Chapter 10 Valuation and Rates of Return Discussion 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 Microsoft as compared to United Airlines? Because Microsoft has less risk than United Airlines, Microsoft 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: a. The real rate of return b. The inflation premium c. 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 (the 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 2 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. 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: 1. Divide the annual interest rate by two. 2. Multiply the number of years by two. 3. 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 10-7 to Formula 10-8 in using the dividend valuation model? To go from Formula (10-7) to Formula (10-8): 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 rate of return on common stock are: a. The dividend yield D1/P0. 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 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. Chapter 10 Problems (For the first 20 bond problems, assume interest payments are on an annual basis.) 1. Bond value (LO10-3) The Lone Star Company has $1,000 par value bonds outstanding at 10 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. 9 percent. c. 13 percent. 10-1. Solution: Loan Star Company Calculator Solution: (a) 6 percent yield to maturity N I/Y PV PMT FV 20 6 CPT PV −1,458.80 100 1,000 Answer: $1,458.80 Current bond price (b) 9 percent yield to maturity N I/Y PV PMT FV 20 9 CPT PV −1,091.29 100 1,000 Answer: $1,091.29 Current bond price (c) 13 percent yield to maturity N I/Y PV PMT FV 20 13 CPT PV −789.26 100 1,000 Answer: $789.26 Current bond price a. 6 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 6%) Appendix D PVA = 100 × 11.470 = $1,147.00 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 6%) Appendix B PV = 1,000 × .312 = $312 Total Present Value Present Value of Interest Payments $1,147.00 Present Value of Principal Payment 312.00 Total Present Value or Price of the Bond $1,459.00 10-1. (Continued) b. 9 percent yield to maturity PVA = A × PVIFA (n = 20, i = 9%) Appendix D PVA = $100 × 9.129 = $912.90 PV = FV × PVIF (n = 20, i = 9%) Appendix B PV = $1,000 × .178 = $178.00 $ 912.90 178.00 $1,090.90 c. 13 percent yield to maturity PVA = A × PVIFA (n = 20, i = 13%) Appendix D PVA = $100 × 7.025 = $702.50 PV = FV × PVIF (n = 20, i = 13%) Appendix B PV = $1,000 × .087 = $87.00 $702.50 87.00 $789.50 2. Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if the present yield to maturity is: a. 7 percent. b. 10 percent. c. 13 percent. 10-2. Solution: Midland Oil Calculator Solution: (a) 7 percent yield to maturity N I/Y PV PMT FV 25 7 CPT PV −1,116.54 80 1,000 Answer: $1,116.54 Current bond price (b) 10 percent yield to maturity N I/Y PV PMT FV 25 10 CPT PV −818.46 80 1,000 Answer: $ 818.46 Current bond price (c) 13 percent yield to maturity N I/Y PV PMT FV 25 13 CPT PV −633.50 80 1,000 Answer: $633.50 Current bond price a. 7 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 25, i = 7%) Appendix D PVA = $80 × 11.654 = $932.32 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25, i = 7%) Appendix B PV = $1,000 × .184 = $184 Total Present Value Present Value of Interest Payments $ 932.32 Present Value of Principal Payments 184.00 Total Present Value or Price of the Bond $1,116.32 b. 10 percent yield to maturity PVA = A × PVIFA (n = 25, i = 10%) Appendix D PVA = $80 × 9.077 = $726.16 PV = FV × PVIF (n = 25, i = 10%) Appendix B PV = $1,000 × .092 = $92 $726.16 92.00 $818.16 10-2. (Continued) c. 13 percent yield to maturity PVA = A × PVIFA (n = 25, i = 13%) Appendix D PVA = $80 × 7.330 = $586.40 PV = FV × PVIF (n = 25, i = 13%) Appendix B PV = $1,000 × .047 = $47 $586.40 47.00 $633.40 3. Exodus Limousine Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is: a. 5 percent. b. 15 percent. 10-3. Solution: Exodus Limousine Company Calculator Solution: (a) 5 percent yield to maturity N I/Y PV PMT FV 50 5 CPT PV −1,912.80 100 1,000 Answer: $1,912.80 Current bond price (b) 15 percent yield to maturity N I/Y PV PMT FV 50 15 CPT PV −666.97 100 1,000 Answer: $666.97 Current bond price a. 5 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 50, i = 5%) Appendix D PVA = $100 × 18.256 = $1,825.60 Present Value of Principal Payment PV = FV × PVIF (n = 50, i = 5%) Appendix B PV = $1,000 × .087 = $87 Present Value of Interest Payment $1,825.60 Present Value of Principal Payment 87.00 Total Present Value or Price of the Bond $1,912.60 10-3. (Continued) b. 15 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 50, i = 15%) Appendix D PVA = $1,000 × 6.661 = $666.10 PV = FV × PVIF (n = 50, i = 15%) Appendix B PV = $1,000 × .001 = $1 Present Value of Interest Payment $666.10 Present Value of Principal Payment 1.00 Total Present Value or Price of the Bond $667.10 4. Bond value (LO10-3) Barry’s Steroids Company has $1,000 par value bonds outstanding at 16 percent interest. The bonds will mature in 40 years. If the percent yield to maturity is 13 percent, what percent of the total bond value does the repayment of principal represent? 