# chapter8 - Chapter 8 Valuing Bonds 8-1. a. The coupon...

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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 0 2 \$27.50 3 \$27.50 60 \$27.50 + \$1000

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72 Berk/DeMarzo Corporate Finance: The Core b. The yield curve is Zero Coupon Yield Curve 4.6 4.8 5 5.2 5.4 5.6 0246 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 + YTM 2 ) 2 + + 40 + 1000 + 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 + .09 2 ) + 40 + .09 2 ) 2 + L + 40 + 1000 + .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 + + C + 1000 + .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 + .035) + 40 + .035) 2 + + 40 + 1000 + .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 + .06) + ... + 70 + 1000 + .06) 10 = \$1073.60 b. Before the first coupon payment, the price of the bond is P = 70 + 70 + .06) ... + 70 + 1000 + .06) 9 = \$1138.02 c. After the first coupon payment, the price of the bond will be P = 70 + .06) ... + 70 + 1000 (1 + .06) 9 = \$1068.02

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74 Berk/DeMarzo Corporate Finance: The Core 8-11. a. First, we compute the initial price of the bond by discounting its 10 annual coupons of \$6 and final face value of \$100 at the 5% yield to maturity: NPER Rate PV PMT FV Excel Formula Given: 10 5.00% 6 100 Solve For PV: (107.72) = PV(0.05,10,6,100) Thus, the initial price of the bond = \$107.72. (Note that the bond trades above par, as its coupon rate exceeds its yield). Next we compute the price at which the bond is sold, which is the present value of the bonds cash flows when only 6 years remain until maturity: NPER Rate PV PMT FV Excel Formula Given: 6 5.00% 6 100 Solve For PV: (105.08) = PV(0.05,6,6,100) Therefore, the bond was sold for a price of \$105.08. The cash flows from the investment are therefore as shown in the following timeline: Year 0 1 2 3 4 Purchase Bond -\$107.72 Receive Coupons \$6 \$6 \$6 \$6 Sell Bond \$105.08 Cash Flows -\$107.72 \$6.00 \$6.00 \$6.00 \$111.08 b. We can compute the IRR of the investment using the annuity spreadsheet. The PV is the purchase price, the PMT is the coupon amount, and the FV is the sale price.
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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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chapter8 - Chapter 8 Valuing Bonds 8-1. a. The coupon...

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