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Chapter 10 Problems (For the first 11 bond problems, assume interest payments are on an annual basis.) 10-1. The Lone Star Company has $1,000 par value bonds outstanding at 9 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. Solution: Lone Star Company a. 6 percent yield to maturity Present Value of Interest Payments PVA = A * PVIFA (n = 20, I = 6%) PVA = 90 * 11.470 = $1,032.30 Appendix D 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 Present Value of Principal Payments Total Present Value or Price of the Bond S-298 $1,032.30 312.00 $1,344.30 b. 8 percent yield to maturity PVA = A * PVIFA (n = 20, I = 8%) PVA = $90 * 9.818 = $883.62 Appendix D PV = FV * PVIF (n = 20, I = 8%) PV = $1,000 * .215 = $215 Appendix B $ 883.62 215.00 $1,098.62 c. 12 percent yield to maturity PVA = A * PVIFA (n = 20, I = 12%) PVA = $90 * 7.469 = $672.21 Appendix D PV = FV * PVIF (n = 20, I = 12%) PV = $1,000 * .104 = $104 Appendix B $672.21 104.00 $776.21 10-24. Justin Cement Company has had the following pattern of earnings per share over the last five years: Year Earnings per Share 1997........................................ $4.00 1998........................................ 4.20 1999........................................ 4.41 2000........................................ 4.63 2001........................................ 4.86 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 (2002). S-299 If the required rate of return (K e) is 13 percent, what is the anticipated stock price (P0 ) at the beginning of 2002? Solution: Justin Cement Company Earnings have been growing at a rate of 5 percent per year. 1998 1999 2000 2001 Base Period $4.20/4.00 $4.41/4.20 $4.63/4.41 $4,86/4.63 5% growth 5% growth 5% growth 5% growth The projected EPS for 2002 is $5.10 ($4.86 * 1.05) Dividends for 2002 represent 40% of earnings or $2.04 ($5.10 * 40%) This is the value for D1 . Ke (required rate of return) is 13% and the growth rate is 5%. P0 (2002) = 10-27. D1 $2. 04 $2. 04 = = = $25.50 K e - g 0.13 − 0. 05 0. 08 Hunter Petroleum Corporation paid a $2 dividend last year. The dividend is expected to grow at a constant rate of 5 percent over the next three years. The required rate of return is 12 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 three years. That is, compute D , D , and D ; for example, D is $2.10 ($2.00 * 1.05). S-300 is, compute D1 , D2 , and D3 ; for example, D1 is $2.10 ($2.00 * 1.05). 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 ). P3 = D4 Ke − g (D4 is equal to D3 times 1.05) d. After your 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 P0 , 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 (which, in turn, represents the value of all future dividends). f. Use Formula 10-9 to show that it will provide approximately the same answer as part e. P0 = D1 Ke − g For Formula 10-9 use D1 = $2.10, Ke = 12 percent, and g = 5 percent. (The slight difference between the answers to part e and part f is due to rounding.) Solution: Hunter Petroleum Corporation a. D1 D2 D3 $2.00 (1.05) = $2.10 $2.10 (1.05) = $2.205 $2.205 (1.05) = $2.315 b. Dividends $2.10 $2.205 $2.315 D1 D2 D3 PV(12%) .893 .797 .712 S-301 PV of Dividends $1.875 1.757 1.648 $5.280 c. P3 = P3 = D4 K e -g D4 = $2. 315 (1.05) = $2.431 $2.431 2.431 = = $34.729 .12 − .05 .07 d. PV of P 3 for n = 3, i = 12% $34.729 * .712 = $24.727 e. answer to part b (PV of dividends) answer to part d (PV of P 3) current value of the stock f. P0 = D1 $2. 10 $2.10 = = = $30.00 K e - g .12 − .05 .07 S-302 $ 5.280 24.727 $30.007 S-303