equity markets and share valuation chapter 7. key concepts and skills understand how stock prices...

Equity markets and share valuation

Chapter 7

Key concepts and skills

• Understand how stock prices depend on future dividends and dividend growth

• Be able to compute stock prices using the dividend growth model

• Understand how corporate directors are elected

• Understand how stock markets work• Understand how stock prices are quoted

7-2Copyright 2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al. Slides prepared by David E. Allen and Abhay K. Singh

Chapter outline

• Ordinary share valuation• Some features of ordinary and preference

shares• The share markets


Cash flows for stockholders

• If you own a share of stock, you can receive cash in two ways:1. The company pays dividends.2. You sell your shares, either to another investor in

the market or back to the company.• As with bonds, the price of the stock is the

present value of these expected cash flows.– Dividends → cash income– Selling → capital gains


One-period example

• Suppose you are thinking of purchasing the stock of Moore Oil Inc. – You expect it to pay a $2 dividend in one year. – You believe you can sell the stock for $14 at

that time. – You require a return of 20% on investments of

this risk. – What is the maximum you would be willing to

pay?


One-period example (cont.)• D1 = $2 dividend expected in one year

• R = 20%• P1 = $14

• CF1 = $2 + $14 = $16

• Compute the PV of the expected cash flows

• Calculator:• 16 [FV]; 20 [I/Y]; 1 [N]; [CPT] [PV] = -13.33

33.13$20.1

)142(P0


Two-period example• Now, what if you decide to hold the share for two years? • In addition to the dividend in one year, you expect a dividend of

$2.10 and a share price of $14.70 at the end of year 2. Now how much would you be willing to pay?

• Calculator:• CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1;

• [NPV]; I = 20; [CPT][NPV] = $13.33

33.13$)20.1(

)70.1410.2(

20.1

2P

20


Three-period example• What if you decide to hold the stock for three years? • In addition to the dividends at the end of years 1 and 2, you

expect to receive a dividend of $2.205 at the end of year 3 and a share price of $15.435.

• Now how much would you be willing to pay?

• Calculator:• CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 =

17.64; F03 = 1;• [NPV]; I = 20; [CPT] [NPV] = $13.33

33.13$)20.1(

)435.15205.2(

)20.1(

10.2

20.1

2P

320


Developing the model

• You could continue to push back when you would sell the share.

• You would find that the price of the share is really just the present value of all expected future dividends.


Stock value = PV of dividends

P0 =(1+R)1 (1+R)2 (1+R)3 (1+R)∞

D1 D2 D3 D∞+ + +…+

10 )1(t

tt

R

DP

How can we estimate all future dividend payments?


Estimating dividends: Special cases

• Constant dividend– The firm will pay a constant dividend forever– This is like a preference share– The price is computed using the perpetuity

formula• Constant dividend growth

– The firm will increase the dividend by a constant percentage every period

• Supernormal growth– Dividend growth is not consistent initially, but

settles down to constant growth eventually


Zero growth

• If dividends are expected at regular intervals forever, this is like a preference share and is valued as a perpetuity– P0 = D/R

• Suppose a share is expected to pay a $0.50 dividend every half-year and the required return is 10% with half-yearly compounding. What is the price?– P0 = .50 / (0.1 / 2) = $10


Constant growth stock

• Dividends are expected to grow at a constant percentage per period.

– D1 = D0(1+g)1

– D2 = D0(1+g)2

– Dt = Dt(1+g)t

– D0 = Dividend JUST PAID

– D1 – Dt = Expected dividends7-13

Copyright 2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al. Slides prepared by David E. Allen and Abhay K. Singh

Dividend growth model (DGM)

P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …

P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + … (‘with a constant dividend growth’ g)

1

00 )1(

)1(

tt

t

R

gDP

g-R

D

g-R

g)1(DP 10

0


DGM—Example 1• Suppose Outback Ltd just paid a dividend of

$0.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the share be selling for?

• D0= $0.50• g = 2%• R = 15%

92.3$02.15.

)02.1(50.0P

gR

)g1(DP

0

00


DGM—Example 2

• Suppose Deep Pirates Ltd is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?– D1 = $2.00

– g = 5%– r = 20%

33.13$05.20.

00.2P

gR

DP

0

10


Share price sensitivity to dividend growth (g)

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Sto

ck P

rice

D1 = $2; R = 20%


Share price sensitivity to required return (R)

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25 0.3

Growth Rate

Sto

ck P

rice

D1 = $2; g = 5%


Example 7.3—Gordon Growth Company I

• Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.

• What is the current price?

• Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g.

40$06.16.

00.4P

gR

DP

0

10


Example 7.3—Gordon Growth Company II

• What is the price expected to be in year 4?– P4 = D4(1 + g) / (R – g) = D5 / (R – g)– P4 = 4(1+.06)4 / (.16 - .06) = 50.50

• What is the implied return given the change in price during the 4-year period?– 50.50 = 40(1+return)4; return = 6%– -40[PV]; 50.50[FV]; 4[N]; [CPT][I/Y] = 6%

• The price grows at the same rate as the dividends.


