FUNDAMENTALS OF FINANCE

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Faculty of Business, Economics and Law

FUNDAMENTALS OF FINANCE

Lecture 4: Valuation of Shares

Presented by: Dr Balasingham Balachandran Professor of Finance Department of Finance, La Trobe Business School

Valuation of Shares

Learning Objectives

• Value a share as the present value of its expected future dividends.

• Understand the trade-off between dividends and growth in share valuation.

• Appreciate the limitations of valuing a share based on expected dividends.

• Value a share as the present value of the company’s total payout.

Valuation of Shares

Figure 7.1: Share price quote for JB Hi-Fi (JBH)

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Pearson

Australia

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Pearson

Australia

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564060/

Berk/Fu

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Valuation of Shares

4 These slides have been drafted by the La Trobe University Department of Finance based on Berk (2014).

 As is the case with debt, equity securities are valued by

calculating the present value of all cash flows generated,

consisting of dividends and the share price obtained

when the shares are sold in the market

 However, the future share price is based on the value of

future dividends to be received by the purchaser of the

shares, and the share price when it is sold to the next

investor, and so on

Valuation of shares

Valuation of Shares

Share Basics

 Ordinary share:

 Is a share of ownership in the corporation, which gives its owner rights to vote

on the election of directors, mergers, or other major events.

 As an ownership claim, ordinary shares carry the right to share in the

profits of the corporation through dividend payments.

 Dividends:

 Are periodic payments, usually in the form of cash that are made to

shareholders as a partial return on their investment in the corporation.

 Shareholders are paid dividends in proportion to the amount of shares

they own.

Valuation of Shares

 The logical conclusion is that the value of a share is given

by the present value of all future dividends that the

corporation is expected to pay:

Valuation of shares

where:

P0 = the price of the share at time 0

Divt = the dividend paid in period t

rE = the cost of the equity (required rate of return)

  0

1 1

n t

t t

Div P

r 

 

Valuation of Shares

 Dividends are unstable and unpredictable, and because

the life of equity is infinite, it is difficult to value shares in

practice

 In order to do so, analysts typically make assumptions

about the character of future dividends, giving rise to a

number of dividend valuation models

Dividend valuation models

Valuation of Shares

A One-Year Investor

 Two potential sources of cash flows from shares:

 The firm might pay out cash to its shareholders in the form of a

dividend.

 The investor might generate cash by selling the shares at some

future date.

 Future dividend payments and share price are unknown.

 Investors will be willing to pay a price up to that point that the

investment has a zero NPV – at which the current share price

equals the PV of the expected future dividend and sale price.

The Dividend-Discount Model

Valuation of Shares

The dividend-discount model

A one-year investor:

• Two potential sources of cash flows from owning a share:

• Dividends

• Selling shares

Valuation of Shares

A One-Year Investor

 As the expected cash flows are risky, we cannot discount them with the risk-free interest rate, but need to use the cost of capital for the firm’s equity.

 Equity Cost of Capital rE: The expected return of other investments available in the market with equivalent risk to the firm’s share.

 If current share prices are less than this amount, it would be a positive NPV investment.

 If the share price exceeds this amount, selling it would produce a positive NPV and the share price would quickly fall.

The Dividend-Discount Model

Valuation of Shares

 Valuing share price today:

 Present value of dividend in year 1 PLUS present value of share price (selling price) in year 1

A One-Year Investor

(Eq. 7.1 in your text book in page 196)

Valuation of Shares

 Dividend Yield: The expected annual dividend of the share divided by its current price.

 Capital Gain: The amount the investor will earn on the share, difference between the expected sale price and the original purchase price for an asset.

 Total Return: The sum of the dividend yield and the capital gain rate—the expected return that the investor will earn for a one- year investment in the share.

The Dividend-Discount Model

Valuation of Shares

 The expected total return of a stock should equal its equity cost of

capital – it should equal the expected return of other investments

available in the market with equivalent risk:

(Eq. 7.2 in your text book in page 196)

Total Return

The Dividend-Discount Model

Valuation of Shares

Problem:

 Suppose you expect Crazy Carlin’s to pay an annual dividend of $0.56 per share in the coming year and to trade $45.50 per share at the end of the year.

