Chapter 10Discussion Questions 10-1. How is valuation of any financial asset related to future cash flows? The valuation of a financial asset is equal to the present value of future cash flows. 10-2. Why might investors demand a lower rate of return for an investment in Exxon Mobil as compared to United Airlines? Because Exxon Mobil has less risk than United Airlines, Exxon Mobil has relatively high returns and a strong market position; United Airlines has had financial difficulties and emerged from bankruptcy in 2006. 10-3. What are the three factors that influence the required rate of return by investors? The three factors that influence the demanded rate of return are: The real rate of return The inflation premium The risk premium 10-4. If inflationary expectations increase, what is likely to happen to yield to maturity on bonds in the marketplace? What is also likely to happen to the price of bonds? If inflationary expectations increase, the yield to maturity (required rate of return) will increase. This will mean a lower bond price. 10-5. Why is the remaining time to maturity an important factor in evaluating the impact of a change in yield to maturity on bond prices? The longer the time period remaining to maturity, the greater the impact of a difference between the rate the bond is paying and the current yield to maturity (required rate of return). For example, a two percent ($20) differential is not very significant for one year, but very significant for 20 years. In the latter case, it will have a much greater effect on the bond price. S10-1 10-6. What are the three adjustments that have to be made in going from annual to semiannual bond analysis? The three adjustments in going from annual to semiannual bond analysis are: Divide the annual interest rate by two. Multiply the number of years by two. Divide the annual yield to maturity by two. 10-7. Why is a change in required yield for preferred stock likely to have a greater impact on price than a change in required yield for bonds? The longer the life of an investment, the greater the impact of a change in the required rate of return. Since preferred stock has a perpetual life, the impact is likely to be at a maximum. 10-8. What type of dividend pattern for common stock is similar to the dividend payment for preferred stock? The no-growth pattern for common stock is similar to the dividend on preferred stock. 10-9. What two conditions must be met to go from Formula 10-8 to Formula 10-9 in using the dividend valuation model? P0 = D1 Ke - g (10 − 9) To go from Formula (10-8) to Formula (10-9): The firm must have a constant growth rate (g). The discount rate (ke) must exceed the growth rate (g). 10-10. What two components make up the required rate of return on common stock? The two components that make up the required return on common stock are: The dividend yield D1/Po. b. The growth rate (g). This actually represents the anticipated growth in dividends, earnings, and stock price over the long term. 10-11. What factors might influence a firm's price-earnings ratio? The price-earnings ratio is influenced by the earnings and sales growth of the S10-2 firm, the risk (or volatility in performance), the debt-equity structure of the firm, the dividend policy, the quality of management, and a number of other factors. Firms that have bright expectations for the future tend to trade at high P/E ratios while the opposite is true of low P/E firms. 10-12. How is the supernormal growth pattern likely to vary from the normal, constant growth pattern? A supernormal growth pattern is represented by very rapid growth in the early years of a company or industry that eventually levels off to more normal growth. The supernormal growth pattern is often experienced by firms in emerging industries, such as in the early days of electronics or microcomputers. 10-13. What approaches can be taken in valuing a firm's stock when there is no cash dividend payment? In valuing a firm with no cash dividend, one approach is to assume that at some point in the future a cash dividend will be paid. You can then take the present value of future cash dividends. A second approach is to take the present value of future earnings as well as a future anticipated stock price. The discount rate applied to future earnings is generally higher than the discount rate applied to future dividends. S10-3 Chapter 10 Problems 1. Burns Fire and Casualty Company has $1,000 par value bonds outstanding at 11 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is: a. 6 percent. b. 8 percent. c. 12 percent. 10-1. Solution: Burns Fire and Casualty Company a. 6 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 6%) PVA = $110 × 11.470 = $1,261.70 Appendix D Present Value of Principal Payment at Maturity PV = FV × FVIF (n = 20, i = 6%) Appendix B PV = 1,000 × .312 = $312 Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond $1,261.70 312.00 $1,573.70 S10-4 079. i = 8%) PV = $1.88 c. i = 8%) PVA = $110 × 9.000 × .59 S10-5 .818 = $1.294.215 = $215 Appendix D Appendix B $1.079.104 = $104 Appendix D Appendix B $821.00 $925. i = 12%) PV = $1.59 PV = FV × PVIF (n = 20. i = 12%) PVA = $110 × 7. 8 percent yield to maturity PVA = A × PVIFA (n = 20.98 PV = FV × PVIF (n = 20.00 $1. 