10-4. Solution: Barry’s Steroids Calculator Solution: 13 percent yield to maturity N I/Y PV PMT FV 40 13 CPT PV −1,229.03 160.0 1,000 Answer: $1,229.03 Total present value of the bond N I/Y PV PMT FV 40 13 CPT PV −7.53 0 1,000 Answer: $7.53 Present value of the principal payment PV of principal payment = $7.53 = .613% Bond value $1,229.03 Present Value of Interest Payments PVA = A × PVIFA (n = 40, i = 13%) Appendix D PVA = $160 × 7.634 = $1,221.44 Present Value of Principal Payment PV = FV × PVIF (n = 40, i = 13%) Appendix B PV = $1,000 × .008 = $8.00 Present Value of Interest Payments $1,221.44 Present Value of Principal Payment 8.00 Total Present Value or Price of the Bond $1,229.44 5. Bond value (LO10-3) Essex Biochemical Co. has a $1,000 par value bond outstanding that pays 15 percent annual interest. The current yield to maturity on such bonds in the market is 17 percent. Compute the price of the bonds for the following maturity dates: a. 30 years b. 20 years c. 4 years 10-5. Solution: Essex Biochemical Calculator Solution: (a) 30 years to maturity N I/Y PV PMT FV 30 17 CPT PV −883.41 150.0 1,000 Answer: $883.41 Bond price (b) 20 years to maturity N I/Y PV PMT FV 20 17 CPT PV −887.44 150.0 1,000 Answer: $887.44 Bond price (c) 4 years to maturity N I/Y PV PMT FV 4 17 CPT PV −945.14 150.0 1,000 Answer: $945.14 Bond price a. 30 years to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 17%) Appendix D PVA = $150 × 5.829 = $874.35 PV = FV × PVIF (n = 30, i = 17%) Appendix B PV = $1,000 × .009 = $9.00 Total Present Value Present Value of Interest Payments $874.35 Present Value of Principal Payment 9.00 Total Present Value or Price of the Bond $883.35 10-5. (Continued) b. 20 years to maturity PVA = A × PVIFA (n = 20, i = 17%) Appendix D PVA = $150 ×5.628 = $844.20 PV = FV × PVIF (n = 20, i = 17%) Appendix B PV = $1,000 × .043 = $43.00 $ 844.20 43.00 $887.20 c. 4 years to maturity PVA = A × PVIFA (n = 4, i = 17%) Appendix D PVA = $150 × 2.743 = $411.45 PV = FV × PVIF Appendix B PV = $1,000 × .534 = $534 $ 411.45 534.00 $945.45 6. Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 9 percent annual interest. The current yield to maturity on such bonds in the market is 12 percent. Compute the price of the bonds for the following maturity dates: a. 30 years b. 15 years c. 1 year 10-6. Solution: Kilgore Natural Gas Calculator Solution: (a) 30 years to maturity N I/Y PV PMT FV 30 12 CPT PV −758.34 90 1,000 Answer: $758.34 Bond price (b) 15 years to maturity N I/Y PV PMT FV 15 12 CPT PV −795.67 90 1,000 Answer: $795.67 Bond price (c) 1 year to maturity N I/Y PV PMT FV 1 12 CPT PV −973.21 90 1,000 Answer: $973.21 Bond price a. 30 years to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 12%) Appendix D PVA = $90 × 8.055 = $724.95 PV = FV × PVIF (n = 30, i = 12%) Appendix B PV = $1,000 × .033 = $33 Total Present Value Present Value of Interest Payments $724.95 Present Value of Principal Payment 33.00 Total Present Value or Price of the Bond $757.95 10-6. (Continued) b. 15 years to maturity PVA = A × PVIFA (n = 15, i = 12%) Appendix D PVA = $90 × 6.811 = $612.99 PV = FV × PVIF (n = 15, i = 12%) Appendix B PV = $1,000 × .183 = $183 $612.99 183.00 $795.99 c. 1 year to maturity PVA = A × PVIFA Appendix D PVA = $90 × .893 = $80.37 PV = FV × PVIF Appendix B PV = $1,000 × .893 = $893.00 $ 80.37 893.00 $973.37 7. Bond maturity effect (LO10-3) Toxaway Telephone Company has a $1,000 par value bond outstanding that pays 6 percent annual interest. If the yield to maturity is 8 percent, and remains so over the remaining life of the bond, the bond will have the following values over time: Remaining Maturity Bond Price 15 $795.67 10 $830.49 5 $891.86 1 $973.21 Graph the relationship in a manner similar to the bottom half of Figure 10-2. Also explain why the pattern of price change takes place. 10-7. Solution: Toxaway Telephone Company As the time to maturity becomes less and less, the importance of the difference between the rate the bond pays and the yield to maturity becomes less significant. Therefore, the bond trades closer to par value. 8. Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 11 percent to 8 percent: a. What is the bond price at 11 percent? b. What is the bond price at 8 percent? c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent? 10-8. Solution: a. $920.30 b. $1,196.80 c. Sales price (8%) $1,196.80 Purchase price (11%) 920.30 Profit $ 276.50 9. Interest rate effect (LO10-3) Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) increase from 9 to 12 percent. a. What is the bond price at 9 percent? b. What is the bond price at 12 percent? c. What would be your percentage return on the investment if you bought when rates were 9 percent and sold when rates were 12 percent? 