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1、4-1Chapter 4The Valuation of The Valuation of Long-Term Long-Term SecuritiesSecurities 2001 Prentice-Hall, Inc.Fundamentals of Financial Management, 11/eCreated by: Gregory A. Kuhlemeyer, Ph.D.Carroll College, Waukesha, WI4-2The Valuation of The Valuation of Long-Term SecuritiesLong-Term Securitiesu
2、uDistinctions Among Valuation ConceptsDistinctions Among Valuation ConceptsuuBond ValuationBond Valuation（债券价值）（债券价值）（债券价值）（债券价值）uuPreferred Stock ValuationPreferred Stock Valuation（优先股价值）（优先股价值）（优先股价值）（优先股价值）uuCommon Stock ValuationCommon Stock Valuation（普通股价值）（普通股价值）（普通股价值）（普通股价值）uuRates of Return
3、 (or Yields)Rates of Return (or Yields)（回报率）（回报率）（回报率）（回报率）4-3What is Value?What is Value?uuuGoing-concern valueGoing-concern value（持续经营价值）（持续经营价值）（持续经营价值）（持续经营价值）represents the amount a firm could be represents the amount a firm could be sold for as a continuing operating sold for as a continuing o
4、perating business.business.uuuLiquidation value Liquidation value （清算价值）（清算价值）（清算价值）（清算价值）represents the amount of money that represents the amount of money that could be realized if an asset or group could be realized if an asset or group of assets is sold separately from its of assets is sold sepa
5、rately from its operating organization.operating organization.4-4What is Value?What is Value?(2) (2) a firma firm: total assets minus liabilities : total assets minus liabilities and preferred stock as listed on the and preferred stock as listed on the balance sheet.balance sheet.uuuBook valueBook v
6、alue（账面价值）（账面价值）（账面价值）（账面价值） represents represents either either (1) (1) an assetan asset: the accounting value of an : the accounting value of an asset - the assets cost minus its asset - the assets cost minus its accumulated accumulated depreciation; depreciation; 4-5What is Value?What is Value?uu
7、uIntrinsic valueIntrinsic value（固有价值）（固有价值）（固有价值）（固有价值） represents the price a security represents the price a security “ought to have” based on all “ought to have” based on all factors bearing on valuation.factors bearing on valuation.uuuMarket valueMarket value （市场价值）（市场价值）（市场价值）（市场价值）represents t
8、he market price at represents the market price at which an asset trades.which an asset trades.4-6Bond ValuationBond ValuationuuImportant TermsImportant TermsuuTypes of BondsTypes of BondsuuValuation of BondsValuation of BondsuuHandling Semiannual Handling Semiannual CompoundingCompounding4-7Importan
9、t Bond TermsImportant Bond TermsuuThe The maturity valuematurity value（到期价值）（到期价值）（到期价值）（到期价值） ( (MVMV) or face value) or face value票面价值票面价值票面价值票面价值 of a of a bond is the stated value. In the bond is the stated value. In the case of a U.S. bond, the face case of a U.S. bond, the face value is usuall
10、y $1,000. value is usually $1,000. uuA A bondbond（债券）（债券）（债券）（债券） is a long-term is a long-term debt instrument issued by a debt instrument issued by a corporation or government.corporation or government.4-8Important Bond TermsImportant Bond TermsuuThe The discount ratediscount rate 贴现率贴现率贴现率贴现率(cap
11、italization rate) is dependent on (capitalization rate) is dependent on the risk of the bond and is composed the risk of the bond and is composed of the risk-free rate plus a premiumof the risk-free rate plus a premium（溢价）（溢价）（溢价）（溢价） for risk. for risk.uuThe bonds The bonds coupon ratecoupon rate 票
12、面利率票面利率票面利率票面利率is is the stated rate of interest; the annual the stated rate of interest; the annual interest payment divided by the interest payment divided by the bonds face value.bonds face value.4-94-10柳化股份2011年公司债券2013年付息公告五、本次付息方法五、本次付息方法1、本公司已与中、本公司已与中证登上海分公司登上海分公司签订了了委托代理委托代理债券券兑付、付、兑息息协议，委托