12 percent yield to maturity PVA = A × PVIFA (n = 20. (Continued) b.000 × .469 = $821.59 104.98 215.10-1. b.16 PV = FV × PVIF (n = 25. Compute the current price of the bonds if the present yield to maturity is: a. i = 7%) Appendix B PV = $1. 10-2.32 184. i = 10%) PV = $1.654 = $932.092 = $92 $ 932.2.00 $1.077 = $726.32 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25. 10 percent yield to maturity PVA = A × PVIFA (n = 25. i = 10%) PVA = $80 × 9.32 Appendix D Appendix B $726. Midland Oil has $1.00 $818. 7 percent. 7 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 25.184 = $184 Total Present Value Present Value of Interest Payments Present Value of Principal Payments Total Present Value or Price of the Bond b.000 par value bonds outstanding at 8 percent interest. i = 7%) PVA = $80 × 11.116. c. The bonds will mature in 25 years.16 S10-6 . 13 percent.16 92.000 × . 10 percent. Solution: Midland Oil a.000 × . 000 × .256 = $1. 5 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 50. 13 percent yield to maturity PVA = A × PVIFA (n = 25. i = 5%) PVA = $100 × 18.825.60 S10-7 . (Continued) c. 15 percent.047 = $47 Appendix D Appendix B $586.40 47.912. The bonds will mature in 50 years. i = 5%) PV = $1. Solution: Exodus Limousine Company a.40 3.60 Present Value of Principal Payment PV = FV × PVIF (n = 50. Exodus Limousine Company has $1. 5 percent.000 × .10-2. b.60 87. Compute the current price of the bonds if the percent yield to maturity is: a. i = 13%) PVA = $80 × 7. i = 13%) PV = $1.000 par value bonds outstanding at 10 percent interest. 10-3.087 = $87 Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond Appendix D Appendix B $1.330 = $586.00 $633.00 $1.825.40 PV = FV × PVIF (n = 25. 10 1.000 × .10 Referring back to Problem 3.10 PV = FV × PVIF (n = 50.00 = = . Solution: Exodus Limousine Company (continued) PV of Principal Payment $1. i = 15%) PV = $1.661 = $666. (Continued) b. 15 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 50. what percent of the total bond value does the repayment of principal represent? 10-4.000 × 6.001 = $1 Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond 4.00 $667. i = 15%) PVA = $1. part b.10-3.150% Bond Value $667.10 S10-8 . Appendix D Appendix B $666. 10-5. i = 8%) PVA = $110 × 11.00 $1. b.238. i = 8%) PVA = $110 × 8.238.49 Appendix D Appendix B $1.5.49 315.258 = $1.49 PV = FV × PVIF (n = 15.559 = $941. 30 years.337.38 99. i = 8%) PV = $1.38 S10-9 .000 × . Solution: Harrison Ford Auto Company a. 30 years to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 30.315 = $315 Appendix D Appendix B $ 941.256. c.38 Present Value of Principal Payment PV = FV × PVIF (n = 30. i = 8%) PV = $1. 15 years.099 = $99 Total Present Value Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond b.00 $1. 1 year. Compute the price of these bonds for these maturity dates: a.000 × .000 par value bond outstanding that pays 11 percent interest. The current yield to maturity on each bond in the market is 8 percent. Harrison Ford Auto Company has a $ 1. 15 years to maturity PVA = A × PVIFA (n = 15. 926 = $926. 30 years. i = 12%) PV = $1.000 × .86 PV = FV × PVIF (n = 1.86 926. 15 years.00 $1. Kilgore Natural Gas has a $1.00 Appendix D Appendix B $ 101.055 = $724. 1 year.95 33.926 = $101. i = 8%) PVA = $110 × .033 = $33 Total Present Value Present Value of Interest Payments Present Value of Principal Payment Total Present Value or Price of the Bond Appendix D Appendix B $724. Compute the price of the bonds for these maturity dates: a. i = 8%) PV = $1.95 PV = FV × PVIF (n = 30.000 par value bond outstanding that pays 9 percent annual interest. 1 year to maturity PVA = A × PVIFA (n = 1.95 S10-10 .86 6. 30 years to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 30. c. b. i = 12%) PVA = $90 × 8. 10-6.027.000 × . (Continued) c.10-5. The current yield to maturity on such bonds in the market is 12 percent. Solution: Kilgore Natural Gas a.00 $757. 000 × .811 = $612.99 c. 15 years to maturity PVA = A × PVIFA (n = 15.00 Appendix D Appendix B $ 80.37 893.000 × .00 $973. 1 year to maturity PVA = A × PVIFA (n = 1.183 = $183 Appendix D Appendix B $612. i = 12%) PV = $1.37 PV = FV × PVIF (n = 1. i = 12%) PVA = $90 × 6.00 $795.893 = $893.37 S10-11 . i = 12%) PVA = $90 × .893 = $80. (Continued) b.10-6.99 183. i = 12%) PV = $1.99 PV = FV × PVIF (n = 15. .. What is the bond price at 8 percent? b. $1.. What would be your percentage loss on the investment if you bought when rates were 8 percent and sold when rates were 12 percent? 10-9. For problem 6 graph the relationship in a manner similar to the bottom half of Figure 10-2.196..80 S10-12 ..... Also explain why the pattern of price change occurs....30 9....30 Profit. for a bond that matures in 20 years........$ 276.. $1.....80 Purchase price (11%).. $1... 700 Using Table 10-2.7.......50 Profit $276.....196........ Sales price (8%)....04% Purchase Pr ice $920... 920.80 b.. What is the bond price at 12 percent? c...... Solution: Kilgore Natural Gas (Continued) 8. 10-7............ Solution: Assumes 12% Yield to Maturity 15 Years 10 5 a. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent? 800 10-8....$1......196.196..assume interest rates in the market (yield to maturity) go from 8 percent to 12 percent... Assume interest rates in the market (yield to maturity) decline 9% Bond...