10-9. Solution: a. $1,090.90 b. $850.90 c. Purchase price (9%) $1,090.90 Sales Price (12%) 850.90 Loss ($240.00) 10. Interest rate effect (LO10-3) Using Table 10-1, assume interest rates in the market (yield to maturity) are 14 percent for 20 years on a bond paying 10 percent. a. What is the price of the bond? b. Assume five years have passed and interest rates in the market have gone down to 12 percent. Now, using Table 10-2 for 15 years, what is the price of the bond? c. What would your percentage return be if you bought the bonds when interest rates in the market were 14 percent for 20 years and sold them 5 years later when interest rates were 12 percent? 10-10. Solution: a. $735.30 b. $864.11 c. Sales price (12%) $864.11 Purchase Price (14%) 735.30 Profit $128.81 11. Effect of maturity on bond price (LO10-3) Using Table 10-2: a. Assume the interest rate in the market (yield to maturity) goes down to 8 percent for the 10 percent bonds. Using column 2, indicate what the bond price will be with a 10-year, a 15-year, and a 20-year time period. b. Assume the interest rate in the market (yield to maturity) goes up to 12 percent for the 10 percent bonds. Using column 3, indicate what the bond price will be with a 10-year, a 15-year, and a 20-year period. c. Based on the information in part a, if you think interest rates in the market are going down, which bond would you choose to own? d. Based on information in part b, if you think interest rates in the market are going up, which bond would you choose to own? 10-11. Solution: a. Maturity Bond price 10 year $1,134.00 15 year 1,171.19 20 year 1,196.36 b. Maturity Bond price 10 year $887.00 15 year 863.78 20 year 850.61 c. Based on information in part a, you would want to own the longest-term bond possible to maximize your gain. d. Based on information in part b, you would want to own the shortest-term bond possible to minimize your loss. 12. Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage Systems. His broker quotes a price of $1,180. Jim is concerned that the bond might be overpriced based on the facts involved. The $1,000 par value bond pays 14 percent interest, and it has 25 years remaining until maturity. The current yield to maturity on similar bonds is 12 percent. Compute the new price of the bond and comment on whether you think it is overpriced in the marketplace. 10-12. Solution: Jim Busby – Disk Storage Systems Calculator Solution: (a) N I/Y PV PMT FV 25 12 CPT PV −1,156.86 140 1,000 Answer: $1,156.86 New bond price (b) The bond has a value of $1,156.86. This indicates his broker is quoting a higher price at $1,180. Present Value of Interest Payments PVA = A × PVIFA (n = 25, i = 12%) Appendix D PVA = $140 × 7.843 = $1,098.02 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25, i = 12%) Appendix B PV = $1,000 × .059 = $59 $1,098.02 59.00 $1,157.02 The bond has a value of $1,157.02. This indicates his broker is quoting too high a price at $1,180. 13. Effect of yield to maturity on bond price (LO10-3) Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described next: Real rate of return 4% Inflation premium 6 Risk premium 5 Total return 15% 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. The bonds have 20 years remaining until maturity. Compute the new price of the bond. 10-13. Solution: Tom Cruise Lines Inc. First compute the new required rate of return (yield to maturity). Real rate of return 4% Inflation premium 3 Risk premium 5 Total return 12% Then, use this value to find the price of the bond. Calculator Solution: Present value of interest payments N I/Y PV PMT FV 20 12 CPT PV −1,224.08 150 1,000 Answer: $1,224.08 New bond price Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 12%) Appendix D PVA = $150 × 7.469 = $1,120.35 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 12%) Appendix B PV = $1,000 × .104 = $104 $1,120.35 104.00 $1,224.35 14. Analyzing bond price changes (LO10-3) Katie Pairy Fruits Inc. has a $1,000, 20-year bond outstanding with a nominal yield of 15 percent (coupon equals 15% × $1,000 = $150 per year). Assume that the current market-required interest rate on similar bonds is now only 12 percent. a. Compute the current price of the bond. b. Find the present value of 3 percent × $1,000 (or $30) for 20 years at 12 percent. The $30 is assumed to be an annual payment. Add this value to $1,000. c. Explain why the answers in parts a and b are basically the same. (There is a slight difference due to rounding in the tables.) 10-14. Solution: Katie Pairy Fruits Inc. Calculator Solution: N I/Y PV PMT FV 20 12 CPT PV −1,224.08 150 1,000 Answer: $1,224.08 Bond price N I/Y PV PMT FV 20 12 CPT PV −224.08 30 0 Answer: $224.08 + 1,000 = 1,224.08 Bond price a. Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 12%) Appendix D PVA = $150 × 7.469 = $1,120.35 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 12%) Appendix B PV = $1,000 × .104 = $104 $1,120.35 104.00 $1,224.35 b. PVA = A × PVIFA (n = 20, i = 12%) Appendix D PVA = $30 × 7.469 = $224.07 $1,000.00 224.07 $1,224.07 c. The answer to part a of $1,224.35 and part b of $1,224.07 are basically the same because in both cases we are valuing the present value of a $30 differential between actual return and required return for 20 years. In part b, we take the present value of the $30 differential to arrive at $224.07. We then add this value to the $1,000 par value that is exactly equal to its market value because the remaining 12 percent coupon ($150 – $30 = $120 coupon) equals the 12 percent market rate. When the coupon rate equals the required rate, the market value equals the par value. In part a, we accomplish the same goal by valuing all future benefits at a three percent differential between stated return (coupon = 12%) and required return (10%) to arrive at $1,224.35. 15. Effect of yield to maturity on bond price (LO10-2 and 3) Media Bias Inc. issued bonds 10 years ago at $1,000 per bond. These bonds had a 40-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 in time as described next: Real rate of return 2% Inflation premium 5 Risk premium 5 Total return 12% Assume that 10 years later, due to good publicity, the risk premium is now 2 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 30 years remaining until maturity. Compute the new price of the bond. 10-15. Solution: Media Bias Inc. First compute the new required rate of return (yield to maturity) Real rate of return 2% Inflation premium 5% Risk premium 2% 9% Total required return Then, use this value to find the price of the bond. Calculator Solution: N I/Y PV PMT FV 30 9 CPT PV −1,308.21 120 1,000 Answer: $1,308.21 Bond price Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 9%) Appendix D PVA = $120 × 10.274 = $1,232.88 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 30, i = 9%) Appendix B PV = $1,000 × .075 = $75.00 Total Present Value Present Value of Interest Payments $1,232.88 Present Value of Principal Payment 75.00 Total Present Value or Price of the Bond $1,307.88 16. Effect of yield to maturity on bond price (LO10-2 and 3) Wilson Oil Company issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point in time as described next: Real rate of return 8% Inflation premium 3 Risk premium 4 Total return 15% Assume that 10 years later, due to bad publicity, the risk premium is now 7 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity. Compute the new price of the bond. 10-16. Solution: Wilson Oil Company First compute the new required rate of return (yield to maturity). Real rate of return 8% Inflation premium 3% Risk premium 7% 18% Total required return Then, use this value to find the price of the bond. Calculator Solution: N I/Y PV PMT FV 15 18 CPT PV −847.25 150 1,000 Answer: $847.25 Bond Price Present Value of Interest Payments PVA = A × PVIFA (n = 15, i = 18%) Appendix D PVA = $150 × 5.092 = $763.80 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 15, i = 18%) Appendix B PV = $1,000 × .084 = $84.00 $763.80 84.00 Bond Price = $847.80 17. Deep discount bonds (LO10-3) Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 14 percent. a. What is the current price of the bonds? b. By what percent will the price of the bonds increase between now and maturity? c. What is the annual compound rate of growth in the value of the bonds? (An approximate answer is acceptable.) 10-17. Solution: Lance Whittingham IV – Leisure Time Corporation Calculator Solution: (a) N I/Y PV PMT FV 18 14 CPT PV −353.26 40 1,000 Answer: $353.26 Bond price a. Current price of the bonds Present Value of Interest Payments PVA = A × PVIFA (n = 18, i = 14) Appendix D PVA = $40 × 6.467 = $258.68 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 18, i = 14%) Appendix B PV = $1,000 × .095 = $95.00 $258.68 95.00 $353.68 b. Percent increase at maturity Maturity Value $1,000.00 Current price – 353.68 Dollar increase $ 646.32 c. Compound rate of growth The bond will grow by 182.74 percent over 18 years. Using Appendix A, the future value of $1, and the interest factor of 2.828 (1 + 1.8274), we see the growth rate is between 5 and 6 percent. 18. Yield to maturity – A calculator or Excel is required (LO10-3) Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which of course is also the amount of principal to be paid at maturity. The bonds are currently selling for $690. They have 10 years remaining to maturity. The annual interest payment is 13 percent ($130). Compute the approximate yield to maturity. 10-18. Solution: Calculator Solution: N I/Y PV PMT FV 10 CPT I/Y 20.53 −690 130 1,000 Answer: 20.53% 19. Yield to maturity – A calculator or Excel is required (LO10-3) Stilley Resources bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 5 percent. If the price of the bond is $841.51, what is the yield to maturity? 10-19. Solution: N I/Y PV PMT FV 4 CPT I/Y 10 −841.51 50 1,000 Answer: 10% 20. Yield to maturity – A calculator or Excel is required (LO10-3) Evans Emergency Response bonds have 6 years to maturity. Interest is paid semiannually. The bonds have a $1,000 par value and a coupon rate of 8 percent. If the price of the bond is $1,073.55, what is the annual yield to maturity? 