 If investments with equivalent risk to Crazy Carlin’s shares have an expected return of 6.80%, what is the most you would pay today for Crazy Carlin’s share?

 What dividend yield and capital gain rate would you expect at this price?

Example 1 Share prices and returns

Valuation of Shares

Solution:

Plan:

 We can use Eq. 7.1 to solve for the beginning price we would pay

now (P0) given our expectations about dividends (Div1=0.56) and

future price (P1=$45.50) and the return we need to expect to earn to

be willing to invest (rE=6.8%).

 We can then use Eq.7.2 to calculate the dividend yield and capital

gain.

(Eq. 7.1)

FORMULA!

Example.1 Share prices and returns

Valuation of Shares

Execute:

 Using Eq.7.1:

 Referring to Eq.7.2 we see that at this price, Crazy Carlin’s dividend

yield is:

Div1/P0 = 0.56/43.13 = 1.30%

 The expected capital gain is: $45.50 - $43.13 = $2.37 per share, for a

capital gain rate of 2.37/43.13 = 5.50%. 16

Example 1 Share prices and returns

Valuation of Shares

Evaluate:

 At a price of $43.13, Crazy Carlin’s expected total return is 1.30%

+ 5.50% = 6.80%, which is equal to its equity cost of capital.

 This amount is the most we would be willing to pay for the share.

 If we paid more, our expected return would be less than 6.8% and

we would rather invest elsewhere.

Example 1 Share prices and returns

Valuation of Shares

Problem:

 Suppose you expect Koch Industries to pay an annual

dividend of $2.31 per share in the coming year and to

trade $82.75 per share at the end of the year. If

investments with equivalent risk to Koch’s Share have an expected return of 8.9%, what is the most you would

pay today for Koch’s Share? What dividend yield and capital gain rate would you expect at this price?

Practice Question 1

Valuation of Shares

Practice Question 1

Execute:

• Referring to Eq. 7.2 we see that at this price, Koch’s dividend yield is Div1/P0 = 2.31/78.11 = 2.96%. The expected capital gain is $82.75

- $78.11 = $4.64 per share, for a capital gain rate of 4.64/78.11 =

5.94%.

P 0  Div

1  P

1 r E

 $2.31$82.75

1.089  $78.11

Valuation of Shares

Practice Question 1

Evaluate:

• At a price of $78.11, Koch’s expected total return is 2.96% + 5.94% = 8.90%, which is equal to its equity cost of capital (the return being

paid by investments with equivalent risk to Koch’s). This amount is the most we would be willing to pay for Koch’s Share. If we paid more, our expected return would be less than 8.9% and we would

rather invest elsewhere.

Valuation of Shares

A Multiyear Investor

 We now extend the intuition we developed for the one-year investor’s

return to a multiyear investor.

 Eq.7.1 depends upon the expected share price in one year, P1.

 But suppose we planned to hold the shares for two years. Then we

would receive dividends in both year 1 and year 2 before selling the

shares, as shown in the following timeline:

The Dividend-Discount Model

Valuation of Shares

 Setting the hare price equal to the present value of the future cash flows:

 As a two-year investor, we care about the dividend and share price in year 2.

 A one-year investor will care about them indirectly as they will affect the sale price at

the end of year 2.

(Eq. 7.3)

The Dividend-Discount Model

FORMULA!

Valuation of Shares

A single N-year investor - Dividend Discount Model.

 The price of the stock is equal to the present value of all of the

expected future dividends it will pay.

(Eq. 7.4)

The Dividend-Discount Model

FORMULA!

(Eq. 7.5)

Valuation of Shares

Constant Dividend Growth Model

 A constant used approximation is to assume that dividends will grow at a

constant rate, g, forever.

 The value of the firm depends on the dividend level of next year,

divided by the equity cost of capital adjusted by the growth rate.

(Eq. 7.6 in your text book in page 199)

Estimating Dividends in the Dividend-Discount Model

FORMULA!

Constant dividend growth model

Valuation of Shares

 There are two critical features of this formula that need

to be understood to apply it correctly

 First, the model does not take into account any dividend

that has just been paid (i.e. Div0, the dividend at time 0)

 Second, the model assumes that the equity cost of

capital must be greater than the growth rate (i.e. rE > g)

– otherwise the value of the stock is negative, which

makes no sense

Constant dividend growth model

Valuation of Shares

Problem:

 Greta’s Garbos is a waste collection company.