$1... Solution: a...90 Purchase price (9%)...... $920...... $850.. a........000 a.. Go to Table 10-1 which is based on bonds paying 10 percent interest for 20 years.....000 Par Value from 11 percent to Bond Value 8 percent: $1...30 b. What is the bond price at 11 percent? b.80 30 25 c......50 = = 30.. What is the bond price at 8 percent? 900 c. ..........Sales price (12%)....80 S10-13 ..9% Purchase Price $1..........196............ 850.............$ (345......90 Loss ............90) Loss ($345...........90) = = 28. Based on information in Part a. Using column 2.50 b.170. Maturity 5 year 15 year 30 year Maturity 5 year 15 year 30 year Bond price $1.80 Bond price 927.10. indicate what the bond price will be with a 5-year. Assume the interest rate in the market (yield to maturity) goes down to 8 percent for the 10 percent bonds. Using Table 10-2: a. Based on the information in part a.30 1. d. if you think interest rates in the market are going up. if you think interest rates in the market are going down. and a 30-year time period.90 1. which bond would you choose to own? d. S10-14 . b.080. a 15-year. indicate what the bond price will be with a 5-year. you would want to own the longest-term bond possible to maximize your gain. which bond would you choose to own? 10-10. a 10-year. Using column 3. Assume the interest rate in the market (yield to maturity) goes up to 12 percent for the 10 percent bonds. Solution: a. c.224. Based on information in Part b. and a 30-year period. you would want to own the shortest-term bond possible to minimize your loss. Based on information in part b. c.11 838.50 864. Solution: Jim Busby – Disk Storage Systems Present Value of Interest Payments PVA = A × PVIFA (n = 25.02 59.02 The bond has a value of $1.000 × .157.180.059 = $59 $1.180.000 par value bond pays 14 percent interest.157.098. and it has 25 years remaining until maturity. i = 12%) Appendix B PV = $1. The $ 1. S10-15 . Compute the new price of the bond and comment on whether you think it is overpriced in the marketplace. This indicates his broker is quoting too high a price at $1. 10-11. His broker quotes a price of $1. The current yield to maturity on similar bonds is 12 percent.02.11.843 = $1. Jim is concerned that the bond might be overpriced based on the facts involved. Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage Systems.098.00 $1.02 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25. i = 12%) PVA = $140 × 7. Compute the new price of the bond.. Tom Cruise Lines...021.. Total return.. Present Value of Interest Payments PVA = A × PVIFA (n = 20.. Inflation premium..... Real rate of return Inflation premium Risk premium Total return 3% 3 4 10% Then use this value to find the price of the bond...514 = $1........ These bonds had a 25-year life when issued and the annual interest payment was then 12 percent.. This return was in line with the required returns by bondholders at that point as described below: Real rate of return.00 $1..170.. 3% 5 4 12% Assume that five years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds... i = 10%) Appendix B PV = $1.....68 149.. Risk premium...000 per bond..149 = $149 $1......... Inc......68 S10-16 ...... Inc. i = 10%) PVA = $120 × 8...12.....021. The bonds have 20 years remaining until maturity. Solution: Tom Cruise Lines.000 × . First compute the new required rate of return (yield to maturity)...... issued bonds five years ago at $1..68 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20. 10-12.. 170.68 are basically the same because in both cases we are valuing the present value of a $20 differential between actual return and required return for 20 years. The $20 is assumed to be an annual payment.000. b.13. Explain why the answers to problem 13b and problem 12 are basically the same. c.00 par value to determine a value of $1.000 (or $20) for 20 years at 10 percent. In problem 13b we take the present value of the $20 differential to arrive at $170.000. Solution: Further Analysis of Problem 12 a. PVA = A × PVIFA (n = 20.170.28 b. Further analysis of problem 12: a.28.170. We then add this value to the $1. (There is a slight difference due to rounding in the tables.170.28. we accomplish the same goal by valuing all future benefits at a two percent differential between actual return and required return to arrive at $1.170.28 and problem 12 of $1. i = 10%) PVA = $20 × 8.) 10-13.28 $1. Find the present value of 2 percent × $1.00 170.68. $1.000.514 = $170. Appendix D S10-17 . Add this value to $1. In problem 12.28 c. The answer to problem 13b of $1. . 10-14.... i = 9%) PVA = $110 × 10....205.130.000 per bond. Compute the new price of the bond.. Solution: Good News Razor Co.130. Present Value of Interest Payments PVA = A × PVIFA (n=30.. The bonds have 30 years remaining until maturity.000 × .... Good News Razor Co......... Inflation premium.... i = 9%) Appendix B PV = $1.... These bonds had a 40 year life when issued and the annual interest payment was then 12 percent. First compute the new required rate of return (yield to maturity) 2% 4% 3% 9% total required return Then use this value to find the price of the bond....14.00 Total Present Value Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond $1..075 = $75................14 75.....14 S10-18 .274 = $1. the risk premium is now 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds....00 $1...14 Appendix D Real rate of return Inflation premium Risk premium Present Value of Principal Payment at Maturity PV = FV × PVIF (n=30... This return was in line with the required returns by bondholders at that point in time as described below: Real rate of return. issued bonds 10 years ago at $1. due to favorable publicity... Total return.... Risk premium.. 