Introduction to Stock Introduction to Stock ValuationValuation

Valuing StocksValuing Stocks

• Recall:Recall:

Stocks have no maturityStocks have no maturity

Cash inflows from stock are:Cash inflows from stock are:– DividendsDividends– Sale PriceSale Price

Stock ValueStock Value

• PV of all future PV of all future estimatedestimated dividends dividends

• Dividends are Dividends are notnot known with known with certainty in advancecertainty in advance

• Dividends must be Dividends must be estimatedestimated

• Future sale price must be Future sale price must be estimatedestimated

Stock ValueStock ValueP

E(D ) E(P )

1 r

E(D )

1

E(D ) E(P )

1

1

E(D )

1

E(D )

(1 )

E(P )

(1 )

o1 1

1

2 2

1 22

22

r

r

r

r r r

E( ) is a reminder that these are estimates!!

‘‘r’r’

• In context of stocks, ‘r’ which we In context of stocks, ‘r’ which we have so far called ‘interest rate’ or have so far called ‘interest rate’ or ‘yield’ or ‘discount rate’ has a special ‘yield’ or ‘discount rate’ has a special namename

• It is called ‘required rate of return’It is called ‘required rate of return’

• It is the return investors demand for It is the return investors demand for buying and holding stockbuying and holding stock

Dividend Discount Dividend Discount Model (DDM)Model (DDM)

PD

r

D

r

D

rm

m01 2

21 1 1

( ). . .

( ).........

• r = required rate of return on stockr = required rate of return on stock

• ALL future dividends must be ALL future dividends must be estimatedestimated– “ “ from here to eternity!!!”from here to eternity!!!”

Simplifying Simplifying AssumptionAssumption

• Dividends grow at a constant Dividends grow at a constant growth rate (g)growth rate (g)

DD00 = current dividend paid = current dividend paidDD11 = D = D00 (1+g) (1+g)DD22 = D = D1 1 (1+g) = D(1+g) = D00 (1+g) (1+g)22

DD33 = D = D22 (1+g) = D (1+g) = D00 (1+g) (1+g)33

...and so on...and so on

ExampleExample• given: g = 5%, Dgiven: g = 5%, D00 = $2 = $2

DD00 = $2 (this is known) = $2 (this is known)

DD11 = D = D00 (1+.05) = $2.10 (1+.05) = $2.10

DD22 = 2.10 = 2.10 (1+.05) = D(1+.05) = D00 (1+05) (1+05)2 2 = = $2.205$2.205

DD33 = 2.205 (1+.05) = D = 2.205 (1+.05) = D00 (1+.05) (1+.05)3 3 = = $2.315$2.315

Constant GrowthConstant Growth

• If dividends can be assumed to grow If dividends can be assumed to grow at a constant rate,at a constant rate,

• The valuation of stock becomes The valuation of stock becomes much simplermuch simpler

Constant Growth DDMConstant Growth DDM

• Notice it is much simpler to estimate:Notice it is much simpler to estimate:

• You need only THREE inputs: D1, r, gYou need only THREE inputs: D1, r, g

ExampleExample

• GivenGiven: D: D00 = $2.00 g = 5% r = = $2.00 g = 5% r = 9%9%

DD11 = $2.10 = $2.10

PP00 = D = D11 / (r - g) = 2.10 / (.09-.05) / (r - g) = 2.10 / (.09-.05)

= $ 52.50 = $ 52.50

Example 2Example 2

• Kinesis Keyboards will begin paying Kinesis Keyboards will begin paying dividend in year 5 of $4.50 per share. dividend in year 5 of $4.50 per share. The dividend in subsequent years is The dividend in subsequent years is expected to grow at a constant rate of expected to grow at a constant rate of 11%. The required rate of return is 11%. The required rate of return is 18%. What is the stock price 18%. What is the stock price expected at the end of year 4?expected at the end of year 4?

• AnswerAnswer: $64.28: $64.28

Constant Growth Constant Growth ImplicationImplication

• ImplicationImplication: Stock Price also grows : Stock Price also grows at the constant rate gat the constant rate g

• Kinesis example: Kinesis example: What is PWhat is P55? What is P? What is P66??AnswerAnswer::

• NoteNote: P: P66 = P = P55 x (1+g) x (1+g)

What if company pays no What if company pays no dividends?dividends?

• Many companies do not pay Many companies do not pay dividends dividends currentlycurrently

• All profits are retained in the firm All profits are retained in the firm and invested in the firmand invested in the firm

• Can companies continue to not pay Can companies continue to not pay dividends forever?dividends forever?

No dividends… (contd.)No dividends… (contd.)

• Sooner or later, company will not Sooner or later, company will not have enough investment have enough investment opportunities within the firmopportunities within the firm

• Sooner or later, companies will Sooner or later, companies will HAVEHAVE to begin paying dividends to begin paying dividends

ExampleExample• Keep Inside Co. is estimated to pay its first Keep Inside Co. is estimated to pay its first

dividend in year 4 of $3.50 which is dividend in year 4 of $3.50 which is expected to grow at a constant rate of 6% expected to grow at a constant rate of 6% thereafter. What is the current stock thereafter. What is the current stock price? r = 10%price? r = 10%

• TrickTrick: Calculate P: Calculate P33 and discount that value and discount that value back to t = 0back to t = 0

• Answer: $ __________Answer: $ __________

A twist:A twist:

• Rearranging constant growth Rearranging constant growth formula:formula:

r = Dividend Yield + Capital Gainsr = Dividend Yield + Capital Gains

Example:Example:

• Sunriver Resorts stock price is $40 Sunriver Resorts stock price is $40 and will pay $2.50 dividend next and will pay $2.50 dividend next year. You estimate the dividend year. You estimate the dividend growth of 10%. What is the return growth of 10%. What is the return on Sunriver stock?on Sunriver stock?

