CHAPTER 5 Bonds and Their Valuation

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1 CHAPTER 5 Bonds and Their Valuation Key features of bonds Bond valuation Measuring yield Assessing risk Key Features of a Bond 1 Par value: Face amount; paid at maturity Assume $1,000 2 Coupon interest rate: Stated interest rate Multiply by par value to get dollars of interest Generally fixed (More ) 3 Maturity: Years until bond must be repaid Declines 4 Issue date: Date when bond was issued 5 Default risk: Risk that issuer will not make interest or principal payments 5-3 How does adding a call provision affect a bond? 5-4 Issuer can refund if rates decline That helps the issuer but hurts the investor Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds Most bonds have a deferred call and a declining call premium PV Financial Asset Valuation n r CF CF + CF ( 1+r ) ( 1+ r ) ( 1+r ) 5-5 Value CF 1 CF 2 CF n 1 n n The discount rate (r i ) is the opportunity cost of capital, ie, the rate that could be earned on alternative investments of equal risk r i r * + IP + LP + MRP + DRP for debt securities 5-6

2 V B What s the value of a 10-year, 10% coupon bond if r d 10%? $100 $1, $ r ( 1+ r d ) ( 1+ r ) d d % V? ( ) ,000 $ $ $38554 $1, , The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t 10: PV annuity PV maturity value Value of bond $ $1, What would happen if expected inflation rose by 3%, causing r 13%? 5-10 What would happen if inflation fell, and r d declined to 7%? ,21071 When r d rises, above the coupon rate, the bond s value falls below par, so it sells at a discount If coupon rate > r d, price rises above par, and bond sells at a premium Suppose the bond was issued 20 years ago and now has 10 years to maturity What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%? Bond Value ($) 1,372 1,211 r d 10% 1, r d 7% M r d 13% Years remaining to Maturity

3 5-13 What s yield to maturity? 5-14 At maturity, the value of any bond must equal its par value The value of a premium bond would decrease to $1,000 The value of a discount bond would increase to $1,000 A par bond stays at $1,000 if r d remains constant YTM is the rate of return earned on a bond held to maturity Also called promised yield 5-15 What s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? r d? ,000 PV 1 PV 10 PV M 887 Find r d that works! V B 887 INT M INT N ( + r d) ( 1+ r d ) ( + r d) 90 Find r d , 1+r d ( 1+ r d) ( ) ( 1+ r d) N If coupon rate < r d, bond sells at a discount 5-17 If coupon rate r d, bond sells at its par value If coupon rate > r d, bond sells at a premium If r d rises, price falls Price par at maturity Find YTM if price were $1, Sells at a premium Because coupon 9% > r d 708%, bond s value > par 5-18

4 Current yield Capital gains yield Exp total return Definitions Annual coupon pmt Current price Change in price Beginning price Exp YTM + Curr yld 5-19 Exp cap gains yld 5-20 Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM 1091% Current yield $90 $ % 5-21 YTM Current yield + Capital gains yield Cap gains yield YTM - Current yield 1091% % 076% Could also find values in Years 1 and 2, get difference, and divide by value in Year 1 Same answer 5-22 What s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk? Interest rate risk: Rising r d causes bond s price to fall r d 1-year Change 10-year Change 5% $1,048 $1,386 10% 1,000 48% 1, % 15% % % Value 1,500 1, year 1-year Long-term bonds: High interest rate risk, low reinvestment rate risk Short-term bonds: Low interest rate risk, high reinvestment rate risk Nothing is riskless! 0 0% 5% 10% 15% r d

