Salaar - Finance Capital Markets Spring Semester 2010 Lahore School of Economics Salaar farooq – Assistant Professor

Salaar - Finance Common Stock Valuation Common Stock Valuation

Salaar - Finance Chapter 10 Common Stock Valuation Learning Objectives Common Stock Valuation Dividend Growth model Zero Growth Constant Growth Multiple growth model Intrinsic Value & Market price Relative Valuation Techniques (P/E,P/S,P/S) Components of Required Return

Salaar - Finance Capital Market Securities Fixed Income (Bonds) Treasuries Agencies Municipals Corporates Equities Preferred Stock Common Stock

Salaar - Finance Stocks It is an equity ownership in a corporation, initially issued to raise capital Points to keep in mind (vs Bonds) C/F’s are NOT known in advance Life of stocks is forever – no maturity Difficult to observe required rate of return for discounting

Salaar - Finance How do we come up with the Price of a Stock? PV of all future expected C/F’s? Assumptions will be needed! Assume a dividend the stock will pay. Assume a selling price at the end of 1 year. Come up with a required rate of return. Stocks

Salaar - Finance Stocks Valuation Assumptions will be needed! Assume a dividend the stock will pay. Assume a selling price at the end of 1 year. Come up with a required rate of return. Example: For 1 year Stock selling price is $70 Stock dividend will be $10 U need a 25% return PV will be 80/(1.25) = $64 (u should pay today)

Salaar - Finance Example: For 1 year Stock selling price is $70 (P1) Stock dividend will be $10 (D1) U need a 25% return (R) PV will be 80/(1.25) = $64 (Po) (u should pay today) Therefore we can write: Po = (D1+P1) / (1+R) NOTE: coming up with a stock end year is not easy!! Stocks Valuation

Salaar - Finance Example: For 1 year t1, would be found the same way by assuming the year 2 price & dividend: P1 = (D2+P2) / (1+R) Here then P1 really equals the P1 we used at Po. Thus we can substitute: Stocks Valuation

Salaar - Finance Example: For 1 year substituting P1 in Po equation: Po = (D1+ (D2+P2)/1+R) / (1+R) = D1/(1+R)^1 + D2/(1+R)^2 + P2/(1+R)^2 If u repeat this forever, the P2 ultimately has a PV of almost ZERO!! Stocks Valuation

Salaar - Finance Formula: Po = E Dn / (1+R)^n PV of all future dividends… as a general valuation framework. Dividends to infinity are still a problem at this stage! Stocks Valuation

Salaar - Finance The problem of NO dividends…. This formula assumes the company will pay something at some point in its life to its shareholders. A Corp where money goes in but nothing comes out doesn’t exist. Or shouldn’t exist! Stocks Valuation

Salaar - Finance Special Cases…. of dividends Zero-growth: Here the dividend is constant, D1=D2=D So, the value of the stock is a Perpetuity (ordinary), Po = D/R same as PV = C/r Stocks Valuation

Salaar - Finance Example zero-growth Suppose a company pays Rs. 10 dividend always. If this policy is forever,… What’s the stock price if the required return is 20%? Stocks Valuation

Salaar - Finance Example zero-growth Suppose a company pays Rs. 10 dividend always. If this policy is forever,… What’s the stock price if the required return is 20%? Po = 10 / 0.2 = Rs 50 per share Stocks Valuation

Salaar - Finance Zero Growth Example: A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%. What’s the price per share today? Stocks Valuation

Salaar - Finance Zero Growth Example: A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%. What’s the price per share today? Po = Do / k 2/.2 = 10 Stocks Valuation

Salaar - Finance Special Cases…. of dividends Constant Growth Model: Suppose the dividend grows at a constant rate g. If dividend just paid is Do, then the next D1 is: D1 = Do x (1+g) & for 2 periods is: D2 = Do x (1+g)^2 (FV formula) D2 = (Do x (1+g)) x (1+g) Stocks Valuation

Salaar - Finance Growing Perpetuity: An asset where the C/F’s grow at a constant rate forever. Putting these dividends in the formula: Po = Do(1+g)^1/(1+R)^1 + Do(1+g)^2/(1+R)^2 we can write this simply as: Po = Do x (1+g) / R-g OR D1 / R - g Stocks Valuation

Salaar - Finance Dividend Growth Model: Determines the Stock Price with constant growth dividends. Po = Do x (1+g) / R-g OR D1 / R - g (g<R) Stocks Valuation

Salaar - Finance Example: Suppose Do = 2.30, R=13%, g=5%. Whats the price per share? Stocks Valuation

Salaar - Finance Stocks Valuation Example: Suppose Do = 2.30, R=13%, g=5%. Whats the price per share? D1 / R - g (g<R) 2.3 x (1.05) / ( ) / 0.8= 30.19

Salaar - Finance Stocks Valuation Note: You can use this to find the stock price at any point in time! Just find the D for that year, grow it at (1+g) & then divide by R-g

Salaar - Finance Stocks Valuation Example: Suppose Do = 2.30, R=13%, g=5%. What’s the price per share in 5 years? D6 / R - g (g<R)

Salaar - Finance Stocks Valuation Example: Suppose Do = 2.30, R=13%, g=5%. What’s the price per share in 5 years? Formula is: Dt+1 / R - g (g<R)

Salaar - Finance Stocks Valuation Example: Suppose Do = 2.30, R=13%, g=5%. What’s the price per share in 5 years? D6 / R - g (g<R) 2.3 x (1.05)^5 / ( ) 2.935x(1.05) / 0.8 = /.08 = 38.53

Salaar - Finance Stocks Valuation Example: Suppose Company T’s next dividend will be $4. Required return is 16%. Dividend increases by 6% every year. What’s the price per share today? & in 4 years?

