1、Corporate Finance Lecture Five许志 西南财经大学金融学院What is Bond?Definition A bond is a legally binding agreement between a borrower and a lender:Specifies the principal amount of the loan.Specifies the size and timing of the cash flows:In dollar terms(fixed-rate borrowing)As a formula(adjustable-rate borrow
2、ing)许志 西南财经大学金融学院Some Relative Conceptions Coupon The stated interest payment made on a bond.Face Value(par value)The principal amount of a bond that is repaid at the end of the term.Coupon Rate The annual coupon divided by the face value of a bond.Maturity Specified date on which the principal amou
3、nt of a bond is paid.许志 西南财经大学金融学院Example of a Bond Consider a U.S.government bond listed as 6 3/8 of December 2009.The Par Value of the bond is$1,000.Coupon payments are made semi-annually(June 30 and December 31 for this particular bond).Since the coupon rate is 6 3/8 the payment is$31.875.On Janu
4、ary 1,2002 the size and timing of cash flows are:02/1/1875.31$02/30/6875.31$02/31/12875.31$09/30/6875.031,1$09/31/12许志 西南财经大学金融学院How to Value Bonds Identify the size and timing of cash flows.Discount at the correct discount rate.If you know the price of a bond and the size and timing of cash flows,t
5、he yield to maturity is the discount rate.Note:Yield to Maturity(YTM)is the rate required in the market on a bond.许志 西南财经大学金融学院Pure Discount BondsInformation needed for valuing pure discount bonds:Time to maturity(T)=Maturity date-todays date Face value(F)Discount rate(r)TrFPV)1(Present value of a p
6、ure discount bond at time 0:00$10$20$1TF$T许志 西南财经大学金融学院 Pure Discount Bonds:ExampleFind the value of a 30-year zero-coupon bond with a$1,000 par value and a YTM of 6%.11.174$)06.1(000,1$)1(30TrFPV00$10$20$29000,1$30许志 西南财经大学金融学院Level-Coupon BondsInformation needed to value level-coupon bonds:Coupon
7、payment dates and time to maturity(T)Coupon payment(C)per period and Face value(F)Discount rateTTrFrrCPV)1()1(11Value of a Level-coupon bond=PV of coupon payment annuity+PV of face value0C$1C$2C$1TFC$T许志 西南财经大学金融学院 Level-Coupon Bonds:ExampleFind the present value(as of January 1,2002),of a 6-3/8 cou
8、pon T-bond with semi-annual payments,and a maturity date of December 2009 if the YTM is 5-percent.On January 1,2002 the size and timing of cash flows are:02/1/1875.31$02/30/6875.31$02/31/12875.31$09/30/6875.031,1$09/31/1275.089,1$)025.1(000,1$)025.1(11205.875.31$1616PV许志 西南财经大学金融学院Further Concepts1.
