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# Ch005A - Appendix 5A The Term Structure of Interest Rates...

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Appendix 5A: The Term Structure of Interest Rates, Spot Rates, and Yields to Maturity 5A.1 a. The present value of any coupon bond is the present value of its coupon payments and face value. Match each cash flow with the appropriate spot rate. For the cash flow that occurs at the end of the first year, use the one-year spot rate. For the cash flow that occurs at the end of the second year, use the two-year spot rate. P = C 1 / (1+r 1 ) + (C 2 +F) / (1+r 2 ) 2 = \$60 / (1.1) + (\$60 + \$1,000) / (1.11) 2 = \$54.55 + \$860.32 = \$914.87 The price of the bond is \$914.87. b. The yield to the maturity is the discount rate, y , which sets the cash flows equal to the price of the bond. P = C 1 / (1+ y ) + (C 2 +F) / (1+ y ) 2 \$914.87 = \$60 / (1+ y ) + (\$60 + \$1,000) / (1+ y ) 2 y = .1097 = 10.97% The yield to maturity is 10.97%. 5A.2 The present value of any coupon bond is the present value of its coupon payments and face value. Match each cash flow with the appropriate spot rate. P = C 1 / (1+r 1 ) + (C 2 +F) / (1+r 2 ) 2 = \$50 / (1.10) + (\$50 + \$1,000) / (1.08) 2 = \$45.45 + \$900.21 = \$945.66 The price of the bond is \$945.66. 5A.3 Apply the forward rate formula to calculate the one-year rate over the second year. (1+r 1 ) × (1+ f 2 ) = (1+r 2 ) 2 (1.09) ×

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Ch005A - Appendix 5A The Term Structure of Interest Rates...

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