2% 4 5 11% Assume that 10 years later. .209 = $209...... Total return...... due to bad publicity. This return was in line with the required returns by bondholders at that point in time as described below: Real rate of return.... These bonds had a 25-year life when issued and the annual interest payment was then 8 percent....28 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 15.. Solution: Wilson Oil Company First compute the new required rate of return (yield to maturity)....... Compute the new price of the bond. Wilson Oil Company issued bonds five years ago at $1..... Inflation premium.. 2% 3 3 8% Assume that 10 years later. 10-15.15..... The bonds have 15 years remaining until maturity.. Present Value of Interest Payments PVA = A × PVIFA (n = 15.000 per bond.28 209.......000 × .00 Bond Price = $784........... i = 11%) PVA = $80 × 7......191 = $575..28 S10-19 ... i = 11%) Appendix B PV = $1. Real rate of return Inflation premium Risk premium 2% 3% 6% 11% total required return Then use this value to find the price of the bond.. Risk premium..00 $575.. the risk premium is now 6 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. 96 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 16. a.00 $530. S10-20 .000. Compound rate of growth The bond will grow by 88. Solution: Lance Whittingham IV – Leisure Time Corporation a. i = 10%) Appendix D PVA = $40 × 7.000 par value bond pays 4 percent annual interest and has 16 years remaining to maturity.883 (1+. i = 10%) Appendix B PV = $1.824 = $312. These represent bonds that are trading at well below par value.03 percent based on interpolation).8834). Using Appendix A. What is the current price of the bonds? b. we see the growth rate is between 4 and 5 percent (4. The current yield to maturity on similar bonds is 10 percent.34% current price 530.96 $ 469.96 c. By what percent will the price of the bonds increase between now and maturity? c.16.000 × .04 = = 88. The $1. What is the annual compound rate of growth in the value of the bonds? (An approximate answer is acceptable.34 percent over 16 years.218 = $218 $312.96 b. the future value of $1 and the interest factor of 1. Current price of the bonds Present Value of Interest Payments PVA = A × PVIFA (n = 16.96 218. He has his eye on a bond issued by the Leisure Time Corporation.) 10-16.00 – 530.04 dollar increase $469. Lance Whittingham IV specializes in buying deep discount bonds. Percent increase at maturity Maturity Value Current price Dollar increase Percent increase = $1. 17. The bonds are currently selling for $850. using Formula 10-2.4 (Principal payment) $1.000.54% $910 $910 S10-21 .000) $90 + $150 10 = $510 + 400 $90 + = $90 + 15 $105 = = 11. which is also the amount of principal to be paid at maturity. The annual interest payment is 9 percent ($90). Solution: Crane Optical Company Approximate Yield to Maturity is represented by Y' Annual interest payment + Y' = Principal payment − Price of the bond Number of years to maturity . They have 10 years remaining to maturity. Compute the approximate yield to maturity. 10-17.6 ($850) + .000 − 850 10 = . Bonds issued by the Crane Optical Company have a par value of $1.6 (Price of the bond) + .4 ($1. The annual interest payment is 13. Compute the approximate yield to maturity.060 S10-22 .100) + . are selling for $1.4 ($1. Solution: West Motel Chain Approximate Yield to Maturity is represented by Y' Annual interest payment + Y'= Principal payment − Price of the bond Number of years to maturity .18. Bonds issued by the West Motel Chain have a par value of $1.6 ($1.4 (Principal payment) $1.000. 10-18.000 − 1. using Formula 10-2.5 percent ($135).100. and have 20 years remaining to maturity.100 20 = .6 (Price of the bond) + .26% $1.000) $135 + − $100 20 = $660 + 400 $135 + = $135 − 5 $130 = = 12.060 $1. 469 = $1. we could infer the yield is somewhat below 13.112. we can reasonably infer the answer is between 12 and 13 percent based on the information in problem 14.32 Present Value of Principal Payment at Maturity PV = FV × PVIF PV = $1. So we next use a higher rate of 13 percent. Solution: West Motel Chain (Continued) In using the trial and error approach in this instance.32 104.008.5 percent because the bonds are trading above the par value of $1. Present Value of Interest Payments PVA = A × PVIFA (n = 20.00 $1.38 Appendix D Appendix D S10-23 .32 The discount rate of 12 percent gives us too high a present value in comparison to the bond price of $1. You may choose to use a handheld calculator instead. Let's begin the trial and error process at 12 percent.104 = $104 $1. i = 13%) PVA = $135 × 7.100. i = 12%) PVA = $135 × 7. Even if we did not have this information. 