Interest Rate Risk Laurel, Inc., and Hardy Corp. both have 6.5 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has 3 years to maturity, whereas the Hardy Corp. bond has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then? Illustrate your answers by graphing
To determine:The percentage change in the price of the bonds in the given situations and the graph showing the changes.
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
Given,
The yield to maturity of the bonds of both companies is 6.5%.
The bonds of L Company mature after 3 years.
The bonds of H Company mature after 20 years.
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 L company,
Substitute $947.47(refer working note) for the new price and $1,000 for the original pricein the above formula.
The change in bonds price is (5.25%).
For H company,
Substitute $809 (refer working note) for the new price and $1,000 for the original price in the above formula.
The change in bonds price is (19.1%).
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 L company,
Substitute $1.055.51 (refer working note) for the new price and $1,000 for the original price in the above formula.
The change in bonds price is 5.55%.
For H company,
Substitute $1,262.31 (refer working note) for the new price and $1,000 for the original price in the above formula.
The change in bonds price is 26.23%.
The graph showing the changes in the price is:
Fig 1
- The graph shows the change in prices of the L Company and H Company.
- The x-axisrepresents the yield to maturity.
- The y-axisrepresents the value of the bonds.
- The line in the graph shows the change in the prices of the bond with the increase and decrease in the yield to maturity.
Working note:
Calculation of thesemi-annual interest on bonds of L Company,
The semi-annual interest is $32.5.
Calculation of the semi-annual interest on bonds of H Company,
The semi-annual interest is $32.5.
Calculation of the price of bonds if yield to maturity is 8.5%:
For L Company,
The value of the bond is $947.97.
For H Company,
The value of the bond is $809.
Calculation of the price of bonds if yield to maturity is 4.5%:
For L Company,
The value of the bond is $1,055.51.
For H Company,
The value of the bond is $1,262.31.
Calculation of
Calculation of
Calculation of
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Calculation of
Calculation of
Calculation of
Calculation of
Thus, the percentage change in price when the rate is increased by 2% for L Company is 5.25%and for H Company is19.1%. The percentage change in price when the rate is decreased by 2% for L Company is5.55% and for H Company is 26.23%.
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Chapter 8 Solutions
EBK CORPORATE FINANCE
- Bond J has a coupon rate of 4.2 percent. Bond K has a coupon rate of 14.2 percent. Both bonds have ten years to maturity, a par value of $1,000, and a YTM of 9.4 percent, and both make semiannual payments. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. b. If interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. a. Percentage change in price b. Percentage change in price Bond J 9.40 % % Bond K 12.83 %arrow_forward(Interest Rate risk) Bond S has 4 years to maturity. Bond T has 30 years to maturity. Both have 9% coupons paid semi-annually, and are priced at par value. If the interest rate(yield to maturity) suddenly drops by 3.8%, the percentage change in the price of Bond T is ____________% (Round your answer to a two-decimal number.) (Interest Rate risk) Bond S has 4 years to maturity. Bond T has 30 years to maturity. Both have 9% coupons paid semi-annually, and are priced at par value. If the interest rate(yield to maturity) suddenly rises by 3.1%, the percentage change in the price of Bond S is ____________% (Keep two decimal numbers and the sign.)arrow_forwardQuantitative Problem: Today, interest rates on 1-year T-bonds yield 1.7%, interest rates on 2-year T-bonds yield 2.5%, and interest rates on 3-year T-bonds yield 3.4%. a. If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places. b. If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places. c. If the pure expectations theory is correct, what is the yield on 1-year T-bonds two years from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.arrow_forward
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