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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,McGraw-Hill/Irwin,Copyright,2007 by The McGraw-Hill Companies,Inc.All rights reserved,.,Stock Valuation,Chapter 6,Key Concepts and Skills,Understand how stock prices depend on future dividends and dividend growth,Be able to compute stock prices using the dividend growth model,Understand how growth opportunities affect stock values,Understand the PE ratio,Understand how stock markets work,Chapter Outline,6.1The Present Value of Common Stocks,6.2Estimates of Parameters in the Dividend-Discount Model,6.3Growth Opportunities,6.4The Dividend Growth Model and the NPVGO Model,6.5Price-Earnings Ratio,6.6Some Features of Common and Preferred Stock,6.7The Stock Markets,6.1 The PV of Common Stocks,The value of any asset is the present value of its expected future cash flows.,Stock produces two kinds of cash flows:,Dividends,The sale price,The PV of Common Stocks,Is the value of a stock equal to,:,1.The discounted present value of the sum of next periods dividend plus next periods stock price,or,2.The discounted present value of all future dividends?,Valuation of Different Types of Stocks,Zero Growth(,零增长),Constant Growth(,持续增长),Differential Growth(,差异增长),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 present value of a perpetuity:,Case 2:Constant Growth,Since future cash flows grow at a constant rate 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.,Constant Growth Example,Suppose an investor is considering the purchase of a share of the Utah Mining Company.The stock will pay a$3 dividend a year from today.This dividend is expected to grow at 10 percent per year(,g=,10%)for the foreseeable future.The investor thinks that the required return(,r,)on this stock is 15 percent,given her assessment of Utah Minings risk.(We also refer to,r,as the discount rate of the stock.)What is the value of a share of Utah Mining Companys stock?,Constant Growth Example,Using the constant growth formula of case 2,P,0,=DIV,1,/(R-g)=$,3,/(0.15-0.10)=$60,P,0,is quite dependent on the value of,g.,If,g,had been estimated to be 12.5percent,the value of the share would have been,P,0,=DIV,1,/(R-g)=$,3,/(0.15-0.125)=$120,Constant Growth Example,Because of,P,0,s dependency on,g,one must maintain a healthy sense of skepticism when using this constant growth of dividends model.,Furthermore,note that,P,0,is equal to infinity when the growth rate,g,equals the discount rate,R.,Because stock prices do not grow infinitely,an estimate of,g,greater than,r,implies an error in estimation.,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 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.,Case 3:Differential Growth,Assume that dividends will grow at rate,g,1,for,N,years and grow at rate,g,2,thereafter.,.,.,.,.,.,.,Case 3:Differential Growth,Dividends will grow at rate,g,1,for,N,years and grow at rate,g,2,thereafter,0 1 2,NN,+1,Case 3:Differential Growth,We can value this as the sum of:,an,N,-year annuity growing at rate,g,1,plus the discounted value of a perpetuity growing at rate,g,2,that starts in year,N,+1,Case 3:Differential Growth,Consolidating gives:,Or,we can“cash flow”it out.,Zero-Growth,、,Constant-Growth and Differential-Growth Patterns,A Differential Growth Example 1,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%.,With the Formula,With Cash Flows,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,.,A Differential Growth Example 2,Consider the stock of Elixir Drug Company,which has a new back-rub ointment and is enjoying rapid growth.The dividend for a share of stock a year from today will be$1.15.During the next four years,the dividend will grow at 15 percent per year(,g,1=15%).After that,growth(,g,2)will be equal to 10 percent per year.Can you calculate the present value of the stock if the required return(,r,)is 15 percent?,A Differential Growth Example 2,we first calculate the present value of the dividends at the end of each of the first five years.,Second,we calculate the present value of the dividends beginning at the end of year 6.,A Differential Growth Example 2,Calculate Present Value of First Five Dividends,The present value of dividend payments in years 1 through 5 is
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