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Consider a five-year, 8 percent annual coupon bond selling at par of $1,000. a. What is the...

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Finance

Consider a five-year, 8 percent annual coupon bond selling atpar of $1,000.

a. What is the duration of this bond?

b. If interest rates increase by 20 basis points, what is theapproximate change in the market price using the durationapproximation?

Answer & Explanation Solved by verified expert
4.3 Ratings (724 Votes)

a

Period Cash Flow Discounting factor PV Cash Flow Duration Calc
0 ($1,000.00) =(1+YTM/number of coupon payments in the year)^period =cashflow/discounting factor =PV cashflow*period
1             80.00                                                             1.08                    74.07                  74.07
2             80.00                                                             1.17                    68.59                137.17
3             80.00                                                             1.26                    63.51                190.52
4             80.00                                                             1.36                    58.80                235.21
5       1,080.00                                                             1.47                  735.03              3,675.15
      Total              4,312.13

b

Macaulay duration =(? Duration calc)/(bond price*number of coupon per year)
=4312.13/(1000*1)
=4.312127
Modified duration = Macaulay duration/(1+YTM)
=4.31/(1+0.08)
=3.99271
Using only modified duration
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-3.99*0.002*1000
=-7.99
%age change in bond price=Mod.duration prediction/bond price
=-7.99/1000
=-0.8%
New bond price = bond price+Modified duration prediction
=1000-7.99
=992.01

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Transcribed Image Text

Consider a five-year, 8 percent annual coupon bond selling atpar of $1,000.a. What is the duration of this bond?b. If interest rates increase by 20 basis points, what is theapproximate change in the market price using the durationapproximation?

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