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Bond Stock Problems solutions l

# Bond Stock Problems solutions l - 1 An Ohio savings bond...

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Unformatted text preview: 1. An Ohio savings bond can be converted to \$25 at maturity six years from purchase. If the state bonds are to be competitive with U Bonds paying 8% annual interest (compounded annually), at what price will the state sell its bonds? Assume no cash payments on savings b to redemption. FV6 n Interest rate PV \$25 6 8% \$15.75 zero-coupn bond Price 2. Determine the value of a \$1,000 Canadian Pacific Limited perpetual 4 percent debenture (bond) at the following rates of return. a. 4% \$1,000 b. 5% \$800 c. 6% \$667 consol; \$1,333.33 3. Consider Allied Signal Corporation's 9 7/8 percent bonds that mature on June 1, 2002. Assume that the interest on these bonds compounded annually. Determine the value of a \$1,000 denomination Allied Signal Corporation bond as of June 1, 1993, to an investor the bond until maturity and whose required rate of return is Coupon Price Par Value Pmt \$1,187.31 \$1,000.00 \$98.75 \$1,052.46 \$1,000.00 \$98.75 \$937.71 \$1,000.00 \$98.75 a. 7% b. 9% c. 11% d. What would be the value of the Allied Signal Corporation bonds at an 8% required rate of return if the interest were paid and compounded semiannually? \$1,118.68 \$1,117.13 \$1,000.00 \$49.38 coupon bond 4. Creative Financing, Inc. is planning to offer a \$1,000 par value 15-year maturity bond with a coupon interest rate that changes every 5 coupon rate for the first 5 years is 10%, 10.75% for the next 5 years, and 11.5% for the final 5 years. If you require an 11% rate of return o this quality and maturity, what is the maximum price you would pay for the bond? (Assume interest is paid annually at the end of each year Time Cash Flow PV Maturity Value \$1,000.00 1 \$100.0 Interest rate 11% 2 \$100.0 Coupon 1-5 10% 3 \$100.0 Coupon 6-10 10.75% 4 \$100.0 Coupon 11-15 11.50% 5 \$100.0 Price \$964 6 \$107.5 7 \$107.5 8 \$107.5 9 10 11 12 13 14 15 \$107.5 \$107.5 \$115.0 \$115.0 \$115.0 \$115.0 \$1,115.0 5. Allied Signal Corporation has a series of zero coupon bonds outstanding that mature on August 1, 2007. The bonds were issued on 1982 for \$125. Determine the yield to maturity (to the nearest tenth of 1 percent) if the bonds are purchased at the a. Issue price in 1982. b. Market price on August 1, 1983 of \$743.75. c. Why are the returns calculated in Parts a and b different? **Assume that maturity value is \$1,000 Time 25 years 24 years PV FV 125 \$1,000.00 743.75 \$1,000.00 6. Determine the value of a share of Litton Industries Series B \$2.00 cumulative preferred stock to an investor who requires the follow return: a. 9% 9% \$22.22 b. 10% 10% \$20.00 c. 12% 12% \$16.67 7. Dooley, Inc., has outstanding \$100 million (par value) bonds that pay an annual coupon rate of interest of 10.5%. Par value of ea \$1,000. The bonds are scheduled to mature in 20 years. Because of Dooley's increased risk, investors now require a 14% rate of return o similar quality with 20 years remaining until maturity. The bonds are callable at 110% of par at the end of 10 years. a. What price would the bonds sell for assuming investors do not expect them to be called? b. What price would the bonds sell for assuming investors expect them to be called at the end of 10 years? Coupon rate 10.50% Call Premium 110% Maturity Value \$1,000 # periods to maturity 20 # periods to call 10 YTM 14% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 8. Waters, Inc., has outstanding a \$100 million (face value) issue of bonds. The bonds pay a coupon rate of interest of 8 percent per annum were first issued, they sold at face value of \$1,000 per bond. The bonds now have 12 years remaining until maturity. They are "puttab bondholder at face value in 5 years. The bonds are not callable by the company. If you require a 9 percent return on bonds such as these until maturity and 8.2 percent on bonds such as these with 12 years remaining until maturity, how much would you pay for one of these bon Time CF(no