CALCULATING THE YIELD ON A BOND
Consider a bond that has a current price of 90; that is, if the par value of the bond is $1,000, the bond’s price is 90% of $1,000 or $900. And suppose that this bond has five years remaining to maturity and an 8% coupon rate. With five years remaining to maturity, the bond has 10 six-month periods remaining.
With a coupon rate of 8%, this means that the cash flows for interest is $40 every six months. For a given bond, we therefore have the following information:
Present value = $900
Number of periods to maturity = 10
Cash flow every six months = $40
Additional cash flow at maturity = $1,000
The six-month yield, r_{d}, is the discount rate that solves:
\$ 900=\left[\sum_{t=1}^{10} \frac{\$ 40}{\left(1+r_{d}\right)^{t}}\right]+\frac{\$ 1,000}{\left(1+r_{d}\right)^{10}}
Using a calculator or spreadsheet, we calculate the six-month yield as 5.315% [PV = $900; N = ’10; PMT = $40; FV = $1,000]. Bond yields are generally stated on the basis of an annualized yield, referred to as the yield to maturity on a bond-equivalent basis. This measure is analogous to the APR with semiannual compounding. Therefore, yield to maturity is 10.63%.