13、中，委托中证登上海分公司登上海分公司进行行债券券兑付、付、兑息。本公司最息。本公司最迟在本年度付息日前第二个交在本年度付息日前第二个交易日将本年度易日将本年度债券的利息足券的利息足额划付至中划付至中证登上海分公司登上海分公司指定的指定的银行行账户。如本公司未按。如本公司未按时足足额将将债券券兑付、付、兑息息资金划入中金划入中证登上海分公司指定的登上海分公司指定的银行行账户，则中中证登上海分公司将根据登上海分公司将根据协议终止委托代理止委托代理债券券兑付、付、兑息息服服务，后，后续兑付、付、兑息工作由本公司自行息工作由本公司自行负责办理，相理，相关关实施事宜以本公司的公告施事宜以本公司的公告为准
14、。准。4-11termperpetual bond 永久永久债券券non-zero coupon-paying非零息票支付非零息票支付债券券zero-coupon bond 零息零息债券，或券，或贴现债券券Interpolate 插插值法法Yield-to-Maturity 到期回报率到期回报率Discount Bond 贴现债券贴现债券Premium Bond 溢价债券溢价债券par Bond 平价债券平价债券4-12Different Types of BondsDifferent Types of BondsA A perpetual bondperpetual bond 永久债券永久债
15、券永久债券永久债券is a bond is a bond that that nevernever matures. It has an infinite matures. It has an infinite life.life.(1 + kd)1(1 + kd)2(1 + kd) V =+ . +III= S S t=1(1 + kd)tIor I (PVIFA kd, )V = I / kd Reduced Form4-13Perpetual Bond ExamplePerpetual Bond ExampleBond P has a $1,000 face value and Bond
16、 P has a $1,000 face value and provides an provides an 8% coupon8% coupon. The appropriate . The appropriate discount rate is 10%discount rate is 10%. What is the value of . What is the value of the the perpetual bondperpetual bond? ? I I I = $1,000 ( = $1,000 ( 8%8%) ) = = $80$80$80. . k k kddd = =
17、 10%10%10%. . V V V = = I I I / / k k kddd Reduced FormReduced Form = = $80$80$80 / / 10%10%10% = = $800 $800 $800. .4-14Different Types of BondsDifferent Types of BondsA A non-zero coupon-paying bondnon-zero coupon-paying bond（非（非（非（非零零零零息票支付债券）息票支付债券）息票支付债券）息票支付债券）is a coupon-paying bond is a coup
18、on-paying bond with a finite life.with a finite life.(1 + kd)1(1 + kd)2(1 + kd)nV =+ . +II + MVI= S Sn nt=1(1 + kd)tIV = I (PVIFA kd, n) + MV (PVIF kd, n) (1 + kd)n+MV4-15Bond C has a $1,000 face value and provides Bond C has a $1,000 face value and provides an an 8% annual coupon8% annual coupon fo
19、r for 30 years30 years. The . The appropriate appropriate discount rate is 10%discount rate is 10%. What is the . What is the value of thevalue of the coupon bondcoupon bond? ?Coupon Bond ExampleCoupon Bond ExampleV V V= = $80 $80 (PVIFA(PVIFA10%10%, , 3030) + ) + $1,000 $1,000 (PVIF(PVIF10%10%, , 3
20、030) ) = = $80$80 (9.427(9.427) + ) + $1,000 $1,000 (.057(.057) ) Table IVTable IVTable IV Table IITable IITable II = $754.16 + $57.00= $754.16 + $57.00= = $811.16 $811.16 $811.16. .4-16Different Types of BondsDifferent Types of BondsA A zero-coupon bondzero-coupon bond （零息债券，或贴（零息债券，或贴（零息债券，或贴（零息债券
21、，或贴现债券）现债券）现债券）现债券）is a bond that pays no interest is a bond that pays no interest but sells at a deep discount from its but sells at a deep discount from its face value; it provides compensation to face value; it provides compensation to investors in the form of price investors in the form of price
22、 appreciationappreciation（价格上涨）（价格上涨）（价格上涨）（价格上涨）. .(1 + kd)nV =MV= MV (PVIFkd, n) 4-17V V= = $1,000 $1,000 (PVIF(PVIF10%10%, , 3030) )= = $1,000 $1,000 (.057(.057) )= = $57.00 $57.00Zero-Coupon Zero-Coupon Bond ExampleBond ExampleBond Z has a $1,000 face value and Bond Z has a $1,000 face value and
23、 a a 30-year30-year life. The appropriate life. The appropriate discount rate is 10%discount rate is 10%. What is the . What is the value of thevalue of the zero-coupon bondzero-coupon bond? ?4-18Semiannual CompoundingSemiannual Compounding(1) Divide (1) Divide k kd d by by 2 2(2) Multiply (2) Multi
24、ply n n by by 2 2(3) Divide (3) Divide I I by by 2 2Most bonds Most bonds in the U.S. in the U.S. pay interest pay interest twice a year (1/2 of the annual twice a year (1/2 of the annual coupon).coupon).Adjustments neededAdjustments needed: :4-19(1 + kd/2 2 ) 2 2*n(1 + kd/2 2 )1Semiannual Compoundi
25、ngSemiannual CompoundingA A non-zero coupon bondnon-zero coupon bond adjusted for adjusted for semiannual compounding.semiannual compounding.V =+ . +I / 2I / 2 + MV= S S2 2*n nt=1(1 + kd /2 2 )tI / 2= I/2 (PVIFAkd /2 ,2*n) + MV (PVIFkd /2 , 2*n) (1 + kd /2 2 ) 2 2*n+MVI / 2(1 + kd/2 2 )24-20V V V= =