10-20. Solution: Semiannual: Payment: $1000 × .08 = $80/2 = $40 n: 6 years × 2 payments per year = 12 N I/Y PV PMT FV 12 CPT I/Y 3.25 −1,073.55 40 1,000 3.25% × 2 = 6.5% annual rate (For the next two problems, assume interest payments are on a semiannual basis.) 21. Bond value––semiannual analysis (LO10-3) Heather Smith is considering a bond investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual interest rate of 11 percent and the interest is paid semiannually. The yield to maturity on the bonds is 14 percent annual interest. There are seven years to maturity. Compute the price of the bonds based on semiannual analysis. 10-21. Solution: Heather Smith and Locklear Airlines 11%/2 = 5.5% semiannual interest rate 5.5% × $1,000 = $55 semiannual interest 7 × 2 = 14 number of periods (n)14%/2 = 7% yield to maturity expressed on a semiannual basis Calculator Solution: N I/Y PV PMT FV 14 7 CPT PV −868.82 55 1,000 Answer: $868.82 Bond price Present Value of Interest Payments PVA = A × PVIFA (n = 14, i = 7%) Appendix D PVA = $55 × 8.745 = $480.98 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 14, i = 7%) Appendix B PV = $1,000 × .388 = $388 Present Value of Interest Payments $480.98 Present Value of Principal Payment 388.00 Total Present Value or Price of the Bond $868.98 22. Bond value––semiannual analysis (LO10-3) You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 10 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 15 years to maturity. a. Compute the price of the bonds based on semiannual analysis. b. With 10 years to maturity, if yield to maturity goes down substantially to 8 percent, what will be the new price of the bonds? 10-22. Solution: Olsen’s Clothing Stores Calculator Solution: (a) N I/Y PV PMT FV 30 5 CPT PV −1,000.00 50 1,000 Answer: $1,000.00 Bond price (b) N I/Y PV PMT FV 20 4 CPT PV −1,135.90 50 1,000 Answer: $1,135.90 Bond price a. Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 5%) Appendix D PVA = $50 × 15.372 = $768.60 Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 30, i = 5%) Appendix B PV = $1,000 × .231 = $231 $768.60 231.00 $999.60 b. PVA = A × PVIFA (n = 20, i = 4%) Appendix D PVA = $50 × 13.590 = $679.50 PV = FV × PVIF (n = 20, i = 4%) Appendix B PV = $1,000 × .456 = $456 $679.50 456.00 $1,135.50 23. Preferred stock value (LO10-4) The preferred stock of Denver Savings and Loan pays an annual dividend of $5.70. It has a required rate of return of 6 percent. Compute the price of the preferred stock. 10-23. Solution: Denver Savings and Loan 24. North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed dividend of $6 per share. With the passage of time, yields have soared from the original 6 percent to 14 percent (yield is the same as required rate of return). a. What was the original issue price? b. What is the current value of this preferred stock? c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price of the preferred stock be affected? 10-24. Solution: North Pole Cruise Lines a. Original price b. Current value c. The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security, its price is inversely related to yields as would be true with bond prices. The present value of an income stream has a higher present value as the discount rate declines, and a lower present value as the discount rate increases. 25. Preferred stock value (LO10-4) X-Tech Company issued preferred stock many years ago. It carries a fixed dividend of $12.00 per share. With the passage of time, yields have soared from the original 10 percent to 17 percent (yield is the same as required rate of return). a. What was the original issue price? b. What is the current value of this preferred stock? c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price of the preferred stock be affected? 10-25. Solution: X-Tech Company a. Original price b. Current value c. The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security, its price is inversely related to yields as would be true with bond prices. The present value of an income stream has a higher present value as the discount rate declines, and a lower present value as the discount rate increases. 26. Analogue Technology has preferred stock outstanding that pays a $9 annual dividend. It has a price of $76. What is the required rate of return (yield) on the preferred stock? 10-26. Solution: Analogue Technology (All of the following problems pertain to the common stock section of the chapter.) 27. Common stock value (LO10-5) Stagnant Iron and Steel currently pays a $12.25 annual cash dividend (D0). They plan to maintain the dividend at this level for the foreseeable future as no future growth is anticipated. If the required rate of return by common stockholders (Ke) is 18 percent, what is the price of the common stock? 