Question

In: Finance

What is the bond’s Macaulay duration of a 2.5 years, 8 percent semiannual coupon bond selling...

What is the bond’s Macaulay duration of a 2.5 years, 8 percent semiannual coupon bond selling at par of $1,000?

A. 2.5 years.

B. 2.45 years.

C. 1.94 years.

D. 2.31 years.

E. 1.75 years

Solutions

Expert Solution

Period
(in years)
Payment Present value factor Present value Duration
         0.50 $      40.00 0.961538462 $      38.46 $      19.23
         1.00 $      40.00 0.924556213 $      36.98 $      36.98
         1.50 $      40.00 0.888996359 $      35.56 $      53.34
         2.00 $      40.00 0.854804191 $      34.19 $      68.38
         2.50 $ 1,040.00 0.821927107 $    854.80 $ 2,137.01
$ 1,000.00 $ 2,314.95
Macaulay duration             2.31

Macaulay duration = $2,314.95 / $1,000 = 2.31 years

Answer is 2.31 years

Each period interest = $1,000 X 8% X 6/12 = $40

Last period payment = $40 + $1,000 principal = $1,040

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