Question
What condition must exist if a bond's coupon rate is to equal both the bond's current yield and its yield to maturity? Assume the market rate of interest for this bond is positive. a. There is no condition under which this can occur. b. The bond must be priced at par. c. The bond must be a zero coupon bond and mature in exactly one year. e. The clean price of the bond must equal the bond's dirty price.
Ask by Coleman Ingram. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The bond must be priced at par.
Solution
The bond's coupon rate equals its current yield if the coupon (coupon amount per period) divided by the market price equals the coupon divided by the face (par) value, which immediately implies that the market price must equal the par value. Additionally, the yield to maturity (YTM) will equal the coupon rate when the bond is priced at par. Therefore, for the coupon rate to equal both the current yield and the YTM (given a positive market rate of interest), the bond must be priced at par.
Answer: b. The bond must be priced at par.
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Simplify this solution Beyond the Answer
For a bond's coupon rate to equal both its current yield and yield to maturity, it must be priced at par, which means its market price is equal to its face value. When a bond sells at par, the coupon payments received by the investor are exactly equal to the yield generated from the bond, thus aligning all three measures. Additionally, a bond priced at par signifies that the market interest rate aligns perfectly with the bond's coupon rate. This equilibrium ensures that investors receive exactly the return they expect, resulting in a harmonious financial scenario for bondholders!