5 True or False: All 10-year bonds have the same price and reinvestment rate risk 5-25 False! Low coupon bonds have less reinvestment rate risk but more price risk than high coupon bonds Semiannual Bonds Multiply years by 2 to get periods 2n 2 Divide nominal rate by 2 to get periodic rate r d /2 3 Divide annual INT by 2 to get PMT INT/2 2n r d /2 OK INT/2 OK 5-27 Find the value of 10-year, 10% coupon, semiannual bond if r d 13% 5-28 You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10-year semiannual bond Which would you prefer? 2(10) 13/2 100/ The semiannual bond s EFF% is: m i Nom EFF% m % 1025% > 10% EFF% on annual bond, so buy semiannual bond If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond? Semiannual bond has r Nom 10%, with EFF% 1025% Should earn same EFF% on annual payment bond, so: At a price of $98480, the annual and semiannual bonds would be in equilibrium, because investors would earn EFF% 1025% on either bond

6 What four factors affect the cost of money? Production opportunities Time preferences for consumption Risk Expected inflation Real versus Nominal Rates r* Real risk-free rate T-bond rate if no inflation; 1% to 4% r r RF Any nominal rate Rate on Treasury securities r r* + IP + DRP + LP + MRP Here: r Required rate of return on a debt security r* Real risk-free rate IP Inflation premium DRP Default risk premium LP Liquidity premium MRP Maturity risk premium 5-33 Premiums Added to r* for Different Types of Debt 5-34 ST Treasury: only IP for ST inflation LT Treasury: IP for LT inflation, MRP ST corporate: ST IP, DRP, LP LT corporate: IP, DRP, MRP, LP 5-35 Bond Ratings Provide One Measure of Default Risk What factors affect default risk and bond ratings? 5-36 Investment Grade Junk Bonds Moody s Aaa Aa A Baa Ba B Caa C S&P AAA AA A BBB BB B CCC D Financial performance Debt ratio Coverage ratios, such as interest coverage ratio or EBITDA coverage ratio Current ratios (More )

7 Provisions in the bond contract Secured versus unsecured debt Senior versus subordinated debt Guarantee provisions Sinking fund provisions Debt maturity Other factors Earnings stability Regulatory environment Potential product liability Accounting policies (More ) 5-39 What is the term structure of interest rates? What is a yield curve? Term structure: the relationship between interest rates (or yields) and maturities A graph of the term structure is called the yield curve 5-40 How can you construct a hypothetical Treasury yield curve? Estimate the inflation premium (IP) for each future year This is the estimated average inflation over that time period Step 2: Estimate the maturity risk premium (MRP) for each future year 5-41 Assume investors expect inflation to be 5% next year, 6% the following year, and 8% per year thereafter Step 1: Find the average expected inflation rate over years 1 to n: n Σ INFL t t 1 IP n n IP 1 5%/10 500% IP 10 [ (8)]/10 75% IP 20 [ (18)]/20 775% Must earn these IPs to break even versus inflation; that is, these IPs would permit you to earn r* (before taxes) 5-42

8 5-43 Assume the MRP is zero for Year 1 and increases by 01% each year Step 2: Find MRP based on this equation: MRP t 01%(t - 1) MRP 1 01% x 0 00% MRP 10 01% x 9 09% MRP 20 01% x 19 19% 5-44 Step 3: Add the IPs and MRPs to r*: r RFt r* + IP t + MRP t r RF Quoted market interest rate on treasury securities Assume r* 3%: r RF1 3% + 5% + 00% 80% r RF10 3% + 75% + 09% 114% r RF20 3% + 775% + 19% 1265% Hypothetical Treasury Yield Curve Interest Rate (%) 1 yr 80% 15 Maturity risk premium 10 yr 114% 20 yr 1265% Inflation premium Real risk-free rate Years to Maturity 5-46 What factors can explain the shape of this yield curve? This constructed yield curve is upward sloping This is due to increasing expected inflation and an increasing maturity risk premium 5-47 What kind of relationship exists between the Treasury yield curve and the yield curves for corporate issues? Corporate yield curves are higher than that of the Treasury bond However, corporate yield curves are not necessarily parallel to the Treasury curve The spread between a corporate yield curve and the Treasury curve widens as the corporate bond rating decreases Interest Rate (%) Hypothetical Treasury and Corporate Yield Curves 52% 59% 5-48 BB-Rated AAA-Rated 60% Treasury yield curve Years to 0 maturity

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