10-27. Solution: Stagnant Iron and Steel 28. Bio Science Inc. will pay a common stock dividend of $3.20 at the end of the year (D1). The required return on common stock (Ke) is 14 percent. The firm has a constant growth rate (g) of 9 percent. Compute the current price of the stock (P0). 10-28. Solution: BioScience Inc. 29. Common stock value under different market conditions (LO10-5) Ecology Labs Inc. will pay a dividend of $6.40 per share in the next 12 months (D1). The required rate of return (Ke) is 14 percent and the constant growth rate is 5 percent. a. Compute P0. (For parts b, c, and d in this problem, all variables remain the same except the one specifically changed. Each question is independent of the others.) b. Assume Ke, the required rate of return, goes up to 18 percent. What will be the new value of P0? c. Assume the growth rate (g) goes up to 9 percent. What will be the new value of P0? Ke goes back to its original value of 14 percent. d. Assume D1 is $7.00. What will be the new value of P0? Assume Ke is at its original value of 14 percent and g goes back to its original value of 5 percent. 10-29. Solution: Ecology Labs Inc. a. b. c. d. 30. Maxwell Communications paid a dividend of $3 last year. Over the next 12 months, the dividend is expected to grow at 8 percent, which is the constant growth rate for the firm (g). The new dividend after 12 months will represent D1. The required rate of return (Ke) is 14 percent. Compute the price of the stock (P0). 10-30. Solution: Maxwell Communications 31. Common stock value based on determining growth rate (LO10-5) Justin Cement Company has had the following pattern of earnings per share over the last five years: Year Earnings per Share 2006 $5.00 2007 5.30 2008 5.62 2009 5.96 2010 6.32 The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future. Dividends represent 40 percent of earnings. Project earnings and dividends for the next year (2011). If the required rate of return (Ke) is 13 percent, what is the anticipated stock price (P0) at the beginning of 2011? 10-31. Solution: Justin Cement Company Earnings have been growing at a rate of 6 percent per year. Base Period (2007/2006) – 1 = 6% growth ($5.30/$5.00) (2008/2007) – 1 = 6% growth ($5.62/$5.30) (2009/2008) – 1 = 6% growth ($5.96/$5.62) (2010/2009) – 1 = 6% growth ($6.32/$5.96) The projected EPS for 2011 is $6.70 = ($6.32 × 1.06). Dividends for 2011 represent 40 percent of earnings or $2.68 ($6.70 × 40%). This is the value for D1. Ke (required rate of return) is 13 percent and the growth rate is 6 percent. 32. Common stock required rate of return (LO10-5) A firm pays a $4.80 dividend at the end of year one (D1), has a stock price of $80, and a constant growth rate (g) of 5 percent. Compute the required rate of return (Ke). 10-32. Solution: 33. Common stock required rate of return (LO10-5) A firm pays a $1.50 dividend at the end of year one (D1), has a stock price of $155 (P0), and a constant growth rate (g) of 10 percent. a. Compute the required rate of return (Ke). Indicate whether each of the following changes would make the required rate of return (Ke) go up or down. (Each question is separate from the others. That is, assume only one variable changes at a time.) No actual numbers are necessary. b. The dividend payment increases. c. The expected growth rate increases. d. The stock price increases. 10-33. Solution: a. b. If the dividend payment increases, the dividend yield (D1/P0) will go up, and the required rate of return (Ke) will also go up. This assumes that the stock price doesn’t rise in response to the increased dividend. If the market demands the same required return as before the dividend increase, the stock price will rise to a new level. c. If the expected growth rate (g) increases, the required rate of return (Ke) will go up. d. If the stock price increases, the dividend yield (D1/P0) will go down, and the required rate of return (Ke) will also go down. 34. Trump Office Supplies paid a $3 dividend last year. The dividend is expected to grow at a constant rate of 7 percent over the next four years. The required rate of return is 14 percent (this will also serve as the discount rate in this problem). Round all values to three places to the right of the decimal point where appropriate. a. Compute the anticipated value of the dividends for the next four years. That is, compute D1, D2, D3, and D4—for example, D1 is $3.21 ($3.00 × 1.07). b. Discount each of these dividends back to the present at a discount rate of 14 percent and then sum them. c. Compute the price of the stock at the end of the fourth year (P4). (D5 is equal to D4 times 1.07) d. After you have computed P4, discount it back to the present at a discount rate of 14 percent for four years. e. Add together the answers in part b and part d to get P0, the current value of the stock. This answer represents the present value of the four periods of dividends, plus the present value of the price of the stock after four periods (which, in turn, represents the value of all future dividends). f. Use Formula 10-8 to show that it will provide approximately the same answer as part e. For Formula 10-8, use D1 = $3.21, Ke = 14 percent, and g = 7 percent. (The slight difference between the answers to part e and part f is due to rounding.) g. If current EPS is equal to $5.32 and the P/E ratio is 1.1 times higher than the industry average of 8, what would the stock price be? h. By what dollar amount is the stock price in part g different from the stock price in part f? i. In regard to the stock price in part f, indicate which direction it would move if (1) D1 increases, (2) Ke increases, and (3) g increases. 