow stock? $17.65 ♥ 3.62. Dexter Company stock sells at $53 a share. The annual dividend on this stock is $2 per share this year and it should be $2.25 per share next year, which is in line with its long-term growth rate. Find the required rate of return on this stock. 16.75% ♥ Multiple Choice Questions 1. For a bond selling at its face value, 5 years before maturity, A. the yield to maturity equals its current yield B. the bond should have zero coupon C. the coupon rate is more than its current yield D. the coupon rate must be equal to the prime rate 2. For the yield-to-maturity of a bond to be equal to its current yield, A. the bond must be selling at a discount B. the bond should have zero coupon C. the bond must sell at its face value D. coupon rate must be equal to the prime rate 3. A bond is listed in WSJ as Ford 8.5s17 and priced as 85. This means A. Its semiannual interest payment is $85 B. Its maturity date is unknown C. Its price is $85 D. Its current yield is 10%. 4. For a perpetual bond, A. It is not possible to calculate its current yield B. The face amount is unknown C. The market price is inversely proportional to the interest rates D. The coupon rate is not known 5. Gordon's growth model does not assume that A. the rate of growth of dividends is constant B. the growth will continue forever C. the company must pay all its earnings in dividends D. the required rate of return by the stockholders is greater than the rate of growth of the company