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1、5-0,CHAPTER,5,How to ValueBonds and Stocks(p106),5-1,Chapter Outline,5.1Definition and Example of a Bond5.2How to Value Bonds5.3Bond Concepts5.4The Present Value of Common Stocks5.5Estimates of Parameters in the Dividend-Discount Model5.6Growth Opportunities5.7The Dividend Growth Model and the NPVGO
2、 Model(Advanced)5.8Price Earnings Ratio5.9 Stock Market Reporting5.10 Summary and Conclusions,5-2,Valuation of Bonds and Stock,First Principles:Value of financial securities=PV of expected future cash flows To value bonds and stocks we need to:Estimate future cash flows:Size(how much)and Timing(when
3、)Discount future cash flows at an appropriate rate:The rate should be appropriate to the risk presented by the security.,5-3,5.1Definition and Exampleof a Bond,A bond is a certificate showing that a borrower owes a specified sum,it is a legally binding agreement between a borrower and a lender:Speci
4、fies 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 borrowing),5-4,5.1Definition and Exampleof 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
5、.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 January 1,2005 the size and timing of cash flows are:,5-5,5.2How to Value Bonds,Identify the size and timing of cash flows.Discount at the correct discoun
6、t rate.If you know the price of a bond and the size and timing of cash flows,the yield to maturity(YTM)is the discount rate.Yield to maturity(YTM)is bond jargon for the discount rate that equates the price of a bond with the discounted value of its coupons and face(par)value.In other words,present v
7、alue=price when r=YTM.The yield to maturity represents the current market interest rate for a bond.,5-6,5.2How to Value Bonds,We now consider how to value following different types of bonds:Pure discount bondsLevel-coupon bondsConsols,5-7,Pure Discount Bonds(p106),The pure discount bond is perhaps t
8、he simplest kind of bond.It promises a single payment at a fixed future date.Pure discount bonds are often called zero-coupon bonds or zeroes.We will use the terms zero,bullet and discount interchangeably to refer to bonds that pay no coupons.,5-8,Pure Discount Bonds(p106),Information needed for val
9、uing pure discount bonds:Time to maturity(T)=Maturity date-todays dateFace value(F)Discount rate(r),Present value of a pure discount bond at time 0:,5-9,Pure Discount Bonds:Example,Find the value of a 30-year zero-coupon bond with a$1,000 par value and a YTM of 6%.,5-10,Example of pure discount bond
10、s:,What is the price of a 25-year,pure discount bond that pays$50 at maturity if the current yield-to maturity is 8 percent?0 1 2 25|-|-|-|$50PV0=50(1.08)25=$7.30,5-11,Level-Coupon Bonds,Information needed to value level-coupon bonds:Coupon payment dates and time to maturity(T)Coupon payment(C)per p
11、eriod and Face value(F)Discount rate,Value of a Level-coupon bond=PV of coupon payment annuity+PV of face value,5-12,Level-Coupon Bonds:Example,Find the present value(as of January 1,2004),of a 6-3/8 coupon T-bond with semi-annual payments,and a maturity date of December 2009 if the YTM is 5-percent
12、.On January 1,2004 the size and timing of cash flows are:,5-13,Example of level-coupon bonds:,What is the value of a two-year$1000 par value bond paying 10%coupon semiannually if the required-return is 8%compounded semi-annually?Coupon=$1000 0.1/2=$50 every six monthPV=F/(1+r)T+C 1/r 1/r(1+r)T=($100
13、0)/(1.04)4+($50)(1/0.04 1/(0.04 1.044)=$1036,5-14,Consols,Consols are bonds that never stop paying a coupon,have no final maturity date,and therefore never mature.A consol is a perpetuity.PV=C/R,5-15,5.3Bond Concepts,Bond prices and market interest rates move in opposite directions.2.When coupon rat
14、e=YTM,price=par value.When coupon rate YTM,price par value(premium bond)When coupon rate YTM,price par value(discount bond)A bond with longer maturity has higher relative(%)price change than one with shorter maturity when interest rate(YTM)changes.All other features are identical.4.A lower coupon bo
15、nd has a higher relative price change than a higher coupon bond when YTM changes.All other features are identical.,5-16,YTM and Bond Value,When the YTM coupon,the bond trades at a premium.,When the YTM=coupon,the bond trades at par.,When the YTM coupon,the bond trades at a discount.,800,1000,1100,12
16、00,1300,$1400,0,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,Discount Rate,Bond Value,5-17,Maturity and Bond Price Volatility,Consider two otherwise identical bonds.The long-maturity bond will have much more volatility with respect to changes in the discount rate,5-18,Coupon Rate and Bond Price
17、Volatility,Consider two otherwise identical bonds.The low-coupon bond will have much more volatility with respect to changes in the discount rate,5-19,Example of U.S.Corporate Bond,Bonds Cur Yld.Vol.Close Net Chg.ChryF 131/4 99 11.8 5 112 1/8 7/8This entry represents Chry F that mature in the year 1
