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3. A $1000 face value bond with a maturity of 2 years and a 6.8750% coupon rate paying semiannual

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## 3. A $1000 face value bond with a maturity of 2 years and a 6.8750% coupon rate paying semiannual

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**MGT 326 Bond & Stock Sample Problems v1.1**1. What is the retail price of a 5 year, $1,000 face value bond that with a coupon rate of 6.0000% with semi-annual payments if its current yield to maturity is 8.0000%? m = 2, T = 5; n =m x T = 10 1) Find coupon payment: CPN = FV(rCPN/m) = $1,000(0.06/2) = $30 2) Find VB: P/Y=1, N=10, I/Y=3, PMT=30, FV=1000; CPT,PV: VB = $918.89 OR P/Y=2, N=10, I/Y=8, PMT=30, FV=1000; CPT,PV: VB = $918.89 2. A $1000 face value bond with a maturity of 3 years and a 7.0000% coupon rate paying annual interest is currently selling for $1,012.83. What is the yield to maturity of this bond? 1) Find coupon payment: CPN = FV(rCPN/m) = $1,000(0.07/1) = $70 2) Find YTM: P/Y=1, N=3, PV=-1012.83, PMT=70, FV=1000; CPT,I/Y: YTM = 6.5154% 3. A $1000 face value bond with a maturity of 2 years and a 6.8750% coupon rate paying semiannual interest is currently selling for $985.57. What is the yield to maturity of this bond? m = 2, T = 2; n =m x T = 4 1) Find coupon payment: CPN = FV(rCPN/m) = $1,000(0.068750/2) = $34.375 2) Find YTM: P/Y=1, N=4, PV=-985.57, PMT=34.375, FV=1000; CPT,I/Y: I/Y = 3.8335; YTM= 3.8335(2) = 7.6669% OR P/Y=2, N=4, PV=-985.57, PMT=34.375, FV=1000; CPT,I/Y: YTM= 7.6669% 4. You are considering purchasing a $10,000 face value bond with 16.5 years to maturity and a coupon rate of 5.6600% with semiannual payments is selling for $10,185.00. The bond’s YTM is 5.8150%. What is the bond seller’s rate of return? 1) Find Fair Market Value: CPN = FV(rCPN/m) = 10,000(0.0566/2) = $283.00 m=2, T=16.5; n = 2 x 16.5 = 33 P/Y=2, N=33, I/Y=5.815, PMT=283, FV=10000, CPT,PV = VB = $9,836.97 2) Find Broker’s rate of return on sales ($10,185 - $9,836.97 ) / $9,836.97 = 3.5380% 5. At the beginning of the year a $5,000 face value bond paying a coupon rate of 9.2500% APR with quarterly payments and 18 years maturity had a YTM of 9.3500%. At the end of the year the bond sold at par (excluding fees and transaction costs). What is the bond’s total yield for the year? Total Yield = EAR(rCPN) + Capital Gains Yield 1) Find EAR(rCPN) = (1 + rCPN/m)m – 1= (1 + 0.0925/4)4 – 1 = 9.5758% 2) Find VB(@t = 0): m=4, T= 18: m = m x T = 72 CPN = $5,000(0.0925/4) = $115.625 P/Y=4, N=72, I/Y=9.35, PMT= 115.625, FV=5000; CPT,PV: VB0 = $4,956.655 3) Find Cap Gains Yld: (VB1 – VB0)/VB0 = ($5,000 - $4,956.655)/ $4,956.655 = 0.008745 = 0.8745% Total Yield = 9.5758% + 0.8745% = 10.4503%**MGT 326 Bond & Stock Sample Problems v1.1**6. Two bonds, (Bond A & Bond B, both of equal bond rating) are offered by two different brokers. Which bond is more fairly priced by its respective broker? (Show all computations and/or calculator inputs) [Hint: Recall that return (percentage profit) is (Sales Price - Fair Market Value) / Fair Market Value ] Bond A 1) Find Retail Price: CPN = FV(rCPN/m) = 5,000(0.065/2) = $162.50 m=2, T=3; n = 2 x 3 = 6 P/Y=2, N=6, I/Y=6, PMT=162.5, FV=5000, CPT,PV = VB = $5,067.77 2) Find Broker’s rate of return on sales ($5,150 - $5,067.77) / $5,067.77 = 1.6237% Bond B 1) Find Retail Price: CPN = FV(rCPN/m) = 1,000(0.05/4) = $12.50 m=4, T=1.5; n = 4 x 1.5 = 6 P/Y=4, N=6, I/Y=4, PMT=12.5, FV=1000, CPT,PV = VB = $1,014.49 2) Find Broker’s rate of return on sales ($1,040.00 - $1,014.49) / $1,014.49 = 2.5147% Bond A is more fairly priced 7. A share of common stock has just paid a dividend of $1.45 (D0). The stock is expected to have a constant long-term