Bond Valuation Chapter 6 Brealey-Myers-Marcus 6th Edition Business Finance 620 Topics Covered Bond characteristics Basic terminology Coupon rates and bond yields Bond pricing techniques For coupon-paying (fixed-rate) corporate bonds Bond risks Interest rate risk Default risk Other forms of corporate debt Pricing zero-coupon bonds Basic Terminology A bond represents a loan to the issuer. The face value is the dollar amount loaned. Must be repaid by the issuer by the bond’s maturity Also called the par value or maturity value The coupon is the dollar amount of interest paid to the bond owners at specific intervals. Remains constant for the life of the bond Not all bonds pay coupons. The coupon rate equals the bond’s annual interest payment, expressed as a percent of its face value. Remains constant for the life of the bond Bond Yields Current Yield A bond’s annual interest payment, expressed as a percent of the bond’s market price Annual return “at the moment” on the price paid, regardless of the bond’s maturity Can vary over the life of a bond Yield To Maturity (YTM) Discount rate that equates the PV of a bond’s future cash flows to its current price Average annual rate of return an investor can expect on the price paid today if the bond is held to maturity Can vary over the life of a bond Coupon Rate and Bond Yields Application A 5-year corporate bond with a $1,000 par value pays a $65 annual coupon. If the bond currently sells for $985, what is the bond’s coupon rate? Current yield? YTM? The bond’s coupon rate is 6.5%: The coupon rate never changes over a bond’s lifetime. Coupon Rate and Bond Yields Application The bond’s current yield is 6.6%: The bond’s yield to maturity is 6.9%: You need a financial calculator to solve this formula for YTM. How should these yields be interpreted? Bond Quotes Corporate bonds Prices are quoted as a percent of the par value ($1,000). A quote of 96.43 represents 96.43% of par ($1,000). A bond quoted at 96.43 trades at $964.30. Government bonds Prices are quoted in 32nds of a percent of par. A quote of 94:13 would represent a price of 94.406% of par, which equals $944.06. (note use of colon “:”) What is the price of a corporate bond quoted at 105.86? What is the price of a federal agency bond quoted at 102:16? Asked and Bid Prices The asked price is the price investors pay to buy a bond from a bond dealer. The minimum price the dealer will accept to sell The bid price is the price investors receive when they sell a bond to a bond dealer. The maximum price the dealer will pay to buy The difference between the asked and bid price is called the spread (dealer’s commission). Bond Pricing General Framework The general formula for a bond’s price: CPN is the coupon, PAR is the face value, and R is the yield to maturity (expected rate of return). Because the coupon stream represents an annuity, the formula can be simplified: Bond Pricing Application Consider a 5-year corporate bond with a $1,000 par value and a $60 annual coupon. If investors seek a 7% annual rate of return, how much should they be willing to pay for the bond today? Note the relative importance of the repayment of the bond’s principal, compared to the coupon stream. The PV of the coupon stream is 25.7% of the bond’s price. The PV of the principal repayment is 74.3% of the price. What happens to this mix as a bond’s maturity increases? Bond Pricing Another Perspective Suppose you deposit $959 in an account earning 7% APR, compounded annually, for 5 years. How does this example illustrate the logic of bond pricing? Year Starting Balance Interest Rate Initial Ending Balance Amount Withdrawn Final Ending Balance 1 $ 959 7% $ 1,026 $ 60 $ 966 2 966 7% 1,034 60 974 3 974 7% 1,042 60 982 4 982 7% 1,051 60 991 5 991 7% 1,060 60 1,000 Bond Pricing Understanding Required Returns Investors need to be compensated to bear risk. As such, investors are said to “require” a certain return. The return bond investors seek is called the market yield on comparable debt. The term “comparable debt” refers to bonds with the same risk as the bond in question. Two bonds have the same risk if they have: the same maturity the credit quality (credit rating). Remember a key principle of CAPM: Securities with the same market risk should have the same expected return. Bond Pricing Application Continued Returning to our bond example – how does the bond price change if investors seek a 5% rate of return? Now, how does the price change if investors seek