Interest Rates and Interest Rates and Bond ValuationBond Valuation Chapter 5Chapter 5 Key Concepts and SkillsKey Concepts and Skills Understand bond values and why they fluctuate Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields Chapter OutlineChapter Outline 5.1Bonds and Bond Valuation 5.2More on Bond Features 5.3Inflation and Interest Rates 5.4Determinants of Bond Yields 5.1 Bonds and Bond Valuation5.1 Bonds and Bond Valuation A bond is a legally binding agreement between a borrower and a lender that specifies the: Par (face) value(面值) Coupon rate(票面利率) Coupon payment(票面利息) Maturity Date(到期日) The yield to maturity(到期收益率) is the required market interest rate on the bond. Bond ValuationBond Valuation Primary Principle: Value of financial securities = PV of expected future cash flows Bond value is, therefore, determined by the present value of the coupon payments and par value. Interest rates are inversely related to present (i.e., bond) values. The Bond Pricing EquationThe Bond Pricing Equation Suppose a corporate issued a 5-year bond with 8% coupon on January 1 of 2013. The Par Value of the bond is $1,000. Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). Since the coupon rate is 8%, the payment is $40. On January 1 of 2013 the size and timing of cash flows will be: Bond ExampleBond Example On January 1, 2013, the required yield is 6%. How can we calculate the bond value? Now assume that the required yield is 12%. What is the bonds value now? Now assume that the required yield is also 8%. What is the bonds value now? Bond ConceptsBond Concepts qBond prices and market interest rates move in opposite directions. qWhen coupon rate = YTM, price = par value (par bond) qWhen coupon rate YTM, price par value (premium bond) qWhen coupon rate YTM, price par value (discount bond) Suppose a firm were to issue a bond with 10 years to maturity. The face value of the bond is $1,000 and the annual coupon is $100. What is the value of the bond if the required market interest rate is 8%/10%/12%? When the required market interest rate is 8% When the required market interest rate is 10% When the required market interest rate is 12% What is the value of the bond 2 years after issuing? When the required market interest rate is 8% When the required market interest rate is 10% When the required market interest rate is 12% qWhen the required market interest rate is constant: qThe value of par bond will maintain unchanged. qThe value of premium bond will gradually decrease with the coming of maturity date. It = par value at maturity date. qThe value of discount bond will gradually increase with the coming of maturity date. It = par value at maturity date. Interest Rate RiskInterest Rate Risk qChange in price due to changes in interest rates: qAll other things being equal, the longer the time to maturity, the greater the interest rate risk. qAll other things being equal, the lower the coupon rate, the greater the interest rate risk. Have a try!Have a try! Suppose a firm has a bond with 20 years to maturity. The face value of the bond is $20,000. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six months over the last 6 years. If the required return on the bond is 8% compounded semiannually, What is the current price of the bond? Computing Yield to MaturityComputing Yield to Maturity Yield to maturity is the rate implied by the current bond price. Finding the YTM requires trial and error and is similar to the process for finding R with an annuity. Suppose we are interested in a 6-year, 8% coupon bond. The face value of the bond is $1000 and the price of the bond is $1115. What is the YTM of this bond? Current Yield vs. Yield to MaturityCurrent Yield vs. Yield to Maturity Current Yield = annual coupon / price Yield to maturity = Current yield + Capital gains yield Example: 10% coupon bond, with annual coupons, face value of 1,000, 20 years to maturity, $1,196.31 price Current yield = 100 / 1196.31 = 8.36% Price in one year (assuming no change in YTM) = 1,192.06 Capital gains yield = (1192.06 1196.31) / 1196.31 =-.36% YTM = 8.36 - .36 = 8% Pure Discount Bonds(Pure Discount Bonds(纯贴现债券纯贴现债券) ) Make no periodic interest payments (coupon rate = 0%) The entire yield to maturity comes from the difference between the purchase price and the par value. Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Information needed for valuing pure discount bonds: Time to maturity (T) Face value (F) Discount rate (r) Present value of a pure discount bond at time 0: