Bond Yields.
An AT&T bond has 10 years until maturity, a coupon rate of 8 percent, and sells for $1,100.
a. What is the current yield on the bond?
b. What is the yield to maturity?
I believe you are missing something; either the market rate of return or the face value of the bond.
Yes
To calculate the current yield and yield to maturity, you are correct in stating that we need either the market rate of return (also known as the required rate of return) or the face value of the bond.
However, we can solve this problem using other given information. Let's start by calculating the missing variable to determine both the current yield and the yield to maturity.
The coupon rate of 8 percent implies that the bond pays an annual coupon payment equal to 8% of the bond's face value. Since we are missing the face value, we can calculate it using the coupon payment, coupon rate, and the bond's selling price.
Let's calculate the face value:
Coupon payment = Coupon rate * Face value
$88 = 8% * Face value
Dividing both sides of the equation by 0.08 (8%), we get:
Face value = $88 / 0.08 = $1,100
Now that we have the face value, we can proceed to calculate the current yield and yield to maturity.
a. Current Yield:
The current yield is the annual coupon payment divided by the bond's current market price, expressed as a percentage.
Current Yield = (Annual Coupon Payment / Market Price) * 100
In this case, the annual coupon payment is 8% of the bond's face value, which is $1,100. Therefore, the annual coupon payment is:
$88 = 8% * $1,100
Using the given information that the bond sells for $1,100, we can calculate the current yield using the formula:
Current Yield = ($88 / $1,100) * 100
b. Yield to Maturity:
The yield to maturity (YTM) is the total return anticipated by an investor who holds the bond until maturity. It considers both the coupon payments and the capital appreciation or depreciation of the bond's market price.
To calculate the yield to maturity, we need the present value of all the cash flows generated by the bond until maturity. These cash flows consist of the annual coupon payments and the bond's face value at maturity.
Since we have the face value, we can calculate the present value of the annual coupon payment using the bond's selling price as the present value. Then we can sum all the present values and solve for the yield to maturity using trial and error or a financial calculator.
Unfortunately, without the market rate of return or any other information, we cannot determine the yield to maturity in this scenario.
It is important to note that yield to maturity accounts for the time value of money and is a more accurate measure of the bond's return compared to the current yield, which only considers the coupon payments relative to the bond's price.