10-19. Optional: For Problem 18.19.000 × . Present Value of Interest Payments PVA = A × PVIFA (n = 20.025 = $948.000. use the techniques in Appendix 10A to combine a trial and error approach with interpolation to find a more exact answer.008. 32 –1. i = 13%) Appendix B PV = $1.112.16 (1%) = 12.38 The discount rate of 13 percent provides too low a value.16%.035.32/$76.00 $ 12.087 = $87 $ 948.000 × .38 87.32 –1. Using interpolation: $1.94 (1%) = 12% + .100.32 PV at 12% bond price 12% + $12. (Continued) Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20.94 PV at 12% PV at 13% $1. The actual value falls between 12 and 13 percent.035.00 $1.38 $ 76.10-19. S10-24 .16% The answer is 12.112. 000 × . The yield to maturity on the bonds is 10 percent annual interest.00 $817. Compute the price of the bonds based on semiannual analysis.256 = $730.000 bonds have a quoted annual interest rate of 8 percent and the interest is paid semiannually. The $1.24 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 50.) 20.24 S10-25 . i = 5%) PVA = $40 × 18. i = 5%) Appendix B PV = $1. 10-20.(For the next two problems.000 = $40 semiannual interest 25 × 2 = 50 number of periods (n) 10%/2 = 5% yield to maturity expressed on a semiannual basis (i) Present Value of Interest Payments PVA = A × PVIFA (n = 50. Solution: Robert Brown III—Southwest Technology 8% interest/2 = 4% semiannual interest rate 4% × $1. There are 25 years to maturity.24 87.087 = $87 $730. Robert Brown III is considering a bond investment in Southwest Technology Company. assume interest payments are on a semiannual basis. 590 = $951.55 b.137. With 10 years to maturity. i = 6%) PVA = $70 × 13.55 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 30. You are called in as a financial analyst to appraise the bonds of the Holtz Corporation. b. a. Solution: Holtz Corporation a. what will be the new price of the bonds? 10-21.21. Present Value of Interest Payments PVA = A × PVIFA (n = 30. if yield to maturity goes down substantially to 8 percent. Compute the price of the bonds based on semiannual analysis.000 par value bonds have a quoted annual interest rate of 14 percent. i = 4%) PV = $1. There are 15 years to maturity.456 = $456 Appendix D Appendix B $ 951.407. The $1. The yield to maturity on the bonds is 12 percent annual interest.000 × . which is paid semiannually.30 PV = FV × PVIF (n = 20. i = 6%) Appendix B PV = $1.55 174.00 $1.30 S10-26 . i = 4%) PVA = $70 × 13.174 = $174 $ 963.000 × .30 456.765 = $963.00 $1. PVA = A × PVIFA (n = 20. What is the current value of this preferred stock? c. S10-27 . It carries a fixed dividend of $6 per share. Dp Kp = $6. Original price D p $6.86 .00 = $42. and a lower present value as the discount rate increases. Solution: North Pole Cruise Lines a.00 Pp = = = $100 Kp . yields have soared from the original 6 percent to 14 percent (yield is the same as required rate of return). Current value $6. The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security.09 North Pole Cruise Lines issued preferred stock many years ago. a. The preferred stock of Ultra Corporation pays an annual dividend of $6.30 = $70 .30. Pp = 23. The present value of an income stream has a higher present value as the discount rate declines. With the passage of time. how will the price of the preferred stock be affected? 10-23. If the yield on the Standard & Poor’s Preferred Stock Index declines.14 c. Compute the price of the preferred stock.22. It has a required rate of return of 9 percent.06 b. its price is inversely related to yields as would be true with bond prices. Solution: Ultra Corp. 10-22. What was the original issue price? b. 91% $110 Analogue Technology has preferred stock outstanding that pays a $9 annual dividend. It plans to maintain the dividend at this level for the foreseeable future as no future growth is anticipated. It has a price of $110.50 Ke .10 annual cash dividend (D0). What is the required rate of return (yield) on the preferred stock? 10-24. Solution: Analogue Technology Kp = Dp Pp = $9 = 11. P0 = D0 $2.10 = = $17.84% $76 (All of the following problems pertain to the common stock section of the chapter.) 26. What is the required rate of return (yield) on the preferred stock? 10-25. currently pays a $2.12 S10-28 .24. It has a price of $76. Dp Pp = $12 = 10. Solution: Static Electric Co. If the required rate of return by common stockholders (Ke) is 12 percent. Venus Sportswear Corporation has preferred stock outstanding that pays an annual dividend of $12. what is the price of the common stock? 10-26. Solution: Venus Sportswear Corporation Kp = 25. Static Electric Co. what will be the new value of P0? d.00 .27. Assume Ke.50 = = $30.05 Friedman Steel Company will pay a dividend of $1. goes up to 12 percent.50 = = $21. The required return on common stock (Ke) is 14 percent.50 $1.20 = = = $64.14 − .20 at the end of the year (D1). P0 = 28. Each question is independent of the others.10 − .09 . D1 Ke − g $1. c.20 $3.05 . what will be the new value of P0? c. D1 $3.50 $1.43 .00 K e . Assume D1 is $2. will pay a common stock dividend of $3.50 per share in the next 12 months (D1). Solution: BioScience Inc. Compute P0. Assume the growth rate (g) goes up to 7 percent. (For parts b.05 $1. and d in this problem all variables remain the same except the one specifically changed. 