9、Bond prices and market interest rates move in opposite directions.2.When coupon rate=YTM,price=par value.When coupon rate YTM,price par value(premium bond)When coupon rate YTM,price par value(discount bond)3.A bond with longer maturity has higher relative(%)price change than one with shorter maturit
10、y when interest rate(YTM)changes.All other features are identical.4.A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes.All other features are identical.许志 西南财经大学金融学院YTM and Bond Value8001000110012001300$140000.010.020.030.040.050.060.070.080.090.1Discou
11、nt RateBond Value6 3/8When the YTM coupon,the bond trades at a discount.许志 西南财经大学金融学院 Maturity and Bond Price VolatilityCConsider two otherwise identical bonds.The long-maturity bond will have much more volatility with respect to changes in the discount rateDiscount RateBond ValueParShort Maturity B
12、ondLong Maturity Bond许志 西南财经大学金融学院 Coupon Rate and Bond Price VolatilityConsider two otherwise identical bonds.The low-coupon bond will have much more volatility with respect to changes in the discount rateDiscount RateBond ValueHigh Coupon BondLow Coupon Bond许志 西南财经大学金融学院Useful Links for Bonds A go
13、od bond site to visit is http:/ has loads of useful information.Information for bond investors can be found at .Learn all about government bonds of U.S.at www.ny.frb.org 中国债券信息网： 和讯债券频道：http:/ 西南财经大学金融学院 The Present Value of Common Stocks Dividends versus Capital Gains Valuation of Different Types o
14、f Stocks Zero Growth Constant Growth Differential Growth许志 西南财经大学金融学院Case 1:Zero Growth Assume that dividends will remain at the same level foreverrPrrrPDiv)1(Div)1(Div)1(Div03322110321DivDivDivSince future cash flows are constant,the value of a zero growth stock is the present value of a perpetuity
15、:许志 西南财经大学金融学院Case 2:Constant Growth)1(DivDiv01gSince future cash flows grow at a constant rate forever,the value of a constant growth stock is the present value of a growing perpetuity:grP10DivAssume that dividends will grow at a constant rate,g,forever.i.e.2012)1(Div)1(DivDivgg3023)1(Div)1(DivDivg
16、g.许志 西南财经大学金融学院Case 3:Differential Growth Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.To value a Differential Growth Stock,we need to:Estimate future dividends in the foreseeable future.Estimate the future stock price
17、when the stock becomes a Constant Growth Stock(case 2).Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.许志 西南财经大学金融学院Case 3:Differential Growth)(1Div10g Dividends will grow at rate g1 for N years and grow at rate g2 thereafter
18、210)(1DivgNg)(1Div10)(1)(1Div)(1Div2102gggNN0 1 2NN+1许志 西南财经大学金融学院Case 3:Differential GrowthWe can value this as the sum of:an N-year annuity growing at rate g1TTArggrCP)1()1(111plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1NBrgrP)1(Div21N许志 西南财经大学金融学院Case 3:Dif
19、ferential GrowthTo value a Differential Growth Stock,we can useNTTrgrrggrCP)1(Div)1()1(121N11许志 西南财经大学金融学院 A Differential Growth Example A common stock just paid a dividend of$2.The dividend is expected to grow at 8%for 3 years,then it will grow at 4%in perpetuity.Given investors assessment of this
20、company,they think that the required return on this stock is 12 percent.What is the stock worth?许志 西南财经大学金融学院With the FormulaNTTrgrrggrCP)1(Div)1()1(121N113333)12.1(04.12.)04.1()08.1(2$)12.1()08.1(108.12.)08.1(2$P3)12.1(75.32$8966.154$P31.23$58.5$P89.28$P许志 西南财经大学金融学院A Differential Growth Example08)
