BD_SM_c08 - Chapter 8 Valuing Bonds 8-1 a The coupon...

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Chapter 8 Valuing Bonds 8-1. a. The coupon payment is: Coupon Rate Face Value 0.055 $1000 CPN $27.50 Number of Coupons per Year 2 ×× == = b. The timeline for the cash flows for this bond is (the unit of time on this timeline is six-month periods): 8-2. a. The maturity is 10 years. b. The coupon rate is 4%. c. The face value is $1000. 8-3. a. Use the following equation: 1/n n n FV 1Y TM P ⎛⎞ += ⎜⎟ ⎝⎠ 1/1 11 100 1 YTM YTM 4.70% 95.51 = 1/2 100 T M Y T M 4 . 8 0 % 91.05 = 1/3 33 100 T M Y T M 5 . 0 0 % 86.38 = 1/4 44 100 1 YTM YTM 5.20% 81.65 = 1/5 55 100 1 YTM YTM 5.50% 76.51 = 1 $27.50 0 2 $27.50 3 $27.50 60 $27.50 + $1000
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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 0246 Maturity (Years) Yield to Maturity c. The yield curve is upward sloping 8-4. a. 100 P $90.27. (1.05)(1.055) == b. 100 P$ 8 0 . 5 7 . (1.05)(1.055)(1.0575)(1.0595) c. 6.05% 8-5. a. 22 0 40 40 40 1000 YTM $1,034.74 .01876 YTM 3.75% YTM YTM YTM 2 (1 ) ) ) 2 + =+ + + = = ++ + " b. 0 40 40 40 1000 PV L $934.96. .09 .09 .09 ) ) ) 2 + + + = + 8-6. 25 C C C 1000 900 C $36.26, so the coupon rate is 3.626% (1 .06) (1 .06) (1 .06) + + + = + " 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.
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Chapter 8 Valuing Bonds 73 8-9. a. 21 4 40 40 40 1000 $1,068.83 (1 .03375) (1 .03375) (1 .03375) + ++ + = + " b. 4 40 40 40 1000 $1,054.60 (1 .035) (1 .035) (1 .035) + + = + " 8-10. a. When it was issued, the price of the bond was 10 70 70 1000 P ... $1073.60 (1 .06) + =+ + = b. Before the first coupon payment, the price of the bond is 9 70 70 1000 P 70 ... $1138.02 + + = c. After the first coupon payment, the price of the bond will be 9 70 70 1000 P ... $1068.02 (1 .06) (1 .06) + =+= 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)
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74 Berk/DeMarzo Corporate Finance 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. The length of the investment N = 4 years. We then calculate the IRR of investment = 5%. Because the YTM was the same at the time of purchase and sale, the IRR of the investment matches the YTM. NPER Rate PV PMT FV Excel Formula Given: 4 –107.72 6 105.08 Solve For Rate: 5.00% = RATE(4,6,-107.72,105.08) 8-12.
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BD_SM_c08 - Chapter 8 Valuing Bonds 8-1 a The coupon...

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