10-27. Compute the current price of the stock (P0). The firm has a constant growth rate (g) of 9 percent.g . b. Inc.) b.05 ..07 S10-29 . the required rate of return. a. Solution: Friedman Steel Company P0 = a. The required rate of return (Ke) is 10 percent and the constant growth rate is 5 percent. BioScience. what will be the new value of P0? 10-28.12 − . .08 0.......57 2008...00 ..... (Continued) c. d.10 − .00 2005.24 P0 = 30.00 = = $40....00 . $3...24 $3...... 3.... $3.. the dividend is expected to grow at 8 percent.. what is the anticipated stock price at the beginning of 2009? S10-30 ...03 $2.. 3.....07 . Compute the price of the stock (P0)..... Dividends represent 30 percent of earnings.10-28..37 2007... The required rate of return (Ke) is 14 percent......00 (1.................. a...........78 The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future...... Over the next 12 months..50 = = $50..... 29..24 = = $54 ... which is the constant growth rate for the firm (g)... Round all values in this problem to two places to the right of the decimal point........06 Haltom Enterprises has had the following pattern of earnings per share over the last five years: Year Earnings per Share 2004..........50 $1. Solution: Maxwell Communications P0 = D1 Ke − g D1 = D 0 (1 + g) = $3.. b.. $1....05 ... 3....05 Maxwell Communications paid a dividend of $3 last year.18 2006..... If the required rate of return (Ke) is 10 percent.. The new dividend after 12 months will represent D1.00 $2... Project earnings and dividends for the next year (2009)..........10 − ..... 10-29.14 − ....08) = $3... 3. 18 $3. Earnings have been growing at a rate of 6 percent per year.78 (1. Ke (required rate of return) is 10% and the growth rate is 6%. This is the value for D1.06 .04 A firm pays a $4.01 Dividend for 2009 represent 30% of earnings or $1.10 − . D1 $1. Solution: Haltom Enterprises a.00 D1 .57 6% growth 6% growth 6% growth 6% growth The projected EPS for 2009 is $3. has a stock price of $70.06) = $4.18/3.37/3.00 $3.10-30. b. Compute the required rate of return.78/3.90 dividend at the end of year one (D1). Solution: Rearranging P0 = Ke = Ke = D1 +g P0 $4.20 = = = $30 K e − g .37 $3. P0 (2005) = 31.g S10-31 .57/3. Ke .20. 2004 2005 2006 2007 2008 Base Period $3.90 + 6% = 7% + 6% = 13% $70.20 $1. 10-31. and a constant growth rate (g) of 6 percent. Solution: a. Ke .32. A firm pays a $1. c. has a stock price of $40 (P0). The stock price increases. The expected growth rate increases. the required rate of return (Ke) will go up. (For parts b. and a constant growth rate (g) of 8 percent.90 + 8% = 4. the dividend yield (D1/P0) will go up. and the required rate of return (Ke) will also go up. 10-32.00 D1 . If the stock price increases.) b. If the dividend payment increases. assume only one variable changes at a time. and d below. d. Rearranging P0 = Ke = Ke = D1 +g P0 $1. Compute the required rate of return (Ke). c.75% $40.75% + 8% = 12. No actual numbers are necessary. the dividend yield (D1/P0) will go down. d. a.90 dividend at the end of year one (D1). The dividend payment increases. If the expected growth rate (g) increases. S10-32 .g b. c. and the required rate of return (Ke) will also go down. Also indicate whether each of the following changes would make the required rate of return (Ke) go up or down. and g = 5 percent. Compute the price of the stock at the end of the third year (P3). f.00 × 1. of dividends.) S10-33 . This answer represents the present value of the first three periods. Cellular Systems paid a $3 dividend last year. After you have computed P3. D2. Ke = 12 percent. (The slight difference between the answers to part e and part f is due to rounding. P3 = D4 Ke − g (D4 is equal to D3 times 1. b. and D3. The dividend is expected to grow at a constant rate of 5 percent over the next two years. P0 = D1 Ke − g (10-9) For Formula 10-9 use D1 = $3. Add together the answers in part b and part d to get P0. Discount each of these dividends back to the present at a discount rate of 12 percent and then sum them. D1 is $3. That is. Round all values throughout this problem to three places to the right of the decimal point. e.15 ($3. a. represents the value of all future dividends). Round all values to three places to the right of the decimal point where appropriate. c. Use Formula 10-9 to show that it will provide approximately the same answer as part e.05). in turn. the current value of the stock. for example.15. discount it back to the present at a discount rate of 12 percent for three years. plus the present value of the price of the stock after three periods (which. compute D1.05) d. Compute the anticipated value of the dividends for the next three years. The required rate of return is 12 percent (this will also serve as the discount rate in this problem).33. 