Copyright 2014 by Diane Scott Docking 1 Stock Valuation Video: How the Market Really works.

Copyright 2014 by Diane Scott Docking 1

Stock Valuation

Video: How the Market Really works

http://www.youtube.com/watch?v=UC31Oudc5Bg


Learning Objectives Understand how to calculate stock returns Understand how stock prices (values) are

determined when dividends grow at a constant rate dividend growth is nonconstant

Identify factors that affect stock prices


Stock Valuation The price of a share of stock is the total value of

the company divided by the number of shares outstanding

Stock price by itself doesn’t represent firm value Number of shares outstanding

Stock price is determined by the demand and supply for the shares

Investors try to value stocks and purchase those that are perceived to be undervalued by the market

New information creates re-evaluation

4Copyright 2014 by Diane Scott Docking

Stock Returns

The returns on a stock over one period (Rt) can be divided into capital gains and dividend returns:

Pt = stock price at time t

Dt = dividends paid over time t – 1 to t

(Pt – Pt – 1) / Pt – 1 = capital gain over time t – 1 to t

Dt / Pt – 1 = return from dividends paid over time t – 1 to t

The returns on a stock over one period (Rt) can be divided into capital gains and dividend returns:

Pt = stock price at time t

Dt = dividends paid over time t – 1 to t

(Pt – Pt – 1) / Pt – 1 = capital gain over time t – 1 to t

Dt / Pt – 1 = return from dividends paid over time t – 1 to t

111

1

1

t

tt

t

tt

t

tt P

PD

P

PP

P

DR

Dividend Yield

Capital Gains Rate


Example: Determining Rate of Return

Union Corporation currently pays an annual dividend of

$1.00. The current stock price is $50. At the end of 1

year, the stock price is $55.

What is Union Co.’s annual rate of return on its stock?

return totalgains capitaldividend

1

1

11

12%10%2%50

6

50

5

50

1

50

5055

50

1

t

tt

t

t

P

PP

P

DR


Example: Stock Return CalculationJake buys 10 shares of AVU stock at $55.10 and sells it 1

year later for $56.30 after collecting a $0.30 dividend per

share.

1. What is Jake’s pre-tax holding period return?


1

1

1_1

%178.2%544.010.55

50.1

10.55

20.1

10.55

30.

10.55

10.5530.56

10.55

30.

2.722%

t

tt

t

tBT P

PP

P

DR


Example: Stock Return Calculation (cont.)2. If the dividend is taxed at the ordinary rate = 28% and the

capital gains at 15%, what is Jake’s after tax holding period return?


1

1

1_1

%851.1%392.0

10.55

236.1

10.55

02.1

10.55

216.

10.55

85.20.1

10.55

72.30.

15.110.55

10.5530.5628.1

10.55

30.

11

2.243%

ratecg

t

ttrateord

t

tAT t

P

PPt

P

DR


Example: 2 year Stock Return Calculation

Jake buys 10 shares of AVU stock at $55.10 and sells it 2

years later for $56.30 after collecting a $0.30 dividend per

share per year.

1. What is Jake’s pre-tax holding period return?CF0 = - $55.10

CF1 = $.30

CF2 = $.30 + $56.30 = $56.60

Therefore IRR = 1.6246%

OR

PV = -$55.10

n = 2

PMT = .30

FV = $56.30

YTM = 1.6246%


Stock Valuation Methods

The Dividend-Discount Model Estimating Dividends in the Dividend-Discount

Model Total Payout and Free Cash Flow Valuation

Models Valuation Based on Comparable Firms Valuation Using P/E Ratios Economic Value Added (EVA) Approach Information, Competition, and Stock Prices


Dividend-Discount Model

The Dividend-Discount Model Zero or No growth in dividends, but unlimited life Zero growth in dividends, but limited life Constant growth in dividends Nonconstant growth in dividends



The price of a stock reflects the present value of the stock's future dividends

D0 = dividend in period 0 expected to remain constant forever

rs = discount rate or required rate of return on the stock

Zero Growth in Dividends

sr

DP 0

0

Perpetuity Dividend Model


Example: Zero Dividend Growth Model

Joan’s Fabric Corp. pays an annual dividend of $5.00 per share on its Preferred stock. This dividend is expected to remain constant into the future. The expected rate of return on the stock is 6.50%. What is the current market price of the stock?

92.76$065.

