McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.0 Chapter 6 Interest Rates and Bond Valuation

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved Bonds and Bond Valuation

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.2 Bonds and Bond Valuation When a corporation (or government) wishes to borrow money from the public on a long term basis, it usually does so by issuing, or selling, debt securities that are generally called Bonds.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.3 Bond Features and Prices A Bond is normally an interest-only loan. The borrower (corporation or government) pays interest every period Principal is repaid at the end of the loan Example: Beck corporation wants to borrow $1,000 for 30 years: The interest rate on similar debt is 12% Beck will pay $120 in interest every year for 30 years.12 x $1,000 = $120 Beck will repay the $1,000 principal at the end of 30 years

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.4 Bond Features and Prices Coupon: the stated interest payment made on a bond. In our example: The $120 regular interest payments that Beck promises to make. The bond will pay $120 per year for the life of the bond.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.5 Bond Features and Prices The amount that will be repaid at the end of the loan is called the bond’s Face Value, or Par Value. Face Value: is the principal amount of a bond that is repaid at the end of the term. Usually $1,000 for corporate bonds Government bonds frequently have much larger face, or par, values A bond that sells for its par value is called: a par value bond

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.6 Bond Features and Prices Coupon Rate: is the annual coupon divided by the face value of a bond. In our previous example: $120/1,000 = 12% The bond has a 12% coupon rate

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.7 Bond Features and Prices The number of years until the face value is paid is called the bond’s time to Maturity: Maturity: is the date on which the principal amount of a bond is paid. Frequently 30 years for corporate bonds – at the time of original issuance, but varies. Once a bond has been issued, the number of years, or time to maturity, declines as time goes by.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.8 Bond Values and Yields As time passes, interest rates change in the marketplace. The cash flows from a bond (coupon payments) stay the same. Therefore, the value of the bond will fluctuate. When interest rates rise, the present value of the bond’s remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is worth more.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.9 Bond Values and Yields To determine the (present) value of a bond at a particular point in time, we need to know: The number of periods remaining until maturity (n) The face value (FV) The coupon (PMT) Note: Bond coupon payments are annuities. The market interest rate for bonds with similar features (i) Yield to Maturity (YTM): the rate required in the market on a bond. “yield” for short.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.10 Bond Values and Yields Example 1: Bottom of Page 146 and 147 Suppose the Xanth Co. were to issue a bond with: 10 years to maturity (n) An annual coupon of $80 (annuity)(PMT) Similar bonds have a YTM of 8% (i) Always assume a $1,000 Face Value (FV) Unless told otherwise The Xanth bond will pay $80 per year for the next 10 years in coupon interest. In 10 years, Xanth will pay $1,000 to the owner of the bond. What would the bond sell for? (i.e. What’s the PV) Use the Financial Calculator and solve for PV: $1,000 Sells for face value because the coupon rate on the bond = the going market rate.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.11 Bond Values and Yields Example 1 Con’t: Bottom of Page 147 and 148 Suppose a year has gone by. The Xanth bond now has nine years to maturity. If the interest rate in the market has risen to 10 percent, what will the bond be worth? Use your financial calculator to solve for PV. N = 9 I = 10 PMT = 80 FV = 1,000 PV =

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.12 Bond Values and Yields Example 1 Con’t: Bottom of Page 147 and 148 This bond, with its 8% coupon, is priced to yield 10% at $885. Because the bond pays less than the going rate (8% vs. 10%) investors are only willing to lend something less than the $1,000 promised repayment. A bond that sells for less than face value (at a discount) is called a Discount Bond.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.13 Bond Values and Yields Example 1 Con’t: Page 148 What would the Xanth bond sell for if interest rates had dropped by 2 percent instead of rising by 2 percent? N = 9 I = 6 (8 – 2 = 6) Pmt = 80 FV = 1000 PV = - 1, Now the bond sells at a premium and is called a Premium Bond.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.14 Bond Values and Yields Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lump sum Remember, as interest rates increase the PV’s decrease So, as interest rates increase, bond prices decrease and vice versa

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.15 Bond Values and Yields Relationship Between Coupon and Yield If YTM = coupon rate, then bond price = par value Remember: YTM = Market interest rate for bonds with similar features If YTM > coupon rate, then bond price < par value Selling at a discount, called a discount bond If YTM par value Selling at a premium, called a premium bond

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.16 Bond Values and Yields Graphical Relationship Between Bond Price and Yield-to-maturity

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.17 Interest Rate Risk The risk that arises for bond owners from fluctuating interest rates is called interest rate risk. Depends on how sensitive the bonds price is to interest rate changes. This interest rate sensitivity directly depends on two things: The time to maturity The coupon rate

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.18 Interest Rate Risk Time to Maturity The longer the time to maturity the greater the interest rate risk. For long term bonds: Even a relatively small change in interest rates “compounded” for 30 years, can have a significant effect on the present value of the bond. For short term bonds: The present value of the bond isn’t greatly affected by a small change in interest rates, if the amount is to be received in one year.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.19 Interest Rate Risk Coupon Rate The lower the coupon rate, the greater the interest rate risk. The value of a bond depends on the present value of its coupons and face amount. If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the face amount to be received at maturity. All other things equal, its value will fluctuate more as interest rates change The bond with the higher coupon has a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate.

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.20 Interest Rate Risk Figure 6.2 Interest Rate Risk and Time to Maturity

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.21 Finding the Yield to Maturity Yield-to-maturity is the rate implied by the current bond price Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $ Will the yield be more or less than 10%? N = 15 PV = FV = 1000 PMT = 100 (1,000 x.10 = $100) I = 11% Note: PMT and FV need to have the same sign PV the opposite sign

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.22 Finding the Yield to Maturity Semiannual Coupons Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1, What is the YTM? N = 40 (20 x 2 = 40) PV = -1, PMT = 50 (1000 x.10 = 100 / 2 = 50) FV = 1000 I = 4% (4 x 2 = 8) Note: the annual YTM of 8% is less than the coupon rate of 10% Therefore, the bond sells for more than face value

McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 6.23 Chapter 6: Suggested Homework Know chapter theories, concepts, and definitions Re-read the chapter and review the Power Point Slides Suggested Homework: The Chapter Review and Self-Test Problems: Page and 6.2 Answers are provided in the book just after the problems Questions and Problems: Page 178 2, 3, 4, 6, and 7 Use your financial calculator to work the problems. Refer to the Solutions Manual to confirm your answers.