26、 $40 $40 (PVIFA(PVIFA5%5%, , 3030) + ) + $1,000 $1,000 (PVIF(PVIF5%5%, , 3030) ) = = $40$40 (15.373(15.373) + ) + $1,000 $1,000 (.231(.231) ) Table IVTable IVTable IV Table IITable IITable II = $614.92 + $231.00= $614.92 + $231.00= = $845.92 $845.92 $845.92Semiannual Coupon Semiannual Coupon Bond Ex
27、ampleBond ExampleBond C has a $1,000 face value and provides Bond C has a $1,000 face value and provides an an 8% semiannual coupon8% semiannual coupon for for 15 years15 years. The . The appropriate appropriate discount rate is 10% (annual rate)discount rate is 10% (annual rate). . What is the valu
28、e of theWhat is the value of the coupon bondcoupon bond? ?4-21Preferred StockPreferred Stock is a type of stock is a type of stock that promises a (usually) fixed that promises a (usually) fixed dividend, but at the discretion of dividend, but at the discretion of the board of directors.the board of
29、 directors.Preferred Stock ValuationPreferred Stock ValuationPreferred Stock has preference over Preferred Stock has preference over common stock in the payment of common stock in the payment of dividends and claims on assets.dividends and claims on assets.4-22Preferred Stock ValuationPreferred Stoc
30、k ValuationThis reduces to a This reduces to a perpetuityperpetuity! !(1 + kP)1(1 + kP)2(1 + kP) V =+ . +DivPDivPDivP= S S t=1(1 + kP)tDivPor DivP(PVIFA kP, )V = DivP / kP4-23Preferred Stock ExamplePreferred Stock ExampleDivDivDivPPP = $100 ( = $100 ( 8% 8% ) = ) = $8.00$8.00$8.00. . k k kPPP = = 10
31、%10%10%. . V V V = = DivDivDivPPP / / k k kPPP = = $8.00$8.00$8.00 / / 10%10%10% = = $80 $80 $80Stock PS has an Stock PS has an 8%,8%, $100 par value $100 par value issue outstanding. The appropriate issue outstanding. The appropriate discount rate is 10%discount rate is 10%. What is the value . Wha
32、t is the value of the of the preferred stockpreferred stock? ?4-24Common Stock ValuationCommon Stock ValuationuuPro rata share of future earnings Pro rata share of future earnings after all other obligations of the after all other obligations of the firm (if any remain).firm (if any remain).uuDivide
33、nds Dividends maymay be paid out of be paid out of the pro rata share of earnings.the pro rata share of earnings.Common stock Common stock represents a represents a residual ownership position in the residual ownership position in the corporation.corporation.4-25Common Stock ValuationCommon Stock Va
34、luation(1) Future dividends(1) Future dividends(2) Future sale of the common (2) Future sale of the common stock sharesstock sharesWhat cash flows will a shareholder receive when owning shares of common stock?4-26Dividend Valuation ModelDividend Valuation ModelBasic dividend valuation model accounts
35、 Basic dividend valuation model accounts for the PV of all future dividends.for the PV of all future dividends.(1 + ke)1(1 + ke)2(1 + ke) V =+ . +Div1Div Div2= S S t=1(1 + ke)tDivtDivDivt t: : Cash dividend Cash dividend at time tat time tk ke e: : Equity investors Equity investors required returnre
36、quired return4-27Adjusted Dividend Adjusted Dividend Valuation ModelValuation ModelThe basic dividend valuation model The basic dividend valuation model adjusted for the future stock sale.adjusted for the future stock sale.(1 + ke)1(1 + ke)2(1 + ke)nV =+ . +Div1Divn n + Pricen nDiv2n n:The year in w
37、hich the firms shares are expected to be sold.Pricen n:The expected share price in year n n. 4-28Dividend Growth Dividend Growth Pattern AssumptionsPattern AssumptionsThe dividend valuation model requires the The dividend valuation model requires the forecast of forecast of allall future dividends.