 Suppose Greta’s Garbos plans to pay $2.30 per share in

dividends in the coming year.

 If its equity cost of capital is 7% and dividends are expected to

grow by 2% per year in the future, estimate the value of Greta’s

Garbos shares.

Example 2 Valuing a firm with constant dividend growth

Valuation of Shares

Solution:

Plan:

 Because the dividends are expected to grow perpetually at a constant

rate, we can use Eq.7.6 to value Greta’s Garbos.

 The next dividend (Div1) is expected to be $2.30, the growth rate (g)

is 2% and the equity cost of capital (rE) is 7%.

Execute:

Example 2 Valuing a firm with constant dividend growth

Valuation of Shares

Evaluate:

 You would be willing to pay 20 times this year’s dividend of

$2.30 to own Greta’s Garbos shares because you are buying a

claim to this year’s dividend and to an infinite growing series of

future dividends.

Example 2 Valuing a firm with constant dividend growth

Valuation of Shares

 Suppose Target Corporation plans to pay $0.68 per

share in dividends in the coming year. If its equity cost

of capital is 10% and dividends are expected to grow

by 8.4% per year in the future, estimate the value of

Target’s share.

Practice Question 2

Valuing a firm with constant dividend growth

Valuation of Shares

Solution:

Plan:

• Because the dividends are expected to grow

perpetually at a constant rate, we can use Eq. 7.6 to

value Target. The next dividend (Div1) is expected to

be $0.68, the growth rate (g) is 8.4% and the equity

cost of capital (rE) is 10%.

Practice Question 2

Valuing a firm with constant dividend growth

Valuation of Shares

 Execute:

Practice Question 2

Valuing a firm with constant dividend growth

P 0  Div

r E  g

 $0.68

.10 .084  $42.50

Evaluate:

•You would be willing to pay 62.5 times this year’s dividend of $0.68 to own Target share because you are

buying claim to this year’s dividend and to an infinite growing series of future dividends.

Valuation of Shares

Dividend vs. investment and growth

 Often firms face a trade-off: increasing growth may require investment, and money spent on investment cannot be used to pay dividends.

 What determines the rate of growth of a firm’s dividend?

 We can define a firm’s dividend payout rate as the fraction of earnings that the firm pays as dividends each year:

(Eq. 7.8 in page 200)

Estimating Dividends in the Dividend-Discount Model

Valuation of Shares

Dividend payout rate

 The firm’s dividend each year is equal to the firm’s earnings per share (EPS) multiplied by its dividend payout rate.

 The firm can, therefore, increase its dividend in three ways:

1. It can increase its earnings (net income).

2. It can increase its dividend payout rate.

3. It can decrease its number of shares outstanding.

Estimating Dividends in the Dividend-Discount Model

Valuation of Shares

A simple model of growth

 A firm can do two things with its earnings: it can pay them out to

investors, or it can retain and invest them.

 If all increases in future earnings result exclusively from new

investment made with retained earnings, then:

(Eq. 7.9 in page 201)

FORMULA!

Estimating Dividends in the Dividend-Discount Model

Change in earnings = New

investment x

Return on new

investment

Valuation of Shares

Retention rate

 New investment equals the firm’s earnings multiplied by its

retention rate, or the fraction of current earnings that the firm

retains:

(Eq. 7.10 in page 201)

FORMULA!

Estimating Dividends in the Dividend-Discount Model

New Investment = Earnings x Retention rate

Valuation of Shares

 Substituting Eq.7.10 into Eq.7.9 and dividing by earnings gives

an expression for the growth rate of earnings:

 The equation shows that a firm can increase its growth by

retaining more of its earnings, but will have to reduce its

dividends.

(Eq. 7.11)

Estimating Dividends in the Dividend-Discount Model

FORMULA!

Earnings growth rate = Change in Earnings

Earnings

g = Retention

rate x

Return on new

investment (Eq. 7.12)

Valuation of Shares

Estimating the growth rate

Example 3:

In the year ended December 2007, National Australia Bank generated

EPS of 269 cents, paid a dividend of 182 cents per share, and its

return on new investment was estimated at 17%. What is the

expected future earnings and dividend growth rate?