Constant growth model conditions

1. Dividend expected to grow at g forever.2. Stock price expected to grow at g forever.3. Expected dividend yield is constant.4. Expected capital gains yield is constant and

equal to g.5. Expected total return, R, must be > g.6. Expected total return (R):

= expected dividend yield (DY) + expected growth rate (g) = dividend yield + g


Non-constant growth problem statement

• Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the share?

• Remember that we have to find the PV of all expected future dividends.


Non-constant growth problem—Solution

• Compute the dividends until growth levels off– D1 = 1(1.2) = $1.20– D2 = 1.20(1.15) = $1.38– D3 = 1.38(1.05) = $1.449

• Find the expected future price– P2 = D3 / (R – g) = 1.449 / (.2 - .05) = $9.66

• Find the present value of the expected future cash flows– P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = $8.67


Non-constant + Constant growth

• Basic PV of all future dividends formula


R

D

R

D

R

D

R

DP

1. . .

111 33

22

11

0

Dividend growth model

gR

DP tt 1

Non-constant + Constant growth (cont.)


22

22

11

0 )1(11 R

P

R

D

R

DP

gR

DP

then 2,t after constant g If

)R1(

DP Because

32

3tt

t2

Non-constant growth followed by constant growth


0

1.0000

0.9583

6.7083

1 2 3rs=20%

8.6667 = P0

g = 20% g = 15% g = 5%

D0 = 1.00 1.20 1.38 1.449

$1.449P2 = ^

0.20 – 0.05= $9.66

Quick quiz: Part 1

• What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?

• What if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return remains at 15%.


33.13$15.

00.20 P

17.17$03.15.

)03.1(00.2P0

Using the DGM to find R

• Start with the DGM:


gP

D g

P

g)1(D R

g-R

D

g - R

g)1(DP

0

1

0

0

100

Rearrange and solve for R:

Finding the required return— Example

• Suppose a firm’s shares are selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?– R = [1(1.05)/10.50] + .05 = 15%

• What is the dividend yield?– 1(1.05) / 10.50 = 10%

• What is the capital gains yield?– g = 5%


Summary of share valuationTable 7.1


Features of ordinary shares

• Voting rights– Stockholders elect directors– Cumulative voting vs straight voting– Proxy voting

• Classes of share– ‘One share, one vote’


Features of ordinary shares (cont.)

• Other rights– Share proportionally in declared

dividends– Share proportionally in remaining assets

during liquidation– Pre-emptive right

• Right of first refusal to buy new stock issue to maintain proportional ownership if desired


Dividend characteristics

• Dividends are not a liability of the firm until declared by the Board of Directors– A firm cannot go bankrupt for not declaring

dividends

• Dividends and taxes– Dividends are not tax deductible for a firm– Taxed as ordinary income for individuals – Dividends received by corporations have a

minimum 100% exclusion from taxable income7-33

Copyright 2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al. Slides prepared by David E. Allen and Abhay K. Singh

Features of preference shares

• Dividends– Stated dividend must be paid before dividends

can be paid to ordinary shareholders– Dividends are not a liability of the firm and

preference dividends can be deferred indefinitely

– Most preference dividends are cumulative— any missed preference dividends have to be paid before ordinary dividends can be paid

• Preference shares generally do not carry voting rights


The share markets

• Primary vs secondary markets– Primary = new-issue market– Secondary = existing shares traded among

investors• Dealers vs brokers

– Dealer: Maintains an inventory Ready to buy or sell at any time Think ‘Used car dealer’

– Broker: Brings buyers and sellers together Think ‘Real estate broker’


Australian Stock Exchange (ASX)• Australian Stock Exchange (ASX)—1987

– Result of amalgamation of state-based exchanges• 1987—Introduction of Stock Exchange Automated

Trading System (SEATS)• 1998—Demutualisation of ASX• 2006—Merger with Sydney Futures Exchange and

now called Australian Securities Exchange • New Zealand Stock Exchange

– Created in 1974– 1991—Introduction of Computer Based Trading

System– Demutualised in 2002


ASX and NZX operations• Operational goal = Attract order flow• Both ASX and NZX are auction markets

– Agency trading—Brokers buying and selling for clients

– Principal trading—Brokers buying and selling their own accounts

• Orders– Limit order—specified sell/buy price– Market order—at best market price

• Trading in both ASX and NZX takes place on computer network


Share market reportingFigure 7.2


Work the Web

• Click on the information icon to go to <http://markets.smh.com.au/apps/qt/index.ac>

• Search for other equities like the one in the last example

• Understand the reported figures


http://markets.smh.com.au/apps/qt/index.ac



Quick quiz: Part 2

• You observe a share price of $18.75. You expect a dividend growth rate of 5% and the most recent dividend was $1.50. What is the required return?

• What are some of the major characteristics of ordinary shares?

• What are some of the major characteristics of preference shares?

7-40Copyright 2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E. Allen and Abhay K. Singh.

Chapter 7

7-41

END

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