38、The future dividends. The following dividend growth rate assumptions following dividend growth rate assumptions simplify the valuation process.simplify the valuation process.Constant GrowthConstant GrowthNo GrowthNo GrowthGrowth PhasesGrowth Phases4-29Constant Growth ModelConstant Growth ModelThe Th
39、e constant growth model constant growth model assumes that assumes that dividends will grow forever at the rate dividends will grow forever at the rate g g. .(1 + ke)1(1 + ke)2(1 + ke) V =+ . +D0(1+g)D0(1+g) =(ke - g)D1D D1 1: :Expected dividend paid at time 1.Expected dividend paid at time 1.D D0 0
40、: Dividend paid recently : Dividend paid recently g g : : The constant growth rate.The constant growth rate.k ke e: : Investors required return.Investors required return.D0(1+g)24-30Constant Growth Constant Growth Model ExampleModel ExampleStock CG has an expected Stock CG has an expected growth rat
41、e of growth rate of 8%8%. Each share of stock just received an . Each share of stock just received an annual annual $3.24 dividend $3.24 dividend per share. The per share. The appropriate appropriate discount rate is 15%discount rate is 15%. What . What is the value of the is the value of the common
42、 stockcommon stock? ?D D1 1 = = $3.24$3.24 ( 1 + ( 1 + .08.08 ) = ) = $3.50$3.50V VCGCG = = D D1 1 / ( / ( k ke e - - g g ) = ) = $3.50$3.50 / ( / ( .15.15 - - .08.08 ) ) = = $50 $504-31Zero Growth ModelZero Growth ModelThe The zero growth model zero growth model assumes that assumes that dividends
43、will grow forever at the rate dividends will grow forever at the rate g g = 0.= 0.(1 + ke)1(1 + ke)2(1 + ke) VZG =+ . +D1D =keD1D D1 1: :Dividend paid at time 1.Dividend paid at time 1.k ke e: : Investors required return.Investors required return.D24-32Zero Growth Zero Growth Model ExampleModel Exam
44、pleStock ZG has an expected Stock ZG has an expected growth rate growth rate of of 0%0%. Each share of stock just received an . Each share of stock just received an annual annual $3.24 dividend $3.24 dividend per share. The per share. The appropriate appropriate discount rate is 15%discount rate is
45、15%. What . What is the value of the is the value of the common stockcommon stock? ?D D1 1 = = $3.24$3.24 ( 1 + ( 1 + 0 0 ) = ) = $3.24$3.24V VZGZG = = D D1 1 / ( / ( k ke e - - 0 0 ) = ) = $3.24$3.24 / ( / ( .15.15 - - 0 0 ) ) = = $21.60 $21.604-33D0(1+g1)tDn(1+g2)tGrowth Phases ModelGrowth Phases
46、ModelThe The growth phases model growth phases model assumes assumes that dividends for each share will grow that dividends for each share will grow at two or more at two or more differentdifferent growth rates. growth rates.(1 + ke)t(1 + ke)tV =S St=1nS St=n+1 +4-34D0(1+g1)tDn+1Growth Phases ModelG
47、rowth Phases ModelNote that the second phase of the Note that the second phase of the growth phases model growth phases model assumes that assumes that dividends will grow at a constant rate dividends will grow at a constant rate g g2 2. . We can rewrite the formula as:We can rewrite the formula as:
48、(1 + ke)t(ke - g2)V =S St=1n+1(1 + ke)n4-35Calculating Rates of Calculating Rates of Return (or Yields)Return (or Yields)1. Determine the expected 1. Determine the expected cash flowscash flows. .2. Replace the intrinsic value (V) with 2. Replace the intrinsic value (V) with the the market price (Pm
49、arket price (P0 0) ). .3. Solve for the 3. Solve for the market required rate of market required rate of return return that equates the that equates the discounted discounted cash flows cash flows to the to the market pricemarket price. . Steps to calculate the rate of return (or yield).4-36Determin
