Chapter 3 Financial Markets PDF

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Chapter 3 Riley 1. BSW Corporation has a bond issue outstanding with an annual coupon rate of 6.4 percent paid quarterly and four years remaining until maturity. The par value of the bond is $1,000. Determine the fair present value of the bond if market conditions justify a 13.5 percent, compounded quarterly, required rate of return. $783.30 Calculations (BA II PLUS Calculator): N= (4x4)= 16 I/Y= (13.5/4)= 3.375 PMT = (6.4/4) = 1.6 = 16 FV = 1000 2. Calculate the yield to maturity on the following bonds. a. A 8.1 percent coupon (paid semiannually) bond, with a $1,000 face value and 21 years remaining to maturity. The bond is selling at $890. 9.13% b. An 5.2 percent coupon (paid quarterly) bond, with a $1,000 face value and 10 years remaining to maturity. The bond is selling at $916. 6.36% c. An 7.2 percent coupon (paid annually) bond, with a $1,000 face value and 8 years remaining to maturity. The bond is selling at $1,066. 6.13% Calculations: a. N= (21x2) = 42 PV = -890 PMT = 81 FV = 1000 b. N= 10 PV = -916 PMT = 52 FV = 1000 c. N= 8 PV = -1066 PMT = 72 FV = 1000 3. Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $1,000, have 12 years remaining to maturity, and have a required rate of return of 11.5 percent. a. The bond has a 7.8 percent coupon rate. $765.40 b. The bond has a 9.8 percent coupon rate. $892.21 c. The bond has a 11.5 percent coupon rate. $1000 Calculations: a. N= 12 I/Y = 11.5 PMT = 78 FV = 1000 b. N= 12 I/Y = 11.5 PMT = 98 FV = 1000 c. N= 12 I/Y = 11.5 PMT = 115 FV = 1000

4. A $1,000 par value bond with five years left to maturity pays an interest payment semiannually with a 9 percent coupon rate and is priced to have a 8.3 percent yield to maturity. If interest rates surprisingly increase by 0.5 percent, by how much would the bond's price change? Bond's price DECREASED by $19.91 Calculations: N= 5 I/Y = 8.3 PMT = 90 FV = 1000 PV = ? PV = 1027.73 N= 5 I/Y = 8.8 (8.3 + .05) PMT = 90 FV = 1000 PV = ? PV = 1007.82 1027.73-1007.82 = 19.91 5. A preferred stock from Hecla Mining Co. (HLPRB) pays $2.40 in annual dividends. If the required rate of return on the preferred stock is 6 percent, what is the fair present value of the stock? $40 Calculations: P1 = [D0 (1+g)]/(i-g) = 2.40/.06 = 40 6. Financial analysts forecast Limited Brands (LTD) growth for the future to be 11.2 percent. LTD's most recent dividend was $1.10. What is the fair present value of Limited Brands's stock if the required rate of return is 15.2 percent? $30.58 Calculations: P1 = [D0 (1+g)]/(i-g) = [1.10 (1+.112)] / (.152-.112) = 30.58 7. A stock you are evaluating just paid an annual dividend of $3.60. Dividends have grown at a constant rate of 1.2 percent over the last 15 years and you expect this to continue. a. If the required rate of return on the stock is 13.7 percent, what is its fair present value? $29.15 b. If the required rate of return on the stock is 16.7 percent, what should the fair value be four years from today? $24.65 Calculations: a. P1 = [D0 (1+g)]/(i-g) = [3.60 (1+.012)] / (.137-.012) = 29.15 b. P4= [$3.60(1 + 0.012)^5] / (0.167 − 0.012) = 24.65 8. A company recently paid a $1.00 dividend. The dividend is expected to grow at a 15.7 percent rate. At a current stock price of $89.29, what return are shareholders expecting? 17.00% Calculations: P1 = [D0 (1+g)]/(i-g) 89.29= [1.00 (1+.157)]/ (i-.157) 89.29(i-.157) = 1.157 i-.157 = .0129 i=.1699

