advertisement

AGEC 424 Lab 8 Bond Problems 1. Smith Blarney is trying to sell my grandmother a semiannual, 10% coupon, $1000 face value bond with 12 years to maturity. Currently the market requires a 6% rate of return on bonds of this risk. What is this bond worth? 1a. Smith Blarney is also trying to sell my grandmother a semiannual, 6% coupon, $1000 face value bond with 12 years to maturity. Currently the market requires a 6% rate of return on bonds of this risk. What is this bond worth? Do you need to do calculations with your financial calculator to figure this answer? 2. Smith Blarney is also trying to sell Grandma a semiannual, 4% coupon, $1000 face value bond priced at $1075. The bond has 5 years to maturity. What yield to maturity would Grandma earn if she buys this bond? 2b. Smith Blarney is also trying to sell Grandma a semiannual, 9% coupon, $1000 face value bond priced at $1000. The bond has 5 years to maturity. What yield to maturity would Grandma get if she buys this bond? Do you need to do calculations with your financial calculator to figure this answer? 3. What is the current yield of the above bond (in number 2a)? Why is the current yield greater than the YTM of the bond? 4. Thompson Tires Inc. has an outstanding semiannual, 12% coupon, $1000 face value bond that is selling for $1185 and has 10 years to maturity. What is the YTM? 5. Assume the Thompson Tires bond in #4 is callable in 5 years with a $50 call premium. What is the YTC? 6. Smith Blarney is back trying to sell Grandma a 10 year, callable, semiannual, $1000 face value, 12% coupon bond. It is callable in 1 year with a $100 call premium. If comparable bonds of this risk yield 6% and you expect this bond to be called, what is its value? Key Lab 8 bond problems 1. N=24 I=3 Compute PV=1338.71 PMT=50 FV=1000 1a. N=24 I=3 Compute PV=1000 PMT=30 FV=1000 No computation is required because when the coupon rate and required return (YTM) are the same the bond value will be its par value. 2. N=10 Compute I=1.19963x2=2.399% PV= -1075 PMT=20 FV=1000 2b. N=10 Compute I=4.5x2=9% PV= -1000 PMT=45 FV=1000 No, you do not need to do computations. If a bond is priced at par, its YTM is the same as its coupon rate. 3. 40/1075 = 3.72%. The current yield is above the YTM because the expected capital gains are negative (the bond is priced above par). 4. N=20 Compute I=4.569x2= 9.14% PV= -1185 PMT=60 FV=1000 5. N=10 Compute I=4.11966x2= 8.24% PV= -1185 PMT=60 FV=1050 6. N=2 I=3 Compute PV= 1151.66 PMT= 60 FV=1100 1 Stock Problems (constant growth model) 1. Assume a dividend today of $2.50 with anticipated growth over the next three years of 10%. The estimated dividend at the third year is: a. $3.25 b. $3.28 c. $3.33 d. none of the above 2. Sharbaugh Inc.’s most recent dividend was $2.00 per share. The dividend is expected to grow at a rate of 4% per year for the foreseeable future. If the market return is 13% on investments with comparable risk, what should the stock sell for today? a. $16.00 c. $23.11 e. $52.00 b. $22.22 d. $50.00 3. A stock just paid a $2.00 dividend that is anticipated to grow at 6% indefinitely. Similar stocks are returning about 13%. The estimated selling price of this stock is: a. $30.29 b. $15.38 c. $16.31 d. $28.57 4. A stock just paid an annual dividend of $2.00, which is expected to remain constant indefinitely. The market return is 14%. The estimated selling price of the stock is: a. $1.76 b. $14.29 c. $10.43 d. none of the above 5. A share of stock is currently selling for $20.80. If the dividend just paid is $2.00 and investors are seeking a 14% return, what is the anticipated rate of constant growth? a. 1% b. 4% c. 0% d. none of the above 6. A share of stock is currently selling for $31.80. If the anticipated constant growth rate for dividends is 6% and investors are seeking a 16% return, what is the dividend just paid? a. $1.91 b. $3.18 c. $3.00 d. $5.09 1. ANS: C 2.50(1.1)3 = $3.33 2. ANS: C (2.00 1.04)/(.13 – .04) = $23.11 3. ANS: A P0 = D0(1 + g)/(k – g) = 2(1.06)/(.13 – .06) = $30.29 4. ANS: 2/.14 = $14.29 B 5. ANS: B P0 = D0(1 + g)/(k – g) 20.80 = 2(1 + g)/(.14 – g) g = 4% 6. ANS: C P0 = D0(1 + g)/(k – g) 31.80 = D0(1 + .06)/(.16 – .06) D0 = $3 1. You are considering investing in B & B, Inc.’s stock and your broker has told you that you can purchase it for $72. You require a return 12% for this type of investment. The last dividend (D0) that B & B paid was $4 and a 6% constant growth rate is anticipated. Should you purchase B & B, Inc.? a. No, because the stock is overpriced by $1.33. b. No, because the stock is overpriced by $3.33. c. Yes, because the stock is underpriced by $1.33. d. Yes, because the stock is underpriced by $3.33. 