Salaar - Finance

Capital MarketsCapital Markets

Spring Semester 2010Spring Semester 2010

Lahore School of EconomicsLahore School of Economics

Salaar farooq – Assistant Professor

Salaar - Finance

Common Stock ValuationCommon Stock Valuation

Salaar - Finance

Chapter 10Common 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 price @ end year is not easy!!

Stocks Valuation

Salaar - Finance

Example: For 1 year

P1 @ 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) / (0.13-0.05)

2.415 / 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 / (0.13-0.05)

2.935x(1.05) / 0.8 = 3.0822/.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/ (.16-.06) = 4/.1 = $40 = Po

What’s the price per share in 4 yrs?

Find D5 first, D1 (1+g)^4 = 4(1.06)^4 = 5.05

5.05/0.1 = 50.50 = P4

Salaar - Finance

Stocks Valuation

Notice here:

P4 = Po (1+g)^4

50.50 = 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 ValuationConstant 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 ValuationConstant 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/ (.16-.07) = 23.78 = Po

What’s the price per share in 4 yrs?

Find D5 first, D1 (1+g)^4 = 2.14(1.07)^4 = 2.81

2.81/.09 = Rs 31.22 = 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

If IV > 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

Salaar - Finance

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

Salaar - Finance

Salaar - Finance

Salaar - Finance

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

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 ReturnEXAMPLE

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 ReturnEXAMPLE

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

= 1/20 + 10%

= 5% + 10% = 15%

Salaar - Finance

Components of Required ReturnEXAMPLE

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 ReturnEXAMPLE

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)

= 3/60 + 0.08

= 0.05 + .08 = 13%

Salaar - Finance

In class practice of Ch-10

NEXT: TECH ANALYSIS