BMGT343 Chapter 10 Bond Prices Yields Bond Characteristics bond security that obligates the issuer to make specified payments to the holder over a period of time a bond is the IOU of the borrower a typical coupon bond obligates the issuer to make semiannual payments of interest coupon payments to the bondholder for the life of the bond when the bond matures the issuer repays the debt by paying the bond s par value face value coupon rate bond s annual interest payment per dollar of par value semiannual divide coupon by 2 bonds usually are issued with coupon rates set just high enough to induce investors to pay par value to buy the bond o o zero coupon bonds make no coupon payments these bonds are issued at prices considerably below par value and the investor s return comes solely from the difference between issue price and the payment of par value at maturity Treasury Bonds Notes treasury notes have maturities 1 10 years treasury bonds are issued from 10 30 years bond prices are quotes as a percentage of par value o bid price of the bond is 100 10 100 10 32 100 313 of par value 1 003 13 the yield to maturity is often interpreted as a measure of the average rate of return to an investor who purchases the bond for the ask price and holds it until its maturity date the quoted price does not include the interest that accrues between coupon payment date the sale invoice price of the bond is the amount the buyer actually pays accrued interest annual cpn pmt 2 x days since last cpn pmt days separating cpn pmts o Corporate Bonds most bonds are traded over the counter in a network of bond dealers linked by a computer quotation system the rating column is the estimation of bond safety by the 3 major bond rating agencies callable bonds allow the issuer to repurchase the bond at a specified call price before the maturity date o the firm might retire the high coupon debt and issue new bonds at a lower coupon rate to reduce interest payments The proceeds from the new bond issue are used to pay for the repurchase of the existing higher coupon bonds at the call price called refunding convertible bonds give bondholders an option to exchange each bond for a specified number of shares of common stock o conversion ratio gives the number of shares for which each bond may be exchanged o market conversion value current value of the shares for which the bond may be exchanged o conversion premium excess of the bond price over its conversion value put bond bond that the holder may choose either to exchange for par value at some date or extend for a given number of years floating rate bonds bonds with coupon rates periodically reset according to specified market rate Preferred Stock like bonds preferred stock promises to pay a specified stream of dividends unlike bonds failure to pay the promised dividend does not result in bankruptcy Instead the dividends owed simply cumulate and the common stockholders may not receive any dividends until the preferred stockholders have been paid in full in the event of bankruptcy the claim of preferred stock holders to the firm s assets has lower priority than that of bondholders preferred stock commonly pays a fixed dividend it is in effect a perpetuity the dividend rate is linked to a measure of current market interest rate and is adjusted at regular intervals dividends on preferred stock are not considered tax deductable expenses to the firm reduces their attractiveness International Bonds foreign bonds are issued by a borrower from a country other than one in which the bond is sold the bond is denominated I the currency of the country in which it is marketed Eurobonds are bonds issued in the currency of one country but not sold in other national markets Innovation in the Bond Market inverse floaters coupon rate on these bonds falls when the general level of interest rates rises asset backed securities income from a specified group of assets is used to service the debt pay in kind bonds issuers of pay in kind bonds may choose to pay interest either in cash or in additional bonds catastrophe bonds used as a way to transfer catastrophe risk from insurance companies to the capital markets investors in these bonds receive compensation in the form of higher coupon rates for taking on the risk indexed bonds make payments that are tied to the general price index or the price of a particular commodity the cash flows are fixed in real terms o o nominal return interest price appreciation initial price real return 1 nominal return 1 inflation Bond Pricing the nominal risk free rate equals the sum of real risk free rate of return premium above the real rate to compensate for expected inflation bond value present value of coupons present value of par value bond value coupon 1 r t par value 1 r t o o o the firm term on the right hand side of the equation is the present value of an annuity the second term is the present value of a single amount the final payment on the bond s par value 1 1 r t is the PV factor price of the bond coupon x 1 r x 1 1 1 r t par value x 1 1 r t the bond price will fall as market interest rates rise this property of bond prices is called convexity because of the convex shape of the bond price curve progressive increases in the interest rate result in progressively smaller reductions in the bond price o o o interest rate fluctuations present the main source of risk in the bond market the force discounting is greatest for the longest term bonds short term treasury securities such as t bills are considered the safest Bond Pricing between Coupon Dates invoice price flat price accrued interest when a bond pays its coupon the flat price equals invoice price because interest 0 Bond Yields Yield to maturity YTM discount rate that makes the present value of a bond s payments equal to its price average rate of return that will be earned on a bond if it is bought now and held until maturity to calculate YTM we solve the bond price equation for the interest rate given the bond s price the semiannual yield would be doubled and reported as a bond equivalent yield o o o o o n number of periods until maturity I interest rate per period PV present value sometimes entered as a negative value FV future value of the bond usually 1 000 PMT amount of the coupon payments zero coupon bonds pmt 0 Current yield annual coupon divided by bond price Premium bonds bonds selling above par value Discount bonds bonds selling below par value Yield to Call at very low market rates the