© 2003 The McGraw-Hill Companies, Inc. All rights reserved.

Stock Valuation

Chapter

Eight

8.2 Chapter Outline

Common Stock Valuation Common Stock Features Preferred Stock Features Stock Market Reporting

8.3 Cash Flows for Shareholders 8.1

If you buy a share of stock, you can receive cash in two ways Dividends Selling your shares

As with any asset, the market price of common stock is equal to the present value of the expected future cash flows the stock will generate

8.4 One Period Example

Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?

Compute the PV of the expected cash flows

33.13$20.1

142

1

r

PriceSaleDivPV 1

StockCalculator Approach16 FV0 PMT1 N20 IPV $13.33

8.5 Two Period Example

Now what if you decide to hold the stock for two years? In addition to the $2 dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay now?

33.13$20.1

70.1410.2

20.1

2

11

2

22

r

PriceSaleDiv

r

DivPV 1

StockCalculator Approach0 CFj

2 CFj

16.80 CFj20 I2nd NPV $13.33

8.6 Three Period Example

Finally, what if you decide to hold the stock for three periods? 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 stock price of $15.435. Now how much would you be willing to pay?

33.13$20.1

435.15205.2

20.1

10.2

20.1

2

1

Pr

11

32

33

22

r

iceSaleDiv

r

Div

r

DivPV 1

Stock

Calculator Approach0 CFj

2 CFj

2.10 CFj17.64 CFj20 I2nd NPV $13.33

8.7 Developing The Model

We could continue this process for many time periods In fact, the price of the stock is just the present value of all

expected future dividends So, how can we estimate all future dividend payments?

8.8 Estimating Dividends: Special Cases

Constant dividend The firm will pay a constant dividend forever Market instrument – preferred stock Price is computed using the level perpetuity formula [PV = C/r]

Constant dividend growth The firm will increase the dividend by a constant percent every

period Market instrument – common stock Price is computed using a growing perpetuity formula

[PV = C/(r-g)]

Supernormal growth Dividend growth is high initially, but later settles down to a

long-run constant growth rate

8.9 Zero Growth Rate

The dividends on most preferred stocks are expressed as a constant percentage of the share’s face value

Suppose a preferred share is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding.

What is the price?

00.20$

410.050.0

r

DivPV 1

StockPreferred

8.10 Constant Growth Rate

To value a common stock, we usually assume the dividend stream will grow at some constant growth rate over time

With a little algebra, this reduces to:

g-r

Div

g-r

g)1(DivP 10

0

r1

1Div...

r1

1Div

r1

1Div

r1

1Div

r1

Div...

r1

Div

r1

Div

r1

DivP

03

30

2

200

33

221

0

gggg

8.11 Constant Growth: Example 1

Suppose Big D, Inc. just paid a dividend of $.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 stock be selling for?

92.3$0.02-0.15

)02.1(50.0

g-r

g)1(DivP 0

0

8.12 Constant Growth: Example 2

Suppose TB Pirates, Inc. 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?

3.331$0.05-0.20

00.2

g-r

DivP 1

0

8.13 Stock Price Sensitivity to Dividend Growth, g

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Stoc

k Pr

ice

Div1 = $2; r = 20%

8.14 Stock 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

Required Return

Stoc

k Pr

ice

Div1 = $2; g = 5%

8.15 Gordon Growth Company – Example 1

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?

0.004$0.06-0.16

00.4

g-r

DivP 1

0

8.16 Gordon Growth Company – Example 2

What is the price expected to be in year 4?

0.505$0.06-0.16

06.100.4

g-r

1Div

g-r

DivP

4

41

54

g

8.17 Gordon Growth Company - Continued

What is the holding period return (capital gains yield) due to the capital gain over the four year period?

%25.2600.40

00.4050.50

0

01

P

PPHPR

8.18 Non-constant Dividend Growth

Suppose a firm is expected to increase dividends by 20% in one year and by 15% in year 2. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend that was just paid was $1 and the required return is 20%, what is the price of the stock?

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

∞0 4321

$1.00

15%20% 5% 5% 5%

8.19 Non-constant Dividend Growth - Continued

Compute the dividends until growth levels off

Find the present value of the expected future cash flows

∞0 4321

$1.00

15%20% 5% 5% 5%

$1.45$1.20 $1.38

67.8$

20.1

1

05.020.0

45.1

20.1

38.1

20.1

20.1

1

1Div

r1

Div

r1

DivP

22

23

221

0

rgr

8.20 Calculating the Required Rate of Return

Start with the constant dividend growth formula:

The required rate of return on a common stock can always be decomposed into: Dividend yield Capital gain or loss

gP

Div

g P

g)(1Div r

for rand solve rearrange

g-r

Div

r - g

g)(1DivP

0

1

0

0

1

00

8.21 Example – Finding the Required Return

Suppose a firm’s stock is 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?

What is the dividend yield?

15%

0.0510.50

1.00(1.05)

g P

g)(1Div r

0

0

What is the capital gains yield?

% 110.50

1.00(1.05)

P

g)(1Div YieldDividend

0

0

0

5%

0.05

g GainCapital

8.22 Table 8.1 - Summary of Stock Valuation

8.23 Common Stock – Features

Voting Rights

1- Cumulative voting- total number of votes each shareholder may cast =

(# of shares owned) x (# of directors to be elected)

All directors are elected at the same time. Cumulative voting favors minority stockholders.

2- Straight voting- directors are elected one at a time (i.e., each directors is voted on one at a time). Straight voting favors majority shareholders.

Staggered elections- only a portion of the board is elected in any one year. This makes it difficult for minority shareholder to elect a specific director.

8.24 Example- Voting Rights

A company has two shareholders: “A” (owns 50 shares); “B” (owns 249 shares). There are 5 directors to be elected and 7 candidates running (T, U, V, W, X, Y, Z). “A” wants candidate Z to be on the board. B wants candidates T, U, V, W, and Y.

Using Straight voting- “A” has 50 votes and “B” has 249 votes. Since each director is voted on one at a time “B” will be able to vote in all his candidates and “A” will not be able to vote in his candidate.

Using Cumulative voting-

“A” has 50 x 5 = 250 votes (all for Z)

“B” has 249 x 5 = 1,245 votes (÷ 5 = 249 for T, U, V, W, and Y)

Therefore, Z wins the most votes. “B” cannot arrange votes to block Z.

8.25 Common Stock – Features (cont.)

Other Rights Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Right to vote on major issues – e.g. mergers Preemptive right – the right to purchase new stock to

maintain proportional ownership, if desired (i.e., the right to buy new shares proportionately)

ExampleIf an investor has 1% of ownership and 1 million new shares are issued.

The investor will have first rights to buy 10,000 of the new shares.

8.26 Common Stock – Features (cont.)

Classes of stock- one has voting power, one has high dividends Dual class shares

Voting & not-voting (restricted) Allows founders to retain control while raising new equity

e.g. Class A: 1 vote per share, 100% of dividends

Class B: 10 votes per share, zero dividends (usually not publicly traded)

Coattail provision Protects non-voting shareholders in the event of a take-over bid (it

allows the non-voting shareholders either the right to vote or to convert their shares into voting shares that can be tendered to the takeover bid)

8.27 Dividends

Dividend size is determined by the board of directors Dividends are not a liability of the firm until a dividend has

been declared by the board Consequently, a firm cannot go bankrupt for not declaring

dividends Dividends and Taxes

Dividend payments are not considered a business expense and are not tax deductible

Dividends received by individual shareholders are partially sheltered by the dividend tax credit (13⅓ %)

Dividends received by corporate shareholders are not taxed, thus preventing the double taxation of dividends

8.28 Preferred Stock Valuation

Preferred stock is a hybrid security with features of bonds and common stock.

Its bond features is that preferred stockholders have preference over common stockholders and have no voting rights.

Its common stock features is that dividends on preferred stock do not have to be paid (i.e., dividends go into arrears and don’t have to be paid on time).

8.29 Preferred Stock - Characteristics

Preferred stock has priority over common stock upon liquidation

Dividends Most preferred stock has a stated dividend that must be

paid before common dividends can be paid Dividends are not a liability of the firm and preferred

dividends can be deferred indefinitely Most preferred dividends are cumulative – any missed

dividends on preferred stock have to be paid before a dividend can be paid on common stock

Preferred stock generally does not carry voting rights

8.30 Preferred Stock & Taxes

Companies with a low tax rate cannot make use of the tax shield available from interest

Therefore, they have an incentive to issue preferred shares, which typically pay a dividend lower than a comparable interest rate. The dividend is non-taxable in the hands of the recipient corporation.

The loophole was partially closed in 1987 by forcing issuers of preferreds to pay a tax of 40% of the preferred dividend.

However, it may still be cheaper to use preferreds than debt for the firm with a zero marginal tax rate

8.31 Stock Market Reporting 8.4

Stock market quotations are published in the newspapers and are also available on-line (usually with 15-minute delays)

In Canada, large cap stocks trade on the TSX Quotes and corporate information on stocks that trade on the

TSX can be found at the exchange’s website

8.32 Figure 8.1 – Sample Stock Market Quotation