4-1Common Stock Valuation

Part I: Difficulties

Uncertain cash flowsUncertain cash flowsEquity is the residual claim on the firm’s Equity is the residual claim on the firm’s

cash flowscash flows

Life of the firm is foreverLife of the firm is forever

Required Rate of Return (the discount Required Rate of Return (the discount rate, rate, r r ) is not easily observed) is not easily observed

4-2

Discounted Cash Flow Valuation

You own a share of stock today. What do You own a share of stock today. What do you get for holding it for you get for holding it for oneone period? period?DividendDividendPrice when you sell the stock: PPrice when you sell the stock: P11

What Determines PWhat Determines P11??

PV = Price = D P

0 01 1( )1 r

4-3

Discounted Cash Flow Valuation

P = D P

12 2( )1 r

So we can substitute the above formula So we can substitute the above formula into the formula for Pinto the formula for P00..

22

221

221

0 r)+(1

P +

r)+(1

D +

r)+(1

D =

)1(

)1()P + (D D

= PVr

r

What determines PWhat determines P22??

4-4

Discounted Cash Flow Valuation

The price of a stock equals the The price of a stock equals the present value of all the firm’s present value of all the firm’s forecasted dividends discounted by forecasted dividends discounted by the required rate of return, r.the required rate of return, r.

We use 3 different sets of We use 3 different sets of assumptions about future dividends assumptions about future dividends to simplify the above formula.to simplify the above formula.

Price = D

r +

D

(1+ r) +

D

(1+ r) + . . . 0

1 22

33( )1

4-5

(I) Zero Growth Dividend Model

Firm’s dividends are constant over time.Firm’s dividends are constant over time. No growth in the dividendNo growth in the dividend

Stream of constant cash flows foreverStream of constant cash flows foreverPrice equity as a Price equity as a perpetuityperpetuity

PV = Price = D

0 0 r

4-6

Common Stock Valuation:Zero dividend growth model

A firm’s dividend is expected to stay A firm’s dividend is expected to stay constant forever at $1 per share. The constant forever at $1 per share. The required rate of return is 10% per year.required rate of return is 10% per year.

What is the current price of the stock?What is the current price of the stock?

4-7

(II) Constant Growth Dividend Model

Forecasted Dividends grow at a constant Forecasted Dividends grow at a constant raterateOnly need to forecast the dividend growth rate Only need to forecast the dividend growth rate

and not an indefinite number of dividendsand not an indefinite number of dividends

Stream of constant growing cash flows Stream of constant growing cash flows foreverforeverPrice equity as a Price equity as a growinggrowing perpetuityperpetuity

g)-(r

D =

g) -(r

g)+(1D = Price = PV 10

00

4-8Common Stock Valuation:Constant Growth Dividend Model

A firm A firm just paidjust paid a $10 per share dividend. a $10 per share dividend. Future dividends are expected to grow at Future dividends are expected to grow at an annual rate of 5% per year. The an annual rate of 5% per year. The required rate of return is 10% per year.required rate of return is 10% per year.

What is the current price of the stock?What is the current price of the stock?

4-9

For many firms (especially those in new or high-tech For many firms (especially those in new or high-tech industries), dividends are low and expected to grow industries), dividends are low and expected to grow rapidly. As product markets mature, dividends are rapidly. As product markets mature, dividends are then expected to slow to some “steady state” rate. then expected to slow to some “steady state” rate. How should stocks such as these be valued?How should stocks such as these be valued?

Answer: We return to the fundamental theory of value - the value Answer: We return to the fundamental theory of value - the value today equals the present value of all future cash flows.today equals the present value of all future cash flows.

Put another way, the Put another way, the non-constant growth modelnon-constant growth model suggests that suggests that

PP00 = present value of dividends in the non-constant growth = present value of dividends in the non-constant growth

period(s) + present value of dividends in the “steady period(s) + present value of dividends in the “steady state” period.state” period.

t

annuitygrowing r

g

gr

CPV

1

11

4-10(III) Differential Growth Dividend Model

Forecasted Dividends grow at a constant Forecasted Dividends grow at a constant rate, grate, g11 for a certain number of years and then for a certain number of years and then

grow at a second growth rate, ggrow at a second growth rate, g2.2.

Example:Example: The dividend of a company has The dividend of a company has just been paid out, and equals $1. During the just been paid out, and equals $1. During the next 18 years the dividend will grow at 14% next 18 years the dividend will grow at 14% per year. After this high growth period the per year. After this high growth period the dividend will grow at 10% per year forever. dividend will grow at 10% per year forever. What is the price of the stock if the required What is the price of the stock if the required return is 15%?return is 15%?

4-11

Answer

Create timeline with relevant dividendsCreate timeline with relevant dividends DD11=$1 x 1.14 = $1.14=$1 x 1.14 = $1.14

DD1818=$1 x (1.14)=$1 x (1.14)18 18 = $10.57= $10.57

DD1919=D=D1818 x (1.10)=$11.63 x (1.10)=$11.63

PV growing annuity with C=DPV growing annuity with C=D11, r = 15%, g=14%, r = 15%, g=14%

PVPVt=18t=18 growing perpetuity, with C=D growing perpetuity, with C=D1919, r = 15%, g=10%, r = 15%, g=10%

Discount perpetuity an additional 18 yearsDiscount perpetuity an additional 18 years

4-12

Rearranging the dividend growth model

PP00 = = DD11 / ( / (rr – – gg))

rr – – gg = = DD11 / / PP00

rr = = DD11 / / PP00 + + gg total return = dividend yield + capital gains yieldtotal return = dividend yield + capital gains yield

Dippy Inc. is selling for $20 and is Dippy Inc. is selling for $20 and is expected to pay a dividend of $1 next expected to pay a dividend of $1 next year, growing at 10% per year. What is the year, growing at 10% per year. What is the total return on this stock?total return on this stock?

Answer: $1 / $20 + 10% = 15%Answer: $1 / $20 + 10% = 15%