Chapter 7 Interest Rates and Bond Valuation Bonds Bond Valuation coupon stated interest payment on a bond face value Par value principal amount of a bond that is repaid at the end of the term coupon rate annual coupon divided by the face value of a bond maturity specified date on which the principal amount of a bond is paid yield to maturity rate required in the market of a bond current yield capital gains yield when interest rates rise the present value of bond s cash flows declines bond is worth less Total bond value present value annuity present value Bond value PV of coupons PV of par Bond Value PV of annuity PV of lump sum Bond has a face value F a coupon of C paid per period t periods to maturity yield of r per period Bond value C x 1 1 1 r t r F 1 r t On calc N years to maturity I yield to maturity PMT coupon rate x face value FV par value Coupon Yield Relationship 1 2 3 If YTM coupon rate par value bond price If YTM coupon par value bond price If YTM coupon par value bond price Interest rate risk risk that arises for bond owners from fluctuating interest rates the longer time to maturity the greater the interest rate risk the lower the coupon rate the greater the interest rate risk current yield annual coupon price effective annual yield 1 r t 1 coupon rate PMT FV More About Bond Features Main differences between debt and equity interest payments on debt are an expense tax deductable dividends are not tax deductable 1 debt is not an ownership interest in the firm 2 3 unpaid debt is a liability creditors can seize assets on debt not equity equity represents an ownership interest debt securities are typically called notes debentures or bonds indenture written agreement between the corporation and the lender detailing the terms of a debt issue deed or trust Yield to call n time to call FV bond premium PV selling price I YTC registered form form of a bond issue in which the registrar of the company records ownership of each bond bearer form form of a bond issue in which the bond is issued without record of the owner s name collateral securities that are pledged as a security for payment of debt mortgage securities secured by a mortgage on the real property of the borrower debenture an unsecured debt usually with a maturity of 10 years or more note an unsecured debt usually with a maturity under 10 years sinking fund account managed by the bond trustee for early bond redemption call provision an agreement giving the corporation the option to repurchase a bond at a specified price prior to maturity call premium amount by which the call price exceeds the par value of a bond deferred call provision a call provision prohibiting the company from redeeming a bond prior to a certain date call protected bond a bond that during a certain period cannot be redeemed by the issuer protective covenant part of the indenture limiting certain actions that might be taken during the term of the loan Some Different Types of Bonds Government Bonds Zero Coupon Bonds Floating Rate Bonds when the government wishes to borrow money for more than 1 year it sells treasury notes bonds to the public treasury issues have no default risk issues are exempt from state income taxes state local gov ts issue municipal bonds have varying degrees of default risk exempt from federal income taxes zero coupon bond bond that makes no coupon payments and is thus initially prices at a deep discount floating rate bond coupon payments interest rates are adjustable o holder has the right to redeem the note at par on the coupon payment date after some specified amount of time o coupon rate has a floor and ceiling capped at a maximum and minimum warrant gives the buyer of a bond the right to purchase shares of stock in the company at a fixed price income bond coupon payments can depend on company income convertible bond can be swapped for a number of shares of stock put bond allows holder to force the issuer to buy back the bond at a stated price Other Bonds Bond Markets the number of bonds issues far exceeds the number of stock issues bid price price a dealer is willing to pay for a security asked price price a dealer is willing to take for a security bid ask spread difference between the bid price and the asked price clean price price of a bond net of accrued interest this is the price that is typically quoted dirty price price of a bond including accrued interest price the buyer actually pays Inflation Interest Rates real rates interest rates or rates of return that have been adjusted for inflation nominal rates interest rates or rates of return that have not been adjusted for inflation the nominal rate on an investment is the change in the number of dollars you have the real rate on an investment is the change in how much you can buy with your dollars change in buying power Fisher Effect relationship between nominal returns real returns and inflation o 1 R 1 r x 1 h o Approximation R r h R nominal rate r real rate h inflation either discount nominal cash flows at a nominal rate or discount real cash flows at a real rate o PV C 1 1 1 r t r PV C t 1 r t Determinants of Bond Yields term structure of interest rates relationship between nominal interest rates on default free pure discount securities and time to maturity pure time value of money inflation premium portion of a nominal interest rate that represents compensation for expected future inflation interest rate risk premium compensation investors demand for bearing interest rate risk treasury yield curve plot of the yields on treasury notes and bonds relative to maturity default risk premium portion of a nominal interest rate or bond yield that represents compensation for the possibility of default