Chapter

Common Stock Valuation

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 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

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 Capital Market Securities

 Fixed Income (Bonds)

 Treasuries
 Corporates

 Equities
 Preferred Stock
 Common Stock

3
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

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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!
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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 = V0

V0 = Σ Expected Cash Flows/ (1 + k)t

Where:
k is the appropriate Discount Rate
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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.

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Discounted Cash Flow
Techniques
Two different approaches to the cash flows & discount
rates can be used in the valuation of stocks:

1. Value the Equity of the Firm, using the required rate of

Return to shareholders.

2. Value the entire firm using the Weighted Average Cost

of Capital (WACC).

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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.

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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 = (D1+P1) / (1+k)
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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)

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Dividend Discount Model

Formula:

Po = Σ [Dn/ (1+K)n]

Present Value of all future dividends as a

general valuation framework!

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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.

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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

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 The Zero Growth Rate Model

Zero-growth:
A Dividend Stream resulting from Fixed dollar
Dividend equal to the current Dividend, Do.
So,
Value of the stock is a Present value of a Perpetuity!

Po = D/K

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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?

Po = Do / k
= 2/0.2
= 10

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The Constant Growth Rate
Model
The constant Growth rate Case for the DDM reflects a
dividend stream that is expected to grow at a constant
rate g, forever.
Which implies:
If dividend just paid is Do, then the next D1 is:
D1 = Do*(1+g)
Dividend for period 2, D2:
D2 = D1*(1+g)
= [Do*(1+g)] * (1+g)
= Do *(1+g)2
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The Constant Growth Rate Model

Stock Price with constant growth dividends:

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

OR
P0 = D1 / (K – g)

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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.

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The Constant Growth Rate Model -
example

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

share?

P0 = D1 / (k – g)
= 2.3 *(1.05) / (0.13 - 0.05)
= 2.415 / 0.8
= 30.19

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 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

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The Constant Growth Rate Model
example

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

share in 5 years?

P5 = D6 / (K – g)
= [2.3 *(1.05)^5] / (0.13-0.05)
= [2.935x(1.05)] / 0.8
= 3.0822 / .08
= 38.53

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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?

P0 = D1 / (k – g)
= 4/(.16-.06)
= 4/.1
= $40

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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.
Price in 4 years?
P4 = D5 / (k – g)
D5 = D1 * (1+g)4
= 4(1.06)4
= 5.05
P4 = 5.05/0.1
= 50.50
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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

P0 = PV of Dividends during the non Constant
period
PLUS
PV of Dividends during the constant
Growth Period

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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.

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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
= Ʃ [Dt /(1+k)t] + {[Dn+1 /(k-g)]*[(1/1+k)n]}
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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?
0 k = 12%
1 2 3 Years
| gs = 5%
| gs = 5%
| gn = 10%
|
1.00 1.05 1.1025 1.21275
P0 = ? P̂2 = 60.6375 = 1.21275
CFt 0 1.05 61.7400 0.12  0.10
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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.
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 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?
Time line:
0 k = 10% 1 2 3 4 Years
| g1 = 4%
| g2 = 5%
| g3 = 6%
| gn = 7%
|
2.00 2.08 2.1840 2.31504 2.4770928
P0 = ?
2.4770928
P̂ = 82.56976 =
0.10  0.07
3

CFt 0 2.08 2.1840 84.88480

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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:

CF0= 0; CF1= 2.08; CF2= 2.1840; and CF3=
84.8848;
I = 10; and press NPV to get NPV = P0 = $67.47.

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 Intrinsic Value & Market Price

If
Intrinsic Value > Market Price = under-valued

Intrinsic Value < Market Price = over-valued

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Discounted Cash flow
approaches
1. Dividend Discount Model
2. Free Cash Flow to Equity (FCFE) Model
3. Free Cash Flow to Firm (FCFF) Model

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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

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Free Cash Flow to equity Model
– Special Cases
1. Zero Growth Case
P0 = FCFE / K

2. Constant Growth Case

P0 = FCFE1 / (K – G)

3. Multiple Growth Case

P0 = PV of FCFE during the non Constant
period
PLUS
PV of FCFE during the constant Growth
Period
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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 36
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
= 300 + 50 – 50 – 100 – 60 +4
= 144 Million
FCFE Per Share = 144 / 20
= $ 7.2 Per Share

Step 2: Calculate Intrinsic Value

P0 = 7.2 / 0.13 = $55.38

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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.
 The company’s free cash flow is expected to grow at 38
a
Free Cash Flow to equity Model –
Constant Growth example
Step 1: Calculate Free Cash Flow To Equity
FCFE= NI + NCC – Debt repayments – Capital
Expenditures – Investment in Working
capital + New Debt Issues
= 300 + 50 – 50 – 100 – 60 +4
= 144 Million
FCFE Per Share = 144 / 20
= $ 7.2 Per Share

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Free Cash Flow to equity Model –
Constant Growth example
Step 2: Calculate Intrinsic Value

