# BD_SM08 - Chapter 8 Valuing Bonds 8-1 a The coupon payment...

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Unformatted text preview: Chapter 8 Valuing Bonds 8-1. a. The coupon payment is: CPN = Coupon Rate × Face Value Number of Coupons per Year = 0.055 × \$1000 2 = \$27.50 b. The timeline for the cash flows for this bond is (the unit of time on this timeline is six-month periods): P = 100/(1.055) 2 = \$89.85 8-2. a. The maturity is 10 years. b. (20/1000) * 2 = 4% so the coupon rate is 4%. c. The face value is \$1000. 8-3. a. Use the following equation: 1 + YTM n = FV n P 1/n 1 + YTM 1 = 100 95.51 1/1 ⇒ YTM 1 = 4.70% 1 + YTM 1 = 100 91.05 1/2 ⇒ YTM 1 = 4.80% 1 + YTM 3 = 100 86.38 1/3 ⇒ YTM 3 = 5.00% 1 + YTM 4 = 100 81.65 1/4 ⇒ YTM 4 = 5.20% 1 + YTM 5 = 100 76.51 1/5 ⇒ YTM 5 = 5.50% 1 \$27.50 2 \$27.50 3 \$27.50 60 \$27.50 + \$1000 72 Berk/DeMarzo • Corporate Finance b. The yield curve is Zero Coupon Yield Curve 4.6 4.8 5 5.2 5.4 5.6 2 4 6 Maturity (Years) Yield to Maturity c. The yield curve is upward sloping 8-4. a. 2 P 100(1.055) \$89.85 = = b. P = 100/(1.0595) 4 = \$79.36 c. 6.05% 8-5. a. \$1,034.74 = 40 (1 + YTM 2 ) + 40 (1 + YTM 2 ) 2 + L + 40 + 1000 (1 + YTM 2 ) 20 ⇒ YTM = 7.5% Using the annuity spreadsheet: NPER Rate PV PMT FV Excel Formula Given: 20-1,034.74 40 1,000 Solve For Rate: 3.75% =RATE(20,40,-1034.74,1000) Therefore, YTM = 3.75% × 2 = 7.50% b. PV = 40 (1 + .09 2 ) + 40 (1 + .09 2 ) 2 + L + 40 + 1000 (1 + .09 2 ) 20 = \$934.96. Using the spreadsheet With a 9% YTM = 4.5% per 6 months, the new price is \$934.96 NPER Rate PV PMT FV Excel Formula Given: 20 4.50% 40 1,000 Solve For PV: (934.96) =PV(0.045,20,40,1000) Chapter 8 Valuing Bonds 73 8-6. 900 = C (1 + .06) + C (1 + .06) 2 + L + C + 1000 (1 + .06) 5 ⇒ C = \$36.26, so the coupon rate is 3.626% We can use the annuity spreadsheet to solve for the payment: NPER Rate PV PMT FV Excel Formula Given: 5 6.00%-900.00 1,000 Solve For PMT: 36.26 =PMT(0.06,5,-900,1000) Therefore, the coupon rate is 3.626% 8-7. Bond A trades at a discount. Bond D trades at par. Bonds B and C trade at a premium. 8-8. Bonds trading at a discount generate a return from both receiving the coupons and from receiving a face value that exceeds the price paid for the bond. As a result, the yield to maturity of discount bonds exceeds the coupon rate. 8-9. a. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. b. 40 (1 + .035) + 40 (1 + .035) 2 + L + 40 + 1000 (1 + .035) 14 = \$1,054.60 NPER Rate PV PMT FV Excel Formula Given: 14 3.50% 40 1,000 Solve For PV: (1,054.60) =PV(0.035,14,40,1000) 8-10. a. When it was issued, the price of the bond was P = 70 (1 + .06) + ... + 70 + 1000 (1 + .06) 10 = \$1073.60 b. Before the first coupon payment, the price of the bond is P = 70 + 70 (1 + .06) ... + 70 + 1000 (1 + .06) 9 = \$1138.02 c. After the first coupon payment, the price of the bond will be P = 70 (1 + .06) ... + 70 + 1000 (1 + .06) 9 = \$1068.02 8-11. 74 Berk/DeMarzo •...
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## This note was uploaded on 12/28/2009 for the course FEWEB CORPFIN taught by Professor Dorsman during the Spring '09 term at Vrije Universiteit Amsterdam.

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BD_SM08 - Chapter 8 Valuing Bonds 8-1 a The coupon payment...

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