10-34. Solution: Trump Office Supplies a. D1 $3.00 (1.07) = $3.21 D2 3.21 (1.07) = 3.435 D3 3.435 (1.07) = 3.675 D4 3.675 (1.07) = 3.932 b. Dividends PV(14%) PV of Dividends D1 $3.21 .877 $ 2.815 D2 3.435 .769 2.642 D3 3.675 .675 2.481 D4 3.932 .592 2.328 $10.266 c. d. PV of P4 for n = 4, i = 14% $60.10 × .592 = 35.579 e. Answer to part b (PV of dividends) 10.266 Answer to part d (PV of P4) 35.579 Current value of the stock $45.845 f. 10-34. (Continued) g. Price = P/E × EPS P/E = 8 × 1.1 = 8.8 Price = 8.8 × $5.32 = $46.816 h. Part g $46.816 Part f 45.857 .959 i. 1) D1 increases, stock price increases 2) Ke increases, stock price decreases 3) g increases, stock price increases Calculator Solution: (b) N I/Y PV PMT FV 1 14 CPT PV −2.816 0 3.210 Answer: $2.82 PV of D1 N I/Y PV PMT FV 2 14 CPT PV −2.643 0 3.435 Answer: $2.64 PV of D2 N I/Y PV PMT FV 3 14 CPT PV −2.481 0 3.675 Answer: $4.83 PV of D3 N I/Y PV PMT FV 4 14 CPT PV −2.328 0 3.932 Answer: $2.33 PV of D4 Total = 2.82 + 2.64 + 2.48 + 2.33 = $10.27. (d) N I/Y PV PMT FV 4 14 CPT PV −35.584 0 60.10 Answer: $35.58 PV of P4 35. Common stock value based on PV calculations (LO10-5) Beasley Ball Bearings paid a $4 dividend last year. The dividend is expected to grow at a constant rate of 2 percent over the next four years. The required rate of return is 15 percent (this will also serve as the discount rate in this problem). Round all values to three places to the right of the decimal point where appropriate. a. Compute the anticipated value of the dividends for the next four years. That is, compute D1, D2, D3, and D4—for example, D1 is $4.08 ($4 × 1.02). b. Discount each of these dividends back to present at a discount rate of 15 percent and then sum them. c. Compute the price of the stock at the end of the fourth year (P4). (D5 is equal to D4 times 1.02.) d. After you have computed P4, discount it back to the present at a discount rate of 15 percent for four years. e. Add together the answers in part b and part d to get P0, the current value of the stock. This answer represents the present value of the four periods of dividends, plus the present value of the price of the stock after four periods, (which, in turn, represents the value of all future dividends). f. Use Formula 10-8 to show that it will provide approximately the same answer as part e. For Formula 10-8, use D1 = $4.08, Ke = 15 percent, and g = 2 percent. (The slight difference between the answers to part e and part f is due to rounding.) g. If current EPS were equal to $4.98 and the P/E ratio is 1.2 times higher than the industry average of 6, what would the stock price be? h. By what dollar amount is the stock price in part g different from the stock price in part f? i. In regard to the stock price in part f, indicate which direction it would move if (1) D1 increases, (2) Ke increases, and (3) g increases. 10-35. Solution: Beasley Ball Bearings a. D1 $4.000 (1.02) = $4.08 D2 $4.080 (1.02) = 4.162 D3 $4.162 (1.02) = 4.245 D4 $4.245 (1.02) = 4.330 b. Dividends PV(15%) PV of Dividends D1 $4.080 .870 $ 3.550 D2 4.162 .756 3.146 D3 4.245 .658 2.793 D4 4.330 .572 2.477 $11.966 c. d. PV of P4 for n = 4, i = 15% $33.977 × .572 = $19.435 e. Answer to part b (PV of dividends) $11.966 Answer to part d (PV of P4) 19.435 Current value of the stock $31.401 f. g. Price = P/E × EPS P/E = 6 × 1.2 = 7.20 Price = 7.20 × $4.98 = $35.86 10-35. (Continued) h. Part g $35.86 Part f –31.39 $ 4.47 i. 1) D1 increases, stock price increases 2) Ke increases, stock price decreases 3) g increases, stock price increases Calculator Solution: (b) N I/Y PV PMT FV 1 15 CPT PV −3.550 0 4.080 Answer: $3.550 PV of D1 N I/Y PV PMT FV 2 15 CPT PV −3.146 0 4.162 Answer: $3.146 PV of D2 N I/Y PV PMT FV 3 15 CPT PV −2.793 0 4.245 Answer: $2.793 PV of D3 N I/Y PV PMT FV 4 15 CPT PV −2.477 0 4.330 Answer: $2.477 PV of D4 Total = 3.550 + 3.146 + 2.793 + 2.477 = $11.966 (d) N I/Y PV PMT FV 4 15 CPT PV −19.426 0 33.977 Answer: $19.426 PV of P4 COMPREHENSIVE PROBLEM Preston Products (Dividend valuation model, P/E ratio) (LO10-5) Mel Thomas, the chief financial officer of Preston Resources, has been asked to do an evaluation of Dunning Chemical Company by the president and Chair of the Board, Sarah Reynolds. Preston Resources was planning a joint venture with Dunning (which was privately traded), 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. Dunning Chemical paid a dividend at the end of year one of $1.30, the anticipated growth rate was 10 percent, and the required rate of return was 14 percent. a. What is the value of the stock based on the dividend valuation model (Formula 10-8)? b. Indicate that the value you computed in part a is correct by showing the value of D1, D2, and D3 and discounting each back to the present at 14 percent. D1 is $1.30 and it increases by 10 percent (g) each year. 