Question

Bond X is noncallable and has 20 years to maturity, a 10% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 9%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer #1

Price of the bond = Sum of PV of all the cash inflows

Price of the bond at the end of 5 years = Sum of PV of all the cash inflows from year 6 to year 20

Please refer to the table for the calculations-

Time | Cash Inflows | PV of cash inflows @9% interest rate |

6 | 100 | 59.6 |

7 | 100 | 54.7 |

8 | 100 | 50.2 |

9 | 100 | 46.0 |

10 | 100 | 42.2 |

11 | 100 | 38.8 |

12 | 100 | 35.6 |

13 | 100 | 32.6 |

14 | 100 | 29.9 |

15 | 100 | 27.5 |

16 | 100 | 25.2 |

17 | 100 | 23.1 |

18 | 100 | 21.2 |

19 | 100 | 19.4 |

20 | 1100 | 196.3 |

Price at the end of 5 years | 702.3 |

We will be willing to pay $702.3 for Bond X today

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market) have expectations that in 5 years, the yield to maturity on
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