Winter Semester 2010 Lahore School of Economics pdf

Dividend Discount Model - Assumptions  Dividend paying stock  Required Return by investors is greater than the Growth Rate of Dividends... Dividend discount models -Multiple Growth Rat

BSC III Winter Semester 2010

Lahore School of

Economics

Chap 10 Common Stock Valuation Investments

Common Stock Valuation

Learning Objectives

 Common Stock Valuation

 Dividend Growth model

 Zero Growth

 Constant Growth

 Multiple growth model

 Intrinsic Value & Market price

 Relative Valuation Techniques (P/E,P/S,P/S)

 Components of Required Return

Capital Market Securities

 Fixed Income (Bonds)

Common Stock

It is an equity ownership in a corporation, initially issued to raise capital

Points to keep in mind!

C/F’s are NOT known in advance

Life of stocks is forever – no maturity

Difficult to observe required rate of return for discounting

Common stock valuation

The two approaches to valuing common stock using fundamental security analysis are:

1. Discounted Cash flow techniques

2. Relative valuation techniques

Common stock valuation

The two approaches to valuing common stocks using fundamental security analysis are:

1. Discounted Cash flow techniques

Attempts to estimate the value of a stock today using a present value analysis.

2. Relative valuation techniques

A stock is valued relative to other stocks based on the basis of ratios.

Key difference!

Discounted Cash Flow

Techniques

The estimated value of a security is equal to the

discounted value (Present Value) of the future stream of cash flows that an investor expects to receive from the security:

Estimated Value of any security = V 0

V 0 = Expected Cash Flows / ( 1 + K ) t

Where:

K is the appropriated Discount Rate

Discounted Cash Flow

Techniques

To use Discounted Cash flow Model, an investor must:

1. Estimate the amount & timing of future stream of Cash

flows.

2. Estimate an appropriate Discount Rate

3. Use these two components in PV Model to estimate the

value of the security, which is then compared to the

current Market Price of the security.

Discounted Cash Flow

Discounted Cash Flow Techniques

How to come up with the Price of a Stock?

Assumptions:

Assume a dividend the stock will pay.

Assume a selling price at the end of 1 year

Come up with a required rate of return.

Discounted Cash Flow Techniques

- Example

Example:

Stock selling price after 1 year is $70

Stock dividend will be $10

Investors require 25% return

PV = 80 /( 1.25 )

= $64

Discounted Cash Flow Techniques

- Example

Example:

Stock selling price after 1 year is $70

Stock dividend will be $10

Investors require 25% return

PV = 80 /( 1.25 )

= $64

Or,

Po = ( D 1 +P 1 ) / ( 1+k )

Discounted Cash Flow Techniques

P1 at t1, could also be found the same way by

assuming year 2 price & dividend :

P1 = ( D2+ P2) / ( 1 + K )

Discounted Cash Flow Techniques

Substituting P1 in Po equation:

Po = ( D1+ ( D2+ P2)/( 1 + K ) ) / ( 1 + K )

= [ D1/( 1+K )1] + [ D2/( 1 + K )2] + [ P2/( 1 + K )2]

Dividend Discount Model

Formula:

Po = E [ Dn/ ( 1 + K )n]

Present Value of all future dividends as a general valuation framework!

Dividend Discount Model

1. Investors must value a stream of dividends that may be

paid forever , since common stock has no maturity

value.

2. The dividend Stream is uncertain :

 There is no specified number of dividends, if in fact

any are paid at all.

 Dividends are Expected to grow in most cases.

Dividend Discount Models – Special cases

Growth Rate Cases for the DDM:

 The Zero Growth rate Case

 The Constant Growth rate Case

 The Multiple Growth rate Case

The Zero Growth Rate Model

The Zero Growth rate model- Example

A company pays a dividend of $2 per share, which is not expected to change Required return is 20% What’s the price per share today?

Discounted Cash Flow Techniques – Zero Growth - Example

A company pays a dividend of $2 per share, which is not

expected to change Required return is 20% What’s the

price per share today?

P o = D o / k

= 2 / 0.2

= 10

The Constant Growth Rate

The Constant Growth Rate ModelStock Price with constant growth dividends:

Po = Do *( 1 + g ) / ( K - g ) OR

P0 = D1 / ( K – g )

Dividend Discount Model -

Assumptions

 Dividend paying stock

 Required Return by investors is greater than the Growth Rate of Dividends.

 Dividends will grow at a constant Rate forever

The Constant Growth Rate Model - example

Suppose Do = 2.30 , K=13 %, g=5% What’s the price per

share?

The Constant Growth Rate Model - example

Suppose Do = 2.30 , K=13 %, g=5% What’s the price per

The Constant Growth Rate Model

Constant Growth Model can be used to find

the stock price at any point in time!