put) Maturity Value \$1,000 0 Time to Bond Maturity 12 1 \$80 Time to Put Maturity 5 2 \$80 Coupon Rate 8% 3 \$80 YTM Putable 9% 4 \$80 YTM Non-Putable 8.20% 5 \$80 Put Premium 0% 6 \$80 7 \$80 8 \$80 9 \$80 10 \$80 11 \$80 12 \$1,080 Price 9. General Cereal common stock dividends have been growing at an annual rate of 7 percent per year over the past 10 years. Current di \$1.70 per share. What is the current value of a share of this stock to an investor who requires a 12 percent rate of return if the following exist? a. Dividends are expected to continue growing at the historic rate for the foreseeable future. Dividends are expected to continue growing at the historic rate for the foreseeable future. b. The dividend growth rate is expected to increase to 9 percent per year. Dividend growth rate is expected to increase to 9 percent per year. c. Dividend growth rate is expected to decrease to 6.5 percent per year. Dividend 0 \$1.70 ke 12% 10. The common stock of General Land Development Company (GLDC) is expected to pay a dividend of \$1.25 next year and current \$25. Assume that the firm's future dividend payments are expected to grow at a constant rate for the foreseeable future. Determine t growth rate of GLDC's dividends (and earnings), assuming that the required rate of return of investors is 12 percent. Dividend 1 P0 ke g stop \$1.25 \$25 12% 7% \$25.00 \$25.00 11. Cascade Mining Company expects its earnings and dividends to increase by 7 percent per year over the next 6 years and then relatively constant thereafter. The firms currently (that is, as of year 0) pays a dividend of \$5 per share. Determine the value of a share stock to an investor with a 12 percent required rate of return. Dividend cash flow Dividend 0 \$5 0 \$5.00 ke 12% 1 \$5.35 \$5.35 g(1-6) 7% 2 \$5.72 \$5.72 g(7-α) 0% 3 \$6.13 \$6.13 P0 \$57.31 4 \$6.55 \$6.55 5 \$7.01 \$7.01 6 \$7.50 \$7.50 7 \$7.50 \$7.50 8 \$7.50 \$7.50 9 \$7.50 \$62.50 \$70.00 10 \$7.50 12. Over the past 5 years, the dividends of the Gamma Corporation have grown from \$0.70 per share to the current level of \$1.30 per s This growth rate is expected to continue for the foreseeable future. What is the value of a share of Gamma Corporation common stock to who requires a 20 percent return on her investment? Dividend -5 \$0.70 div 1 \$1.47 Dividend 0 ke g P0 \$1.30 20% 13.18% \$21.57 13. Simtek currently pays a \$2.50 dividend (D0) per share. Next year's dividend is expected to be \$3 per share. After next year, div expected to increase at a 9 percent annual rate for 3 years and a 6 percent annual rate thereafter. What is the current value of a share of Simtek stock to an investor who requires a 15 percent return on his or her investment? a. If the dividend in year 1 is expected to be \$3 and the growth rate over the following 3 years is expected to be only 7 percent and then 6 percent thereafter, what will the new stock price be? b. cash flow Dividend 0 \$2.50 0 Dividend 1 \$3.00 1 \$3.00 \$3.00 g (2-4) 9% 2 \$3.27 \$3.27 g (5-α) 6% 3 \$3.56 \$3.56 ke 15% 4 \$3.89 \$3.89 P0 \$35.81 5 \$4.12 \$4.12 \$34.14 6 \$4.37 \$4.37 7 \$4.63 \$4.63 8 \$4.90 \$4.90 9 \$5.20 \$61.23 \$66.43 10 \$5.51 14. Suppose General Electric common stock is selling at \$68 a share, and its present dividend, D0 , is \$2 a share. If investors are req percent annual return, what annual growth rate are they expecting, assuming a constant growth valuation model is appropriate for General E P0 Dividend 0 ke g \$68 \$2 14% 15. A security analyst has forecast the dividends of Hedges enterprises for the next 3 years. His forecast is: D1 = \$1.50; D2 = \$ \$2.20. He has also forecast a selling price in 3 years of \$48.50. The rate of return for common stock with risk level comparable to that enterprises is 14%. What is the value of Hedges stock? 