Valuation of Shares

Estimating the growth rate

Example:

In the year ended December 2007, National Australia Bank generated

EPS of 269 cents, paid a dividend of 182 cents per share, and its

return on new investment was estimated at 17%. What is the

expected future earnings and dividend growth rate?

  %5.5055.017.068.01 investment on Returnrate Retention



g

68.0269182ratioPayout 

Valuation of Shares

 An alternative approach to estimating the growth

is based on historical dividends

 If we can assume that historical dividends are a

good indication of future dividends, the historical

growth rate can be used as an estimate of the

future growth rate

 This involves finding the geometric average

growth rate of previous dividends

Estimating the growth rate

Valuation of Shares

4.40

dn=d0(1+g) n

We can do this by taking the equation for the future value of a single amount:

Estimating the growth rate

1 0

 n n

d g

Valuation of Shares

Estimating the growth rate

Example 4:

The table at right shows the dividends paid

by XYZ Ltd at the end of each of the years

shown. What is the geometric average

historic growth rate of dividends? What is

the value of an XYZ share at the end of

2009, if this growth will continue forever

and the required rate of return is 15%?

Year Dividend

2005 $1.19

2006 $1.32

2007 $1.40

2008 $1.55

2009 $1.68

Valuation of Shares

Estimating the growth rate

Example:

The table at right shows the dividends paid

by XYZ Ltd at the end of each of the years

shown. What is the geometric average

historic growth rate of dividends? What is

the value of an XYZ share at the end of

2009, if this growth will continue forever

and the required rate of return is 15%?

Year Dividend

2005 $1.19

2006 $1.32

2007 $1.40

2008 $1.55

2009 $1.68

%91 19.1

68.1 1 4

 n n

d g

Valuation of Shares

Estimating the growth rate

Example:

The table at right shows the dividends paid

by XYZ Ltd at the end of each of the years

shown. What is the geometric average

historic growth rate of dividends? What is

the value of an XYZ share at the end of

2009, if this growth will continue forever

and the required rate of return is 15%?

Year Dividend

2005 $1.19

2006 $1.32

2007 $1.40

2008 $1.55

2009 $1.68

    52.30$

09.015.0

09.168.11 01

0 

 



 

 

gDiv

Div P

Valuation of Shares

 Crane Sporting Goods expects to have earnings per share of $6 in the coming

year. Rather than reinvest these earnings and grow, the firm plans to pay out all

of its earnings as a dividend.

 With these expectations of no growth, Crane’s current share price is $60.

 Suppose Crane could cut its dividend payout rate to 75% for the foreseeable future and use the retained earnings to open new stores.

 The return on investment in these stores is expected to be 12%.

 If we assume that the risk of these new investments is the same as the risk of its existing investments, then the firm’s equity cost of capital is unchanged.

 What effect would this new policy have on Crane’s share price?

Example 5 Cutting dividends for profitable growth

Valuation of Shares

Solution:

Plan:  We need to calculate its equity cost of capital and determine Crane’s dividend

and growth rate under the new policy.

 Because we know that Crane currently has a growth rate of 0 (g = 0), a dividend of $6 and a price of $60, we can use Eq.7.7 to estimate rE.

 Next, the new dividend will simply be 75% of the old dividend of $6.

 Finally, given a retention rate of 25% and a return on new investment of 12%, we can calculate the new growth rate (g) and calculate the price of Crane’s shares if it institutes the new policy.

Example 5 Cutting dividends for profitable growth

Valuation of Shares

Execute:

 Using Eq.7.7 to estimate rE we have:

 In other words, to justify Crane’s share price under its current policy, the

expected return of other shares with equivalent risk must be 10%.

 Next, we consider the new dividend policy.

 If Crane reduces its dividend payout rate to 75%, then from Eq.7.8 its

dividend this coming year will fall to Div1= EPS1 x 75% = $6 x 75% =

$4.50.

Example 5 Cutting dividends for profitable growth

Valuation of Shares

Execute (cont’d):

 At the same time, because the firm will now retain 25% of its earnings to

invest in new stores, its growth rate will increase to:

g = Retention rate x Return on new investment = 25% x 12% = 3%

 Assuming Crane can continue to grow at this rate, we can calculate its

share price under the new policy using the constant dividend growth

model:

Example 5 Cutting dividends for profitable growth

Valuation of Shares

Evaluate:

 Crane’s share price should rise from $60 to $64.29 if the company

cuts its dividend in order to increase its investment and growth,

implying that the investment has positive NPV.

