Suppose an 8% coupon, 30year bond is selling at 1,276.76 what average rate of return would be earned by an investor purchasing the bond at this price? We find the interest rate at which the present value of the remaining 60 semiannual payments equal the bond price.
This is the rate consistent with the observed price of the bond. Therefore, we solve for r in the following equation:
1,276.76 = [pic] $40 + $1000 (1+ r)t (1+ r)60
Or equivalently, 1,276.76 = 40 × Annuity factor (r , 60) + 1,000 × PV factor (r , 60)
These equations have only one unknown variable, the interest rate, r . you can use a financial calculator or spreadsheet to confirm that the solution is r = .03, or 3% per half year. This is considered the bond ‘s yield to maturity.
The financial press reports yields on an annualized basis, and annualizes the bond’s semiannual yield using simple interest techniques , resulting in an annual percentage rate ,or APR. Yields annualized using simple interest are also called “bond equivalent yields.”
Example 14.4: Yield to Call
Suppose the 8% coupon, 30- year maturity bond sells for $1,150 and is callable in 10 years at a call price of $1,100. its yield to maturity (YTM) and yield to call would be calculated using the following inputs
Yield to call Yield to Maturity
|Coupon payment $40 $40 |
|Number of Semiannual Periods 20 periods 60 periods |
|Final Payment $1,100