Interest Rate Risk The Faulk Corp. has a 6 percent coupon bond outstanding. The Gonas Company has a 14 percent bond outstanding. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 10 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? What if interest rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bonds?
To determine: The percentage change in the price of the bonds.
Coupon Rate:
The coupon rate refers to the rate at which interest is earned on the face value of a bond every year. This is the rate at which yield is funded from a fixed-income security.
Yield to Maturity:
The yield to maturity is the total yield or return, which is derived from a bond until the time of the maturity. For this, it is assumed that the bond will be held until the maturity and would not be called.
Interest Rate Risk:
The interest rate risk refers to the risk, which is associated with a bond because of the fluctuations of the interest rate. The value of the bond differs with the change in the interest rate.
Explanation of Solution
Solution:
Given,
The yield to maturity of the bonds of both companies is 10%.
The bonds of both the company mature after 12 years.
The F Company has a 6% coupon rate outstanding.
The G Company has a 14% coupon rate outstanding.
Calculation of the change in the price of bonds when the interest rate is increased by 2%:
The formula to calculate the change in price is,
For F company,
Substitute $623.53 (refer working note) for the new price and $724 for the original price in the above formula.
The change in bonds price is (13.87%).
For G company,
Substitute $1,125.57 (refer working note) for the new price and $1,276 for the original price in the above formula.
The change in bonds price is (11.79%).
Calculation of the change in the price of bonds when the interest rate is decreased by 2%:
The formula to calculate the change in price is,
For F company,
Substitute $847.41 (refer working note) for the new price and $724 for the original price in the above formula.
The change in bonds price is 17.04%.
For G company,
Substitute $1,457.29 (refer working note) for the new price and $1,276 for the original price in the above formula.
The change in bonds price is 14.21%.
Working note:
Calculation of the semi-annual interest on bonds of F Company:
The semi-annual interest is $30.
Calculation of the semi-annual interest on bonds of G Company:
The semi-annual interest is $70.
Calculation of the price of bonds if yield to maturity is 10%:
For F Company,
The value of the bond is $724.
For G Company,
The value of the bond is $1,276.
Calculation of the price of bonds if yield to maturity is 12%:
For F Company,
The value of the bond is $623.53.
For G Company,
The value of the bond is $1,125.57.
Calculation of the price of bonds if yield to maturity is 8%:
For F Company,
The value of the bond is $847.41.
For G Company,
The value of the bond is $1,457.29.
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Thus, the percentage change in price when the rate isincreased by 2% for F Company is (13.87%) and for G Company is (11.79%). The percentage change in price when the rate is decreased by 2% for F Company is 17.04% and for G Company is 14.21%.
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