Question

In: Finance

Consider a 3-year bond with 14 percent semi-annual coupon payments and currently priced to yield 12...

Consider a 3-year bond with 14 percent semi-annual coupon payments and currently priced to yield 12 per cent per annum.

  1. Calculate duration of the bond.
  2. What is the percentage of price change if interest rate increases to 12.15% per annum?

Solutions

Expert Solution

Assuming the Face value of the Bond $1000

A Semi annual Period (w) Cash Flows (x) Discounting fator @ YTM 6% PV of cash flows (x) w*x
1 70                                              0.9434                       66.04         66.04
2 70                                              0.8900                       62.30      124.60
3 70                                              0.8396                       58.77      176.32
4 70                                              0.7921                       55.45      221.79
5 70                                              0.7473                       52.31      261.54
6 1070                                              0.7050                     754.31 4,525.85
Price of Bond                 1,049.17 5,376.13
Duration = Sum(w*x)/Sum(x)
=(5376.13/1049.17)/2                          2.56 Years
Volatility of Bond=( Duration/ YTM)
=(2.56/1.12) 2.285714286
If Yeild changes by 1% the Bond price will change by 2.285%
B If Yeild is increased by .15% then price of bond
=1049.17*(.15/100)*(2.2857)                          3.60
Price of the bond(1049.17-3.60) 1045.57
Percentage decreae in price(1045.57/1049.17)-1 -0.343%

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