dividend growth rate of 5% p.a. If rs is 9.400% what is the price of one share of this stock? P0 = D0(1 + g) / (rs –g) = $1.45(1 + 0.05) / (0.094 – 0.05) = $34.60 8. A firm’s stock is expected to pay a dividend of $1.50 per share at the end of the 2009. The firm's NI is expected to grow at an annual rate of 2.8500%. The stock price was $39.23 at the beginning of 2009. By the end of 2009 the price of the firm’s stock is expected to rise to $40.35. What is this stock's expected total yield? E(Total Yield) = E(Div Yld) + E(Cap Gains Yld) = $1.50/$39.23 + ($40.35 - $39.23) / $39.23 = 3.8236% + 2.8550% = 6.6786%**MGT 326 Bond & Stock Sample Problems v1.1**9. The stock of DAA Corp. is currently selling for $45 per share. The firm’s most recent dividend was $3. The firm's dividends are expected to grow at a rate of 10% per year for the next three years (i.e. until t=3). After this time, the dividends are expected to grow at a constant rate of 5% per year for the foreseeable future. The stock's required rate of return is 11%. Is the stock of DAA Corp. undervalued or overvalued and by how much? Normal Growth (gN= 5%, t=3 & onward) Dinfinity Supernormal Growth (gSN=10%, t=0 thru t=3) D7 D6 D5 D4 D3 D2 D1 D0 = $3.00 0 1 2 3 4 5 6 7 t = ? (infinity) Horizon Value rs = 11.0% 1) Find D1, D2 & D3: Opt 1: D1 = $3.00(1+0.10) = $3.3000; D2 = $3.30(1+0.10) = $3.6300; D3 = $3.63(1+0.10) = $3.9900 Opt 2: D1 = $3.00(1+0.10) = $3.3000; D2 = $3.00(1+0.10)2 = $3.6300; D3 = $3.00(1+0.10)3 = $3.9900 Opt 3: D1 = N=1, I/Y=10, PV=3; CPT,FV: $3.3000; D2 = N=2, I/Y=10, PV=3; CPT,FV: $3.6300; D3 = N=3, I/Y=10, PV=3; CPT,FV: $3.9930 2) Find PV at t=0 of D1, D2 & D3 and sum them Uneven Cash flow approach: CF, 2nd CLR WORK (Clear cash flow worksheet) 0, ENTER ↓, 3.30, ENTER ↓, ↓, 3.63, ENTER ↓, ↓, 3.993, ENTER NPV, 11, ENTER ↓, CPT: NPV = $8.8388 3) Find Horizon Value: D3(1 + gN) / (rs – gN) = $3.993(1 + 0.05) / (0.11 – 0.05) = $69.8775 Note: This is the theoretical value of the stock three years from today. 4) Find PV at t=0 of Horizon Value: P/Y=1, N=3, I/Y=11, PV=69.8775; CPT,PV = $51.0938 5) P0 = $8.8388 + $51.06 = $59.93 $45 - $59.93= -$14.93; The stock is under valued by $14.93**MGT 326 Bond & Stock Sample Problems v1.1**10. The stock of Gigantic Jim’s Large & Tall Men’s Clothiers Inc. is currently selling for $75 per share. The firm pays dividends each quarter and they are expected to grow at a rate of 15% per year for the next nine months. After this time, the dividends are expected to grow at a constant rate of 8% per year for the foreseeable future. The firm’s most recent dividend was $0.50. The stock's required rate of return is 11%. What is the theoretical value of this stock? Normal Growth (gN= 8%, t=3 & onward) Dinfinity Supernormal Growth (gSN=15%, t=0 thru t=3) D7 D6 D5 D4 D3 D2 D1 D0 = $0.50 0 1 2 3 4 5 6 7 t = ? (infinity) Horizon Value rs = 11.0% 1) Find D1, D2 & D3: D0 = $0.50 Solution Opt 1: D1 = $0.50(1+0.15/4) = $0.5188; D2 = $.5188(1+0.15/4) = $0.5382;D3 = $0.5382(1+0.15/4) = $0.5584 Solution Opt 2: D1 = $0.50(1+0.15/4) = $0.5188; D2 = $0.50(1+0.15/4)2 = $0.5382;D3 = $0.50(1+0.15/4)3 = $0.5584 Solution Opt 3: D1 =[P/Y=4,N=1, I/Y=15, PV=0.5; CPT,FV] $0.5188; D2 = [N=2, I/Y=15, PV=0.5; CPT,FV] $0.5382; D3 = [N=3, I/Y=15, PV=0.5; CPT,FV] $0.5584 2) Find PV at t=0 of D1, D2, D3 & D4 and sum them Uneven Cash flow approach: CF, 2nd CLR WORK (Clear cash flow worksheet) 0, ENTER ↓, 0.5188, ENTER ↓, ↓, 0.5382, ENTER ↓, ↓, 0.5584, ENTER NPV, 2.75, ENTER (I/Y = 11/4 = 2.75) ↓, CPT: NPV = $1.5294 3) Find Horizon Value: D3(1 + gN /m) / (rs/m – gN/m) = $0.5584(1 + 0.08/4) / (0.11/4 – 0.08/4) = $75.9424 4) Find PV at t=0 of Horizon Value: P/Y=4, N=3, I/Y=11, FV=75.9424; CPT,PV = $70.0066 5) P0 = $1.5294 + $70.0066 = $71.54