18、999 and have a coupon rate of 131/4.Cur Yld=coupon payment/current priceIf you buy this Chrysler bond,the asked price is 112.125%of par value.,5-20,Multiple Choice Questions,1.A pure discount bond A)does not have any face value.B)pays interest annually.C)pays interest semiannually.D)does not pay a c
19、oupon.E)None of the above.,5-21,Answer:D,5-22,2.A level coupon bond A)pays the same principal every period.B)pays the same taxes every period.C)is a zero coupon annuity.D)pays an annuity over the life of the bond.E)None of the above.,5-23,Answer:D,5-24,3.The coupon of a bond is A)its time period to
20、maturity.B)its current price.C)its face value.D)its yield to maturity.E)the amount of the interest payment.,5-25,Answer:E,5-26,4.A consol A)always sells at a premium.B)always sells at a discount.C)is an agent that makes interest payments.D)is a perpetuity.E)does not pay any interest.,5-27,Answer:D,5
21、-28,5.A bond is listed in The Wall Street Journal as a 12 3/4s of July 2009.This bonds pays A)$127.50 in July and January.B)$63.75 in July and January.C)$127.50 in July.D)$63.75 in July.E)None of the above.,5-29,Answer:BRationale:Bonds pay semiannually,therefore in July and January of$1000(.1275)(.5
22、)=$63.75.,5-30,6.If its yield to maturity is less than its coupon rate,a bond will sell at a _,and increases in market interest rates will _.A)discount;decrease this discount.B)discount;increase this discount.C)premium;decrease this premium.D)premium;increase this premium.E)None of the above.,5-31,A
23、nswer:C,5-32,5.4The Present Valueof Common Stocks,The valuation principles are the same for stocks and bonds.The current price of a share of stock is the present value of expected future cash flows:i.e.the expected dividend plus expected price at the end of the holding period.The value of common sto
24、ck depends only on the timing,size,and riskiness of expected future dividends.This is the essence of the dividend valuation model.How do we estimate future dividends?,5-33,5.4The Present Valueof Common Stocks,Obviously,it is not feasible to estimate dividends for each period individually.To make the
25、 above valuation formula(equation 5.4 from the text)operational,we introduce three models for estimating future dividends:zero growth,constant dividend growth,and differential growth.The three dividend growth models apply to firms in different stages of its life cycle.Young companies usually have a
26、high growth rate.After a while they slow down and grow at a more normal rate.Finally,they may shrink or go out of business entirely.,5-34,Case 1:Zero Growth,Assume that dividends will remain at the same level forever,Since future cash flows are constant,the value of a zero growth stock is the presen
27、t value of a perpetuity:,5-35,Example of a zero growth stock:,Suppose a firms earnings and dividends are expected to remain constant at$1 per share forever.The discount rate appropriate for the risk of the dividends is 10%.The value of the firm is thenPrice=($1)/(.1)=$10 per share.,5-36,The zero gro
28、wth model fits many mature companies surprisingly well if cash flows and the discount rate are estimated in real terms.It fits exactly in real terms when nominal cash flows are expected to increase at the rate of inflation.,5-37,Case 2:Constant Growth,Since future cash flows grow at a constant rate
29、forever,the value of a constant growth stock is the present value of a growing perpetuity:,Assume that dividends will grow at a constant rate,g,forever.i.e.,5-38,Example of a constant growth stock:,Suppose a firm just paid a dividend of$10 per share.Future dividends are expected to increase at a 5%a
30、nnual rate.The required return is 25%per year.The value of the firm is estimated as:Divl=Div0(1+g)=($10)(1.05)=$10.50Price=Divl/(r g)=($10.50)/(.25.05)=$52.50.Read example on p114-115,5-39,Case 3:Differential Growth,Assume that dividends will grow at different rates in the foreseeable future and the
31、n will grow at a constant rate thereafter.This general type of model is especially useful for valuing firms in the growth stage of their life cycle.To value a Differential Growth Stock,we need to:Estimate future dividends in the foreseeable future.Estimate the future stock price when the stock becom
32、es 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.,5-40,Case 3:Differential Growth,Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter,.,.,.,.,.,.,5-41,Case 3:
33、Differential Growth,Dividends will grow at rate g1 for N years and grow at rate g2 thereafter,5-42,Case 3:Differential Growth,We can value this as the sum of:an N-year annuity growing at rate g1,plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1,5-43,Case 3:Differen
34、tial Growth,To value a Differential Growth Stock,we can use,Or we can cash flow it out.,5-44,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.What is the stock worth?The discount rate is 12%.
