Bonds and Their Valuation.ppt

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1、,CHAPTER 4Bonds and Their Valuation,Key features of bondsBond valuationMeasuring yieldAssessing 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

2、),3.Maturity: Years until bondmust be repaid. Declines.4.Issue date: Date when bondwas issued.5.Default risk: Risk that issuer will not make interest or principal payments.,How does adding a call provision affect a bond?,Issuer can refund if rates decline. That helps the issuer but hurts the investo

3、r.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.,Whats 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

4、 investor, shortens average maturity.But not good for investors if rates decline after issuance.,1.Call x% at par per year for sinking fund purposes.2.Buy bonds on open market.Company would call if rd is below the coupon rate and bond sells at a premium. Use open market purchase if rd is above coupo

5、n rate and bond sells at a discount.,Sinking funds are generally handledin 2 ways,Financial Asset Valuation,PV,=,CF,1,+,r,.,.,.,+,CF,1,+,r,1,n,1,2,2,1,CF,r,n,.,r,.,+,+,+,The discount rate (ri) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal

6、 risk.,ri = r* + IP + LP + MRP + DRP,for debt securities.,Whats the value of a 10-year, 10% coupon bond if rd = 10%?,V,r,B,d,$100,$1,000,1,1,10,10,.,.,.,+,$100,1,+,r,d,100,100,10%,100 + 1,000,V = ?,.,= $90.91 + . . . + $38.55 + $385.54= $1,000.,+,+,+,1,r,+,d,10 10 100 1000NI/YR PV PMTFV -1,000,The b

7、ond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:,INPUTS,OUTPUT,10 13 100 1000NI/YR PV PMTFV -837.21,When kd rises, above the coupon rate, the bonds value falls below par, so it sells at a discount.,What would happen if expected inflation rose by 3%, causing r = 1

8、3%?,INPUTS,OUTPUT,What would happen if inflation fell, and rd declined to 7%?,10 7 100 1000NI/YR PV PMTFV -1,210.71,If coupon rate rd, price rises above par, and bond sells at a premium.,INPUTS,OUTPUT,Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its

9、 value over time if the required rate of return remained at 10%, or at 13%, or at 7%?,M,Bond Value ($),Years remaining to Maturity,1,372,1,211,1,000,837,775,3025 20 15 10 5 0,rd = 7%.,rd = 13%.,rd = 10%.,At maturity, the value of any bond must equal its par value.The value of a premium bond would de

10、crease to $1,000.The value of a discount bond would increase to $1,000.A par bond stays at $1,000 if rd remains constant.,Whats “yield to maturity”?,YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”,Whats the YTM on a 10-year, 9% annual coupon, $1,000 par val

11、ue bond that sells for $887?,90,90,90,0,1,9,10,rd=?,1,000,PV1 . . .PV10PVM,887,Find rd that “works”!,.,10 -887 90 1000NI/YR PV PMTFV10.91,V,INT,r,M,r,B,d,N,d,N,1,1,1,.,+,INT,1,+,r,d,887,90,1,1,000,1,1,10,10,r,r,d,d,+,90,1,+,r,d,Find rd,+,+,+,+,+,+,+,+,INPUTS,OUTPUT,.,If coupon rate rd, bond sells at

12、 a premium.If rd rises, price falls.Price = par at maturity.,Find YTM if price were $1,134.20.,10 -1134.2 90 1000NI/YR PV PMTFV7.08,Sells at a premium. Because coupon = 9% rd = 7.08%, bonds value par.,INPUTS,OUTPUT,Definitions,Current yield =Capital gains yield = = YTM = +,Annual coupon pmtCurrent p

13、rice,Change in priceBeginning price,Exp totalreturn,Exp Curr yld,Exp capgains yld,Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%.,Current yield= 0.1015 = 10.15%.,$90 $887,YTM= Current yield + Capital gains yield.Cap gains yield = YTM -

14、 Current yield = 10.91% - 10.15% = 0.76%.,Could also find values in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.,Whats interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?,rd,1-year,Change,10-year,Change,5%,$1,048,$1,386,10%,1,000,4.8%,1,000,38

15、.6%,15%,956,4.4%,749,25.1%,Interest rate risk: Rising rd causes bonds price to fall.,0,500,1,000,1,500,0%,5%,10%,15%,1-year,10-year,rd,Value,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 $

16、500,000 playing the lottery. Youll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.,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 re

17、mained constant.,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!,True or False: “All 10-year bonds have the same price and reinvestment rate risk.”False! Low coupon bonds have lessreinvest

18、ment rate risk but more price risk than high coupon bonds.,Semiannual Bonds,1.Multiply years by 2 to get periods = 2n.2.Divide nominal rate by 2 to get periodic rate = rd/2.3.Divide annual INT by 2 to get PMT = INT/2.,2nrd/2 OK INT/2OK NI/YR PV PMTFV,INPUTS,OUTPUT,2(10) 13/2 100/220 6.5 50 1000NI/YR

19、 PV PMTFV -834.72,Find the value of 10-year, 10% coupon,semiannual bond if rd = 13%.,INPUTS,OUTPUT,Spreadsheet Functions for Bond Valuation,See Ch 04 Mini Case.xls for details.PRICEYIELD,You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10-year semiannual

20、 bond. Which would you prefer?,The semiannual bonds EFF% is:,10.25% 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 rNom = 10%, with EFF% = 10.25%. Should earn same EFF

21、% on annual payment bond, so:,INPUTS,OUTPUT,10 10.25 100 1000 N I/YRPV PMT FV -984.80,At a price of $984.80, the annual and semiannual bonds would be in equilibrium, because investors would earn EFF% = 10.25% on either bond.,A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135

22、.90 with an 8% yield to maturity.It can be called after 5 years at $1,050.Whats the bonds nominal yield tocall (YTC)?,10 -1135.9 50 1050 N I/YR PV PMT FV 3.765 x 2 = 7.53%,INPUTS,OUTPUT,rNom = 7.53% is the rate brokers would quote. Could also calculate EFF% to call:EFF% = (1.03765)2 - 1 = 7.672%.Thi

23、s rate could be compared to monthly mortgages, and so on.,If you bought bonds, would you be more likely to earn YTM or YTC?,Coupon rate = 10% vs. YTC = rd = 7.53%. Could raise money by selling new bonds which pay 7.53%.Could thus replace bonds which pay $100/year with bonds that pay only $75.30/year

24、.Investors should expect a call, hence YTC = 7.5%, not YTM = 8%.,In general, if a bond sells at a premium, then (1) coupon rd, so (2) a call is likely.So, expect to earn:YTC on premium bonds.YTM on par & discount bonds.,Disney recently issued 100-year bonds with a YTM of 7.5%-this represents the pro

25、mised 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.,Bond Ratings Provide One Measureof Default Risk,Inves

26、tment Grade,Junk Bonds,Moodys,Aaa,Aa,A,Baa,Ba,B,Caa,C,S&P,AAA,AA,A,BBB,BB,B,CCC,D,What factors affect default risk and bond ratings?,Financial performanceDebt ratioCoverage ratios, such as interest coverage ratio or EBITDA coverage ratioCurrent ratios,(More),Provisions in the bond contractSecured ve

27、rsus unsecured debtSenior versus subordinated debtGuarantee provisionsSinking fund provisionsDebt maturity,(More),Other factorsEarnings stabilityRegulatory environmentPotential product liabilityAccounting policies,Top Ten Largest U.S. Corporate Bond Financings, as of July 1999,IssuerFord Motor Co.AT

28、&TRJR HoldingsWorldComSprint,DateJuly 1999Mar 1999May 1989Aug 1998Nov 1998,Amount$8.6 billion$8.0 billion$6.1 billion$6.1 billion$5.0 billion,Bankruptcy,Two main chapters of Federal Bankruptcy Act:Chapter 11, ReorganizationChapter 7, LiquidationTypically, company wants Chapter 11, creditors may pref

29、er Chapter 7.,If company cant meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business.Company has 120 days to file a reorganization plan.Court appoints a “trustee” to supervise reorganization. Management usually stays in c

30、ontrol.,Company must demonstrate in its reorganization plan that it is “worth more alive than dead.” Otherwise, judge will order liquidation under Chapter 7.,If the company is liquidated, heres the payment priority:1.Secured creditors from sales of secured assets.2.Trustees costs3.Wages, subject to

31、limits4.Taxes5.Unfunded pension liabilities6.Unsecured creditors7.Preferred stock8.Common stock,In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.,