4. What is the duration of a four-year, $1,500 bond that pays a coupon (annual) of...
4. What is the duration of a four-year, $1,500 bond that pays a coupon (annual) of 12% that trades at a yield of 16%. Calculate is the expected change in the bond’s price if interest rates fall by 0.70 percent (70 basis points)?
Homework Answers
Par Value =1500
Coupon =1500*12% =180
YTM =16%
Number of Periods =4
Price of Bond =PV of Coupons+PV of Par Value
=180*((1-(1+16%)^-4)/16%)+1500/(1+16%)^4 =1332.11
Macaulay Duration
=(180*1/(1+16%)+180*2/(1+16%)^2+180*3/(1+16%)^3+1680*4/(1+16%)^4))/1332.11=3.3631
Modified Duration =3.3631/(1+16%) =2.8993 or 2.90
New Price with new YTM of 15.30%
Price of Bond =PV of Coupons+PV of Par Value
=180*((1-(1+15.30%)^-4)/15.30%)+1500/(1+15.30%)^4 =1359.53
Change in Price =1359.53-1332.11 =27.42
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