FIN303 Vicentiu Covrig Bonds and their valuation chapter 7 1 FIN303 Vicentiu Covrig Bond markets Bond A long term debt instrument in which a borrower agrees to make payments of principal and interest on specific dates to the holders of the bond Primarily traded in the over the counter OTC market Most bonds are owned by and traded among large financial institutions Full information on bond trades in the OTC market is not published but a representative group of bonds is listed and traded on the bond division of the NYSE 2 FIN303 Vicentiu Covrig Key Features of a Bond Par value face amount of the bond which is paid at maturity assume 1 000 Coupon interest rate stated interest rate generally fixed paid by the issuer Multiply by par to get dollar payment of interest Maturity date years until the bond must be repaid Issue date when the bond was issued Yield to maturity rate of return earned on a bond held until maturity also called the promised yield Some bonds are callable Call provision Allows issuer to refund the bond issue if rates decline helps the issuer but hurts the investor 3 FIN303 Vicentiu Covrig What is the value of a 10 year 10 annual coupon bond if rd discount rate 10 0 1 2 kd VB n 100 100 100 1 000 100 100 1 000 VB 1 10 1 10 1 10 1 10 10 VB 90 91 38 55 385 54 VB 1 000 4 FIN303 Vicentiu Covrig What is the opportunity cost of debt capital The discount rate rd is the opportunity cost of capital and is the rate that could be earned on alternative investments of equal risk rd r IP MRP DRP LP 5 FIN303 Vicentiu Covrig Using a financial calculator to value a bond We have a bond with a coupon rate of 10 paid annually that matures in 10 years with a face par value of 1 000 and rd is 13 Calculate the bond s value When rd is above the coupon rate the bond s value falls below par and sells at a discount INPUTS 10 13 N I YR OUTPUT PV 837 21 6 100 1000 PMT FV FIN303 Vicentiu Covrig What is the value of a 10 year 10 semiannual coupon bond if rd 13 1 2 3 Multiply years by 2 N 2 10 20 Divide nominal rate by 2 I YR 13 2 6 5 Divide annual coupon by 2 PMT 100 2 50 INPUTS 20 6 5 N I YR OUTPUT PV 834 72 7 50 1000 PMT FV FIN303 Vicentiu Covrig Exam type question You intend to purchase a 10 year 1 000 face value bond that pays interest of 60 every 6 months If your nominal annual required rate of return is 10 percent with semiannual compounding how much should you be willing to pay for this bond a 826 31 b 1 086 15 c 957 50 d 1 124 62 Financial calculator solution Inputs N 20 I 5 PMT 60 FV 1000 Output PV 1 124 62 VB 1 124 62 8 FIN303 Vicentiu Covrig What is the YTM on a 10 year 9 annual coupon 1 000 par value bond selling for 887 Must find the rd that solves this model INT INT M VB 1 N 1 rd 1 rd 1 rd N 90 90 1 000 887 1 10 1 rd 1 rd 1 rd 10 9 FIN303 Vicentiu Covrig Using a financial calculator to find YTM Solving for I YR the YTM of this bond is 10 91 This bond sells at a discount because YTM coupon rate INPUTS 10 N OUTPUT I YR 10 91 10 887 90 1000 PV PMT FV FIN303 Vicentiu Covrig Definitions Annual coupon payment Current yield CY Current price Change in price Capital gains yield CGY Beginning price Expected Expected Expected total return YTM CY CGY YTM yield to maturity rate of return earned on a bond if it is held to maturity 11 FIN303 Vicentiu Covrig A 10 year 10 semiannual coupon bond selling for 1 135 90 can be called in 4 years for 1 050 what is its yield to call YTC The bond s yield to maturity can be determined to be 8 Solving for the YTC is identical to solving for YTM except the time to call is used for N and the call premium is FV INPUTS 8 N OUTPUT I YR 3 568 12 1135 90 50 1050 PV PMT FV FIN303 Vicentiu Covrig Exam type question Consider a 1 000 par value bond with a 7 percent annual coupon The bond pays interest annually There are 9 years remaining until maturity What is the current yield on the bond assuming that the required return on the bond is 10 percent a 10 00 b 8 46 c 7 00 d 8 52 Current yield Annual coupon payment Current price Step 1 Find the price of the bond N 9 I YR 10 PMT 70 FV 1000 and then solve for PV 827 23 VB 827 23 Step 2 Calculate the current yield CY 70 827 23 8 46 13 FIN303 Vicentiu Covrig When is a call more likely to occur In general if a bond sells at a premium then 1 coupon rd so 2 a call is more likely So expect to earn YTC on premium bonds YTM on par discount bonds 14 FIN303 Vicentiu Covrig Bond values over time At maturity the value of any bond must equal its par value If kd remains constant The value of a premium bond would decrease over time until it reached 1 000 The value of a discount bond would increase over time until it reached 1 000 A value of a par bond stays at 1 000 15 FIN303 Vicentiu Covrig What is interest rate or price risk Interest rate risk is the concern that rising kd will cause the value of a bond to fall change 4 8 4 4 1 yr 1 048 1 000 956 rd 5 10 15 10yr 1 386 1 000 749 change 38 6 25 1 The 10 year bond is more sensitive to interest rate changes and hence has more interest rate risk 16 FIN303 Vicentiu Covrig What is reinvestment rate risk Reinvestment rate risk is the concern that kd will fall and future CFs will have to be reinvested at lower rates hence reducing income EXAMPLE Suppose you just won 1 000 000 playing the lottery You intend to invest the money and live off the interest If you choose to invest in series of 1 year bonds that pay a 8 coupon you receive 80 000 in income and have 1 000 000 to reinvest But if 1 year rates fall to 3 your annual income would fall to 30 000 If you choose a 30 year bond that pay a 10 coupon you receive 100 000 in income you can lock in a 10 interest rate and 100 000 annual income for 30 years 17 FIN303 Vicentiu Covrig Conclusions about interest rate and reinvestment rate risk Short term AND OR …