9. a. What is the duration of a two-year bond that pays an annual coupon of 10.4 percent and has a current yield to maturity of 12.5 percent? Use $1,000 as the face value. 1.90 years b. What is the duration of a two-year zero-coupon bond that is yielding 11.5 percent? Use $1,000 as the face value. 2 years Calculations: a. Year 1 CF = 104 1/(1+0.125)^t = 0.8889 PV of CF = 92.44 PV of CF x t = 92.44 Year 2 CF = 1104 1/(1+0.125)^t = 0.7901 PV of CF = 872.30 PV of CF x t = 1744.59 PV of CF for year 1 and 2 = 964.74 PV of CF x t for year 1 and 2 = 1837.04 Duration = 1837.04/964.74 = 1.9042 years b. zero coupon bond = year to maturity 10. Consider the following. a. What is the duration of a four-year Treasury bond with a 5.5 percent semiannual coupon selling at par? 3.64 years b. What is the duration of a three-year Treasury bond with a 5.5 percent semiannual coupon selling at par? 2.81 years c. What is the duration of a two-year Treasury bond with a 5.5 percent semiannual coupon selling at par? 1.92 years Calculations: a. 3644.70/1000 = 3.64 b. 2806.29/1000 = 2.81 c. 1921.13/1000 = 1.92 11. You have discovered that when the required rate of return on a bond you own fell by 0.5 percent from 9.1 percent to 8.6 percent, the fair present value rose from $955 to $965. What is the duration of this bond? Assume annual payments. 2.3 years Calculations: We know −D = [ΔPb/Pb]/[Δrb/(1+ rb)], so −D = (10/955)/(−0.005/1.091) = −2.28 years; D = 2.3 years.

1. Duration is the weighted average time to maturity of the bond's cash flows. 2. Which of the following bond terms are generally positively related to bond price volatility? I. II. III. IV.

Coupon rate Maturity YTM Payment frequency

II only 3. A security has an expected return less than its required return. This security is selling for more than its PV. 4. You would want to purchase a security if P ≤ PV or E(r) ≥ r.

5. A 10-year annual payment corporate bond has a market price of $1,050. It pays annual interest of $100 and its required rate of return is 9 percent. By how much is the bond mispriced? Underpriced by $14.18 6. A 12-year annual payment corporate bond has a market price of $925. It pays annual interest of $60 and its required rate of return is 7 percent. By how much is the bond mispriced? Overpriced by $4.43 7. An eight-year corporate bond has a 7 percent coupon rate. What should be the bond's price if the required return is 6 percent and the bond pays interest semiannually? $1,062.81 8. A corporate bond has a coupon rate of 10 percent and a required return of 10 percent. This bond's price is $1,000.00. 9. A 10-year annual payment corporate coupon bond has an expected return of 11 percent and a required return of 10 percent. The bond's market price is less than its PV. 10. An eight-year annual payment 7 percent coupon Treasury bond has a price of $1,075. The bond's annual E(r) must be 5.80 percent. 11. Corporate Bond A returns 5 percent of its cost in PV terms in each of the first five years and 75 percent of its value in the sixth year. Corporate Bond B returns 8 percent of its cost in PV terms in each of the first five years and 60 percent of its cost in the sixth year. If A and B have the same required return, which of the following is/are true? I. II. III. IV.

Bond A has a bigger coupon than Bond B. Bond A has a longer duration than Bond B. Bond A is less price-volatile than Bond B. Bond B has a higher FPV than Bond A.