21、.2(1$208).2(1$0 1 234308).2(1$)04.1(08).2(1$316.2$33.2$0 1 2 308.62.2$52.2$89.28$)12.1(75.32$52.2$)12.1(33.2$12.116.2$320P75.32$08.62.2$3PThe constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.许志 西南财经大学金融学院The Dividend Growth Model and the NPVGO Model(Advanced)
22、We have two ways to value a stock:The dividend discount model.The price of a share of stock can be calculated as the sum of its price as a cash cow plus the per-share value of its growth opportunities.许志 西南财经大学金融学院Estimates of Parameters in the Dividend-Discount ModelThe value of a firm depends upon
23、 its growth rate,g,and its discount rate,r.Where does g come from?Where does r come from?许志 西南财经大学金融学院Where does g come from?g=Retention ratio Return on retained earnings许志 西南财经大学金融学院Where does r come from?The discount rate can be broken into two parts.The dividend yield The growth rate(in dividends
24、)In practice,there is a great deal of estimation error involved in estimating r.许志 西南财经大学金融学院Growth Opportunities Growth opportunities are opportunities to invest in positive NPV projects.The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100-percent of its ear
25、nings as dividends and the net present value of the growth opportunities.NPVGOrEPSP许志 西南财经大学金融学院The Dividend Growth Model and the NPVGO Model Consider a firm that has EPS of$5 at the end of the first year,a dividend-payout ratio of 30%,a discount rate of 16-percent,and a return on retained earnings
26、of 20-percent.The dividend at year one will be$5 .30=$1.50 per share.The retention ratio is.70(=1-.30)implying a growth rate in dividends of 14%=.70 20%From the dividend growth model,the price of a share is:75$14.16.50.1$Div10grP许志 西南财经大学金融学院The NPVGO Model First,we must calculate the value of the f
27、irm as a cash cow.25.31$16.5$Div10rP Second,we must calculate the value of the growth opportunities.75.43$14.16.875$.16.20.50.350.30grP Finally,75$75.4325.310P许志 西南财经大学金融学院Price Earnings RatioMany analysts frequently relate earnings per share to price.The price earnings ratio is a.k.a.the multiple C
28、alculated as current stock price divided by annual EPS The Wall Street Journal uses last 4 quarters earningsEPSshareper Priceratio P/E Firms whose shares are“in fashion”sell at high multiples.Growth stocks for example.Firms whose shares are out of favor sell at low multiples.Value stocks for example
29、.许志 西南财经大学金融学院Stock Market Reporting52 WEEKSYLDVOLNETHILOSTOCKSYM DIV%PE 100sHILO CLOSE CHG52.7519.06 Gap Inc GPS0.090.5 15 65172 20.50 1919.25-1.75Gap has been as high as$52.75 in the last year.Gap has been as low as$19.06 in the last year.Gap pays a dividend of 9 cents/shareGiven the current price
30、,the dividend yield is%Given the current price,the PE ratio is 15 times earnings6,517,200 shares traded hands in the last days tradingGap ended trading at$19.25,down$1.75 from yesterdays close许志 西南财经大学金融学院Stock Market Reporting52 WEEKSYLDVOLNETHILOSTOCKSYM DIV%PE 100sHILO CLOSE CHG52.7519.06 Gap Inc
31、 GPS0.090.5 15 65172 20.50 1919.25-1.75 Gap Incorporated is having a tough year,trading near their 52-week low.Imagine how you would feel if within the past year you had paid$52.75 for a share of Gap and now had a share worth$19.25!That 9-cent dividend wouldnt go very far in making amends.Yesterday,