07 S10-34 .12 − .007 D1 $3.05 . D1 D2 D3 P3 = P3 = $3.086 × . i = 12% $52. P0 = $ 7.921 37.00 (1.05) = $3.07 d.472 Dividends $3.646 $3.05) = $3.086 $45. D1 D2 D3 b.15 = = = $45. PV of P3 for n = 3.15 $3.472 (1.086 .712 = $37.893 .646 $3.921 c.15 (1.12 − .086 e. D 4 = $3.307 $3.05) = $3.712 PV of Dividends $2.05 .472 $7.797 . Solution: Cellular Systems a.10-33.472 D4 Ke − g PV(12%) . Answer to part b (PV of dividends) Answer to part d (PV of P3) Current value of the stock f.646 = = $52.00 K e − g .636 2.31 (1.307 $3.15 $3.813 2.05) = $3.15 3. compute D1.34. Round all values to three places to the right of the decimal point where appropriate. In regard to the stock price in part f. Compute the price of the stock at the end of the fourth year (P4). By what dollar amount is the stock price in part g different from the stock price in part f ? i. (3) g increases.1 times higher than the industry average of 8. P0 = D1 Ke − g (10-9) For Formula 10-9 use D1 = $3. Discount each of these dividends back to present at a discount rate of 14 percent and then sum them. and D4. discount it back to the present at a discount rate of 14 percent for four years. D2.00 × 1. If current EPS were equal to $5. in turn. indicate which direction it would move if (1) D1 increases. Trump Office Supplies paid a $3 dividend last year. and g = 7 percent. After you have computed P4. the current value of the stock. e. P4 = D5 Ke − g (D5 is equal to D4 times 1. a.07). f. represents the value of all future dividends). The dividend is expected to grow at a constant rate of 7 percent over the next four years. (The slight difference between the answers to part e and part f is due to rounding. The required rate of return is 14 percent (this will also serve as the discount rate in this problem). c.21 ($3.21. D3. (2) Ke increases. (which. what would the stock price be? h. This answer represents the present value of the four periods of dividends. Add together the answers in part b and part d to get P0. That is. S10-35 . for Example. Compute the anticipated value of the dividends for the next four years.07) d. Use Formula 10-9 to show that it will provide approximately the same answer as part e. b.32 and the P/E ratio is 1. Ke = 14 percent. plus the present value of the price of the stock after four periods. D1 is $3.) g. 07) = $4.07 . D 5 = 3.266 35. Solution: Trump Office Supplies a.07) = 3.675 3.07) = $3.592 PV of Dividends $ 2.642 2.769 .435 3.845 D1 $3.932 Dividends $3.328 $10.932 (1.675 (1.266 c.675 3.932 D5 Ke − g PV(14%) .14 − .435 (1.857 K e − g .10 .207 $4.579 $45.21 3.21 (1. i=14% $60.07 .10-34.00 (1.07) = 3.21 $3.435 3.877 . PV of P4 for n=4.07 S10-36 . D1 D2 D3 D4 b.579 e.675 .21 3.592 = 35. Answer to part b (PV of dividends) Answer to part d (PV of P4) Current value of the stock f.481 2. D1 D2 D3 D4 P4 = P4 = $3.207 $4.10 × .07) = 3.07 d.815 2.14 − .21 = = = $45.207 = = $60. P0 = 10. Price = P/E × EPS P/E = 8 × 1.959 1) D1 increases. $46.8 × $5.32 = $46.857 . (Continued) g.8 Price = 8. stock price decreases 3) G increases.10-34. Part g Part f i.1 = 8. stock price increases 2) Ke increases.816 h. stock rice increases S10-37 .816 45. the anticipated growth rate was 10 percent... D1 is $1...... Indicate that the value you computed in part a is correct by showing the value of D1.. What is the stock value based on the P/E ratio approach? Multiply the average P/E ratio you computed times earnings per share....... Olin Corp..30....... a......COMPREHENSIVE PROBLEM Mel Thomas... and D3 and discounting each back to the present at 14 percent..... you also examine the value of the firm based on the price-earnings (P/E) ratio times earnings per share. has been asked to do an evaluation of Dunning Chemical Company by the president and Chair of the Board.. How does this value compare to the dividend valuation model values that you computed in parts a and b? S10-38 ...... 3M.30 and it increases by 10 percent (g) each year.. Assume Dunning Chemical has earnings per share of $2.. you should get an answer approximately equal to the answer in part a.... Du Pont. c.. The P/E ratios were as follows during the time period under analysis: P/E Ratio 15 18 7 19 21 Dow Chemical.. As an alternative measure. Preston Resources was planning a joint venture with Dunning (which was privately traded)....... D2. Georgia Gulf.... the chief financial officer of Preston Resources.... Also discount back the anticipated stock price at the end of year three to the present and add it to the present value of the three dividend payments... Sarah Reynolds... Dunning Chemical paid a dividend at the end of year one of $1... The value of the stock at the end of year three is: P3 = D4 Ke − g D4 = D3 ( 1 + g ) If you have done all these steps correctly.. and Sarah and Mel needed a better feel for what Dunning’s stock was worth because they might be interested in buying the firm in the future.. Since the company is privately traded (not in the public stock market)....................... What is the value of the stock based on the dividend valuation model (Formula 10-9)? b..... you will get your anticipated P/E ratio by taking the average value of five publicly traded chemical companies. and the required rate of return was 14 percent.....10.. . e. 124...... more heavily because it is similar to Dunning Chemical... If in computing the industry average P/E.153.63 PV @ 11% $ 90... i = 11%) PV = $1..65 ( 1% ) = 10% + ....153..76% $90.....02 10% + $1.085... $ 939.63 The discount rate of 11 percent gives us a value slightly lower than the bond price of $1.. By what percent will the stock price change as a result of using the weighted average industry P/E ratio in part d as opposed to that in part c? Present Value of Principal