P0 = Expected FCFE / (K – G)
= 7.2 / (0.13 – 0.06)
= 102.8571

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Free Cash Flow to equity Model –
Multiple Growth example
 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 expected to grow at
a constant rate of 12% for two years & then will grow
at 6%forever. What is the stock’s intrinsic value
today?
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Free Cash Flow to equity Model –
Multiple Growth example
Step 1: Calculate Free Cash Flow To Equity for
year 1
FCFE= NI + NCC – Debt repayments – Capital
Expenditures – Investment in Working
capital + New Debt Issues
= 300 + 50 – 50 – 100 – 60 +4
= 144 Million
FCFE Per Share = 144 / 20
= $ 7.2 Per Share

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Free Cash Flow to equity Model –
Multiple Growth example
Step 2: Calculate FCFE for Non Constant Growth
Period
FCFE in Year 2 = 7.2 * (1 + 0.12)
= 8.0640
FCFE in Year 3 = 8.0640 * (1 +0.12)
= 9.03

Step 3: Calculate FCFE for Constant Growth period

FCFE in Year 4 = 9.03 * ( 1+ 0.06)
= 9.57

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Free Cash Flow to equity Model –
Multiple Growth example
Step 4: Calculate PV of CF during Non Constant
Growth Period
PV = [CF1 / (1+K)] +[CF2/(1+K)2] +
[CF3/(1+K)3]
= [7.2 / (1.13)] + [ 8.06/(1.13)2]+
[9.03/(1.13)3]
= 18.94
Step 5: Calculate PV of CF during Constant
Growth Period
PV = P3 / (1+K)3 P3 =
9.57/0.07
= 136.71/ (1.13)3 = 136.7144
Free Cash Flow to equity Model –
Multiple Growth example
Step 6: Calculate Intrinsic Value

P0 = PV of FCFE during the non Constant

period
PLUS
PV of FCFE during the constant Growth
Period
= 18.94 + 94.75
= 113.69

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Free Cash Flow to Firm Model
FCFF is defined as cash amounts available to be
paid to both bondholders & stockholders.

FCFF = FCFE + Interest (1 – T) +Principle

Repayments – New Debt issues – Preferred
Dividends
OR
FCFF = EBIT(1-T) + NCC – Capital Expenditure –
Change in working Capital
OR
FCFF = NI + NCC + INT (1-T) – Capital
Expenditures – Changes in Working
Capital
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 Free Cash Flow to Firm Model –
Implementing the model
1. Forecast Expected FCFF
2. Estimate the Discount Rate (WACC)
WACC = wd * kd (1-T) + we *ke

3. Calculate the Value of the Corporation

4. Calculate Intrinsic Stock Value
= Value of Corporation MINUS Value of Debt
MINUS Value of Preferred Stock.

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Free Cash Flow to Firm Model –
Special Cases
1. Zero Growth Case
V0 = FCFF / WACC

2. Constant Growth Case

V0 = FCFF1 / (WACC – G)

3. Multiple Growth Case

V0 = PV of FCFF during the non Constant
period
PLUS
PV of FCFF during the constant Growth
Period
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Example
 Free cash flow to firm for Frontier Ceramics is
currently $300 million but is expected to grow by 4%
each year forever. If the company's cost of capital is
10%, how much is it worth? If market value of debt is
$3,000 million and FC has 200 million shares
outstanding, find per share value of FC.

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 Example
 Free cash flow to firm for Frontier Ceramics is currently
$300 million but is expected to grow by 4% each year
forever. If the company's cost of capital is 10%, how much
is it worth? If market value of debt is $3,000 million and FC
has 200 million shares outstanding, find per share value of
FC. $300 M × (1 +4%)
Firm Value = = $5,200 M
WACC − g

If market value of debt is $3,000 million, value of equity is $2,200

million
Ve = Vf − Vd = $5,200 M − $3,000 M = $2,200 M
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 Example
 XYZ has FCFF of 700 million and FCFE of 620 million. XYZ
before-tax cost of debt is 5.7 percent, and its required rate of
return for equity is 11.8 percent. The company expects a target
capital structure consisting of 20 percent debt financing and 80
percent equity financing. The tax rate is 33.33 percent, and
FCFF is expected to grow forever at 5.0 percent. XYZ has debt
outstanding with a market value of 2.2 billion and has 200
million outstanding common shares.

1. What is XYZ’s weighted average cost of capital?

2. What is the value of XYZ’s equity using the FCFF
valuation approach?
3. What is the value per share using this FCFF approach?
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Free Cash Flow to Firm Model –
Example
Today is December 31, 2003. The following
information applies to Addison Airlines:
 After-tax, operating income [EBIT(1 - T)] for the year
2004 is expected to be $400 million.
 The company’s depreciation expense for the year
2004 is expected to be $80 million.
 The company’s capital expenditures for the year
2004 are expected to be $160 million.
 No change is expected in the company’s net
operating working capital.
 The company’s free cash flow is expected to grow at
a constant rate of 5 percent per year.
 The company’s WACC is 10 percent.
 The current market value of the company’s debt is
$1.4 billion. The company currently has 125 million
shares of stock outstanding.
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Free Cash Flow to Firm Model –
Example
Step 1: Calculate the free cash flow amount:
FCFF = EBIT(1-T) + NCC – Capital Expenditure –
Change in working Capital
=$400 million+$80 million-$160
million-$0
=$320 million.