 By using its earnings to invest in projects that offer a rate of return

(12%) greater than its equity cost of capital (10%), Crane has

created value for its shareholders.

Example 5 Cutting dividends for profitable growth

Valuation of Shares

 Prime World (PW) expects to have earnings per share of $0.48 in the

coming year. Rather than reinvest these earnings and grow, the firm

plans to pay out all of its earnings as a dividend. With these

expectations of no growth, PW’s current share price is $10.

 Suppose PW could cut its dividend payout rate to 67% for the

foreseeable future and use the retained earnings to expand. The return

on investment in the expansion is expected to be 11%. If we assume

that the risk of these new investments is the same as the risk of its

existing investments, then the firm’s equity cost of capital is unchanged. What effect would this new policy have on PW’s share price?

Practice Question 3

Cutting dividends for profitable growth

Valuation of Shares

Solution:

Plan:

• To figure out the effect of this policy on PW’s share price, we need to know several things. First, we need to compute its equity cost of

capital. Next we must determine PW’s dividend and growth rate under the new policy.

• Because we know that PW currently has a growth rate of 0 (g = 0), a

dividend of $0.48 and a price of $10, we can use Eq. 7.7 to estimate rE.

Practice Question 3

Cutting dividends for profitable growth

Valuation of Shares

• Next, the new dividend will simply be 67% of the old dividend of $0.48.

Finally, given a retention rate of 33% and a return on new investment

of 11%, we can use Eq. 7.12 to compute the new growth rate (g).

Finally, armed with the new dividend, PW’s equity cost of capital, and its new growth rate, we can use Eq. 7.6 to compute the price of PW’s shares if it institutes the new policy.

Practice Question 3

Cutting dividends for profitable growth

Valuation of Shares

Execute:

• Using Eq. 7.7 to estimate rE we have:

• In other words, to justify PW’s share price under its current policy, the expected return of other stocks in the market with

equivalent risk must be 4.8%.

Practice Question 3

Cutting dividends for profitable growth

r E  Div

P 0

 g  $0.48

$10  0  4.8% 0% 4.8%

Valuation of Shares

Execute (cont’d):

• Next, we consider the consequences of the new policy. If PW reduces

its dividend payout rate to 67%, then from Eq. 7.8 its dividend this

coming year will fall to Div1 = EPS1 x 67% = $0.48 x 67% = $0.32.

• At the same time, because the firm will now retain 33% of its earnings to

invest in new stores, from Eq. 7.12 its growth rate will increase to:

Practice Question 3

Cutting dividends for profitable growth

g = Retention Rate ´ Return on New Investment = 33%´11% = 3.63%

Valuation of Shares

Execute (cont’d):

Assuming PW can continue to grow at this rate, we can compute its share

price under the new policy using the constant dividend growth model of

Eq. 7.6.

Practice Question 3

Cutting dividends for profitable growth

P 0  Div

r E  g

 $0.32

.048 .0363  $27.35

Valuation of Shares

Evaluate:

• PW’s share price should rise from $10 to $27.35 if the company cuts its dividend in order to increase its investment and growth, implying that the

investment has positive NPV. By using its earnings to invest in projects

that offer a rate of return (11%) greater than its equity cost of capital

(4.8%), PW has created value for its shareholders.

Practice Question 3

Cutting dividends for profitable growth

Valuation of Shares

 One common assumption is that dividends will remain

constant, in which case the dividend stream constitutes

a perpetuity

 The value of such a share is given by:

Constant dividend model

Div P

r 

where:

P0 = the current price of the share

Div = the (constant) dividend per period

Valuation of Shares

Constant dividend model

Example 6:

If the required rate of return on a share is 12.5%, the share has

just paid an annual dividend of 30 cents, and this dividend is

expected to remain constant forever, what is the value of the

share?

Valuation of Shares

Constant dividend model

Example:

If the required rate of return on a share is 12.5%, the share has

just paid an annual dividend of 30 cents, and this dividend is

expected to remain constant forever, what is the value of the

share?

0.30 $2.40

0.125 E

Div P

r   

Valuation of Shares

Constant dividend model

Example 7:

Boral Ltd traded at $5.79 on 12 March 2008. The cash dividend

by Boral in the previous year was around 49 cents per share.

What discount rate was being applied by Boral’s investors?

Valuation of Shares

Constant dividend model

Example:

Boral Ltd traded at $5.79 on 12 March 2008. The cash dividend

by Boral in the previous year was around 49 cents per share.

What discount rate was being applied by Boral’s investors?

0.49 5.79

0.0846 8.46%

E E

Div P

r r

  

  

Valuation of Shares

Constant dividend growth model

Example 8:

If the required rate of return on a share is 12.5%, the share has

just paid an annual dividend of 30 cents, and this dividend is

expected to grow at 5% p.a. in perpetuity, what is the value of the

share?

Valuation of Shares

Constant dividend growth model

Example:

If the required rate of return on a share is 12.5%, the share has

just paid an annual dividend of 30 cents, and this dividend is

expected to grow at 5% p.a. in perpetuity, what is the value of the

share?

   01 0

1 0.30 1.05 $4.20

0.125 0.05 E E

Div gDiv P

r g r g

    

  

Valuation of Shares

 Sometimes it is expected that the dividend stream will

settle down in the future to a constant dividend, or a

constantly growing dividend

 In the meantime, the dividends might follow a different

pattern, or no pattern

Uneven dividend streams

Valuation of Shares

 As always, the value of the share is the present value of

all future dividends

 The dividend stream is broken down into two

components:

 The predictable pattern (e.g. a perpetuity or growing

perpetuity) that begins some time in the future

 The dividends that are received between now and then

Uneven dividend streams

Valuation of Shares

Changing growth rates

 Successful young firms have very high initial growth rates and often

retain 100% of their earnings to exploit investment opportunities.

 As they mature, growth slows, earnings exceed their investment

needs and they begin to pay dividends.

 We cannot use the constant dividend model to value such a firm for

two reasons:

1. These firms often pay no dividends when they are young.

2. Their growth rate continues to change over time until they mature.

Estimating Dividends in the Dividend-Discount Model

Valuation of Shares

Uneven dividend streams

Example 9:

What is the value of a share that is expected to pay a dividend of

45 cents in one year, 60 cents in 2 years and 75 cents in three

years? The dividend is then expected to remain constant (at 75

cents) in perpetuity. The required rate of return is 9% p.a.

 This dividend stream can be broken down into two

components:

 Div1 and Div2, each of which must be discounted

 All dividends from Div3 onward, which can be valued using the

constant dividend model

Valuation of Shares

Uneven dividend streams

0 2 3 1

Div1 = 0.45 Div2 = 0.60 Div3 = 0.75

The present value of Div1 is given by

The present value of Div2 is given by

The present value of all dividends

from Div3 onward is given by

4128.0 09.1

45.0 

5050.0 09.1

60.0 2 

3333.8 09.0

75.0 

Valuation of Shares

Uneven dividend streams

0 2 3 1

Div1 = 0.45 Div2 = 0.60 Div3 = 0.75

 However, note that because the first dividend used in the

model is Div3, the present value calculated using the

model applies to year 2

 This must then be discounted

by 2 periods to find the

present value at year 0: 0140.7

09.1

3333.8 2



Valuation of Shares

Uneven dividend streams

0 2 3 1

Div1 = 0.45 Div2 = 0.60 Div3 = 0.75

The complete calculation in this case is therefore:

   

93.7$ 09.1

09.0

75.0

09.1

60.0

09.1

45.0

21 0



 

 

 

EEEE rr

Div

Div P

Valuation of Shares

   

93.7$ 09.1

09.0

75.0

09.1

60.0

09.1

45.0

21 0



 

 

 

EEEE rr

Div

Div P

Uneven dividend streams

0 2 3 1

Div1 = 0.45 Div2 = 0.60 Div3 = 0.75

The complete calculation in this case is therefore:

Valuation of Shares

Uneven dividend streams

0 2 3 1

Div1 = 0.45 Div2 = 0.60 Div3 = 0.75

The complete calculation in this case is therefore:

   

93.7$ 09.1

09.0

75.0

09.1

60.0

09.1

45.0

21 0



 

 

 

EEEE rr

Div

Div P

Valuation of Shares

Example 10 – Non Constant Growth

A company has just paid a dividend of 15 cents

per share and that dividend is expected to grow at

a rate of 20% per annum for the next 3 years and

at a rate of 5% per annum forever after that.

