Presentation on theme: "CHAPTER 8 Bonds and Their Valuation"— Presentation transcript:
1 CHAPTER 8 Bonds and Their Valuation Key features of bondsBond valuationMeasuring yieldAssessing risk
2 Key Features of a Bond1. Par value: Face amount; paid at maturity. Assume $1,000.2. Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.
3 3. Maturity: Years until bond must be repaid. Declines.4. Issue date: Date when bondwas issued.
4 How does adding a “call provision” affect a bond? 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.
5 What is a sinking fund?Provision to pay off a loan over its life rather than all at maturity.Similar to amortization on a term loan.Reduces risk to investor, shortens average maturity.But not good for investors if rates decline after issuance.
6 Sinking funds are generally handled in 2 ways 1. Call x% at par per year for sinking fund purposes.2. Buy bonds on open market.Company would call if kd is below the coupon rate and bond sells at a premium. Use open market purchase if kd is above coupon rate and bond sells at a discount.
8 The discount rate (ki) is the opportunity cost of capital, i. e The discount rate (ki) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk.ki = k* + IP + LP + MRP + DRP.
9 What’s the value of a 10-year, 10% coupon bond if kd = 10%? 100121010%,000V = ?...()VkBd=$100$1,100010.+= $ $ $385.54= $1,000.
10 The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: PVA = PMT * (1- (1+k)n )kPV = FV(1/(1+k)n)V bond = PMT * (1- (1+kd)n + M(1/(1+kd)n)kd
12 With annual compounding, P/Y = 1, and End mode With annual compounding, P/Y = 1, and End mode. Use all TVM keys in the calculation - you have an annuity and a future cash flow outside the annuity.INPUTSN I/YR PV PMT FV-1,000OUTPUT
13 Most bonds pay interest semiannually, so m = 2. You must divide k by 2, multiplyn by 2. The payment will be $50 every 6months.If the market rate of interestincreased to 12%:1V bond = PMT * (1- (1+kd/2)n*2+ M(1/(1+kd /2)n *2)kd /2V bond = 50 * (1- (1+.12/2)10* (1/(1+.12/2)10*2).12/2V bond =50( )+1000(.3118) =This bond trades at a discount to par.
14 What would happen if expected inflation rose by 2%, causing k =12%?. P/Y=2, End modeINPUTSN I/YR PV PMT FVOUTPUTWhen kd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.
15 If the market rate of interest decreased to 8%: 1 V bond = PMT * (1- (1+kd/2)n*2+ M(1/(1+kd /2)n *2)kd /2V bond = 50 * (1- (1+.08/2)10* (1/(1+.08/2)10*2).08/2V bond =50( )+1000(.4564) =This bond trades at a premium to par.
16 What would happen if inflation fell, and kd declined to 8%? P/Y=2, End modeN I/YR PV PMT FV-1,135.90INPUTSOUTPUTPrice rises above par, and bond sells at a premium, if coupon > kd.
17 The bond was issued 20 years ago and now has 10 years to maturity The bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?
18 Years remaining to Maturity Bond Value ($)1,372kd = 7%.1,211kd = 10%.M1,000837kd = 13%.775Years remaining to Maturity
19 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 kd remains constant.
20 What is the “yield to maturity”? YTM is the rate of return earned on a bond held to maturity. Also called the “promised yield.”
21 What’s the YTM on a 10-year, 9% semiannual coupon, $1,000 par value bond that sells for $885.45? 192045kd=?1,000PV1.PV20PVM885.45Find kd that “works”!...
22 If you don’t have a financial calculator, need to use trial and error. Know the price of the bond hasdropped to $885.45, so yield must have gone up.Try 11%, was a 9% coupon bond.1V bond = PMT * (1- (1+kd/2)n*2+ M(1/(1+kd /2)n *2)kd /2= 45 * (1- (1+.11/2)10* (1/(1+.11/2)10*2).11/2=45( )+1000(.3427) =Vbond needs to be higher, so yield needs to belower, but not much lower. Without a financial calculator,an answer of 9% < k < 11% would be sufficient.
24 If coupon rate < kd, discount. If coupon rate = kd, par bond.If coupon rate > kd, premium.If kd rises, price falls.Price = par at maturity.
25 If the price of the bond has increased to $1142.12, yield (market rate of interest) must have gone down.Try 7%, was a 9% coupon bond.1V bond = PMT * (1- (1+kd/2)n*2+ M(1/(1+kd /2)n *2)kd /2= 45 * (1- (1+.07/2)10* (1/(1+..07/2)10*2).07/2=45( )+1000(.5026) =Vbond is approximately equal, so the YTM is 7% .
26 Find YTM if price were $1,INPUTSN I/YR PV PMT FV7.0OUTPUTSells at a premium. Because coupon = 9% > kd = 7.0%, bond’s value > par.
28 Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%.$90$887Current yield == = 10.15%.
29 YTM = Current yield + Capital gains yield. Cap gains yield = YTM – Current yield= 10.91% – 10.15%= 0.76%.Could also find value in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.
30 What’s interest rate (or price) risk What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?Interest rate risk: Rising kd causes bond’s price to fall.kd1-yearChange10-yearChange5%$1,048$1,386+4.8%-4.4%+38.6%-25.1%10%1,0001,00015%956749
32 What is reinvestment rate risk? The risk that CFs will have to be reinvested in the future at lower rates, reducing income.Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.
33 Year 1 income = $50,000. At year-end get back $500,000 to reinvest. If rates fall to 3%, income will drop from $50,000 to $15,000. Had you bought 30-year bonds, income would have remained constant.
34 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!
35 Do all bonds of the same maturity have the same price and reinvestment rate risk? No, low coupon bonds have lessreinvestment rate risk but more price risk than high coupon bonds.
36 A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for $1, with an 8% yield to maturity.It can be called after 4 years at $1,050.What’s the bond’s nominal yield to call (YTC)? The price ofthe bond is now $ , need to find YTC. Try 6%.1V bond = PMT * (1- (1+kd/2)n*2+CP(1/(1+kd /2)n *2)kd /2= 50 * (1- (1+.06/2)4* (1/(1+.06/2)4*2).06/2=50( )+1050(.7894) =Need lower V bond = so YTC must be greater than 6%.
37 With a financial calculator, you are just Solving for the interest rate, using theCall premium as the future value and theTime to possible call as n.INPUTSN I/YR PV PMT FV3.568 x 2 = 7.137%OUTPUT
38 kNom = 7. 137% is the rate brokers would quote kNom = 7.137% is the rate brokers would quote. Could also calculate EFF% to call:EFF% = ( )2 – 1 = 7.26%.This rate could be compared to monthly mortgages, etc.
39 If you bought bonds, would you be more likely to earn YTM or YTC? Coupon rate = 10% vs. YTC = kd = 7.137%. Could raise money by selling new bonds which pay 7.137%.Could thus replace bonds that pay $100/year with bonds that pay only $71.37/year.Investors should expect a call, hence YTC = 7.1%, not YTM = 8%.
40 In general, if a bond sells at a premium, then (1) coupon > kd, so (2) a call is likely. So, expect to earn:YTC on premium bonds.YTM on par & discount bonds.
41 Disney recently issued 100-year bonds with a YTM of 7 Disney recently issued 100-year bonds with a YTM of 7.5%--this represents the promised return. The expected return was less than 7.5% when the bonds were issued.If issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return.
42 Bond Ratings Provide One Measure of Default Risk Investment Grade Junk BondsMoody’s Aaa Aa A Baa Ba B Caa CS&P AAA AA A BBB BB B CCC D
43 What factors affect default risk and bond ratings? Financial performanceDebt ratioTIE ratioCurrent ratio
44 Provisions in the bond contract Secured vs. unsecured debtSenior vs. subordinated debtGuarantee provisionsSinking fund provisionsDebt maturity
45 Other factorsEarnings stabilityRegulatory environmentPotential product liabilityAccounting policies
46 Top Ten Largest U.S. Corporate Bond Financings, as of July 1999 IssuerFord Motor Co.AT&TRJR HoldingsWorldComSprintDateJuly 1999Mar 1999May 1989Aug 1998Nov 1998Amount$8.6 billion$8.0 billion$6.1 billion$5.0 billion