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?
a) The current yield is $80/1100 = 7.27%
b) The yield to maturity (YTM) is the interest rate r for which the present value of all future payments (compounding at interest rate r) equals the amount currently paid. If iterest were paid annually, the YTM would be the value of r that satisfies the equation
80(1+r)^-1 + 80(1+r)^-2 + ... + 80(1+r)^-10 +1000(1+r)^-10 = 1000
You need a calculator to solve that. Most bonds pay interest semiannually, which doubles the number of terms in the equation, and requires that r/2 be used as the compouding rate. The question should have specified whether bond paymenta are annual or semiannual.
Using the bond rate calculator at this website:
http://www.moneychimp.com/calculator/bond_yield_calculator.htm
I get a YTM of 6.602%
To calculate the current yield on the bond, you need to divide the annual coupon payment by the current market price of the bond. In this case, the coupon rate is 8 percent, so the annual coupon payment is $80 (0.08 multiplied by the face value of $1,000). The current market price of the bond is $1,100.
So, the current yield is $80 divided by $1,100, which equals 0.0727 or 7.27%.
To calculate the yield to maturity (YTM) of the bond, you need to find the interest rate at which the present value of all future cash flows (coupon payments and the final principal repayment) equals the market price of the bond.
Using the YTM equation provided, you have a series of future cash flows (coupon payments) and the final principal repayment. The equation requires solving for the interest rate (r) that satisfies the equation.
Since most bonds pay interest semiannually, you need to adjust the equation accordingly. The compounding rate becomes r/2, and the number of terms in the equation doubles.
To solve for the YTM, you can use a bond rate calculator, such as the one provided (http://www.moneychimp.com/calculator/bond_yield_calculator.htm).
Entering the appropriate values (face value of $1,000, coupon rate of 8 percent, number of years until maturity = 10, and market price of $1,100), the calculator will give you the YTM as 6.602%.
Remember to consider the timing of coupon payments and the formula for compounding when using bond yield calculators or performing manual calculations.