BUAD 306 Business Finance Session 5 Bond Valuation and Interest Rates Professor Kristy Jansen Bond valuation The general valuation formula is therefore P The current price of the bond T Maturity date Number of payments over the bond s life C Coupon Par Face value usually 1 000 r The appropriate discount rate or the YTM TTtTTtrParrrCrParrCP 1111111 Roadmap of this class Today Learn how bond markets really work Quoted interest rate for bonds YTM YTM versus coupon Interest rate sensitivity Basic features of corporate bonds Bond ratings Basic features of government bonds Where market interest rates come from The YTM for a bond Inflation and interest rates The yield curve Yield To Maturity YTM The YTM or yield or internal rate of return IRR is the quoted interest rate required in the market for that bond The YTM of a bond is quoted like an APR YTM per period rate r number of periods per period rate r the discount rate for the bond For annual bonds YTM r only for bonds that pay annually 1 1 1 1 1 1 1 Bond valuation Consider a bond with a 10 annual coupon rate 5 years to maturity Assume the YTM is 10 and par value is 1 000 What is the current price of the bond 0 r 1 r 2 r 3 r 4 r Bond Price C C C C 5 C Par 1 000 100 1 10 100 0 10 1 100 1 10 2 1 1 10 5 100 1 10 3 1 000 1 10 5 1 000 100 1 10 4 100 1 10 5 1 000 1 10 5 YTM and bond price The price of the bond and the YTM are inversely related Same bond T 5 coupon 10 but different prices for different YTM 1 500 00 1 400 00 1 300 00 1 200 00 1 100 00 1 000 00 900 00 800 00 700 00 600 00 0 5 10 15 20 Bond prices coupon versus YTM If YTM Coupon rate then Par value Bond price Coupon is at current market conditions so bond is traded at par If YTM Coupon rate then Bond price Par value Coupon is below current market conditions so bond is traded at a If YTM Coupon rate then Bond price Par value Coupon is above current market conditions so bond is traded at a discount premium Another bond valuation example Consider a bond with a 10 annual coupon rate 5 years to maturity and assume its YTM is 8 What is the current price of the bond Is this bond sold at a discount 100 0 08 1 1 1 08 5 1 000 1 08 5 1 079 85 Price Face Value so the bond is sold at a premium Summary basic bond relations Bond prices and interest rates move in opposite directions When a bond s coupon rate is greater than equal to less than its YTM the bond s market value is greater than equal to less than its par value Computing the YTM Finding the YTM is similar to finding r for an annuity with non zero future value Consider a bond with a 10 annual coupon rate 15 years to maturity and a par value of 1 000 The current price is 928 09 Will the yield be more or less than 10 Excel RATE 15 100 928 09 1000 11 Crucial the sign convention YTM with semiannual coupons Most bonds pay coupons every six months The YTM and the coupons of a bond are quoted like an APR YTM period YTM number of periods Annual coupon period coupon number of periods Thus the EAR of a bond is different from its YTM Only in the special case of annual coupon payment will we have YTM EAR YTM with semiannual coupons Only with annual coupon YTM per period rate APR EAR But most bonds pay coupons every six months Finding the YTM is similar to finding r for an annuity First move to per period rate General bond valuation 1 1 1 1 Note Coupons are quoted in ANNUAL units as well YTM with semiannual coupons Suppose a bond with a 10 coupon rate and semiannual coupon has a par value of 1 000 20 years to maturity and is selling for 1197 93 What is the YTM of the bond What is the EAR What is the semiannual coupon payment PMT 1 000 0 10 2 50 How many periods are there N 20 2 40 What is the YTM of this bond PV 1 197 93 FV 1 000 RATE 40 50 1197 93 1000 4 00 YTM 4 2 8 What is the EAR of this bond EAR 1 APR 2 2 1 1 YTM 2 2 1 8 16 Interest rate risk and time to maturity Interest rate risk and time to maturity Bond price versus YTM 30 year bond 1 year bond Interest rate risk the longer the time to maturity the greater the interest rate risk Interest rate risk and coupon rates 18 Bond J has a coupon rate of 3 percent Bond K has a coupon rate of 9 percent Both bonds have 14 years to maturity make semiannual payments and have a YTM of 6 percent If interest rates suddenly rise by 2 percent what is the percentage price change of these bonds What if rates suddenly fall by 2 percent instead What does this problem tell you about the interest rate risk of lower coupon bonds Interest rate risk and coupon rates cont d 1 1 1 1 1 1 0 06 2 14 2 1 0 06 2 14 2 718 54 1 1 0 06 2 14 2 1 0 06 2 14 2 1 281 46 YTM 6 YTM 8 30 2 0 06 2 90 2 0 06 2 30 2 0 08 2 90 2 0 08 2 30 2 0 04 2 90 2 0 04 2 YTM 4 1 1 1 1 1 1 1 000 1 000 1 000 1 000 1 000 1 000 1 1 0 04 2 14 2 1 0 04 2 14 2 893 59 24 36 1 1 0 04 2 14 2 1 0 04 2 14 2 1 532 03 19 55 1 1 0 08 2 14 2 1 0 08 2 14 2 583 42 18 80 1 1 0 08 2 14 2 1 0 08 2 14 2 1 083 32 15 46 Interest rate risk the lower the coupon rate the greater the interest rate risk Bond prices versus YTM If you hold a government bond what risks are you facing 1 The government might not pay 2 Interest rate risk interest rates move over time bond prices change All other things being equal the longer the time to maturity the All other things being equal the lower the coupon rate the greater greater the interest rate risk the interest rate risk The relation between bond prices and interest rates is not linear The effect of time on bond prices The effect of time on bond …