Salaar - Finance Stocks Valuation Example: Suppose next dividend will be $4. Required return is 16%. Dividend increases by 6% every year. D1 = 4, R=16%, g=6%. (since D1 is given, don’t need to grow by g) What’s the price per share today? Po = D1 / R - g (g<R) 4/ ( ) = 4/.1 = $40 = Po What’s the price per share in 4 yrs? Find D5 first, D1 (1+g)^4 = 4(1.06)^4 = /0.1 = = P4

Salaar - Finance Stocks Valuation Notice here: P4 = Po (1+g)^ = 40 x (1.06)^4 So, Stock price grows at the same constant rate as the Dividend! P4 is simply D5/(R-g)

Salaar - Finance Stocks Valuation Constant growth Example: Suppose ODGC pays a dividend of Rs.2 per share which is expected to grow at a constant rate of 7% per year. Investors require a rate of return of 16% given the risk of this stock. D1 = 2*(1.07) = 2.14, R=16%, g=7%. What’s the price per share today? What’s the price per share in 4 yrs?

Salaar - Finance Stocks Valuation Constant growth Example: Suppose ODGC pays a dividend of Rs.2 per share which is expected to grow at a constant rate of 7% per year. Investors require a rate of return of 16% given the risk of this stock. D1 = 2*(1.07) = 2.14, R=16%, g=7%. What’s the price per share today? Po = D1 / R - g (g<R) 2.14/ ( ) = = Po What’s the price per share in 4 yrs? Find D5 first, D1 (1+g)^4 = 2.14(1.07)^4 = /.09 = Rs = P4

Salaar - Finance PART II

Salaar - Finance Stocks Valuation Multiple Growth model Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate. Value = PV of dividends + PV of terminal price = E Do(1+g)^t / (1+k) + Dn(1+g)/(k-g).1/1+k^n illustrate concept

Salaar - Finance Stocks Valuation Intrinsic Value & Market Price IfIV > Mkt Price = under/over-valued? IV < Mkt Px = under/over valued?

Salaar - Finance Stocks Valuation Multiple growth Example: MCB is expanding and is expected to grow at a rate of 20% per year for the next three years. Current dividend is Rs. 2 per share. After this rapid growth, the company is likely to slow down to a normal growth of 7% for the foreseeable future. Required return on this stock is 22%. D1 = 2*(1.20) = 2.40, R=22%, G1= 20%, g=7%. What’s the price per share today? solution in excel - MCB

Salaar - Finance

REAL PROBLEM PRACTICE Use First stage growth = 7% (3yrs) Second stage growth = 5% (perpetuity) Do = 3.68 Required return = 10 year yield + 10% ERP= 15% BASED ON ITS REAL PX, IS IT OVER/UNDER VALUED? Solution in Excel - B

Salaar - Finance

REAL PROBLEM PRACTICE Use – What is the Market pricing on this stock?? First stage growth = 7.7% (3yrs) Second stage growth = 5% (perpetuity) Do = 0.7 Required return = 10 year yield + 10% ERP BASED ON ITS REAL PX, IS IT OVER/UNDER VALUED? Solution in Excel – Main

Salaar - Finance

Relative Valuation Techniques Making Valuations through comparisons P/E = Price to Earnings ratio so if comparable stocks are trading at x15. & Earnings for a stock are equal to: $3 What should be the stock price?45 Forward P/E = Po/E1

Salaar - Finance Relative Valuation Techniques Making Valuations through comparisons P/BV = Price to Book Value (S.Equity) ratio so if comparable stocks are trading at x10. & BV for a stock is equal to: $5 What should be the stock price? 50

Salaar - Finance Relative Valuation Techniques Making Valuations through comparisons P/S = Price to Sales ratio so if comparable stocks are trading at x1. & Sales for a stock is equal to: $5 What should be the stock price? 5

Salaar - Finance Components of Required Return Let’s break down the R, discount rate which we used in the Dividend Discount Model or DDM Po = D1 / (R-g) if we rearrange to solve for R…. then… R-g = D1/Po R = D1/ Po + g

Salaar - Finance Components of Required Return R = D1/ Po + g This means TR has 2 components: D1/Po = Dividend Yield g = same rate as the increase in stock price = Capital gains yield

Salaar - Finance Components of Required Return EXAMPLE R = D1/ Po + g If a stock is selling for $20 per share. Next dividend will be $1 per share. Dividend will grow by 10% per year forever. What is the return on this stock?

Salaar - Finance Components of Required Return EXAMPLE R = D1/ Po + g If a stock is selling for $20 per share. Next dividend will be $1 per share. Dividend will grow by 10% per year forever. What is the return on this stock? R = Div yield + Cap gains yield = 1/ % = 5% + 10% = 15%

Salaar - Finance Components of Required Return EXAMPLE R = D1/ Po + g A stock’s dividend will grow by 8% per year forever. If the stock is selling for $60 per share and next dividend will be $3 per share. What is the required return on this stock?

Salaar - Finance Components of Required Return EXAMPLE R = D1/ Po + g A stock’s dividend will grow by 8% per year forever. If the stock is selling for $60 per share and next dividend will be $3 per share. What is the required return on this stock? R = Div yield (D1/Po) + Cap gains yield (g) = 3/ = = 13%

Salaar - Finance In class practice of Ch-10 NEXT: TECH ANALYSIS