Question

A
bond has a face value of $1000, fixed coupon rate of 8,3% and 3
years to maturity. The discount rate is 3,3%. What is the Macaulay
Duration? State the answer as a number with 2 decimals (for
example, 3.12).

Answer #1

Given that, Face value of bond = $1000

Coupon rate = 8.3%

Discount rate = 3.3%

Term = 3years

Coupon amount = face value × coupon rate

=$1000×8.3%

=$83

Computation of Macaulay duration of bond:

Year | cash flows | Discounted cash flows | year × discounted cash flows | |

1 | $83 |
$80.35 (83/(1+3.3%)^1) |
$80.35 | |

2 | $83 |
$77.79 ($83/(1+3.3%)^2) |
$155.58 | |

3 | $83 |
$75.30 (83/(1+3.3%)^3) |
$225.9 | |

4 | $1083 |
$951.10 (1083/(1+3.3%)^4) |
$3804.4 | |

$1184.54 | $4266.23 |

Macaulay duration = sum of (year× Discounted cash flows) /sum of (Discounted cash flows)

=$4266.23/$1184.54

=$3.60years

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