Question

A zero-coupon bond has a yield to maturity of 8% and a par value of $1,000. If the bond matures in 8 years, at what price should the bond sell today?

a) $501.90

b) $555.28

c) $573.88

d) $540.30

Answer #1

Answer: **Option (d)**

Valuation of Zero Coupon Bond |

Coupon Rate = 0 |

Time Period = 8 Years |

Redemption Value = Twice par = 2*$1,000 = $ 2,000 |

Yield to Maturity = 8% |

Par Value = $ 1,000 |

Price of Bond = Present Value of all future expected Reciepts |

Price of Bond = Present Value of all Coupon payments + Present Value of Redemtion proceeds |

Price of Bond = [0* PVAF(8%, 8 years)] + [$ 1,000 * PV(8%, 8yr)] |

Price of Bond = 0 + [$ 1,000 * (1+0.08)^{-8}] |

Price of Bond = $ 1,000 / (1+0.08)^{8} |

Price of Bond = $ 1,000 * 0.5403 |

Price of Bond = $ 540.30 |

PVF = 1/(1+i)^{n}

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