Assuming a required rate of return of 10%,

calculate the current market price of the share.

Valuation of Shares

Non-Constant Growth 4 step Approach

 Step 1

Calculate the value of the

dividends at the end of

each year, Dt (during the

initial growth period)

 Note: D1=D0(1+g) 1

and D0 = 0.15

YEAR EXPECTED

DIVIDEND

1 D1=0.15(1.2) 1

= 0.18

2 D2=0.15(1.2) 2

=0.216

3 D3=0.15(1.2) 3

=0.2592

Valuation of Shares

0 1 2 3 4 t

D1 D2 D3

Step 2: Discounting

PV(D1)

PV(D2)

PV(D3) Step 2: Discounting

PV(D1)

Step 2: Discounting

PV(D2)

PV(D3)

PV(D1)

Step 2: Discounting

Non-Constant Growth 4 step Approach

Valuation of Shares

Non-Constant Growth 4 step Approach

 Step 2

Find the PV of expected dividends during the

initial growth period.

Year Expected

Dividend

1 0.18 PV(D0) = 0.18/(1.10) 1 = 0.164

2 0.216 PV(D0) = 0.216/(1.10) 2 = 0.179

3 0.2592 PV(D0) = 0.2592/(1.10) 3 =0.195

Valuation of Shares

Non-Constant Growth 4 step Approach

Step 3

Find the value of the share at the end of the initial

growth period.

Note: the share reverts to its long run historical growth rate in year 4. Therefore we

need to determine the price at the end of the initial growth phase which occurs at the

end of period 3.

Valuation of Shares

Non-Constant Growth 4 step Approach

Step 4

Determine the PV of the price found in step 3

and then sum this to the PV of dividends found

in step 2.

Valuation of Shares

Non-Constant Growth Valuation

Valuation of Shares

Limitations of the DDM

Non-dividend-paying stocks:

• Many companies do not pay dividends, thus the dividend- discount model must be modified.

 Uncertainty is associated with forecasting a firm’s future dividends.

Estimating Dividends in the Dividend-Discount Model

Valuation of Shares

Limitations of the DDM

 Uncertainty is associated with forecasting a firm’s future dividends.

 Let’s consider an example, where a firm pays annual dividends of

$0.72.

 With an equity cost of capital of 11% and expected dividend growth of

8%, the DDM implies a share price of:

 With a 10% growth rate however, this estimate would rise to $72 per

share; with a 5% growth rate it would fall to $12 per share.

Estimating Dividends in the Dividend-Discount Model

Valuation of Shares

Figure Share prices for different expected growth rates

Valuation of Shares

Share Repurchase and the total payout model

 So fare we assumed that cash paid out to the shareholders takes the

form of a dividend.

 In recent years, an increasing number of firms have replaced

dividend payouts with share repurchases.

 In a share repurchase, the firm uses excess cash to buy back its own

shares, which reduces cash available for dividends and decreases

the number of shares on issue, increasing its earnings and dividends

per share basis.

Total Payout and Free Cash Flow Valuation Models

Valuation of Shares

 In the dividend-discount model, we valued a share from the

perspective of a single shareholder, discounting the dividends the

shareholder will receive:

P0 = PV (Future dividends per share)

(Eq.7.14)

Share Repurchase and the total payout model

FORMULA!

Valuation of Shares

Total Payout Model

 The total payout model values the firm’s equity instead of a single

(Eq. 7.15)

Total Payout Model

P0 = PV ( Future total dividends and repurchases)

Shares outstanding 0

FORMULA!

Valuation of Shares

Problem:

 Titan Industries has 217million shares outstanding and expects

earnings at the end of this year of $860million.

 Titan plans to pay out 50% of its earnings in total, paying 30% as a

dividend and using 20% to repurchase shares.

 If Titan’s earnings are expected to grow by 7.5% per year and these

payout rates remain constant, determine the share price assuming an

equity cost of capital of 10%.