1 Find the Dividend for that year.

2 Grow it at (1+g)

3 Divide by K-g

The Constant Growth Rate Model - example

Suppose Do = 2.30 , K=13 %, g=5% What’s the

price per share in 5 years?

Hint:

P5 = D6 / ( K – g )

The Constant Growth Rate Model - example

Suppose Do = 2.30 , K=13 %, g=5% What’s the price per

The Constant Growth Rate Model - example

Suppose Company XYZ’s next dividend will be $4

Required return is 16% Dividend increases by 6% every

year, forever.

What’s the price per share today?

& in 4 years ?

The Constant Growth Rate Model - example

Suppose Company XYZ’s next dividend will be $4

Required return is 16% Dividend increases by 6% every

The Constant Growth Rate Model - example

Suppose Company XYZ’s next dividend will be $4

Required return is 16% Dividend increases by 6% every

BSC/BBA III Winter Semester 2010

Lahore School of

Economics

Chap 10 Common Stock Valuation Investments

Common Stock Valuation

Learning Objectives

 Common Stock Valuation

 Dividend Growth model

 Zero Growth

 Constant Growth

 Multiple growth model

 Intrinsic Value & Market price

 Relative Valuation Techniques (P/E,P/S,P/S)

 Components of Required Return

Dividend discount models -Multiple Growth Rate Case

For many companies, it is inappropriate to assume that dividends will grow at a constant rate as Firms typically go through life cycles.

P0 = PV of Expected Future Cash flows

Dividend discount models

-Multiple Growth Rate Case

For many companies, it is inappropriate to assume that dividends will grow at a constant rate as Firms typically go through life cycles.

P0 = PV of Expected Future Cash flows

P 0 = PV of Dividends during the non Constant period

PLUS

PV of Dividends during the constant Growth Period

Multiple Growth Rate Case

To find Value of Stock with Non Constant Growth ,

we go through the following three steps :

1. Find the PV of Dividends during the period of Non

Constant Growth.

2. Find the PV of Stock at the end of Non Constant

Growth period at which point it has become a

constant growth Stock, and discount the price back

to the present.

3. Add these two components to find the intrinsic

Value of the Stock.

Dividend discount models

-Multiple Growth Rate Case

Multiple Growth model

Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate

Dividend discount models

-Multiple Growth Rate Case

Multiple Growth model

Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate

Value = PV of dividends + PV of terminal price

= E [ Dt /( 1 + k )t] + { [ Dn+1 /( k - g ) ] * [ ( 1 / 1 + k )n] }

Multiple Growth Rate Case -

Example

The last dividend paid by Klein Company was $1.00 Klein’s growth rate is expected to be a constant 5

percent for 2 years, after which dividends are

expected to grow at a rate of 10 percent forever

Klein’s required rate of return on equity (ks) is 12

percent What is the current price of Klein’s common stock?

Multiple Growth Rate Case -

Example

The last dividend paid by Klein Company was $1.00 Klein’s growth rate is expected to be a constant 5 percent for 2 years , after which dividends are expected

to grow at a rate of 10 percent forever Klein’s required rate of return on equity (ks) is 12 percent What is the current price of Klein’s common stock?

0 1 2 3 Years | | | |

21275

1

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Multiple Growth Rate Case -

Example

The last dividend paid by Klein Company was $1.00 Klein’s growth rate is expected to be a constant 5

percent for 2 years , after which dividends are

expected to grow at a rate of 10 percent forever

Klein’s required rate of return on equity (ks) is 12

percent What is the current price of Klein’s common stock?

Financial calculator solution:

Enter in Cash register CF0 = 0, CF1 = 1.05, and

CF2 = 61.74.

Then,

Enter I = 12, and press NPV to get NPV=P0= $50.16.

Multiple Growth Rate Case -

Example

Your company paid a dividend of $2.00 last year The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a

constant 7 percent thereafter The required rate of

return on equity (ks) is 10 percent What is the current stock price?

Multiple Growth Rate Case -

constant 7 percent thereafter The required rate of

return on equity (ks) is 10 percent What is the current stock price?

Multiple Growth Rate Case -

Example

Your company paid a dividend of $2.00 last year The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a

constant 7 percent thereafter The required rate of

return on equity (ks) is 10 percent What is the current stock price?

Financial calculator Solution:

CF 0 = 0; CF 1 = 2.08; CF 2 = 2.1840; and CF 3 = 84.8848;

I = 10; and press NPV to get NPV = P0 = $67.47.

Intrinsic Value & Market Price

If

Intrinsic Value > Market Price = under-valued

Intrinsic Value < Market Price = over-valued

Assignment ( 7 Questions )

Q1:A stock is expected to pay $0.45 dividend at the end

of the year The dividend is expected to grow at a constant rate of 4 percent a year, and the stock’s

required rate of return is 11 percent What is the

expected price of the stock 10 years from today?

