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%
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