1 Dividend 1 2 Dividend 2 3 Dividend 3 3 P3 ke P0 \$1.50 \$1.75 \$2.20 \$48.50 14% \$1.32 \$1.35 \$1.48 \$32.74 16. A company pays a current dividend (D0) of \$1.20 per share on its common stock. The annual dividend will increase by 3%, 4% respectively, over the next 3 years, and then by 6% per year thereafter. The appropriate discount rate is 12%. What is the current price of the stock? a. What is the capital gain (or loss) on the stock over the past year? b. 1 Dividend 0 2 Dividend 1 3 Dividend 2 4 Dividend 3 Dividend 4 ke 4 P3 P0 \$1.20 \$1.07 12% 17. Stock in Lockwood Corporation is selling for \$60 per share. Lockwood has paid a dividend of \$4 per share, and the required rate o similar stocks is 12%. Assuming that Lockwood's dividend will grow at a constant rate in the future, what will that growth rate be? P0 Dividend 0 ke g \$60 \$4 12% 18. The Zero Company wishes to determine the required rate of return on its common stock. The prevailing market price, P0, of its comm \$50 per share. The firm expects to pay a dividend, D1, of \$4 at the end of the coming year - 1993. The dividends paid on the outstandin stock over the past 6 years (1987-1992) are given below. Year 1992 1991 1990 1989 1988 1987 Dividend 3.8 3.62 3.47 3.33 3.12 2.97 P0 Dividend 1993 \$50 \$4 The firm has maintained a fixed payout ratio from 1987 to 1992. a. What is the growth rate of earnings and dividends? b. What is the required rate of return on zero company's common stock? 19 If D1 = \$10, D2 = \$20, P0 = \$60 and the required rate of return(r) = .12. What is P2? Dividend 1 Dividend 2 P0 ke P2 \$10 \$20 \$60 12% 20. Investor A can buy a perpetual bond (consol) that pays a coupon rate of \$10 per year. Investor A's required rate of return is 10%. T plans to buy the bond now, hold it for three years, collect the three coupon payments, and then sell it to Investor B. If Investor B purchases the end of year three and has the following alternative required rates of return, what is the present value (price) of the bond to Investor A? PV(P3) P0 PV(Dividends) a. Investor B's required rate of return is 10%. b. Investor B's required rate of return is 8%. c. Investor B's required rate of return is 20%. are to be competitive with U.S. Savings no cash payments on savings bonds prior lowing rates of return. t the interest on these bonds is paid and f June 1, 1993, to an investor who holds 9.88 #periods 9 9 9 18 erest rate that changes every 5 years. The equire an 11% rate of return on a bond of nually at the end of each year.) 07. The bonds were issued on August 1, t the YTM 8.67% 1.24% Par \$1,000.00 \$1,000.00 estor who requires the following rates of est of 10.5%. Par value of each bond is require a 14% rate of return on bonds of years. CF (no call) CF (call) \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$105 \$1,105 \$1,205 \$\$\$\$\$\$\$\$\$\$- nterest of 8 percent per annum. At the time the bonds til maturity. They are "puttable" at the option of the return on bonds such as these with 5 years remaining d you pay for one of these bonds? CF(put) \$80 \$80 \$80 \$80 \$1,080 the past 10 years. Current dividends are rate of return if the following conditions \$36.38 \$61.77 \$32.92 g 7% 9% 6.50% ke 12% 12% 12% E(DIV 1) \$1.82 \$1.85 \$1.81 of \$1.25 next year and currently sells for reseeable future. Determine the implied ercent. er the next 6 years and then to remain etermine the value of a share of Cascade he current level of \$1.30 per share (D0). orporation common stock to an investor er share. After next year, dividends are rn on his or her investment? pected to be only 7 percent EPS g(EPS) rr 25% 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 \$1.20 \$1.50 \$1.88 \$2.34 \$2.93 \$3.66 \$4.58 \$5.72 \$7.15 \$8.94 \$11.18 \$13.97 \$17.46 \$21.83 \$27.28 \$34.11 \$42.63 \$53.29 \$66.61 \$83.27 \$104.08 \$114.49 DPS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \$68.70 \$17.92 a share. If investors are requiring a 14 el is appropriate for General Electric? rr g is: D1 = \$1.50; D2 = \$1.75; D3 = risk level comparable to that of Hedges 0.4 10% \$686.95 dend will increase by 3%, 4%, and 5%, share, and the required rate of return on l that growth rate be? market price, P0, of its common stock is idends paid on the outstanding common uired rate of return is 10%. The investor tor B. If Investor B purchases the bond at ) of the bond to Investor A? ...
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