32、Gap had another rough day in a rough year.Gap“opened the day down”beginning trading at$20.50,which was down from the previous close of$21.00=$19.25+$1.75许志 西南财经大学金融学院Summary and ConclusionsIn this chapter,we used the time value of money formulae from previous chapters to value bonds and stocks.The v
33、alue of a zero-coupon bond isThe value of a perpetuity isTrFPV)1(rCPV 许志 西南财经大学金融学院Summary and Conclusions(continued)The value of a coupon bond is the sum of the PV of the annuity of coupon payments plus the PV of the par value at maturity.The yield to maturity(YTM)of a bond is that single rate that
34、 discounts the payments on the bond to the purchase price.TTrFrrCPV)1()1(11许志 西南财经大学金融学院Summary and Conclusions(continued)A stock can be valued by discounting its dividends.There are three cases:1.Zero growth in dividends2.Constant growth in dividends3.Differential growth in dividendsrPDiv0grP10DivN
35、TTrgrrggrCP)1(Div)1()1(121N11许志 西南财经大学金融学院Excel的应用Yahoo-Finance的债券主页许志 西南财经大学金融学院价值和收益率的计算付息债券的现金流量分析许志 西南财经大学金融学院 价值和收益率的计算债券价值随市场利率的变化而变化许志 西南财经大学金融学院价值和收益率的计算债券发行后的价值许志 西南财经大学金融学院影响债券价值的主要因素 债券的票面金额是债券价格的决定性因素。因为面值是债券到期偿还本金的直接依据，所以从理论上讲，在发行时债券的价格应与面值相等。但由于受市场利率和供求关系的影响，债券的实际发行价格有可能会偏离其票面金额。债券的票面利
36、率与市场平均收益率之间会存在一些差别，因此预先确定的债券票面利率会在债券正式发行时影响债券的价格。此外在债券被持有期间，由于存在着已支付利息和尚未支付的利息，所以债券的交易价格会受市场利率的影响。债券的偿还期限越长，它作为投资工具的风险就越大。按照收益和风险对等的原则，较长期限的债券，要用较高的利率来补偿其风险。债券的信用评级和市场的供求关系也会影响债券价值。许志 西南财经大学金融学院信用风险与债券评级债券的信用评级许志 西南财经大学金融学院Excel中的债券函数Excel债券函数的分类 许志 西南财经大学金融学院Excel中的债券函数 Excel中每个债券计算函数都有若干参数，它们在全部债券
37、类函数中是通用的，并且其中一部分参数本身可以作为计算函数，而以其他参数为参数。所有这些参数可分为3组。第一组参数是价格、收益率、利率：价格(pr)，面值(par)，偿付价格(redemption)，收益率(yld)，利率(rate或coupon)第二组是有关债券计算的各种日期：发行日(issue)，交易日(settlement)，到期日(maturity)，首期付息日(first_coupon)，末期付息日(last_interest)第三组参数是关于日期计算基准的：计息次数(frequency)，日计数基准(basis)许志 西南财经大学金融学院定期付息债券的计算 价格与收益率的计算 PRI
38、CE(settlement,maturity,rate,yld,redemption,frequency,basis)YIELD(settlement,maturity,rate,pr,redemption,frequency,basis）ODDFPRICE(settlement,maturity,issue,first_coupon,rate,yld,redemption,frequency,basis)ODDFYIELD(settlement,maturity,issue,first_coupon,rate,pr,redemption,frequency,basis)ODDLPRICE(s
39、ettlement,maturity,last_interest,rate,yld,redemption,frequency,basis)ODDLYIELD(settlement,maturity,last_interest,rate,pr,redemption,frequency,basis)许志 西南财经大学金融学院定期付息债券的计算关于计息期和利息的计算 ACCRINT(issue,first_interest,settlement,rate,par,frequency,basis)COUPDAYBS(settlement,maturity,frequency,basis)COUPDAY
40、SNC(settlement,maturity,frequency,basis)COUPDAYS(settlement,maturity,frequency,basis)COUPPCD(settlement,maturity,frequency,basis)COUPNCD(settlement,maturity,frequency,basis)COUPNUM(settlement,maturity,frequency,basis)COUPPCD()COUPNCD()交易日COUPDAYSNC()COUPDAYBS()COUPDAYS()COUPNUM()许志 西南财经大学金融学院其他类型债券的
41、计算 到期付息债券的计算 PRICEMAT(settlement,maturity,issue,rate,yld,basis)YIELDMAT(settlement,maturity,issue,rate,pr,basis)ACCRINTM(issue,maturity,rate,par,basis)折价债券的计算 PRICEDISC(settlement,maturity,discount,redemption,basis)YIELDDISC(settlement,maturity,pr,redemption,basis)DISC(settlement,maturity,pr,redempt
42、ion,basis)INTRATE(settlement,maturity,investment,redemption,basis)RECEIVED(settlement,maturity,investment,discount,basis)国库券的计算 TBILLPRICE(settlement,maturity,discount)TBILLYIELD(settlement,maturity,pr)TBILLEQ(settlement,maturity,discount)许志 西南财经大学金融学院Readings for Preparation Chapter 6,Corporate Finance,Ross 6/E,Mcgraw-Hill Chapter 9,Fundamentals of Corporate Finance,Ross 6/E,Mcgraw-Hill Chapter 5,Principles of Corporate Finance,Brealey 7/E,Mcgraw-Hill Excel金融计算专业教程第四章，王晓民，清华大学出版社
