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?
To calculate the current yield on the bond, you need to divide the annual coupon payment by the current market price of the bond. The formula for current yield is:
Current Yield = Annual Coupon Payment / Current Market Price
a. To find the current yield, first calculate the annual coupon payment. The coupon payment is equal to the coupon rate multiplied by the face value of the bond. In this case, the coupon rate is 8 percent and the face value is not given. Let's assume the face value is $1,000 (which is a common assumption for bonds). So the annual coupon payment would be:
Annual Coupon Payment = Coupon Rate * Face Value
= 8% * $1,000
= $80
Next, divide the annual coupon payment by the current market price. In this case, the bond sells for $1,100, so the current yield would be:
Current Yield = $80 / $1,100
≈ 0.0727 or 7.27%
Therefore, the current yield on the bond is approximately 7.27%.
b. The yield to maturity (YTM) represents the total return an investor can expect to earn on a bond if it is held until maturity, considering both the coupon payments and any potential capital gain/loss. Calculating the YTM requires solving a financial equation or using a specialized financial calculator or software.
There isn't a direct formula to calculate YTM manually, but you can use financial tools or online calculators to find it. However, I can guide you through the steps that would typically be involved:
1. Get the cash flows: Determine the cash flows the bondholder will receive. In this case, you would have the annual coupon payments ($80) for 10 years and the face value of the bond ($1,000) at maturity.
2. Estimate the bond's present value: Determine the present value of each future cash flow by discounting them using the bond's yield to maturity. Start with an initial guess for the YTM and adjust it iteratively until the present value equals the current market price ($1,100). The process may require the use of financial formulas or trial-and-error methods.
Please note that the YTM may also be influenced by factors such as prevailing interest rates, credit risk, and market conditions.
In summary, while the current yield can be calculated easily using the provided data, determining the yield to maturity requires more complex calculations or the use of specific financial tools.