II and IV only 12. A corporate bond returns 12 percent of its cost (in PV terms) in the first year, 11 percent in the second year, 10 percent in the third year and the remainder in the fourth year. What is the bond's duration in years? 3.32 years 13. A semiannual payment bond with a $1,000 par has a 7 percent quoted coupon rate, a 7 percent promised YTM, and 10 years to maturity. What is the bond's duration? 7.35 years 14. If an N year security recovered the same percentage of its cost in PV terms each year, the duration would be sum of the years/N. 15. You bought a stock three years ago and paid $45 per share. You collected a $2 dividend per share each year you held the stock and then you sold the stock for $47 per share. What was your annual compound rate of return? 5.84 percent 16. A four-year maturity 0 percent coupon corporate bond with a required rate of return of 12 percent has an annual duration of 4.00 years. 17. A decrease in interest rates will increase the bond's duration. 18. A six-year maturity bond has a five-year duration. Over the next year maturity will decline by one year and duration will decline by less than one year. 19. An annual payment bond has a 9 percent required return. Interest rates are projected to fall 25 basis points. The bond's duration is 12 years. What is the predicted price change? 2.75 percent 20. The duration of a 180-day T-Bill is (in years). 0.493.

Candru 1. The required rate of return on a bond is A. the interest rate that equates the current market price of the bond with the present value of all future cash flows received. B. equivalent to the current yield for non-par bonds. C. less than the E(r) for discount bonds and greate than the E(r) for premium bonds. D. inversely related to a bond's risk and coupon. E. none of the options. 2. Duration is A. the elasticity of a security's value to small coupon changes. B. the weighted average time to maturity of the bond's cash flows. C. the time until the investor recovers the price of the bond in today's dollars. D. greater than maturity for deep discount bonds and less than maturity for premium bonds. E. the second derivative of the bond price formula with respect to the YTM. 3. Which of the following bond terms are generally positively related to bond price volatility? I. II. III. IV. A. B. C. D. E.

Coupon rate Maturity YTM Payment frequency II and IV only I and III only II and III only II only II, III, and IV only

4. The interest rate used to find the present value of a financial security is the A. expected rate of return. B. required rate of return. C. realized rate of return. D. realized yield to maturity. E. current yield. 5. A security has an expected return less than its required return. This security is A. selling at a premium to par. B. selling at a discount to par. C. selling for more than its PV. D. selling for less than its PV. E. a zero coupon bond. 6. A bond that you held to maturity had a realized return of 8 percent, but when you bought it, it had an expected return of 6 percent. If no default occurred, which one of the following must be true? A. The bond was purchased at a premium to par. B. The coupon rate was 8 percent. C. The required return was greater than 6 percent. D. The coupons were reinvested at a higher rate than expected. E. The bond must have been a zero coupon bond. 7. You would want to purchase a security if P ____________ PV or E(r) ____________ r. A. ≥; ≤ B. ≥; ≥ C. ≤; ≥ D. ≤; ≤

8. A 10-year annual payment corporate bond has a market price of $1,050. It pays annual interest of $100 and its required rate of return is 9 percent. By how much is the bond mispriced? A. $0.00 B. Overpriced by $14.18 C. Underpriced by $14.18 D. Overpriced by $9.32 E. Underpriced by $9.32 9. A 12-year annual payment corporate bond has a market price of $925. It pays annual interest of $60 and its required rate of return is 7 percent. By how much is the bond mispriced? A. $0.00 B. Overpriced by $7.29 C. Underpriced by $7.29 D. Overpriced by $4.43 E. Underpriced by $4.43 10. An eight-year corporate bond has a 7 percent coupon rate. What should be the bond's price if the required return is 6 percent and the bond pays interest semiannually? A. $1,062.81 B. $1,062.10 C. $1,053.45 D. $1,052.99 E. $1,049.49 11. A 15-year corporate bond pays $40 interest every six months. What is the bond's price if the bond's promised YTM is 5.5 percent? A. $1,261.32 B. $1,253.12 C. $1,250.94 D. $1,263.45 E. $1,264.79 12. A corporate bond has a coupon rate of 10 percent and a required return of 10 percent. This bond's price is A. $924.18. B. $1,000.00. C. $879.68. D. $1,124.83. E. not possible to determine from the information given. 13. A 10-year annual payment corporate coupon bond has an expected return of 11 percent and a required return of 10 percent. The bond's market price is A. greater than its PV. B. less than par. C. less than its E(r). D. less than its PV. E. $1,000.00. 14. An eight-year annual payment 7 percent coupon Treasury bond has a price of $1,075. The bond's annual E(r) must be A. 13.49 percent. B. 5.80 percent. C. 7.00 percent. D. 1.69 percent. E. 4.25 percent.

