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# Duration and price volatility of bonds

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1. Compute the duration for bond C, and rank the bonds on the basis of their price volatility. The current rate of interest is 8%, so the prices of bonds A and B are \$1,000 and \$1,268, respectively
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BOND COUPON TERM DURATION
A 8% 10 YRS 7.25
B 12% 10 YRS 6.74
C 8% 5YRS ?

Confirm your ranking by calculating the percentage change in the price of each bond when interest rates is rises from 8 to 12%. (Bond A's and B's prices become \$774 and \$1000, respectively?

2.a) what is the price of each of the following bonds (\$1,000 principal), if the current interest rate is 9%?

Firm A Coupon 6%
Maturity 5%

Firm B Coupon 6%
Maturity 20 yrs

Firm C Coupon 15%
Maturity 5 yrs

Firm D Coupon 15%
Maturity 20 yrs

Firm E Coupon 0% (zero coupon bond)
Maturity 5%

Firm F Coupon 0% (zero coupon bond)
Maturity 20%

b) What is the duration of each bond?

c) Rank the bonds in terms of price fluctuations with the least volatile bond first and the most volatile bonds last as judged by each bond's duration

d) Confirm your volatility rankings by determining the percentage change in the price of each bond if interest rates rise to 12%.

e) What generalizations can be made from the above exercise concerning (a) low-versus high-coupon bonds (b) intermediate-versus long-term bonds, and (c) zero coupon bonds?

3). A 10 year bond with a 9% coupon will sell for \$1,000 when interest rates are 9%. What is the duration of this bond? Using duration to forecast the change in the price of the bond, calculate the difference between the forecasted and the actual price change according to the bond valuation model for the following interest rates: 9.2, 9.4, 9.6, 9.8, 10.0, 10.5, 11.0 and 12.0 %