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. The value of the stock at the end of year three is: If you have done all these steps correctly, you should get an answer approximately equal to the answer in part a. c. As an alternative measure, you also examine the value of the firm based on the price-earnings (P/E) ratio times earnings per share. Since the company is privately traded (not in the public stock market), you will get your anticipated P/E ratio by taking the average value of five publicly traded chemical companies. The P/E ratios were as follows during the time period under analysis: P/E Ratio Dow Chemical 15 DuPont 18 Georgia Gulf 7 3M 19 Olin Corp 21 Assume Dunning Chemical has earnings per share of $2.10. What is the stock value based on the P/E ratio approach? Multiply the average P/E ratio you computed times earnings per share. How does this value compare to the dividend valuation model values that you computed in parts a and b? d. If in computing the industry average P/E, you decide to weight Olin Corp. by 40 percent and the other four firms by 15 percent, what would be the new weighted average industry P/E? (Note: You decided to weight Olin Corp. more heavily because it is similar to Dunning Chemical.) What will the new stock price be? Earnings per share will stay at $2.10. e. 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, i = 11%) (Appendix B) PV = $1,000 × .124 = $124 Total Present Value Present value of interest payments $ 939.63 Present value of principal payment at maturity 124.00 Total present value, or price, of the bond $1,063.63 The discount rate of 11 percent gives us a value slightly lower than the bond price of $1,085. The rate for the bond must fall between 10 and 11 percent. Using linear interpolation, the answer is 10.76 percent $1,153.65 PV @ 10% $1,153.65 PV @ 10% 1,063.63 PV @ 11% 1,085.00 bond price $ 90.02 $ 68.65 CP 10-1. Solution: Preston Resources—Dunning Chemical a. b. Future Value of Dividends D1 $1.30 (1.00) = $1.30 D2 $1.30 (1.10) = $1.43 D3 $1.30 (1.10) = $1.573 Present Value of Dividends Dividends PV (14%) (PV of Dividend) D1 $1.30 .877 $1.14 D2 $1.43 .769 $1.10 D3 $1.573 .675 $1.06 $3.30 Value of Stock Price at the end of Year 3 Present Value of Future Stock Price P3 = $43.25 n = 3, i = 14% (Appendix B) PV = $43.25 × .675 = $29.19 Total stock prices: PV of Dividends $ 3.30 PV of Stock Price 29.19 $32.49 CP 10-1. (Continued) c. Average P/E Ratio of Five Chemical Firms Dow Chemical 15 DuPont 18 Georgia Gulf 7 3M 19 Olin Corp. 21 Total 80 Stock Price = P/E × EPS 16 × $2.10 = $33.60 The stock price using the P/E ratio approach is slightly higher than the value using the dividend valuation model approach ($33.60 versus $32.50). d. P/E Ratio Weights Weighted Average Dow Chemical 15 .15 2.25 DuPont 18 .15 2.70 Georgia Gulf 7 .15 1.05 3M 19 .15 2.85 Olin Corp. 21 .40 8.40 17.25 Stock price = P/E × EPS $17.25 × $2.10 = $36.23 CP 10-1. (Continued) e. Stock price (d) $36.23 Stock price (c) 33.60 Appendix 10A–1. Valuation of supernormal growth firm (LO10-5) Surgical Supplies Corporation paid a dividend of $1.12 per share over the last 12 months. The dividend is expected to grow at a rate of 25 percent over the next three years (supernormal growth). It will then grow at a normal, constant rate of 7 percent for the foreseeable future. The required rate of return is 12 percent (this will also serve as the discount rate). a. Compute the anticipated value of the dividends for the next three years (D1, D2, and D3). b. Discount each of these dividends back to the present at a discount rate of 12 percent and then sum them. c. Compute the price of the stock at the end of the third year (P3). d. After you have computed P3, discount it back to the present at a discount rate of 12 percent for three years. e. Add together the answers in part b and part d to get the current value of the stock. (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.) 10A–1. Solution Surgical Supplies Corporation a. D1 $1.12 (1.25) = $1.40 D2 $1.40 (1.25) = $1.75 D3 $1.75 (1.25) = $2.19 b. Supernormal Dividends Discount Rate Ke = 12% Present Value of Dividends During the Supernormal Growth Period D1 $1.40 .893 $1.25 D2 $1.75 .797 1.39 D3 $2.19 .712 1.56 $4.20 c. d. PV of P3 for n = 3, i = 12% $46.80 × .712 = $33.32 e. Answer to part b (PV of dividends) $ 4.20 Answer to part d (PV of P3) 33.32 Current value of the stock $37.52 Solution Manual for Foundations of Financial Management Stanley B. Block, Geoffrey A. Hirt, Bartley R. Danielsen 9780077861612, 9781260013917, 9781259277160
Download
Close
Close
