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FINC3131Business Finance

Chapter 9: Stocks and Their Valuation

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Learning objectives1. Compute the price of a preferred stock.2. Compute the price of common stock under

various assumptions about dividend growth.

Preferred stock

1. Hybrid security.

2. Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends are paid to common stockholders.

3. However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy.

Common Stock

1. Represents ownership

2. Ownership implies control

3. Stockholders elect directors

4. Directors elect management

5. Management’s goal: Maximize the stock price

Dividend growth model

Value of a stock is the present value of the future dividends expected to be generated by the stock.

)r(1D

... )r(1

D

)r(1D

)r(1

D P

s3

s

32

s

21

s

10

^

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Preferred stockPays a fixed dividend forever.

Price of preferred stock is simply the present value of a perpetuity.

Required rate of return on preferred stock.

pps r

DP

psp P

Dr

Preferred stock dividend

Required rate of return on preferred stock/ cost of capital for preferred stock

Price of preferred stock

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Common stockFor common stock, the future cash flows are: Dividends Selling priceThese cash flows are highly uncertain. To find the value of common stock, we make

assumptions about how dividends evolve in the future. We look at 3 set of assumptions:

1. Constant dividend stream2. Dividends grow at constant rate (constant

dividend growth model)3. Non-constant dividend growth

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Constant dividend stream Same amount of dividend is paid for ever. Cash flow stream resembles a perpetuity. Thus, we value the common stock in the same way as

we value the preferred stock. Common stock price, Pe

Cost of equity capital, re

ee r

DP

ee P

Dr

Common stock dividend

Cost of equity capital or required rate of return on equity

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Dividends grow at constant rate 1

1. Assume that dividends grow at a constant rate, g, per period forever.

2. Given this assumption, the price of common stock equals

gr

D

gr

gDP

eee

10 1D0 = Dividend that the firm just paid

Dividend growth rate

Required rate of return on equity

Don’t panic.

D1 = D0(1 + g)

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Dividends grow at constant rate 2

Useful properties.

1. All other things unchanged, • If D0 increases (decreases), Pe increases

(decreases).

• If g increases (decreases), Pe increases (decreases).

• If re increases (decreases), Pe decreases (increases).

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Dividends grow at constant rate 2

1. By rearranging the above equation, we can find the required rate of return on equity

2. For the constant growth model to work, re > g.

gP

Dr

ee 1

Dividend yield

Capital gains yield

Required rate of return on equity

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Constant growth problems 1 Jarrow Company will pay an annual dividend

of $3 per share one year from today. The dividend is expected to grow at a constant rate of 7% permanently. The market requires 15% What is the current price of the stock (to 2 decimal places)?

In this question D1 is already given to you.

Verify that Price = $37.5

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Constant growth problems 2 Johnson Foods Inc. just paid a dividend of $10

(i.e., D0 = 10.00). Its dividends are expected to grow at a 4% annual rate forever. If you require a 15% rate of return on investments of this risk level, what is Johnson Foods’s current stock price? (to 2 decimal places)

Straightforward application of price formula.

Verify that price = $94.55

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Constant growth problems 3 The price of a stock in the market is $62. You

know that the firm has just paid a dividend of $5 per share (i.e., D0 = 5). The dividend growth rate is expected to be 6 percent forever. What is the investors’ required rate of return for this stock (to 2 decimal places)?

Use re = (D1/P) + g.

Verify that re = 14.55%

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Constant growth problems 4 A firm is expected to pay a dividend of

$5.00 on its stock next year. The price of this stock is $40 and the investor’s required rate of return is 20%. The firm’s dividends grow at a constant rate. What is this constant dividend growth rate (g)?

use re = (D1/P) + g

Verify that g = 7.5%

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Constant growth problems 5 In order to use the constant dividend growth

model to value a stock it must be true that:

a. The required rate of return is less than the expected dividend growth rate.

b. The expected dividend growth rate is greater than zero.

c. The next dividend (D1) is expected to be greater than $1.00.

d. The expected dividend growth rate is less than the required rate of return.

Which statement is correct?

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Non-constant dividend growth 11. With this assumption, dividends grow at

different rates for different periods of time. Eventually, dividends will grow at a constant rate forever.

2. Time line is very useful for valuing this type of stocks.

3. To value such stocks, also need the constant growth formula.

4. Best way to learn is through an example.

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Non-constant dividend growth 2 ABC Co. is expected to pay dividends at the end of the

next three years of $2, $3, $3.50, respectively. After three years, the dividend is expected to grow at 5% constant annual rate forever. If the required rate of return on this stock is 15%, what is the current stock price?

T = 0

$2.00 $3.00 $3.50 Dividends grow at 5% forever

T =1 T = 2 T = 3 T = 4

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What to do?

1. Use constant growth formula to find stock price at the end of year 3. Call this stock price P3.

2. Add P3 to dividend received at t=3. This sum is the cash flow for t=3. Find PV of this cash flow.

3. Find PV of dividends at t=1, t=2.

4. Current stock price = sum of 2 and 3.

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Apply the method to find ABC’s stock price

1. P3 = (3.5 x (1.05))/(0.15 – 0.05) = 36.75

2. At t=3, cash flow is 36.75 + 3.50 = 40.25

Current stock price, P0

47.30$

15.1

25.40

15.1

3

15.1

2320 P

If D0 = $2 , r=13% and g = 30% for 3 years before achieving long-run growth

of 6%, what is the PV?

1. Can no longer use just the constant growth model to find stock value.

2. However, the growth does become constant after 3 years.

rs = 13%

g = 30% g = 30% g = 30% g = 6%

P 0.06

$66.543

4.658

0.13

2.301

2.647

3.045

46.114

54.107 = P0

^

0 1 2 3 4

D0 = 2.00 2.600 3.380 4.394

...

4.658

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Another type of non-constant growth problem

Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D0 = 2.00). Investors believe that the firm will grow at 10% annually for the next 2 years and 6% annually forever thereafter. Assuming a required return of 15%, what is the current price of the stock (to 2 decimal places)?

Use timeline to ‘see’ the problem better.

Verify that stock price = $25.29

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Summary1. Find the price/ present value of equity

securities2. Consols, preferred stock are valued using the

same techniques. 3. Common stocks are valued under 3 different

assumptions about dividends• Constant dividends• Dividends grow at constant rate• Dividends grow at different rates

4. Assignment: self-test question ST-3 ST-4problems: 9-1 9-2 9-3 9-6 9-7 9-8 9-11 9-13 9-14