50、ing Bond YTMDetermining Bond YTMDetermine the Yield-to-Maturity Determine the Yield-to-Maturity (YTM) for the coupon-paying bond (YTM) for the coupon-paying bond with a finite life.with a finite life.P0 =S Sn nt=1(1 + kd )tI= I (PVIFA kd , n) + MV (PVIF kd , n) (1 + kd )n+MVkd = YTM4-37Determining t
51、he YTMDetermining the YTMJulie Miller want to determine the YTM Julie Miller want to determine the YTM for an issue of outstanding bonds at for an issue of outstanding bonds at Basket Wonders (BW)Basket Wonders (BW). . BWBW has an has an issue of issue of 10% annual coupon 10% annual coupon bonds bo
52、nds with with 15 years 15 years left to maturity. The left to maturity. The bonds have a current market value of bonds have a current market value of $1,250$1,250. .What is the YTM?What is the YTM?4-38YTM Solution (Try 9%)YTM Solution (Try 9%)$1,250 = $100(PVIFA9%,15) + $1,000(PVIF9%, 15)$1,250 = $1
53、00(8.061) + $1,000(.275)$1,250 = $806.10 + $275.00=$1,081.10Rate is too high!4-39YTM Solution (Try 7%)YTM Solution (Try 7%)$1,250 = $100(PVIFA7%,15) + $1,000(PVIF7%, 15)$1,250 = $100(9.108) + $1,000(.362)$1,250 = $910.80 + $362.00=$1,272.80Rate is too low!4-40.07$1,273.02IRR$1,250 $192.09$1,081 X $2
54、3.02$192YTM Solution (Interpolate)YTM Solution (Interpolate)$23X=4-41.07$1,273.02IRR$1,250 $192.09$1,081 X $23.02$192YTM Solution (Interpolate)YTM Solution (Interpolate)$23X=4-42.07$1273.02YTMYTM $1250$1250 $192.09$1081($23)(0.02) $192YTM Solution (InterpolateYTM Solution (Interpolate插值法插值法插值法插值法) )
55、$23XX =X = .0024YTM = .07 + .0024 = .0724 or 7.24%4-43Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTMP0 =S S2n nt=1(1 + kd /2 )tI / 2= (I/2)(PVIFAkd /2, 2n) + MV(PVIFkd /2 , 2n) +MV 1 + (kd / 2) 2 -1 = YTMDetermine the Yield-to-Maturity Determine the Yield-to-Maturity (Y
56、TM) for the semiannual coupon-(YTM) for the semiannual coupon-paying bond with a finite life.paying bond with a finite life.(1 + kd /2 )2n4-44Determining the Semiannual Determining the Semiannual Coupon Bond YTMCoupon Bond YTMJulie Miller want to determine the YTM Julie Miller want to determine the
57、YTM for another issue of outstanding for another issue of outstanding bonds. bonds. The firmThe firm has an issue of has an issue of 8% 8% semiannual coupon semiannual coupon bonds with bonds with 20 20 years years left to maturity. The bonds left to maturity. The bonds have a current market value o
58、f have a current market value of $950$950. .What is the YTM?What is the YTM?4-45Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM 1 + (kd / 2) 2 -1 = YTMDetermine the Yield-to-Maturity Determine the Yield-to-Maturity (YTM) for the semiannual coupon-(YTM) for the semiannual
59、 coupon-paying bond with a finite life.paying bond with a finite life. 1 + (.042626) 2 -1 = .0871 or 8.71%4-46Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM 1 + (kd / 2) 2 -1 = YTMThis technique will calculate This technique will calculate k kd d. . You must then substi
60、tute it into the You must then substitute it into the following formula.following formula. 1 + (.0852514/2) 2 -1 = .0871 or 8.71% (same result!)4-47Bond Price-Yield Bond Price-Yield RelationshipRelationshipDiscount BondDiscount Bond - The market required - The market required rate of return exceeds
61、the coupon rate rate of return exceeds the coupon rate (Par P(Par P0 0 ). ).Premium BondPremium Bond - - The coupon rate The coupon rate exceeds the market required rate of exceeds the market required rate of return (Preturn (P0 0 Par). Par).Par BondPar Bond - - The coupon rate equals the The coupon
