In: Finance

- An investor buys a 3.8% annual payment bond with 8 years to maturity. The bond is priced at a yield-to-maturity of 5.6%. What is the bond’s Macaulay duration?

Calculation of Macaulay duration of the bond

Maturity Period = | 8 years | |||

Face value (assumed) = | $1,000 | |||

Coupon Rate = | 3.80% | |||

Coupon payment at 3.8% of face value | $38.00 | |||

Yield-to-maturity | 5.60% | |||

Year (t) | Cash Flow from coupon payments and maturity amount (CF) | Present value (PV) discounted at 5.6% [=CF/(1+5.6%)^t] | PV *t | |

1 | $38.00 | $35.98 | $35.98 | |

2 | $38.00 | $34.08 | $68.15 | |

3 | $38.00 | $32.27 | $96.81 | |

4 | $38.00 | $30.56 | $122.23 | |

5 | $38.00 | $28.94 | $144.69 | |

6 | $38.00 | $27.40 | $164.42 | |

7 | $38.00 | $25.95 | $181.65 | |

8 | $1,038.00 | $671.25 | $5,370.02 | |

sum | $886.43 | $6,183.96 | ||

Bond's Price↑ | ||||

Macaulay duration = sum of (PV*t)/sum of PVs = | $6183.96/$886.43 | 6.98 | Years |

Macaulay duration of the bond is 6.98 years

Formulas used in excel calculation:

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