# UT FIN 357 - Chapter 5. Interest Rates and Bond Valuation (60 pages)

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## Chapter 5. Interest Rates and Bond Valuation

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- Pages:
- 60
- School:
- University of Texas at Austin
- Course:
- Fin 357 - Business Finance

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Interest Rates and Bond Valuation J David Miller 2017 Chapter 5 Finance 357 A Typical Bond IBM wants to borrow 1000 and would like to repay the 1 000 in 30 years The interest rate on debt from similar companies is 6 per year 6 X 1 000 60 interest payment per year for 30 years A 1 000 payment will be made at the end of 30 years to repay the loan 2 Bond Terminology Bond payments are called Coupons The amount to be repaid at the end of the loan is the Face Value or Par Value Annual coupon divided by the face value is the Coupon Rate The number of years until the face value is repaid is called the time to Maturity As each year passes the time to maturity decreases by one year 3 IBM Bond using Bond Terminology IBM wants to borrow 1000 and would like to repay the 1 000 in 30 years The interest rate on debt from similar companies is 6 per year Becomes A 30 year IBM bond with a 1 000 face value and a 6 coupon rate The time to maturity is 30 years 4 5 Bond Values and Yields Over time market interest rates change but the coupon on bonds remain the same This causes the present value of bonds to fluctuate As market interest rates rise the present value of bonds fall When interest rates fall the present value of bonds rise To determine the value of a bond once it has been issued we need the time remaining till maturity the face value the coupon and the market interest rate for bonds with similar features 6 Bond Values and Yields con d The interest rate that is required by the market after a bond has been issued is its Yield to Maturity Sometimes it is just called Yield The Yield acts as the bond s discount rate 7 Valuing a Bond IBM issues a 10 year 1 000 bond with an annual coupon of 8 The yield to maturity on this bond is 8 Present Value of Face repayment 1 000 2 1589 463 19 Annuity Present Value 80 X 1 1 1 0810 08 536 81 Total Bond Value 463 19 563 81 1 000 8 Bond Premium vs Discount A bond that is selling for it s face value is often said to be selling at par 1000 face bond selling for 1000 A bond selling for more than its face value is said to be selling at a premium 1000 face bond selling for 1100 A bond selling for less than its face value is said to be selling at a discount 1000 face bond selling for 900 9 Bond Valuation Formula A formula combining both the present value of the face value and an annuity of the coupon payments can be used to value a bond This is an annuity 10 Bond Valuation General Electric issued a bond several years ago This bond has a face value of 1 000 with a 60 annual coupon There are 23 years left until the bond matures What is the present value of the bond if current interest rates are 5 11 General Electric Bond Value General Electric issued a bond several years ago This bond has a face value of 1 000 with a 60 annual coupon There are 23 years left until the bond matures What is the present value of the bond if current interest rates are 5 60 X 1 1 1 05 23 05 1000 1 05 23 809 31 325 57 1 134 88 FV 1000 PMT 60 N 23 I Y 5 PV 1 134 89 12 Current Yield One description of the return on a bond is called Current Yield This calculated by dividing the bond s total annual coupon payments by the market price of the bond Annual Coupon 80 Bond Price 900 Current Yield 80 900 8 89 13 Current Yield Example A 25 year 8 annual coupon Goldman Sachs bond is selling for 658 Interest rates are currently at 6 What is the Current Yield of this bond 14 Current Yield Example Answer A 25 year 8 annual coupon Goldman Sachs bond is selling for 658 Interest rates are currently at 6 What is the Current Yield of this bond Total Annual Coupons 8 1 000 80 Bond Market Price 658 Current Yield 80 658 12 16 15 Semiannual Coupons Most bonds in the US make coupon payments twice a year For example a 30 year 10 coupon bond would make two payments of 50 during the year Bond interest rates are quoted like APRs The above bond with a 10 annual coupon would pay 50 per period for 60 periods of 6 months each 30 years X 2 times per year 60 The method we used with compounding money applies here as well 16 Semiannual Coupon Example A friend of yours wants to sell you a 10 year semiannual IBM bond with a 60 coupon paid Interest rates are currently at 7 What is the present value of this bond 7 interest rate 2 3 5 10 years X 2 periods per yr PV of Coupon 30 X 1 1 1 035 20 035 426 37 PV of Face Value 1000 1 035 20 502 57 FV 1000 I Y 7 2 3 5 N 10 2 20 PMT 60 2 30 PV 928 94 17 Bond Pricing Your parents give you a 1000 face value Microsoft bond as a graduation present The bond pays 70 in total coupon payments but pays them semiannually and there are 20 years until maturity Interest rates are currently at 8 How much was the gift really worth 18 Bond Pricing Answer Your parents give you a 1000 face value Microsoft bond as a graduation present The bond pays 70 in total coupon payments but pays them semiannually and there are 20 years until maturity Interest rates are currently at 8 How much was the gift really worth PV of Coupon 35 X 1 1 1 04 40 04 692 75 PV of Face Value 1000 1 04 40 208 29 FV 1000 I Y 8 2 4 N 20 2 40 PMT 70 2 35 PV 901 04 19 Interest Rate Risk The risk that arises for bond owners from fluctuating interest rates is called interest rate risk The amount of interest rate risk depends on how sensitive its price is to interest rate changes There are two very important rules to remember 1 All other things being equal the longer the time to maturity the greater the interest rate risk 2 All other things being equal the lower the coupon rate the greater the interest rate risk 20 Yield to Maturity YTM Often we will know the price that a bond is selling for along with the coupon and the time remaining until maturity These are helpful to us but what we are really interested in is the bond s yield to maturity The yield we would get if we bought the bond and held it until maturity 21 YTM Explained The yield to …

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