62、 rate equals the market required rate of return (Pmarket required rate of return (P0 0 = Par). = Par).4-48Bond Price-Yield Bond Price-Yield RelationshipRelationship Coupon Rate Coupon Rate Coupon RateMARKET REQUIRED RATE OF RETURN (%)MARKET REQUIRED RATE OF RETURN (%)BOND PRICE ($)1000 Par1600140012
63、0060000 2 4 6 8 1010 12 14 16 185 Year5 Year15 Year15 Year4-49Bond Price-Yield Bond Price-Yield RelationshipRelationshipAssume that the required rate of Assume that the required rate of return on a 15-year, 10% coupon-return on a 15-year, 10% coupon-paying bond paying bond risesrises from 10% to 12%
64、. from 10% to 12%. What happens to the bond price?What happens to the bond price?When interest rates When interest rates riserise, then the , then the market required rates of return market required rates of return riserise and bond prices will and bond prices will fallfall. .4-50Bond Price-Yield Bo
65、nd Price-Yield RelationshipRelationship Coupon Rate Coupon Rate Coupon RateMARKET REQUIRED RATE OF RETURN (%)MARKET REQUIRED RATE OF RETURN (%)BOND PRICE ($)1000 Par16001400120060000 2 4 6 8 1010 12 14 16 1815 Year15 Year5 Year5 Year4-51Bond Price-Yield Bond Price-Yield Relationship (Rising Rates)Re
66、lationship (Rising Rates)Therefore, the bond price has Therefore, the bond price has fallen fallen from $1,000 to $864.from $1,000 to $864.The required rate of return on a 15-year, 10% coupon-paying bond has risen from 10% to 12%.4-52Bond Price-Yield Bond Price-Yield RelationshipRelationshipAssume t
67、hat the required rate of Assume that the required rate of return on a 15-year, 10% coupon-return on a 15-year, 10% coupon-paying bond paying bond fallsfalls from 10% to 8%. from 10% to 8%. What happens to the bond price?What happens to the bond price?When interest rates When interest rates fallfall,
68、 then the , then the market required rates of return market required rates of return fallfall and bond prices will and bond prices will riserise. . 4-53Bond Price-Yield Bond Price-Yield RelationshipRelationship Coupon Rate Coupon Rate Coupon RateMARKET REQUIRED RATE OF RETURN (%)MARKET REQUIRED RATE
69、 OF RETURN (%)BOND PRICE ($)1000 Par16001400120060000 2 4 6 8 1010 12 14 16 1815 Year15 Year5 Year5 Year4-54Bond Price-Yield Relationship Bond Price-Yield Relationship (Declining Rates)(Declining Rates)Therefore, the bond price has Therefore, the bond price has risenrisen from $1,000 to $1,171.from
70、$1,000 to $1,171.The required rate of return on a 15-year, 10% coupon-paying bond has fallen from 10% to 8%.4-55The Role of Bond MaturityThe Role of Bond MaturityAssume that the required rate of return Assume that the required rate of return on both the 5- and 15-year, 10% coupon-on both the 5- and
71、15-year, 10% coupon-paying bonds paying bonds fallfall from 10% to 8%. What from 10% to 8%. What happens to the changes in bond prices?happens to the changes in bond prices?The longer the bond maturity, the The longer the bond maturity, the greater the change in bond price for a greater the change i
72、n bond price for a given change in the market required rate given change in the market required rate of return.of return.4-56Bond Price-Yield Bond Price-Yield RelationshipRelationship Coupon Rate Coupon Rate Coupon RateMARKET REQUIRED RATE OF RETURN (%)MARKET REQUIRED RATE OF RETURN (%)BOND PRICE ($
