What is the current yield on a $1,000 bond with a 5 percent coupon if its market price is Instructions: Enter your responses as a percentage rounded to two decimal places. a. $900? b. $1,000? c. $1,100? % % %
The Correct Answer and Explanation is :
To calculate the current yield on a bond, you use the formula:
[
\text{Current Yield} = \frac{\text{Coupon Payment}}{\text{Market Price of the Bond}} \times 100
]
Where:
- Coupon Payment is the annual interest payment based on the bond’s face value.
- Market Price of the Bond is the price the bond is currently trading for in the market.
For this problem, the bond has a face value of $1,000 and a coupon rate of 5 percent. The coupon payment is calculated as:
[
\text{Coupon Payment} = \text{Face Value} \times \text{Coupon Rate} = 1,000 \times 0.05 = 50
]
Now, let’s calculate the current yield for each scenario:
a. When the market price is $900:
[
\text{Current Yield} = \frac{50}{900} \times 100 = 5.56\%
]
b. When the market price is $1,000:
[
\text{Current Yield} = \frac{50}{1,000} \times 100 = 5.00\%
]
c. When the market price is $1,100:
[
\text{Current Yield} = \frac{50}{1,100} \times 100 = 4.55\%
]
Explanation:
The current yield measures the income (interest) an investor can expect to earn on a bond based on its current market price. It is important to note that the coupon payment is fixed, but the yield changes based on the price at which the bond is purchased.
- If the bond is purchased at a discount (e.g., $900), the current yield is higher because the investor is paying less for the bond but still receiving the same $50 annual coupon payment. This results in a yield greater than the coupon rate.
- If the bond is purchased at par (e.g., $1,000), the current yield is equal to the coupon rate, since the price paid for the bond is exactly its face value.
- If the bond is purchased at a premium (e.g., $1,100), the current yield is lower because the investor is paying more than the face value for the bond, so the return on the investment (the coupon payment) is smaller relative to the price paid for the bond.
In conclusion, the current yield is inversely related to the market price of the bond. As the price rises, the yield falls, and as the price falls, the yield increases.