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CHAPTER SEVEN: BOND ANALYSIS AND INVESTMENT 06/08/2011 1 Bond Values • Bond values are discussed in one of two ways: – The dollar price – The yield to maturity • These two methods are equivalent since a price implies a yield, and vice-versa 06/08/2011 2 Bond Yields • There are several ways that we can describe the rate of return on a bond: – Coupon rate – Current yield – Yield to maturity – Modified yield to maturity – Yield to call – Realized Yield 06/08/2011 3 The Coupon Rate • The coupon rate of a bond is the stated rate of interest that the bond will pay • The coupon rate does not normally change during the life of the bond, instead the price of the bond changes as the coupon rate becomes more or less attractive relative to other interest rates • The coupon rate determines the dollar amount of the annual interest payment: Annual Pmt  Coupon Rate  Face Value 06/08/2011 4 The Current Yield • The current yield is a measure of the current income from owning the bond • It is calculated as: Annual Pmt CY  Face Value 06/08/2011 5 The Yield to Maturity • The yield to maturity is the average annual rate of return that a bondholder will earn under the following assumptions: – The bond is held to maturity – The interest payments are reinvested at the YTM • The yield to maturity is the same as the bond’s internal rate of return (IRR) 06/08/2011 6 The Modified Yield to Maturity • The assumptions behind the calculation of the YTM are often not met in practice • This is particularly true of the reinvestment assumption • To more accurately calculate the yield, we can change the assumed reinvestment rate to the actual rate at which we expect to reinvest • The resulting yield measure is referred to as the modified YTM, and is the same as the MIRR for the bond 06/08/2011 7 The Yield to Call • Most corporate bonds, and many older government bonds, have provisions which allow them to be called if interest rates should drop during the life of the bond • Normally, if a bond is called, the bondholder is paid a premium over the face value (known as the call premium) • The YTC is calculated exactly the same as YTM, except: – The call premium is added to the face value, and – The first call date is used instead of the maturity date 06/08/2011 8 The Realized Yield • The realized yield is an ex-post measure of the bond’s returns • The realized yield is simply the average annual rate of return that was actually earned on the investment • If you know the future selling price, reinvestment rate, and the holding period, you can calculate an ex-ante realized yield which can be used in place of the YTM (this might be called the expected yield) 06/08/2011 9 Calculating Bond Yield Measures • As an example of the calculation of the bond return measures, consider the following: – You are considering the purchase of a 2-year bond (semiannual interest payments) with a coupon rate of 8% and a current price of $964.54. The bond is callable in one year at a premium of 3% over the face value. Assume that interest payments will be reinvested at 9% per year, and that the most recent interest payment occurred immediately before you purchase the bond. Calculate the various return measures. – Now, assume that the bond has matured (it was not called). You purchased the bond for $964.54 and reinvested your interest payments at 9%. What was your realized yield? 06/08/2011 10