A stock that currently trades for $40 per share is

expected to pay a year-end dividend of $2 per share The dividend is expected to grow at a constant rate over time The stock has a required rate of return of 11% What is the stock’s expected price seven years from today ?

Motor Homes Inc (MHI) is presently in a stage of

abnormally high growth because of a surge in the

demand for motor homes The company expects

earnings and dividends to grow at a rate of 20 percent for the next 4 years, after which time there will be no growth (g = 0) in earnings and dividends The

company’s last dividend was $1.50 MHI’s required return on stock is 18% What should be the current common stock price?

A stock is not expected to pay a dividend over the next four years Five years from now, the company anticipates that it will establish a dividend of $1.00 per share Once the dividend is established, the

market expects that the dividend will grow at a

constant rate of 5 percent per year forever The required rate of return on the company’s stock is expected to remain constant at 12% What is the current stock price?

R E Lee recently took his company public through an initial public offering He is expanding the business quickly to take advantage of an otherwise unexploited market Growth for his company is expected to be 40 percent for the first three years and then he expects it

to slow down to a constant 15 percent The most

recent dividend (D0) was $0.75 Based on the most recent returns, his company’s required return is 20% What is the current price of Lee’s stock?

DAA’s stock is selling for $15 per share The firm’s income, assets, and stock price have been growing at

an annual 15 percent rate and are expected to

continue to grow at this rate for 3 more years

Dividend of $0.50 has been declared recently After super normal growth, dividends are expected to grow

at the firm’s normal growth rate of 6 percent The

firm’s required rate of return is 18 percent

Determine whether the stock is under or overvalued State reasons for your answer!

Philadelphia Corporation’s stock recently paid a

dividend of $2.00 per share (D0 = $2), and the stock

is in equilibrium The company has a constant growth rate of 5 percent The required rate of return on its stock is 29.5% Philadelphia is considering a change

in policy that will increase its required return to

33.25% If market conditions remain unchanged,

what new constant growth rate will cause

Philadelphia’s common stock price to remain

unchanged?

BBA III Winter Semester 2010

Lahore School of

Economics

Chap 10 Common Stock Valuation Investments

Common Stock Valuation

Learning Objectives

 Common Stock Valuation

 Dividend Growth model

 Zero Growth

 Constant Growth

 Multiple growth model

 Intrinsic Value & Market price

 Relative Valuation Techniques (P/E,P/S,P/S)

 Components of Required Return

Discounted Cash flow

approaches

1. Dividend Discount Model

2. Free Cash Flow to Equity (FCFE) Model

3. Free Cash Flow to Firm (FCFF) Model

Free Cash Flow to equity Model

Free Cash Flow to Equity (FCFE) is defined as the cash flow remaining after principle & interest payments have been made & Capital Expenditures have been provided for.

FCFE Model differs from the DDM in the sense that FCFE measures what firm could pay out as dividends rather than what they actually paid out.

FCFE = NI + NCC – Debt repayments – Capital Expenditures

– Investment in Working capital + New Debt Issues

Free Cash Flow to equity Model – Special Cases

1 Zero Growth Case

P 0 = FCFE / K

2 Constant Growth Case

P 0 = FCFE 1 / (K – G)

3 Multiple Growth Case

P 0 = PV of FCFE during the non Constant period

PLUS

PV of FCFE during the constant Growth Period

Free Cash Flow to equity Model –

Zero Growth example

An analyst has collected the following information about Franklin Electric:

 Projected NI for the next year $300 million

 Projected depreciation expense for the next year $50 million

 Projected capital expenditures for the next year $ 100 million

 Projected increase in operating working capital next year $60 million.

 Interest Expense for the year was $5 million & Company paid back

50 Million of its debt outstanding but also issued $4 million of new debt

 Cost of equity 13%.

 Number of shares outstanding today 20 million.

 The company’s free cash flow is NOT expected to grow What is the stock’s intrinsic value today?

Free Cash Flow to equity Model –

Zero Growth example

Step 1: Calculate Free Cash Flow To Equity

FCFE = NI + NCC – Debt repayments – Capital

Expenditures – Investment in Working capital + New Debt Issues

Free Cash Flow to equity Model –

Constant Growth example

An analyst has collected the following information about Franklin Electric:

 Projected NI for the next year $300 million

 Projected depreciation expense for the next year $50 million

 Projected capital expenditures for the next year $ 100 million

 Projected increase in operating working capital next year $60 million.

 Interest Expense for the year was $5 million & Company paid back

50 Million of its debt outstanding but also issued $4 million of new debt

 Cost of equity 13%.

 Number of shares outstanding today 20 million.