Payment at Maturity— PV = FV × PVIF (n = 20...65 (Appendix B) $68...124 = $124 Total Present Value— Present value of interest payments.76 percent $1...085.... what would be the new weighted average industry P/E? (Note: You decided to weight Olin Corp.00 Total present value.. $1.10.) What will the new stock price be? Earnings per share will stay at $2..76 ( 1% ) = 10. by 40 percent and the other four firms by 15 percent... Using linear interpolation...63 Present value of principal payment at maturity.000 × ... or price...65 PV @ 10% 1. the answer is 10....d.063. you decide to weight Olin Corp.02 S10-39 ..063.00 bond price $ 68.65 PV@10% 1.. The rate for the bond must fall between 10 and 11 percent. of the bond.. 10 .CP 10-1.10) = $1.730 $1.573 Dividends $1. Future Value of Dividends D1 D2 D3 $1.49 S10-40 .25 .04 Present Value of Future Stock Price P3 = $43. i = 14%) (Appendix B) PV = $43.10 .675 = $29.43 (1.30 $1.10) = $1.30 (1.573 (1.04 b.50 K e − g .14 − .19 Total stock prices: PV of Dividends $ 3.43 $1.25 (n = 3.769 .573 PV (14%) .30 Present Value of Dividends D1 D2 D3 Value of Stock Price at the end of Year 3 P3 = P3 = D4 Ke − g D 4 = D 3 (1 + g) = 1. P0 = D1 $1.06 $3.30 = = = $32.30 $1.10) = $1.00) = $1.730 $1.877 .30 $1. Solution: Preston Resources—Dunning Chemical a.14 − .14 $1.43 $1.25 × .675 (PV of Dividend) $1.19 $32.730 = = $43.10 $1.30 (1.30 PV of Stock Price 29. (Continued) c.15 1. Dow Chemical Dupont Georgia Gulf 3M Olin Corp.05 19 .10 = $33. 21 Total 80 80 = 16 Average P/E 5 Stock Price = P/E × EPS 16 × $2.50).15 2.25 Stock price = P/E × EPS $17.10 = $36.25 18 .25 × $2. Weighted P/E Ratio Weights Average 15 .85 21 . ($33.60 versus $32.15 2.60 The stock price using the P/E ratio approach is slightly higher than the value using the dividend valuation model approach.70 7 .15 2.CP 10-1.23 S10-41 . Average P/E Ratio of Five Chemical Firms Dow Chemical 15 Dupont 18 Georgia Gulf 7 3M 19 Olin Corp.40 17. d.40 8. 83% Beginning amount $33.60 $ 2.23 33.63 = 7.CP 10-1. (Continued) e.63 Change $2. Stock price (d) Stock price (c) Change $36.60 S10-42 . The annual interest payment is 8 percent.00 $901.) 10A–1.823 = $785. i = 9%) Appendix B PV = $1.84 116. Find yield to maturity by combining the trial-and-error approach with interpolation.116 = $116 $785. Bonds issued by the Medford Corporation have a par value of $1. we will try 9 percent.) As a first approximation.000 × . are selling for $865. Present Value of Interest Payments PVA = A × PVIFA (n = 25.84 S10-43 . i = 9%) PVA = $80 × 9. we can assume the yield to maturity must be above the quoted interest rate of 8 percent. (Use an assumption of annual interest payments.84 Appendix D Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25.000. Solution: Medford Corporation Since the bond is trading below par value at $865. and have 25 years to maturity. (The yield to maturity would be 8 percent at a bond value of $1.Appendix 10A–1. as shown in this appendix.000. 00 $ 36.44(1%) = 9.000 × . The actual value for the bond must fall between 9% and 10%. So we next use a higher discount rate of 10 percent. PVA = A × PVIFA (n = 25.10A–1.092 = $92 Appendix D Appendix B $726.077 = $726. Using interpolation.84 –865.16 PV = FV × PVIF (n = 25.00 $818. (Continued) The discount rate of 9 percent gives us too high a present value in comparison to the bond price of $865. the answer is: $901. i = 10%) PVA = $80 × 9.16 The discount rate of 10 percent provides a value lower than the price of the bond.16 92.84 PV at 9% Bond price $36.16 $ 83.68 S10-44 .84 (1%) = 9% + .44% $83.68 9% + PV at 9% PV at 10% $901. i = 10%) PV = $1.84 –818. e.56 $4.893 $1. Compute the anticipated value of the dividends for the next three years (D1.40 . D1 D2 D3 $1. D2. The required rate of return is 12 percent (this will also serve as the discount rate). Compute the price of the stock at the end of the third year (P3). After you have computed P3. The dividend is expected to grow at a rate of 25 percent over the next three years (supernormal growth).75 (1. b.25) = $1.40 (1.797 $2.75 $1. a.39 1. Add together the answers in part b and part d to get the current value of the stock. Surgical Supplies Corporation paid a dividend of $1.40 $1.25) = $1.25 1. (This answer represents the present value of the first three periods of dividends plus the present value of the price of the stock after three periods. and D3).19 . P3 = D4 Ke − g [Review Appendix 10C for the definition of D 4 ] d. It will then grow at a normal.) 10C–1. discount it back to the present at a discount rate of 12 percent for three years.19 Present value of dividends during the supernormal growth period $1.12 (1.20 b. constant rate of 7 percent for the foreseeable future. c. D1 D2 D3 Supernormal Discount rate dividends Ke = 12% $1.712 S10-45 . Solution Surgical Supplies Corporation a.75 .10C–1.25) = $2. Discount each of these dividends back to the present at a discount rate of 12 percent and then sum them.12 over the last 12 months. 52 S10-46 . PV of P3 for n = 3.32 e. P3 = D4 Ke − g D 4 = D 3 (1.05 d.80 .12 − .34 $2. i = 12% $46.07) = $2.34 = = $46.07 0.712 = $33. (Continued) c.34 P3 = $2.80 × . Answer to part b (PV of dividends) Answer to part d (PV of P3) Current value of the stock $ 4.07) = $2.19 (1.10C–1.32 $37.20 33.