Bond Terminology Bond • A security that obligates the issuer to make fixed payments to the bondholder until the maturity of the bond (fixed income security) Face Value (par, principal or maturity value) • Payment made at the maturity of the bond. In the US it is usually $1,000 Coupon • The interest payments made to the bondholder. In the USA coupons are paid twice a year Coupon Rate • Total annual interest payment as percent of bond face value. Only used to calculate coupon. Not used as discount rate, but upon issuance the coupon rate is usually close or equal to the discount or required rate of return.
Bond Terminology and Pricing Bond Price • Equals the present value of all future coupon payments and the future par value payment. Bond Yield • The annualized (APR) discount rate used to calculate the bond’s present value. Also known as the yield to maturity or required rate of return. Current Yield • Annual coupon payments divided by bond price. coupon coupon ( coupon + par )PV = + + .... + (1 + r ) 1 (1 + r ) 2 (1 + r ) t
Bond Pricing Example What is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%. 50 50 1,050PV = + + (1.0215) (1.0215) (1.0215) 3 1 2PV = $1,081.95 Calculator: N=3, I/Y=2.15, PMT=.05x1,000=50, FV=1,000, PV=?
Bond Cash Flows
Bond Pricing Example What is the price of the bond if the required rate of return is 2.15% and the coupons are paid semi- annually? 25 25 25 1,025PV = 1 + 2 + ... + 5 + 6 (1.01075) (1.01075) (1.01075) (1.01075)PV = $1,082.37 Calculator: N=3 years x 2 payments/year=6, I/Y=2.15/2 payments/year = 1.075, PMT=.05x1,000/2 payments/year=25, FV=1,000, PV=?
Semi-Annual Coupons How did the calculation change, given semi-annual coupons versus annual coupon payments? Time Periods Discount RatePaying coupons twice a year, Since the time periods are instead of once doubles the now half years, thetotal number of cash flows to discount rate is also be discounted in the PV changed from the annual formula. rate to the half year rate.
Bond Pricing Example What is the price of the annual bond if the required rate of return is 5.0 %? 50 50 1,050 PV = 1 + 2 + 3 (1.050) (1.050) (1.050) PV = $1,000
Bond Pricing Example What is the price of the annual bond if the required rate of return is 8 %? 50 50 1,050 PV = + + (1.08) (1.08) (1.08) 3 1 2 PV = $922.69
Interest Rate Risk The value of an existing bond falls as interest (discount) rates rise 1,200 1,100 1,000 900 B p d n o $ e c r ) ( i 800 700 0 2 4 6 8 10 12 14 16 Interest rate (%)
Interest Rate Risk The value of an existing bond falls as interest (discount) rates rise. The intuition is that, when buying a bond, we agree on a fixed interest payment. Afterwards, when current interest rates go up, our bond pays less interest than newer bonds, making our bond worth less.
Pricing of Zero-Coupon Bonds Price a 10 year zero-coupon bond at a 12% discount rate. PV = CFt / (1 + r)t = 1000 / (1 + .12)10 Price = 1000 / (1+0.12)10 = $321.97
Bond Yield or Yield to Maturity (YTM) When a normal coupon bond is initially issued its coupon rate should be close to or equal to its yield to maturity (discount rate) But market conditions like changing interest rates can cause the bond prices and yields to change over time while the coupon rate stays constant If given the bond price, you can calculate its YTM by solving for r below. coupon coupon ( coupon + par )PV = + + .... + (1 + r ) 1 (1 + r ) 2 (1 + r ) t
Bond Yields Example What is the YTM of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95. 50 50 1,050 PV = + + (1 + r ) (1 + r ) 1 2 (1 + r ) 3 PV = $1,081.95 YTM = 2.15%
The Yield CurveTerm Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date.Yield Curve - Graph of the term structure.
The Yield Curve Treasury zero coupon bonds (strips) are bonds that make a single payment. The yields on Treasury strips in February 2008 show that investors received a higher yield on longer term bonds. 6 5 4 Yield % 3 2 1 0 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 Maturity (years)
Bond Rates of ReturnRate of Return – actual earnings of aninvestor during a certain period of time perdollar invested in a bond. (coupons + change in price)Rate of return = investment (coupons + Price 1 – Price 0 )Rate of return = Price 0
Bonds and Credit RisksCredit risk is the risk of default by the issuer, which is theinability to pay coupons or face value at maturity. USGovernment debt has no credit risk by convention.Investors require higher yields on riskier bonds.The default premium is the difference between the yields ongovernment bonds and corporate bonds with the samematurity, but more default risk.
Default Risk and Ratings• Rating companies – Moody’s Investor Service – Standard & Poor’s – Duff and Phelps• Rating Categories – Investment grade = BBB, Baa and above – Speculative grade or Junk bonds = BB and below
Bond Ratings StandardMoody s & Poors SafetyAaa AAA The strongest rating; ability to repay interest and principal is very strong.Aa AA Very strong likelihood that interest and principal will be repaidA A Strong ability to repay, but some vulnerability to changes in circumstancesBaa BBB Adequate capacity to repay; more vulnerability to changes in economic circumstancesBa BB Considerable uncertainty about ability to repay.B B Likelihood of interest and principal payments over sustained periods is questionable.Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid.