BondsandTheirValuation(英文版)

1、8 - 1Copyright 2001 by Harcourt, Inc.All rights reserved.CHAPTER 8Bonds and Their ValuationnKey features of bondsnBond valuationnMeasuring yieldnAssessing risk8 - 2Copyright 2001 by Harcourt, Inc.All rights reserved.Key Features of a Bond1.Par value: Face amount; paid at maturity. Assume $1,000.2.Co

2、upon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.8 - 3Copyright 2001 by Harcourt, Inc.All rights reserved.3.Maturity: Years until bondmust be repaid. Declines.4.Issue date: Date when bondwas issued.8 - 4Copyright 2001 by Harcourt, Inc.All rights reserve

3、d.How does adding a “call provision” affect a bond?nIssuer can refund if rates decline. That helps the issuer but hurts the investor.nTherefore, borrowers are willing to pay more, and lenders require more, on callable bonds.nMost bonds have a deferred call and a declining call premium.8 - 5Copyright

4、 2001 by Harcourt, Inc.All rights reserved.Whats a sinking fund?nProvision to pay off a loan over its life rather than all at maturity.nSimilar to amortization on a term loan.nReduces risk to investor, shortens average maturity.nBut not good for investors if rates decline after issuance.8 - 6Copyrig

5、ht 2001 by Harcourt, Inc.All rights reserved.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.Sinking funds ar

6、e generally handled in 2 ways8 - 7Copyright 2001 by Harcourt, Inc.All rights reserved.Financial Asset Values()()()PV =CF1+k. +CF1+k1n1221CFkn.012nkCF1CFnCF2Value.+8 - 8Copyright 2001 by Harcourt, Inc.All rights reserved.nThe discount rate (ki) is the opportunity cost of capital, i.e., the rate that

7、could be earned on alternative investments of equal risk.ki = k* + IP + LP + MRP + DRP.8 - 9Copyright 2001 by Harcourt, Inc.All rights reserved.Whats the value of a 10-year, 10% coupon bond if kd = 10%?( () )( () )( () )VkkBdd= =$100$1,1000111010 . . . +$1001+kd1001000121010%100 + 1,000V = ?.= $90.9

8、1 + . . . + $38.55 + $385.54= $1,000.+8 - 10Copyright 2001 by Harcourt, Inc.All rights reserved.10 10 100 1000NI/YR PV PMTFV -1,000The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: $ 614.46 385.54 $1,000.00PV annuity PV maturity value PV annuity =INPUTSOUTPUT

9、8 - 11Copyright 2001 by Harcourt, Inc.All rights reserved. 10 13 100 1000NI/YR PV PMT FV -837.21When 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 k = 13%?INPUTSOUTPUT8 - 12Copyright 2001 by Har

10、court, Inc.All rights reserved.What would happen if inflation fell, and kd declined to 7%? 10 7 100 1000NI/YR PV PMTFV -1,210.71Price rises above par, and bond sells at a premium, if coupon kd.INPUTSOUTPUT8 - 13Copyright 2001 by Harcourt, Inc.All rights reserved.The bond was issued 20 years ago and

11、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%?8 - 14Copyright 2001 by Harcourt, Inc.All rights reserved.MBond Value ($)Years remaining to Maturity1,3721,2111,0008377753025 20 15 10 5 0kd = 7%.kd = 13%.kd = 1

12、0%.8 - 15Copyright 2001 by Harcourt, Inc.All rights reserved.nAt maturity, the value of any bond must equal its par value.nThe value of a premium bond would decrease to $1,000.nThe value of a discount bond would increase to $1,000.nA par bond stays at $1,000 if kd remains constant.8 - 16Copyright 20

13、01 by Harcourt, Inc.All rights reserved.Whats “yield to maturity”?nYTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”8 - 17Copyright 2001 by Harcourt, Inc.All rights reserved.Whats the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $8

14、87? 9090 9001910kd=?1,000PV1 . . .PV10PVM887Find kd that “works”!.8 - 18Copyright 2001 by Harcourt, Inc.All rights reserved. 10 -887 90 1000NI/YR PV PMT FV 10.91( () )( () )( () )VINTkMkBdNdN= =111 . +INT1+ kd( () )( () )( () )8879011000111010= =kkdd +901+kd,Find kd + + + +INPUTSOUTPUT .8 - 19Copyri

15、ght 2001 by Harcourt, Inc.All rights reserved.nIf coupon rate kd, premium.nIf kd rises, price falls.nPrice = par at maturity. 8 - 20Copyright 2001 by Harcourt, Inc.All rights reserved.Find YTM if price were $1,134.20. 10 -1134.2 90 1000NI/YR PV PMTFV 7.08Sells at a premium. Because coupon = 9% kd =

16、7.08%, bonds value par.INPUTSOUTPUT8 - 21Copyright 2001 by Harcourt, Inc.All rights reserved.DefinitionsCurrent yield = .Capital gains yield = . = YTM = + .Annual coupon pmtCurrent priceChange in priceBeginning priceExp totalreturnExp Curr yldExp capgains yld8 - 22Copyright 2001 by Harcourt, Inc.All

17、 rights reserved.Current yield = 0.1015 = 10.15%.Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%. $90 $8878 - 23Copyright 2001 by Harcourt, Inc.All rights reserved.YTM= Current yield + Capital gains yield.Cap gains yield = YTM Current y

18、ield = 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.8 - 24Copyright 2001 by Harcourt, Inc.All rights reserved.Whats interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?kd1-yearChange 10-year Change5

19、%$1,048$1,38610%1,000+4.8%-4.4%1,000+38.6%-25.1%15%956749Interest rate risk: Rising kd causes bonds price to fall.8 - 25Copyright 2001 by Harcourt, Inc.All rights reserved.05001,0001,5000%5%10%15%1-year10-yearkdValue.8 - 26Copyright 2001 by Harcourt, Inc.All rights reserved.What is reinvestment rate

20、 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. Youll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.8 - 27Copyright 2001 by Harcourt, Inc.All rights

21、 reserved.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.8 - 28Copyright 2001 by Harcourt, Inc.All rights reserved.nLong-term bonds: High interest rate

22、 risk, low reinvestment rate risk.nShort-term bonds: Low interest rate risk, high reinvestment rate risk.nNothing is riskless!8 - 29Copyright 2001 by Harcourt, Inc.All rights reserved.Do all bonds of the same maturityhave the same price and reinvestment rate risk?No, low coupon bonds have lessreinve

23、stment rate risk but more price risk than high coupon bonds.8 - 30Copyright 2001 by Harcourt, Inc.All rights reserved.True or False: “All 10-year bonds have the same price and reinvestment rate risk.”False! Low coupon bonds have less reinvestment rate risk but more price risk than high coupon bonds.

24、8 - 31Copyright 2001 by Harcourt, Inc.All rights reserved.Semiannual Bonds1. Multiply years by 2 to get periods = 2n.2. Divide nominal rate by 2 to get periodic rate = kd/2.3. Divide annual INT by 2 to get PMT = INT/2. 2nkd/2 OK INT/2OK NI/YR PV PMTFVINPUTSOUTPUT8 - 32Copyright 2001 by Harcourt, Inc

25、.All rights reserved. 2(10) 13/2 100/220 6.5 50 1000NI/YR PV PMTFV -834.72Find the value of 10-year, 10% coupon,semiannual bond if kd = 13%.INPUTSOUTPUT8 - 33Copyright 2001 by Harcourt, Inc.All rights reserved.You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky

26、10%, 10-year semiannual bond. Which would you prefer?The semiannual bonds EFF% is:10.25% 10% EFF% on annual bond, so buy semiannual bond.%.25.101210.011mi1%EFF2mNom= = = = = =8 - 34Copyright 2001 by Harcourt, Inc.All rights reserved.If $1,000 is the proper price for the semiannual bond, what is the

27、proper price for the annual payment bond?nSemiannual bond has kNom = 10%, with EFF% = 10.25%. Should earn same EFF% on annual payment bond, so: 10 10.25 100 1000N I/YRPV PMT FV -984.80INPUTSOUTPUT8 - 35Copyright 2001 by Harcourt, Inc.All rights reserved.nAt a price of $984.80, the annual and semiann

28、ual bonds would be in equilibrium, because investors would earn EFF% = 10.25% on either bond.8 - 36Copyright 2001 by Harcourt, Inc.All rights reserved.A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8% yield to maturity.It can be called after 4 years at $1,050.

29、Whats the bonds nominal yield tocall (YTC)? 8 -1135.9 50 1050N I/YR PV PMT FV 3.568 x 2 = 7.137%INPUTSOUTPUT8 - 37Copyright 2001 by Harcourt, Inc.All rights reserved.kNom = 7.137% is the rate brokers would quote. Could also calculate EFF% to call:EFF% = (1.03568)2 1 = 7.26%.This rate could be compar

30、ed to monthly mortgages, etc.8 - 38Copyright 2001 by Harcourt, Inc.All rights reserved.If you bought bonds, would you be more likely to earn YTM or YTC?nCoupon rate = 10% vs. YTC = kd = 7.137%. Could raise money by selling new bonds which pay 7.137%.nCould thus replace bonds that pay $100/year with

31、bonds that pay only $71.37/year.nInvestors should expect a call, hence YTC = 7.1%, not YTM = 8%.8 - 39Copyright 2001 by Harcourt, Inc.All rights reserved.nIn general, if a bond sells at a premium, then (1) coupon kd, so (2) a call is likely.nSo, expect to earn:lYTC on premium bonds.lYTM on par &

32、 discount bonds.8 - 40Copyright 2001 by Harcourt, Inc.All rights reserved.nDisney 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.nIf issuer defaults, investors receive less than the promised ret

33、urn. Therefore, the expected return on corporate and municipal bonds is less than the promised return.8 - 41Copyright 2001 by Harcourt, Inc.All rights reserved.Bond Ratings Provide One Measure of Default RiskInvestment GradeJunk BondsMoodys AaaAaA BaaBa B CaaCS&PAAA AA A BBB BB B CCC D8 - 42Copy

34、right 2001 by Harcourt, Inc.All rights reserved.What factors affect default risk and bond ratings?nFinancial performancelDebt ratiolTIE, FCC ratioslCurrent ratios8 - 43Copyright 2001 by Harcourt, Inc.All rights reserved.nProvisions in the bond contractlSecured vs. unsecured debtlSenior vs. subordina

35、ted debtlGuarantee provisionslSinking fund provisionslDebt maturity8 - 44Copyright 2001 by Harcourt, Inc.All rights reserved.nOther factorslEarnings stabilitylRegulatory environmentlPotential product liabilitylAccounting policies8 - 45Copyright 2001 by Harcourt, Inc.All rights reserved.Top Ten Large

36、st U.S. Corporate Bond Financings, as of July 1999IssuerFord Motor Co.AT&TRJR HoldingsWorldComSprintDateJuly 1999Mar 1999May 1989Aug 1998Nov 1998 Amount$8.6 billion$8.0 billion$6.1 billion$6.1 billion$5.0 billion8 - 46Copyright 2001 by Harcourt, Inc.All rights reserved.BankruptcynTwo main chapters of Federal Bankruptcy Act:lChapter 11, ReorganizationlChapter 7, LiquidationnTypically, company wants Chapter 11, creditors may prefer Chapter 7.8 - 47Copyright 2001 by Harcourt, Inc.All rights reserved.nIf company cant meet its obligations