Question

QUESTION 7 You own two $1,000 par bonds, one in this problem and one in the next. I want to illustrate something else. Both of these bonds are zero coupon bonds, which simply means they pay no coupon. The first bond matures in 3 years, and yields 8%. If the required yield drops to 6% (instantaneously, so the maturity does not change), what is the percentage price change? Answer in percent to three decimal places. Do not enter the percent sign. Do enter the sign if negative. Assume annual compunding. QUESTION 8 OK, this is the second zero coupon bond. This one also has a par value of $1,000. This one matures in 12 years, and yields 8%. If the required yield drops to 6% (instantaneously, so the maturity does not change), what is the percentage price change? Answer in percent to three decimal places. Do not enter the percent sign. Do enter the sign if negative. Assume annual compunding. Again, be sure to compare the results of this problem and the last. The only thing different between the two bonds is maturity. What does this tell you about maturity and the interest rate sensitivity of the bond? I assume by now you have been reminded several times of the relationship between the direction of the interest rate change and the direction of the price change. QUESTION 9 Calculate the value (price) of a $5,000 par value bond which pays quarterly interest at an annual coupon rate of 5.63% and has 9 years until maturity. The yield on similar risk bonds is currently 8.47% (nominal annual with quarterly compounding). Answer in dollars to two decimal places. Do not enter the dollar sign and do not enter commas.

Answer 1

1.
Percentage price change=(Par value/(1+new yield)^maturity)/(Par value/(1+original yield)^maturity)-1=(1000/1.06^3)/(1000/1.08^3)-1=5.76785%

2.
Percentage price change=(Par value/(1+new yield)^maturity)/(Par value/(1+original yield)^maturity)-1=(1000/1.06^12)/(1000/1.08^12)-1=25.1453%

Higher the maturity, higher is the interest rate sensitivity

Interest rates increase and price decreases and vice versa

3.
=5000*5.63%/8.47%*(1-1/(1+8.47%/4)^(4*9))+5000/(1+8.47%/4)^(4*9)=4111.989188