To determine: The price of the bonds after 1 year, 3 years, 8 years, 12 years and 13 years and prepare a graph of bond prices versus time to maturity.
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 its maturity and would not be called.
Effective Annual Rate:
The effective annual rate is the rate, which is incurred or received on various investment or loans. The effective annual rate is affected by the increase in compounding years.
Current Yield:
The current yield represents the return on the bond, which is held by the owner for a year. The current yield is calculated by dividing the annual cash inflow from the current market price.
Explanation of Solution
Solution:
Given,
For M Company,
The bond is a premium bond and makes semi-annual payments.
The coupon rate is 8.5%.
The yield to maturity is 7%.
The maturity period is 13 years.
For MG Company,
The bond is a discount bond and makes semi-annual payments.
The coupon rate is 7%.
The yield to maturity is 8.5%.
The maturity period is 13 years.
Calculation of the value of the bond after 1 year:
The formula to calculate the value of the bond is,
For M Company,
Substitute $42.5 for interest value, $1,000 for the interest value, 1.9 for
The value of the bond is $1,014.25.
For MG Company,
Substitute $35 for interest value, $1,000 for the interest value, 1.88 for
The value of the bond is $985.9.
Calculation of the value of bond after 3 years:
For M Company,
Substitute $42.5 for interest value, $1,000 for the interest value, 5.329 for
The value of the bond is $1,039.98.
For MG Company,
Substitute $35 for interest value, $1,000 for the interest value, 5.2 for
The value of the bond is $961.
Calculation of the value of bond after 8 years:
For M Company,
Substitute $42.5 for interest value, $1,000 for the interest value, 12.094 for
The value of the bond is $1,089.695.
For MG Company,
Substitute $35 for interest value, $1,000 for the interest value, 11.44 for
The value of the bond is $914.1.
Calculation of the value of bond after 12 years:
For M Company,
Substitute $42.5 for interest value, $1,000 for the interest value, 16.06 for
The value of the bond is $1,120.45.
For MG Company,
Substitute $35 for interest value, $1,000 for the interest value, 14.86 for
The value of the bond is $888.3.
Calculation of the value of the bond after 13 years:
For M Company,
Substitute $42.5 for interest value, $1,000 for the interest value, 16.89 for
The value of the bond is $1,126.625.
For MG Company,
Substitute $35 for interest value, $1,000 for the interest value, 15.57 for
The value of the bond is $853.75.
The graph showing the change in the value of bonds with the maturity period is:
Fig 1
- The graph shows the change in the price of bonds with the maturity period.
- The x-axis shows the years of maturity.
- The y-axis shows the price of the bond.
- The value of the bonds of M Company increases with time.
- The value of the bonds of MG Company decreases with time.
Working note:
Calculation of the semi-annual interest for M Company:
The semi-annual interest is $42.5.
Calculation of the semi-annual interest for MG Company:
The semi-annual interest is $35.
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Calculation of the
Thus, the value of the bonds of M Company after 1 year is $1,014.25, after 3 years is $1,039.98, after 8 years is $1,089.695, after 12 years is $1,120.45, and after 13 years is $1,126.625 and the value of the bonds of MG Company after 1 year is $985.9, after 3 years is $961, after 8 years is $914.10, after 12 years is $888.3, and after 13 years is $853.75.
Want to see more full solutions like this?
Chapter 8 Solutions
Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
- Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent. Both bonds have 13 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? Percentage change in price of Bond J=? Percentage change in price of Bond K=? What if rates suddenly fall by 2 percent instead? Percentage change in price of Bond J=? Percentage change in price of Bond K=?arrow_forwardKawesha Corporation has a premium bond making semiannual payments. The bondpays a 9 percent coupon, has a YTM of 7 percent, and has 13 years to maturity. TheModigliani Company has a discount bond making semiannual payments. This bondpays a 7 percent coupon, has a YTM of 9 percent, and also has 13 years to maturity.If interest rates remain unchanged, what do you expect the price of these bonds to be(a) 1 year from now?(b) In 3 years? (c) In 8 years?(d) In 12 years?(e) What’s going on here?arrow_forwardGive typing answer with explanation and conclusion Bond A pays semi-annual coupons, pays its next coupon in 6 months, and matures in 6 years. Bond B pays annual coupons, pays its next coupon in 1 year, and matures in 10 years. Both bonds have a face value of $1,000.00 and both bonds have the same yield-to-maturity. Bond A has a coupon rate of 12.67 percent and is priced at $921.60. Bond B has a coupon rate of 8.24 percent. What is the price of bond B?arrow_forward
- Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7 percent, has a YTM of 5 percent, and has 17 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 5 percent, has a YTM of 7 percent, and also has 17 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In seven years? In 12 years? In 16 years? In 17 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)arrow_forwardBond X is a premium bond making semiannual payments. The bond pays a coupon rate of 8 percent, has a YTM of 6 percent, and has 18 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6 percent, has a YTM of 8 percent, and also has 18 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of Bond X $ Price of Bond Y $ If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In eight years? In 13 years? In 17 years? In 18 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of bond Bond X Bond Y One year $ $ Eight years $ $ 13 years $ $ 17 years $ $ 18 years $ $arrow_forwardThere is a goverment bond that pays %16 annual coupon interest however the payments are semi-annually. The maturity of this bond is 6 years and the par value is 100 TL. Find the price of this bond when market interest rate is %12 ? Explain briefly the relationship between bond prices and bond yields?arrow_forward
- Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7 percent, has a YTM of 5 percent, and has 19 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 5 percent, has a YTM of 7 percent, and also has 19 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In 11 years? In 14 years? In 16 years? In 19 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)arrow_forwardThis is a bond question: A company issues a bond with annual coupons of $1,000 per year and the first coupon is due one year from today. It issues the bond at par, meaning that it is able to sell the bond for a price identical to its face value. If the face value is $5,000, what discount rate is used by investors to price the band?arrow_forwardBond P is a premium bond with a coupon rate of 8 percent. Bond D is a discount bond with a coupon rate of 3 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 5 percent, and have eight years to maturity.1. What is the current yield for bond P and D?2. If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P and bond D?arrow_forward
- Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7 percent, has a YTM of 5 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 5 percent, has a YTM of 7 percent, and also has 13 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In four years? In nine years? In 11 years? In 13 years?arrow_forwardA General Power bond carries a coupon rate of 8.2%, has 9 years until maturity, and sells at a yield to maturity of 7.2%. (Assume annual interest payments.) a. What interest payments do bondholders receive each year? b. At what price does the bond sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. What will happen to the bond price if the yield to maturity falls to 6.2%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) d. If the yield to maturity falls to 6.2%, will the current yield be less, or more, than the yield to maturity?arrow_forwardA General Power bond carries a coupon rate of 9.2%, has 9 years until maturity, and sells at a yield to maturity of 8.2%. (Assume annual interest payments.) a. What interest payments do bondholders receive each year? b. At what price does the bond sell? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. c. What will happen to the bond price if the yield to maturity falls to 7.2%? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. A a. Interest payments b. Price c. Price will byarrow_forward
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
- Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage LearningCorporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan ProfessorPublisher:McGraw-Hill Education