CH06 - Chapter 6 Bonds Note: All problems in this chapter...

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Chapter 6 Bonds Note: All problems in this chapter are available in MyFinanceLab. 1. Plan: We can use Eq. (6.1) to determine the semiannual coupon payment on the bond and then create a timeline for the cash flows using the semiannual coupon payment found earlier. Execute: a. The coupon payment is: Coupon Rate Face Value CPN Number of Coupons per Year 0.055 $1000 2 $27.50 × = × = = b. Using the semiannual coupon payment we can then create a timeline for the cash flows of the bond. The timeline for the cash flows for this bond is (the unit of time on this timeline is six- month periods): 2 100/(1.055) $89.85 P = = Evaluate: We can compute the coupon payment by simply computing the year coupon payment of the face value using the coupon rate and then dividing that by the number of coupon payments per year. Also, in order to compute the value of the bond we need to know the cash flows and this is why we plot out those cash flows in a timeline. 1 $27.50 0 2 $27.50 3 $27.50 20 $27.50 + $1000
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58 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance 2. Plan: We can see that the bond consists of an annuity of 20 payments of $20, paid every 6 months, and one lump-sum payment of $1000 (face value) in 10 years (twenty 6-month periods). We can rearrange Eq. (6.1) in order to find the coupon rate knowing the coupon payment of $20. By rearranging Eq. (6.1) we come up with: coupon rate = (coupon payment/face value) × number of coupon payments per year. Execute: a. The maturity is 10 years. b. (20/1000) × 2 = 4% so the coupon rate is 4%. c. The face value is $1000. Evaluate: The maturity of the bond is the final repayment date of that bond, at which point payments on the bond will terminate. In this case, the bond will make 20 semiannual payments terminating in 10 years. We can find the coupon rate if we know the coupon payment, face value, and number of coupon payments per year by using and rearranging Eq. (6.1). Finally, we know that the face value of the bond is the amount repaid at maturity, in this case $1000. 3. Plan: We can use Eq. (6.2) to compute the yield to maturity for each bond. We can then use Excel to plot the zero-coupon yield curve, which will plot the yield to maturity of investments of different maturities using the yield to maturity on the y -axis and the maturity in years on the x -axis. Execute: a. Using Eq. (6.2) for the first five years to compute the yield to maturity: 1/ 1/1 11 1/2 1/3 33 1/4 44 1/5 55 FV 1Y TM 100 1 YTM YTM 4.70% 95.51 100 1 YTM YTM 4.80% 91.05 100 Y TM 5 . 0 0 % 86.38 100 1 YTM YTM 5.20% 81.65 100 1 YTM YTM 5.50% 76.51 n n n P ⎛⎞ += ⎜⎟ ⎝⎠ = = = = =
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Chapter 6 Bonds 59 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. Evaluate: The yield to maturity of the bond is the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond. We can use Eq. (6.2) knowing the face value, price, and year of each bond in order to find the yield to maturity. We can plot the zero-coupon yield curve using Excel, which will compare the yield to maturity of investments of different maturities.
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CH06 - Chapter 6 Bonds Note: All problems in this chapter...

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