A bond is valued at $99,500. Par is $100,000. The annual coupon is $450. What can you say about this bond? a. The YTM has dropped to a value below 4.5%. b. The YTM is equal to 4.5%. c. The YTM is now above 4.5%.
The correct answer and explanation is:
The correct answer is c. The YTM is now above 4.5%.
The bond is currently valued at $99,500, which is below its par value of $100,000. This indicates that the bond is trading at a discount, meaning its market price is lower than its face value. The coupon payment is $450 annually, which is based on the par value of $100,000. To calculate the bond’s coupon rate, divide the annual coupon payment by the par value: Coupon rate=450100,000=0.0045 or 4.5%\text{Coupon rate} = \frac{450}{100,000} = 0.0045 \text{ or } 4.5\%
Since the bond is priced below par, the Yield to Maturity (YTM) must be higher than the coupon rate. This is because investors demand a higher return to compensate for purchasing the bond at a discount. The YTM represents the total return an investor can expect if the bond is held to maturity, including both the coupon payments and any gain from the bond’s price moving toward par.
For a bond priced below par, the YTM will always exceed the coupon rate. In this case, since the bond is priced at $99,500 (a discount), the YTM is greater than 4.5%. Therefore, the correct choice is c. The YTM is now above 4.5%.
A bond’s price and YTM are inversely related. If the bond price falls below par, the YTM increases because the investor is purchasing the bond at a discount and receiving the same fixed coupon payments. Conversely, if the bond price rises above par, the YTM would decrease as the investor is paying a premium for the same coupon payments.