2 2. You are considering investing in ABC, Inc.’s stock which is selling at $45.95. Similar stocks return 16%. ABC’s last dividend was $4.50 and a 6% constant growth rate is anticipated. Should you purchase ABC, Inc.? a. No, because the stock is overpriced by $1.75. b. No, because the stock is overpriced by $3.85. c. Yes, because the stock is underpriced by $1.75. d. Yes, because the stock is underpriced by $3.85. 3. Toys-r-Cool Inc.’s constant growth stock’s last dividend was $1.50. It is selling for $30.20 in a market in which similar stocks return 12%. Calculate the stock’s anticipated growth rate. a. b. c. d. 6.7% 8.7% 10.9% 12% 4. Charlie Company is expected to grow at an annual rate of 6% indefinitely. The return on similar stocks is currently 11%. Charlie’s board of directors declared a dividend of $1.85 yesterday. What should a share of Charlie Company sell for? a. $39.22 b. $37.00 c. $16.82 d. $17.83 5. What is the value of a share of Henley Inc. to an investor who requires a 12 percent rate of return if Henley’s last dividend was $1.20? Assume earnings and dividends are expected to grow indefinitely at a rate of 7% per year. a. $24.00 b. $18.34 c. $25.68 d. None of the above 6. The current price of Zebar is $32.00 and its last dividend was $.60. What is its return if dividends are expected to grow indefinitely at 8 percent? a. 9.88% b. 11.38% c. 18.75% d. none of the above 1.ANS: A P0 = D0(1 + g)/(k – g) P0 = 4(1.06)/(.06) = $70.67 $72 – $70.67 = $1.33 Stock is overpriced 2. ANS: C P0 = D0(1 + g)/(k – g) P0 = [4.50(1.06)]/(.10) = $47.70 $45.95 – $47.70 = ($1.75) Stock is underpriced 30.20 = [1.50(1 + g)]/(.12 – g) g = 6.7% 4. ANS: A P0 = D0(1 + g)/(k –g) = 1.85(1.06)/(.11 – .06) = $39.22 5. ANS: C P0 = $1.20(1.07)/(.12 –.07) = $25.68 6. ANS: D 3. ANS: A kE = [.60(1.08)/32] + .08 = 10.03% P0 = D0(1 + g)/k – g Stock Problems (two stage growth) 7. Long Life Insurance Inc just paid a dividend of $1.50, and projects supernormal growth at 12% for the next three years. After that growth is expected to slow down to a normal 4% and go on at that rate for the foreseeable future. Similar stocks are earning a return of 10%. How much would you pay for a share of Long Live today? a. $37.70 b. $32.08 c. $26.00 d. $28.28 3 ANS: B D1 = 1.50(1.12) = 1.68 D2 = 1.88 D3 = 2.11 D4 = 2.11(1.04) = 2.19168768 P3 = D4/(.10 – .04) = 36.53 CF0 = 0, C01 = 1.68, C02 = 1.88, C03 = 2.11+36.53=38.64; I = 10 Solve for NPV = $32.11 8. Cantaloupe Growers Corp. is expanding into a new geographic area. Management expects the new market to fuel growth of 22% for three years. After that normal growth of 6% will resume. Cantaloupe’s most recent annual dividend was $1.25. Other fruit companies have been returning about 12% lately. How much should a share of Cantaloupe be worth? a. $33.06 b. $38.00 c. $40.17 d. $68.32 ANS: A D1 = 1.25(1.22) = 1.53 D2 = 1.86 D3 = 2.27 D4 = 2.27(1.06) = 2.4059986 P3 = D4 /(.12 – .06) = 40.10 CF0 = 0, C01 = 1.53, C02 = 1.86, C03 = 2.27+40.10=42.37; I = 12 Solve for NPV = $33.01 9. Frazier Inc. paid a dividend of $4 last year (D0). The firm is expecting dividends to grow at 21% in years 1–2 and 10% in Year 3. After that growth will be constant at 8% per year. Similar investments return 14%. Calculate the value of the stock today. a. $71.49 b. $88.31 c. $91.47 d. $116.10 ANS: C D1 = 4(1.21) = 4.84 D2 = D1(1.21) = 5.8564 D3 = D2(1.10) = 6.442 D4 = D3(1.08) = 6.9574032 P3 = [D4]/(.14 – .08) = 115.95672 Calculator Steps: CF0 = 0, C01 = 4.84, C02 = 5.86, C03 = 6.44 + 115.96 = 122.40; I = 14 Solve for NPV = $91.37 10. Williamson Metals, Inc. paid a dividend last year of $3, and is expecting dividends to grow at an 18% rate in years 1 and 2 followed by constant growth of 6% per year thereafter. Similar stocks return 12%. Calculate the value of the stock today. a. $65.37 b. $73.85 c. $82.91 d. $93.76 ANS: A D1 = 3(1.18) = 3.54 D2 = 3.54(1.18) = 4.18 P2 = [4.1772(1.06)]/(.12 -.06) = 4.427832/.06 = 73.80 4.18 + 73.80 = 77.98 Calculator Steps: CF0 = 0, C01 = 3.54, C02 = 77.98; NPV: I = 12 NPV = $65.33 4