00.500

sr

DP




t = period

Dt = dividend in period t

rs = discount rate or required rate of return on the stock

Zero Growth in Dividends

Non-Perpetuity Dividend Model

1

0)1(t

ts

t

r

DP


Example: 1-period Dividend Growth Model

Mary expects Longs Drug Stores to pay an annual dividend of $.56 per share in the coming year and to trade $45.50 per share at the end of the year. Investments with equivalent risk to Longs’ stock have an expected return of 6.80% What is the most Mary would pay today for

Longs’ stock? What dividend yield and capital gain rate would

Mary expect at this price?


Example: 1-period Dividend Growth Model

What is the most Mary would pay today for Longs’ stock?

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

At this price, Longs’ 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%.

Total return is 1.30% + 5.50% = 6.80%

13.43$)068.1(

50.45

)068.1(

56.0

)1()1(

11

11

11

0

ss r

P

r

DP


Example: Multiyear Dividend Growth Model

Suppose Mary plans to hold the stock for two years. She expects the price to be $45.50 at the end of two years. Mary would receive dividends in both year 1 and year 2 before selling the stock, as shown in the following timeline:



Example: Multi-year Dividend Growth Model


91.40$)068.1(

50.45

)068.1(

56.0

)068.1(

56.0

)1()1()1(

221

22

22

11

0

sss r

P

r

D

r

DP




t = period

Dt = dividend in period t

rs = discount rate

g = the nominal growth rate of earnings over time.

Constant Dividend Growth Model

gr

D

gr

gDP

s

t

s

t

t

10 )1(


Example 1: Constant Dividend Growth Model

Consolidated Edison, Inc. (Con Edison), is a regulated utility company that services the New York City area. Suppose Con Edison just paid $2.30 per share in dividends. Its equity cost of capital is 7% and dividends are expected to grow by 2% per year in the future.

What is the current value of Con Edison’s stock?



What is the current value of Con Edison’s stock?

gr

D

gr

gDP

ss

100

1

02.07.

346.2

02.07.

02.130.20

P

92.46$05.

346.20 P



Suppose Johnson & Johnson plans to pay $2.85 per share in dividends in the coming year. Its equity cost of capital is 9% and dividends are expected to grow by 3% per year in the future.

What is the estimated value of Johnson & Johnson’s stock?



What is the current value of Johnson & Johnson’s stock?

gr

DP

s 1

0

50.47$06.

85.2

03.09.

85.20

P



Firms experience different growth rates: supernormal growth (gs) and normal growth (g) .

A 4-step process to calculate current price1. Find the PV (P0

’) of the dividends during the period of supernormal growth (gs).

2. Find the price of the stock at the end of the supernormal growth period (n), when normal growth (g) begins using the constant dividends growth model.

NonConstant Dividend Growth Model

n

tt

s

ts

r

gDP

1

0'0 )1(

1

gr

ggD

gr

DP

s

ns

s

nn

101 )1()1(



Firms experience different growth rates: supernormal growth (gs) and normal growth (g) .

A 4-step process to calculate current price1. Find the PV (P0

’) of the dividends during the period of supernormal growth (gs).



n

tt

s

ts

r

gDP

1

0'0 )1(

1

gr

ggD

gr

DP

s

ns

s

nn

101 )1()1(



A 4-step process to calculate current price3. Discount this price (Pn) back to time 0 (P0

”).

4. Add the two components of the stock price together.


ns

n

r

PP

)1("

0

"0

'00 PPP


Example: Valuing a Firm with Two Different Growth Rates

Up and Away Corp. is expected to experience supernormal growth of 30% per year for the next 3 years. After that, the growth rate is expected to drop to 5% for the remainder of the firm’s life. Up and Away’s dividend at the end of last year of $1.60 per share. The firm’s cost of capital is 20%.

What is the value of the firm’s stock?



Given: D0 = $1.60; rs = 20%; gs = 30%; g = 5%; n = 3 years

1. Find the PV (P0’) of the dividends during the period of supernormal growth (gs).

3

11

0'0 )20.1(

30.160.1$

)1(

1

tt

tn

tt

s

ts

r

gDP

t Dividend ÷ (1.20)t = PV

1 $1.60(1.30)1 = $2.0800 ÷ (1.20)1 = $1.7333

2 $1.60(1.30)2 = $2.7040 ÷ (1.20)2 = $1.8778

3 $1.60(1.30)3 = $3.5152 ÷ (1.20)3 = $2.0341

∑ = $5.6452 = $5.65 = '0P




gr

ggD

gr

DP

s

ns

s

nn

101 )1()1(

05.20.