Example 11 Valuation with share repurchases

Valuation of Shares

Solution:

Plan:

 Based on the equity cost of capital of 10% and an expected earnings growth rate of 7.5% we can calculate the present value of Titan’s future payouts as a constant growth perpetuity.

 The only input missing here is Titan’s total payouts this year, which we can calculate as 50% of its earnings.

 The PV of all of Titan’s future payouts is the value of its total equity.

Example 11 Valuation with share repurchases

Valuation of Shares

Execute:

 Titan will have total payouts this year of: 50% x $860 million = $430 million

 Using the constant growth perpetuity formula:

 To calculate the share price, we divide by the current number of shares

outstanding:

PV (Future total dividends

and repurchases) =

$430 M = 17.2 billion

0.10 – 0.075

Example 11 Valuation with share repurchases

Valuation of Shares

Evaluate:

 Using the total payout method, we did not need to know the firm’s split between dividends and share repurchases.

 To compare this method with the dividend-discount model, note that Titan will pay a dividend of 30% x $860 million/(217 million shares) = $1.19 per share, for a dividend yield of 1.19/79.26 = 1.50%.

 From Eq.7.7, dividend and share price growth rate is g = rE – Div1/P0= 8.50%.

 This growth rate exceeds the 7.50% growth rate of earnings as Titan’s share count will decline over time owing to its share repurchases.

Example 11 Valuation with share repurchases

Valuation of Shares

Problem:

 3M Co. has 698 million shares outstanding and expects

earnings at the end of this year of $2.96 billion. 3M plans to

pay out 50% of its earnings in total, paying 25% as a

dividend and using 25% to repurchase shares. If 3M’s earnings are expected to grow by 9.2% per year and these

payout rates remain constant, determine 3M’s share price assuming an equity cost of capital of 12%.

Practice Question 4

Valuation of Shares

Solution:

Plan:

• Based on the equity cost of capital of 12% and an expected earnings

growth rate of 9.2% we can compute the present value of 3M’s future payouts as a constant growth perpetuity. The only input missing here

is 3M’s total payouts this year, which we can calculate as 50% of its earnings. The present value of all of 3M’s future payouts is the value of its total equity. To obtain the price of a share, we divide the total

value by the number of shares outstanding (698 million).

Practice Question 4

Valuation of Shares

Execute:

• 3M will have total payouts this year of 50% x $2.96 billion = $1.48

billion. Using the constant growth perpetuity formula, we have:

• This present value represents the total value of 3M’s equity (i.e. its market capitalisation). To compute the share price, we divide by the

current number of shares outstanding:

Practice Question 4

PV(Future Total Dividends and Repurchases) = $1.48 billion

.12 - .092 = $52.86 billion

P 0

= $52.86 billion

698 million shares = $75.73 per share

Valuation of Shares

Evaluate:

• Using the total payout method, we did not need to know the firm’s split between dividends and share repurchases. To compare this

method with the dividend-discount model, note that 3M will pay a

dividend of 25% x $2.96 billion/(698 million shares) = $1.06 per share,

for a dividend yield of $1.06/$75.73 = 1.40%. From Eq. 7.7, 3M’s expected EPS, dividend, and share price growth rate g = rE – Div1/P0 =

12% – 1.4% = 10.6%. This growth rate exceeds the 9.2% growth rate

of earnings because 3M’s share count will decline over time owing to its share repurchases.

Practice Question 4

Valuation of Shares

How would an investor decide whether to buy or sell a

share?

• She would value the share using her own expectations.

• If her expectations were substantially different, she might conclude that the share was over- or under-priced.

• Based on that conclusion, she would buy or sell the share.

Putting it all together

Valuation of Shares

How could a share suddenly be worth more or less after an

earnings announcement?

• As investors digest the news, they update their expectations and buying or selling pressure would then drive the share

price up or down until the buys and sells came into balance.

Putting it all together

Valuation of Shares

What should managers do to raise the share price further?

• The only way to raise the share price is to make value- increasing decisions.

Putting it all together

Valuation of Shares

Lecture Quiz

1. What discount rate do you use to discount the future cash flows of a share?

2. What are three ways that a firm can increase the amount of its future dividend per share?

3. What are the main limitations of the dividend-discount model?

4. How does the total payout model address part of the dividend- discount model’s limitations?