a 6% return on their investment? Let’s summarize these results >>> Bond Pricing Premium, Par and Discount Bonds Bond Value YTM Coupon Rate Price Premium to Par 5% 6% 1,043 Par 6% 6% 1,000 Discount to Par 7% 6% 959 How would you characterize the relation among the bond’s coupon rate, its YTM, and its price? Bonds can trade at par, at a premium to par, or at a discount to par. Results from the application: Bond Prices Over Time 30-Year US Treasury Bond Price Path for Premium Bond Price Path for Discount Bond Today Maturity Interest Rate Risk Bond prices fluctuate as interest rates change. You can see the source of the fluctuation in the bond pricing formula. Not only do bond prices change when interest rates change, but the impact is greater for bonds with longer maturities. Consider the following example: Bond A Bond B 5-year maturity 30-year maturity $40 annual coupon $70 annual coupon $1,000 par value $1,000 par value 4.5% YTM 7.5% YTM If market yields increase “across the board” by 1%, what will happen to each bond’s price? Interest Rate Risk Application Bond Maturity Initial YTM Initial Price New YTM New Price Price Change A 5 years 4.5% 978 5.5% 936 (4.3%) B 30 years 7.5% 941 8.5% 839 (10.8%) What can you conclude about the relation between time to maturity and the sensitivity of bond prices to interest rate fluctuations? What produces this effect? Interest Rate Risk Another Perspective A bond’s par value plays a major role in its price. The longer a bond’s maturity: the more heavily discounted its par value, and the larger the effect of any interest rate change on bond price. Consider the following example: Bond A has 5-year maturity, Bond B has a 20-year maturity. If we change R by 0.5%, which discounting term will be more significantly affected? A B The Yield Curve Treasury STRIPS are Treasury securities whose principal and interest payments have been converted into separate bonds that each make a single payment at maturity. The yields on STRIPS in August 2009 show that investors received a higher yield on longer-term bonds (STRIPS). Why would all investors not buy longer-term bonds and earn higher yields? Why invest in shorter-term bonds with lower yields? US Treasury STRIPS 3Q Yield, August 2009 The Risk of Default Credit risk The risk debt will not be serviced on schedule, to include the possibility that payments will be delayed or the issuer will not be able to pay at all A concern for both corporate and municipal bonds Default premium Additional compensation for bearing credit risk Bond ratings Investment grade rated Baa or better by Moody’s or BBB or better by Standard & Poor’s High-yield (formerly called “junk”) bonds rated below Baa (Moody’s) or BBB (S&P) How did bond ratings fare in the 2008-2009 Great Recession? Default Risk and Bond Ratings Other Forms of Corporate Debt Zero-coupon bonds Trade at a (deep) discount to par and pay the $1,000 face value at maturity, but no periodic coupon interest Return comes entirely from capital gain (loss) Help issuing companies conserve cash Minimize interest rate risk for buy-and-hold investors Floating-rate bonds Coupon rates vary with market conditions – almost always approximating market interest rates. Convertible bonds Investors may be able to convert a bond’s par value into a predetermined number of shares of stock. Investors can participate in stock price appreciation. Pricing Zero-Coupon Bonds Key characteristics: $1,000 par value No interest paid between issue and maturity dates; return comes entirely from capital gains (realized at maturity) YTM quotes are published for zeros of different maturities. Example: How much should you be willing to pay for a 20-year zero with a $1,000 par value and 8% YTM? Note that this is simply a special case of the general bond pricing formula (with all coupons equal to zero). Bond Pricing Understanding the Logic of Comparable Debt Measure Our Bond New Bond Comment Maturity 7 years 7 years Both bonds have the same interest rate risk Credit Rating AA+ AA+ Both bonds have the same default (credit) risk Coupon Rate 6.60% 6.90% Annual Coupon $66 $69 Market Yield (YTM) _______% 6.90% The YTM on a newly issued bond held to maturity is its coupon rate Bond Value Today $ _______ $1,000 The value of the New Bond today is $1,000 (par value) 1) How is the New Bond “comparable” to Our Bond? 2) What minimum rate of return should an investor require from Our Bond? 3) How much should an investor be willing to pay for Our Bond?