• Answer: __________Answer: __________

Required ReturnRequired Return

• Regulators, investors use the Regulators, investors use the previous simple formula to estimate previous simple formula to estimate the required rate of returnthe required rate of return

• Note however, that a simplifying Note however, that a simplifying constant growth assumption has constant growth assumption has been made when we use the formulabeen made when we use the formula

Caution with constant Caution with constant growthgrowth

• WORKS ONLY IF ‘r’ > ‘g’WORKS ONLY IF ‘r’ > ‘g’– Stock prices Stock prices cannotcannot be negative! be negative!

• Constant dividend growth assumption Constant dividend growth assumption may not be realistic in all casesmay not be realistic in all cases

• Avoid the temptation to blindly apply Avoid the temptation to blindly apply the formula!!the formula!!

What if g > r ?What if g > r ?

• Unrealistic to assume constant Unrealistic to assume constant growth for rapidly growing growth for rapidly growing companiescompanies

• Rapid growth cannot last foreverRapid growth cannot last forever– New competition, declining profitsNew competition, declining profits

• Multi-stage (non-constant) growth Multi-stage (non-constant) growth models are employed in such casesmodels are employed in such cases

ExampleExample

• Kinesis Keyboard: DKinesis Keyboard: D00 = $0.50 = $0.50Supergrowth in years 1 to 5: 55%Supergrowth in years 1 to 5: 55%Thereafter, constant growth of 11%Thereafter, constant growth of 11%r = 18%r = 18%What is the What is the currentcurrent stock price? stock price?

• Answer: ________Answer: ________

ApproachApproach• Draw time lineDraw time line

• Compute DCompute D11 to D to D55 at first growth rate at first growth rate

• Compute DCompute D66 at the second growth rate at the second growth rate

• Compute PCompute P5 5 using constant growth DDMusing constant growth DDM

• Take PV (at t = 0) of DTake PV (at t = 0) of D11 to D to D55 and P and P55

• NoteNote: P: P55 incorporates the present values incorporates the present values of of allall dividends D dividends D66 and onwards!! and onwards!!

Step 1Step 1

• D0 = D0 = $ 0.50$ 0.50

• DD11 = D = D00 ( 1+__ ) = ( 1+__ ) = $ _____$ _____

• DD22 = D = D11 ( 1+__ ) = ( 1+__ ) = $ _____$ _____

• DD33 = D = D22 ( 1+__ ) = ( 1+__ ) = $ _____$ _____

• DD44 = D = D33 ( 1+__ ) = ( 1+__ ) = $ _____$ _____

• DD55 = D = D44 ( 1+__ ) = ( 1+__ ) = $ _____$ _____

0 1 2 3 4 5 6

Step 2Step 2

• Estimate DEstimate D66 = D = D55 ( 1 + ____ ) = $ ( 1 + ____ ) = $ __________

• Now estimate PNow estimate P55 using constant using constant growthgrowth

PP55 = D = D66 / (r - g) = ________ = / (r - g) = ________ = $_______$_______

Step 3Step 3

• Now you have all the numbers Now you have all the numbers neededneeded

• Fill in the boxesFill in the boxes

• Show all the dividends and PShow all the dividends and P55 on the on the time linetime line

0 1 2 3 4 5 6

+

Step 4Step 4

• Discount DDiscount D11 - D - D55 and P and P55 back to time back to time t = 0t = 0

• You can use your calculator for this You can use your calculator for this using the and using the and keyskeys

CFj NPV

Using your calculatorUsing your calculator• Enter CFEnter CF00 as: as: $0.0000$0.0000

• Enter CFEnter CF11 as: as: $0.7750$0.7750

• Enter CFEnter CF22 as: as: $1.2013$1.2013

• Enter CFEnter CF33 as: as: $1.8619$1.8619

• Enter CFEnter CF44 as: as: $2.8860$2.8860

• Enter CFEnter CF55 as D as D55 + P + P55:: $75.4071$75.4071

• Enter interest rate:Enter interest rate: 1818• Hit Answer: $ ___________Hit Answer: $ ___________

CFj

CFj

CFj

CFj

CFj

CFj

NPV

I/YR

Another ExampleAnother Example• Mega Growth Co. is growing quickly. Mega Growth Co. is growing quickly.

Dividends are expected to grow at a Dividends are expected to grow at a 30% rate for the next three years, with 30% rate for the next three years, with the rate falling off to 7% thereafter. If the rate falling off to 7% thereafter. If the required return is 23% and the the required return is 23% and the company just paid $1.40 dividend, company just paid $1.40 dividend, what is the current share price?what is the current share price?

• Answer: Answer: $________$________

Supergrowth Example Supergrowth Example 22

• Terminator Brews will pay no Terminator Brews will pay no dividend for the next 2 years. The dividend for the next 2 years. The third year dividend of $1.00 will third year dividend of $1.00 will grow at 30% for the next 3 years. grow at 30% for the next 3 years. Thereafter the growth will level off Thereafter the growth will level off to 10% forever. r = 15%. What is to 10% forever. r = 15%. What is the value of Terminator today?the value of Terminator today?

• Answer: $ 24.09Answer: $ 24.09

RecapRecap• Unlike bonds, cash flows (i.e. dividends) on Unlike bonds, cash flows (i.e. dividends) on

stocks are not known in advancestocks are not known in advance

• They must be estimatedThey must be estimated

• Analysts spend a lot of time and energy on Analysts spend a lot of time and energy on estimating dividends!!estimating dividends!!

• Hence stock valuation is more of an art than Hence stock valuation is more of an art than an exact science!an exact science!