35、,5-45,With the Formula,5-46,A Differential Growth Example(continued),0 1 234,0 1 2 3,The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.,5-47,5.5 Estimates of Parameters in the Dividend-Discount Model,The value of a firm depends upon its growth rate,g,and i
36、ts discount rate,r.Where does g come from?Where does r come from?,5-48,Where does g come from?,g=Retention ratio Return on retained earnings=Retention ratio Return on EquityRetention ratio=1-payout ratioReturn on retained earnings=net income/retained earningsSee example on p117.Retention ratio=0.4,R
37、OE=0.16 g=0.4 0.16=0.064,5-49,The Rockwell Company had net earnings of$127,000 this past year.Dividends were paid of$38,100 on retained earnings of$1,587,500.The estimated growth for Rockwell is A)2.4%B)5.6%C)7.2%D)16.8%E)None of the above,5-50,Answer:B Rationale:g=Retention ratio Return on retained
38、 earnings=(1-($38,100/$127,000)($127,000/$1,587,000)=(1-.3).08=.056=5.6%,5-51,Where does r come from?,P=Div/(r-g),r=(Div/P)+gThe discount rate can be broken into two parts.The dividend yield The growth rate(in dividends)See example on p118Retention ratio=0.4,g=0.064,P=$10payout ratio=dividends/earni
39、ngs=1-0.4=0.6Earnings next year=2000,000 1.064=2,128,000Dividends=$2,128,000 0.6=$1,276,800Dividends per share=1,276,800/1,000,000=1.28 r=1.28/10+0.064=0.192,5-52,Mutiple choice,The Lory Company had net earnings of$127,000 this past year.Dividends were paid of$38,100 on the companys equity of$1,587,
40、500.If Lory has 100,000 shares outstanding with a current market price of$11.625 per share,what is the required rate of return?A)4.2%B)6%C)9%D)14%E)None of the above.,5-53,Answer:CRationale:g=Retention ratio ROE=(1-($38,100/$127,000)($127,000/$1,587,000)=(1-.3).08=.056=5.6%R=Div/P0+g=(.381(1.056)/11
41、.625)+.056=(.40/11.625)+.056=.0346+.056=.0906=9%,5-54,5.6Growth 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 earnings as dividends and the net prese
42、nt value of the growth opportunities.The company pays all of earnings out to stockholders as dividends is frequently called a cash cow.,5-55,EPS/rthe value of the firm if it distributed all earnings to the stockholders.NPVGO-the additional value if the firm retains earnings in order to fund new proj
43、ects.See example on p120EPS=1000,000/100,000=$10,r=0.1,EPS/r=$100NPVGO at date1=210,000/0.1-1000,000=1,100,000NPVGO at date 0=1,100,000/1.1=$1000,000NPVGO per share=1000,000/100,000=$10P=EPS/r+NPVGO=100+10=$110,-1000,000,210,000,5-56,5.7The Dividend Growth Model and the NPVGO Model(Advanced),For a s
44、tock with a steady growth in dividends,we have two ways to value a stock:The dividend discount model.P=Div/(r-g)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.P=EPS/r+NPVGONPVGO=(kEPSROE/r)-kEPS/(r-g)K-retent
45、ion ratio,5-57,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 of 20-percent.The dividend at year one will be$5.30=$1.50 per share.The retention
46、 ratio is.70(=1-.30)implying a growth rate in dividends of 14%=.70 20%(g=retention ratio ROE)From the dividend growth model,the price of a share is:,5-58,The NPVGO Model,First,we must calculate the value of the firm as a cash cow.,Second,we must calculate the value of the growth opportunities.,Final
47、ly,K*EPS=0.7*5=3.5,5-59,Example on p123-125,EPS=10,K=1-0.4=0.6,Div=10*0.4=$4 r=16%,ROE=20%,g=0.6*0.2=0.121.Determine the value use dividend growth model:P=Div/(r-g)=4/(0.16-0.12)=$100,5-60,2.Determine the value use NPVGO modelFirst,we must calculate the value of the firm as a cash cow.P0=EPS/r=10/0.
48、16=$62.5Second,we must calculate the value of the growth opportunities NPVGO=(kEPSROE/r)-kEPS/(r-g)=(0.6100.2/0.16)-0.610/(0.16-0.12)=$37.5P=62.5+37.5=$100,5-61,5.8Price Earnings Ratio,Many analysts frequently relate earnings per share to price.The price earnings ratio is a.k.a.(also called as)the m
49、ultipleCalculated as current stock price divided by annual EPSThe Wall Street Journal uses last 4 quarters earnings,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.,5-62,Price per sh
50、are=EPS/r+NPVGODividing by EPS yields:Price per share/EPS=1/r+NPVGO/EPSThe equation shows that the P/E ratio is related to the net present value of growth opportunities.,5-63,Other Price Ratio Analysis,Many analysts frequently relate earnings per share to variables other than price,e.g.:Price/Cash F