15. A six-year annual payment corporate bond has a required return of 9.5 percent and an 8 percent coupon. Its market value is $20 over its PV. What is the bond's E(r)? A. B. C. D. E.

8.00 percent 10.21 percent 9.98 percent 9.03 percent 3.53 percent

16. Corporate Bond A returns 5 percent of its cost in PV terms in each of the first five years and 75 percent of its value in the sixth year. Corporate Bond B returns 8 percent of its cost in PV terms in each of the first five years and 60 percent of its cost in the sixth year. If A and B have the same required return, which of the following is/are true? I. II. III. IV. A. B. C. D. E.

Bond A has a bigger coupon than Bond B. Bond A has a longer duration than Bond B. Bond A is less price-volatile than Bond B. Bond B has a higher FPV than Bond A. III only I, III, and IV only I, II, and IV only II and IV only I, II, III, and IV

17. A corporate bond returns 12 percent of its cost (in PV terms) in the first year, 11 percent in the second year, 10 percent in the third year and the remainder in the fourth year. What is the bond's duration in years? A. 3.68 years B. 2.50 years C. 4.00 years D. 3.75 years E. 3.32 years 18. A semiannual payment bond with a $1,000 par has a 7 percent quoted coupon rate, a 7 percent promised YTM, and 10 years to maturity. What is the bond's duration? A. 10.00 years B. 8.39 years C. 6.45 years D. 5.20 years E. 7.35 years 19. An annual payment bond with a $1,000 par has a 5 percent quoted coupon rate, a 6 percent promised YTM, and six years to maturity. What is the bond's duration? A. 5.31 years B. 5.25 years C. 4.76 years D. 4.16 years E. 3.19 years 20. If an N year security recovered the same percentage of its cost in PV terms each year, the duration would be A. N. B. 0. C. sum of the years/N. D. N!/N2. E. none of the options.

21. The ___________ the coupon and the ______________ the maturity; the __________ the duration of a bond, ceteris paribus. A. larger; longer; longer B. larger; longer; shorter C. smaller; shorter; longer D. smaller; shorter; shorter E. None of the options presented 22. You bought a stock three years ago and paid $45 per share. You collected a $2 dividend per share each year you held the stock and then you sold the stock for $47 per share. What was your annual compound rate of return? A. 8.89 percent B. 8.51 percent C. 5.84 percent D. 4.44 percent E. 2.96 percent 23. A four-year maturity 0 percent coupon corporate bond with a required rate of return of 12 percent has an annual duration of _______________ years. A. 3.05 B. 2.97 C. 3.22 D. 3.71 E. 4.00 24. A decrease in interest rates will A. decrease the bond's PV. B. increase the bond's duration. C. lower the bond's coupon rate. D. change the bond's payment frequency. E. not affect the bond's duration. 25. A 10-year maturity coupon bond has a six-year duration. An equivalent 20-year bond with the same coupon has a duration A. equal to 12 years. B. less than six years. C. less than 12 years. D. equal to six years E. greater than 20 years. 26. A six-year maturity bond has a five-year duration. Over the next year maturity will decline by one year and duration will decline by A. less than one year. B. more than one year. C. one year. D. N years. E. N/(N-1) years. 27. An annual payment bond has a 9 percent required return. Interest rates are projected to fall 25 basis points. The bond's duration is 12 years. What is the predicted price change? A. -2.75 percent B. 33.33 percent C. 1.95 percent D. -1.95 percent E. 2.75 percent