Step 2:Calculate the firm value today using the

constant growth corporate value model:
V0 = FCFF1 / (WACC – G)
= 320 / (0.10 – 0.05)
= 6,400 Million

This is the total firm value today! 53

Free Cash Flow to Firm Model –
Example
Step 3: Determine the market value of the
equity and price per share:
MVTotal = MVEquity + MVDebt
$6,400 million = MVEquity + $1,400
million
MVEquity = $5,000 million.

This is today’s market value of the firm’s equity.

Divide by the number of shares to find the

current price per share:

$5,000 million/125 million = $40.00.

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 Relative Valuation Techniques
The relative value concept is based on making
comparisons in order to determine value.
Relative Valuation measures include:

1. Price / Earnings Ratio

2. Price / Book Ratio
3. Price / Sales Ratio
4. Price / Cash flows

The most popular relative valuation technique is

based on price to earnings.
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Earnings Multiplier or The P/E
Ratio
The P/E ratio is simply when the investor values
the stock based on expected annual earnings.

P/E Ratio = Market Value per share/Earnings per

share

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The P/E Ratio FOR A Constant
Growth Company-
Determinants
The DDM model specifies the variables that
should determine the value of P/E Ratio.

P0 = D1 / (K – G)

Dividing both sides of Equation by Expected

Earnings (E1):

P0/E1 = (D1/E1) / (K – G)

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Cont.
Thus P/E ratio is determined by:
1. Expected dividend payout ratio
(D1/E1)
2. Required rate of return (k)

3. Growth rate (g)

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Example
Dividend payout = 50%
k = 12%, g = 8%,
P/E = 0.50/(0.12-0.08)
= 12.5

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A small change in either or both k or g will have a
great impact on P/E ratio.

60
P/E Ratio- Example
The Charleston Company is a relatively small,
privately owned firm. Last year the company
had net income of $15,000 and 10,000 shares
were outstanding. The owners were trying to
determine the equilibrium market value for the
stock prior to taking the company public. A
similar firm that is publicly traded had a
price/earnings ratio of 5.0. Using only the
information given, estimate the market value of
one share of Charleston’s stock.
Sol:
EPS = $15,000/10,000 = $1.50.
P/E = 5.0 = P/$1.50.
P = $7.50.
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Price/Book Value
Price to Book Value is calculated as the ratio of
price to stockholder’s Equity as measured on
the Balance Sheet.

P/BV = Price per share/ Book Value per share

For example, a P/B ratio above 1 indicates that

the investors are willing to pay more for the
company than its net assets are worth. This
could indicate that the company has healthy
future profit projections and the investors are
willing to pay a premium for that possibility.
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 If the market book ratio is less than 1,
on the other hand, the company’s stock
price is selling for less than their assets
are actually worth.

63
Price/Book Value - Example
You are given the following information:
Stockholders’ equity = $1,250; price/earnings
ratio = 5; shares outstanding = 25; and
market/book ratio = 1.5. Calculate the market
price of a share of the company’s stock.

Total market value = $1,250(1.5) =

$1,875.
Market value per share = $1,875/25 = $75.

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PRICE/Sales Ratio
The PSR is calculated by dividing a company’s
current stock Price by its revenue per share.

P/S = Price per share/ Revenues per share

65
 P/S RATIO
 Let's assume Company XYZ reports net sales of
$5,000,000 and it currently has 500,000 shares
outstanding. The stock is currently trading at $20.
 Sales per Share = (5,000,000/500,000) = 10
 Price-to-Sales Ratio = 20/10 = 2
 Now we want to compare XYZ to one of its competitors,
Company ABC.
 ABC also reports net sales of $5,000,000 and it also has
500,000 shares outstanding. The stock is trading at
$100.
 Sales per Share = (5,000,000/500,000) = 10
 Price-to-Sales Ratio = 100/10 = 10 66
Components of Required Return

Let’s break down the K, discount rate which we

used in the Dividend Discount Model or DDM
Po = D1 / (K-g)
if we rearrange to solve for K….
then…
K-g = D1/Po
K = (D1/ Po) + g

67
Components of Required Return

K = (D1/ Po) + g

This means TR has two components:

D1/Po = Dividend Yield

g = same rate as the increase in stock price
= Capital gains yield

68
Components of Required Return -
Example
If a stock is selling for $20 per share. Next
dividend will be $1 per share. Dividend will
grow by 10% per year forever.
What is the return on this stock?

69
Components of Required Return -
Example
If a stock is selling for $20 per share. Next
dividend will be $1 per share. Dividend will
grow by 10% per year forever.
What is the return on this stock?
K = Div yield + Cap gains yield
= 1/20 + 10%
= 5% + 10%
= 15%

70