73、)1000 Par16001400120060000 2 4 6 8 1010 12 14 16 1815 Year15 Year5 Year5 Year4-57The Role of Bond MaturityThe Role of Bond MaturityThe 5-year bond price has The 5-year bond price has risenrisen from from $1,000 to $1,080 for the 5-year bond $1,000 to $1,080 for the 5-year bond ( (+8.0%+8.0%). ).The
74、15-year bond price has The 15-year bond price has risenrisen from from $1,000 to $1,171 ($1,000 to $1,171 (+17.1%+17.1%). ). Twice as fastTwice as fast! !The required rate of return on both the 5- and 15-year, 10% coupon-paying bonds has fallen from 10% to 8%.4-58The Role of the The Role of the Coup
75、on RateCoupon RateFor a given change in the For a given change in the market required rate of return, market required rate of return, the price of a bond will change the price of a bond will change by proportionally more, by proportionally more, thethe lowerlower the coupon rate the coupon rate. .4-
76、59Example of the Role of Example of the Role of the Coupon Ratethe Coupon RateAssume that the Assume that the market required rate market required rate of return of return on two equally risky 15-year on two equally risky 15-year bonds is bonds is 10%10%. The coupon rate for . The coupon rate for Bo
77、nd HBond H is is 10%10% and and BondBond L L is is 8%8%. . What is the rate of change in each of What is the rate of change in each of the bond prices if the bond prices if market required market required rates rates fall to 8%?fall to 8%?4-60Example of the Role of the Example of the Role of the Cou
78、pon RateCoupon RateThe price for The price for Bond H Bond H will rise from $1,000 will rise from $1,000 to $1,171 (to $1,171 (+17.1%+17.1%). ).The price for The price for Bond L Bond L will rise from $848 to will rise from $848 to $1,000 ($1,000 (+17.9%+17.9%). ). It rises fasterIt rises faster! !T
79、he price on Bonds H and L prior to the change in the market required rate of return is $1,000 and $848, respectively.4-61Determining the Yield on Determining the Yield on Preferred StockPreferred StockDetermine the yield for preferred Determine the yield for preferred stock with an infinite life.sto
80、ck with an infinite life.P P0 0 = = DivDivP P / / k kP P Solving for Solving for k kP P such thatsuch thatk kP P = = DivDivP P / / P P0 0 4-62Preferred Stock Yield Preferred Stock Yield ExampleExamplek kP P = = $10$10 / / $100$100. .k kP P = = 10%10%. .Assume that the Assume that the annual dividend
81、 annual dividend on on each share of preferred stock is each share of preferred stock is $10$10. . Each share of preferred stock is Each share of preferred stock is currently trading at currently trading at $100$100. . What is What is the the yield yield on preferred stockon preferred stock? ?4-63De
82、termining the Yield on Determining the Yield on Common StockCommon StockAssume the constant growth model Assume the constant growth model is appropriate. Determine the yield is appropriate. Determine the yield on the common stock.on the common stock.P P0 0 = = D D1 1 / ( / ( k ke e - - g g ) )Solvin
83、g for Solving for k ke e such thatsuch thatk ke e = ( = ( D D1 1 / / P P0 0 ) + ) + g g 4-64Common Stock Common Stock Yield ExampleYield Examplek ke e = ( = ( $3$3 / / $30 $30 ) + ) + 5%5%k ke e = = 15%15%Assume that the Assume that the expected dividend expected dividend (D(D1 1) ) on each share of
84、 common stock on each share of common stock is is $3$3. Each share of common stock . Each share of common stock is currently trading at is currently trading at $30 $30 and has an and has an expected expected growth rate growth rate of of 5%5%. . What is What is the the yield yield on common stockon common stock? ?