)05.1()30.1(60.1)1()1( 131304

3

gr

ggD

gr

DP

s

s

s

6067.24$15.

6910.3

05.20.

)05.1(5152.3 1

3

P



3. Discount this price (Pn) back to time 0 (P0”).


24.14$)20.1(

6067.24$

)1()1( 333"

0

s

ns

n

r

P

r

PP

89.19$24.14$65.5$"0

'00 PPP


Example: Comparing Dividend-Growth Models

Jake is considering buying Polo stock which is currently

priced at $62 per share. Polo paid a dividend at the end of

last year of $2.50 per share. Jake’s required rate of return is

5%. Should Jake buy the stock, assuming:

1. The dividend is expected to continue into the foreseeable future?

2. The dividend is expected to grow at a constant rate of 1% into the foreseeable future?

3. The dividend is expected to grow at a rate of 3% for the next 4 years and then at a rate of 1% thereafter?



1. The dividend is expected to continue into the foreseeable future?

Do NOT Buy. Priced too high.

50$05.

50.200

r

DP



2. The dividend is expected to grow at a constant rate of 1% into the foreseeable future?

Yes buy. Priced too low

125.63$

04.

525.2

01.05.

01.150.20

P



3. The dividend is expected to grow at a rate of 3% for the next 4 years and then at a rate of 1% thereafter?

Given: D0 = $2.50; rs = 5%; gs = 3%; g = 1%; n = 4years

Step 1: Find the PV (P0’) of the dividends during the period of supernormal growth (gs).

4

11

0'0 )05.1(

03.150.2$

)1(

1

tt

tn

tt

s

ts

r

gDP

t Dividend ÷ (1.05)t = PV

1 $2.50(1.03)1 = $2.575 ÷ (1.05)1 = $2.4524

2 $2.50(1.03)2 = $2.6523 ÷ (1.05)2 = $2.4057

3 $2.50(1.03)3 = $2.7318 ÷ (1.05)3 = $2.3598

4 $2.50(1.03)4 = $2.8138 ÷ (1.05)4 = $2.3149

∑ = $9.5328 = $9.53 = '0P




gr

ggD

gr

DP

s

ns

s

nn

101 )1()1(

01.05.

)01.1()03.1(50.2)1()1( 141405

4

gr

ggD

gr

DP

s

s

s

0485.71$04.

8419.2

01.05.

)01.1(8138.2 1

4

P



3. Discount this price (Pn) back to time 0 (P0”).


Yes buy. Priced too low

45.58$)05.1(

0485.71$

)1()1( 444"

0

s

ns

n

r

P

r

PP

98.67$45.58$53.9$"0

'00 PPP


Dividends Versus Return and Growth

For another interpretation, note that we can rearrange the constant dividend growth model equation as follows:

Solving for rs:

Solving for g:

gr

DP

s

tt 1

gP

Dr

t

ts 1

t

ts P

Drg 1

0

0

DP

DPrg

t

ts

or


Example: Solving for Investment Return

Carson Co. recently paid a $1.20 dividend. The dividend is expected to grow at a 2% rate. At a current stock price of $36.35, what return are shareholders expecting?

Solve for rs:

02.35.36$

)02.1(20.1$1 gP

Dr

t

ts

%367.505367.02.03367.02.35.36$

224.1$sr


Example: Solving for Growth Rate

Flintstone Co. recently paid a $1.10 dividend. The current stock price of the company is $46.27 and investors expect a 6% return. What is the expected future growth rate in dividends.

Solving for g:

10.127.46

10.17762.2

10.127.46

10.127.4606.

0

0

DP

DPrg

t

ts

%54.35385.3035385.037.47

6762.1g


Limitations of Dividend-Discount Model

We cannot use the constant dividend growth model to value the stock of the following types of firms: Firms that pay no dividends Firms whose growth rate continues to change over

time until they mature

There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model


Limitations of Dividend-Discount Model

We cannot use the constant dividend growth model to value the stock of such a firm for two reasons: These firms often pay no dividends when they are

young Their growth rate continues to change over time until

they mature

There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model

Copyright 2014 by Diane Scott Docking 1 Stock Valuation Video: How the Market Really works.

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t p t p t

t d t p t

time t d t

stock returns

diane scott docking

share of stock

period r t

current stock price