On jan 1, 2012, fin307 is considering the newly issued 10-year aaa corporate bond, which is due jan 1, 2022, with a coupon rate of 6% per year paid every 6 months. the bond is traded at par. suppose the market interest rate declines by 100 bps (i. e., 1%), what is the duration (before interest rate change) and the effect of the market interest decline on the bond price? hint: if your calculator does not have a build-in function for duration, go to excel and do the calculation manually by setting up 6 columns for t (=1, 2, 3…..20), df(discount factor or 1/pv factor), cf (cashflow), pv (present value of cf=cf*df), w(weight=pv/sum of pv or p0), and t*w. then sum up all t*w, then divide by 2 (because here coupon is paid semiannually).

DURATION:  15.52358724

Explanation:

t // cash flow // pv// duration

130  $ 29.27  0.027151915

230  $ 28.55  0.052979346

330  $ 27.86          0.07753075

430  $ 27.18           0.100853008

530  $ 26.52  0.122991473

630  $ 25.87  0.143990017

730  $ 25.24  0.163891076

830  $ 24.62  0.182735695

930  $ 24.02  0.200563568

1030  $ 23.44  0.217413081

1130  $ 22.86  0.233321356

1230  $ 22.31          0.248324281

1330  $ 21.76          0.262456557

1430  $ 21.23          0.27575173

1530  $ 20.71          0.288242226

1630  $ 20.21          0.29995939

1730  $ 19.72          0.310933514

1830  $ 19.23          0.321193874

1930  $ 18.77          0.330768759

201030 $ 628.58  11.66253562

  $ 1,077.95  15.52358724

There is 20 payment as the bond stands for 10 years and does 2 payment per year

payment per year:

1,000 x 6% / 2 = $ 30 interest payment

then, we have the maturity at year-end for $ 1,000

Then, for the PV we use the lump sum:

For last step we do the average for that and multiply by the payment number

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