Question

You find a bond with 5 years until maturity that has a coupon rate of 7.6 percent and a yield to maturity of 5.9 percent. What is the Macaulay duration? Solve by hand.

Answer #1

Let the face value be 1000 .Interest = 1000*.076 = 76

period | cash flow | period *cash flow | PVF @ 5.9% | present value of cash flow [cash flow * PVF] | present value of period *cash flow [ period *cash flow *PVF] |

1 | 76 | 1*76=76 | .94429 | 71.7660 | 76*.94429=71.7660 |

2 | 76 | 2*76 = 152 | .89168 | 67.7677 | 152*.89168= 135.5354 |

3 | 76 | 228 | .84200 | 63.992 | 191.976 |

4 | 76 | 304 | .79509 | 60.4268 | 241.7074 |

5 | 1000+76=1076 | 5380 | .75079 | 807.8500 | 4039.2502 |

6140 | 1071.8025 | 4680.235 |

Macaulay duration = 4680.235/1071.8025

= 4.37 years

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