To determine: The yield to maturity
Introduction:
Yields refer to the return on the investment made by an investor. A bond yield refers to the return earned by the investor on the bond, if he or she holds the bond until the bond matures. It is also known as the yield to maturity.
Answer to Problem 25QP
The yield to maturity of the bond is 5.29 percent.
Explanation of Solution
Given information:
The present time is May 2013. The face value of the bond is $1,000. Assume that the coupon payments are semiannual. The following is the information regarding the Treasury bond that matures in May 2023:
Rate | Maturity | Bid | Asked | Chg | Ask yield |
5.850 | May 23 | 104.1762 | 104.3850 | +0.4513 | ?? |
The formula to calculate annual coupon payment:
The formula to calculate the current price:
The formula to calculate the yield to maturity:
Where,
“C” refers to the coupon paid per period
“F” refers to the face value paid at maturity
“r” refers to the yield to maturity
“t” refers to the periods to maturity
Compute the annual coupon payment:
Hence, the annual coupon payment is $58.5.
Compute the current price of the bond:
The face value of the bond is $1,000. The last asked price is 104.3850% of the face value of the bond.
Hence, the current price of the bond is $1,043.85.
Compute the semiannual yield to maturity of the bond as follows:
The bond pays the coupons semiannually (Assumption). The annual coupon payment is $58.5. However, the bondholder will receive the same is two equal installments. Hence, semiannual coupon payment or the 6-month coupon payment is $29.25
The remaining time to maturity is 10 years
Finding “r” in Equation (1) would give the semiannual yield to maturity. However, it is difficult to simplify the above the equation. Hence, the only method to solve for “r” is the trial and error method.
The first step in trial and error method is to identify the discount rate that needs to be used. The bond sells at a premium in the market if the market rates (Yield to maturity) are lower than the coupon rate. Similarly, the bond sells at a discount if the market rate (Yield to maturity) is higher than the coupon rate.
In the given information, the bond sells at a premium because the market value of the bond is higher than its face value. Hence, substitute “r” with a rate that is lower than the coupon rate until one obtains the bond value close to $1,043.85.
The coupon rate of 5.85 percent is an annual rate. The semiannual coupon rate is 2.925 percent
The attempt under the trial and error method using 2.645 percent as “r”:
The current price of the bond is $1,043.88, when “r” is 2.645 percent. This value is close to 1,043.85. Hence, 2.645 percent is the semiannual yield to maturity.
Compute the annual yield to maturity:
Hence, the yield to maturity is 5.29 percent.
Want to see more full solutions like this?
Chapter 6 Solutions
ESSENTIALS OF CORP.FIN.-W/CODE >CUSTOM<
- 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