Fixed-Income Bond Valuation: Prices and Yields

We will now use discounted cash flow analysis to calculate bond prices and show how the discount rate used as well as a bond’s features, such as its coupon rate and time-to-maturity, affect pricing. The price of a bond and its future cash flows can be used calculate an internal rate of return, known as the yield-to-maturity, which serves as a useful return measure for fixed-income investors under certain assumptions. One of these assumptions that applies to this learning module is that all bond interest and principal cash flows occur as promised. We will explore the relationship between bond prices and bond features, showing how different features affect a bond’s price, and demonstrate pricing both on and between bond coupon dates. Finally, we will introduce matrix pricing, which uses comparable bonds to estimate a bond’s price and yield-to-maturity when neither is known.

Most of the examples and exhibits used throughout the reading can be downloaded as a Microsoft Excel workbook. Each worksheet in the workbook is labeled with the corresponding example or exhibit number in the text.
 

• Bond pricing is an application of discounted cash flow analysis. Bond prices are a function of a bond’s features, including its cash flows and the interest rate(s) used to discount future cash flows.
• By comparing a bond’s price to its face value or its coupon rate to the discount rate, we can identify whether a bond is trading at a discount, at par, or at a premium.
• If the market price of a bond is known, an internal rate of return on the cash flows can be calculated, known as the yield-to-maturity (YTM). The YTM is the single interest rate that equates the present value of future cash flows to the price of the bond.
• A bond investor’s rate of return will equal the YTM if (1) the investor holds the bond to maturity, (2) the issuer makes full coupon and principal payments on the scheduled dates, and (3) the investor reinvests all coupon payments at the same YTM.
• When a bond is priced or traded in between coupon dates, an additional amount must be added for interest that has accrued since the last coupon payment, to compensate the seller, since the buyer will receive the entire next coupon payment.
• To calculate a bond’s accrued interest on any date, we multiply the coupon by the fraction of days elapsed in the coupon period divided by the total days in the coupon period. There are various conventions for counting these days; two common conventions are actual/actual and 30/360.
• A bond’s price changes inversely with changes in its YTM. A bond’s features determine price sensitivity to changes in YTM.
• The lower the coupon rate on a fixed-coupon bond, the greater the percentage price change for a given change in the bond’s yield-to-maturity. Generally, the longer a bond’s time-to-maturity, the greater its percentage price change for a given change in its yield-to-maturity.
• Unlike listed equity securities, most bonds are thinly traded, which complicates price discovery.
• Matrix pricing is a price estimation process for new or illiquid bonds that uses yields on securities with the same or similar features. Matrix pricing is widely used in price quotations for bonds.