28. A bond that pays interest annually has a 6 percent promised yield and a price of $1,025. Annual interest rates are now projected to fall 50 basis points. The bond's duration is six years. What is the predicted new bond price after the interest rate change? (Watch your rounding.) A. $1,042.33 B. $995.99 C. $1,054.01 D. $987.44 E. None of the options presented 29. A bond that pays interest semiannually has a 6 percent promised yield and a price of $1,045. Annual interest rates are now projected to increase 50 basis points. The bond's duration is five years. What is the predicted new bond price after the interest rate change? (Watch your rounding.) A. $1,020.35 B. $1,069.65 C. $1,070.36 D. $1,019.64 E. None of the options presented 30. Convexity arises because A. bonds pay interest semiannually. B. coupon changes are the opposite sign of interest rate changes. C. duration is an increasing function of maturity. D. present values are a nonlinear function of interest rates. E. duration increases at higher interest rates. 31. The duration of a 180-day T-Bill is (in years) A. 0.493. B. 0.246. C. 1. D. 0. E. indeterminate. 32. For large interest rate increases, duration _____________ the fall in security prices, and for large interest rate decreases, duration ______________ the rise in security prices. A. overpredicts; overpredicts B. overpredicts; underpredicts C. underpredicts; overpredicts D. underpredicts; underpredicts E. None of the options presented

Kaywood 1. The dividend yield is defined as: A. the current annual cash dividend divided by the current market price per share. B. the current annual cash dividend divided by the current book value per share. C. next year's expected cash dividend divided by the current market price per share. D. next year's expected cash dividend divided by the current book value per share. E. next year's expected cash dividend divided by next year's expected market price per share. 2. The capital gains yield equals which one of the following? A. Total yield B. Current discount rate C. Market rate of return D. Dividend yield E. Dividend growth rate

3. Kate could not attend the last shareholders meeting and thus she granted the authority to vote on her behalf to the managers of the firm. Which one of the following terms is used to describe the method by which Kate's shares were voted? A. Straight B. Cumulative C. Consent-form D. Proxy E. In absentia 4. What is the market called that allows shareholders to resell their shares to other investors? A. Primary B. Proxy C. Secondary D. Inside E. Initial 5. The price of a stock at year 4 can be expressed as: A. D0 / (R + G4). B. D0 × (1 + R)5. C. D1 × (1 + R)5. D. D4/(R-g). E. D5/(R-g). 6. The required return on a stock is equal to which one of the following if the dividend on the stock decreases by 1 percent per year? A. (P0/D1)-g B. (D1/P0)/g C. Dividend yield + capital gains yield D. Dividend yield - capital gains yield E. Dividend yield × capital gains yield 7. Computing the present value of a growing perpetuity is most similar to computing the current value of which one of the following? A. Non-dividend-paying stock B. Stock with a constant dividend C. Stock with irregular dividends D. Stock with a constant growth dividend E. Stock with growing dividends for a limited period of time 8. The Glass Ceiling paid an annual dividend of $2.20 per share last year. Management just announced that future dividends will increase by 2.8 percent annually. What is the amount of the expected dividend in year 5? A. $2.39 B. $2.41 C. $2.46 D. $2.53 E. $2.58 9. The Pancake House pays a constant annual dividend of $1.25 per share. How much are you willing to pay for one share if you require a 15 percent rate of return? A. $7.86 B. $8.33 C. $10.87 D. $11.04 E. $11.38

10. Klaus Toys just paid its annual dividend of $1.40. The required return is 16 percent and the dividend growth rate is 2 percent. What is the expected value of this stock five years from now? A. $11.04 B. $11.26 C. $11.67 D. $12.41 E. $12.58 11. Blackwell Ink is losing significant market share and thus its managers have decided to decrease the firm's annual dividend. The last annual dividend was $0.90 a share but all future dividends will be decreased by 5 percent annually. What is a share of this stock worth today at a required return of 15 percent? A. $4.07 B. $4.28 C. $4.49 D. $4.72 E. $4.95 12. The common stock of Tasty Treats is valued at $10.80 a share. The company increases its dividend by 8 percent annually and expects its next dividend to be $0.20 per share. What is the total rate of return on this ...