Investments
BSC III
Winter Semester 2010
Lahore School of
Economics
Investments
Chap 10
Common Stock Valuation
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)
Treasuries
Corporates
 Equities
Preferred Stock
Common Stock
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 = V0
V0
= 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
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).
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 = (D1+P1) / (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
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
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?
Po = Do / k
= 2/0.2
= 10
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
The Constant Growth Rate
Model
Stock Price with constant growth dividends:
Po
= Do *(1+g) / (K-g)
P0
= D1 / (K – g)
OR
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
share?
P0
= D1 / (k – g)
= 2.3 *(1.05) / (0.13 - 0.05)
= 2.415 / 0.8
= 30.19
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
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
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
year, forever.
What’s the price per share today?
P0 = D1 / (k – g)
= 4/(.16-.06)
= 4/.1
= $40
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
P4
= D5 / (k – g)
= D1 * (1+g)4
= 4(1.06)4
= 5.05
= 5.05/0.1
= 50.50
Investments
BSC/BBA III
Winter Semester 2010
Lahore School of
Economics
Investments
Chap 10
Common Stock Valuation
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
P0 = PV of Dividends during the non Constant period
PLUS
PV of Dividends during the constant Growth
Period
Multiple Growth Rate Case
1.
2.
3.
To find Value of Stock with Non Constant Growth,
we go through the following three steps:
Find the PV of Dividends during the period of Non
Constant Growth.
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.
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
|
1.00
P0 = ?
CFt 0
k = 12%
gs = 5%
1
|
1.05
1.05
2
3 Years
|
|
gs = 5%
gn = 10%
1.1025
1.21275
P̂2 = 60.6375 = 1.21275
61.7400 0.12  0.10
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 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
2
3
4 Years
k = 10% 1
|
|
|
|
|
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
CFt 0
2.08
2.1840
84.88480
3
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.
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?
Q#2
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?
Q#3
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?
Q#4
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?
Q#5
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?
Q#6
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!
Q#7
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?
Investments
BBA III
Winter Semester 2010
Lahore School of
Economics
Investments
Chap 10
Common Stock Valuation
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.
2.
3.
Dividend Discount Model
Free Cash Flow to Equity (FCFE) Model
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
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
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
= 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
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 a
constant rate of 6% forever. What is the stock’s intrinsic
value today?
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
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
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?
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
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
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
= 136.71
= 94.75
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
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
Free Cash Flow to Firm Model –
Implementing the model
1.
2.
3.
4.
Forecast Expected FCFF
Estimate the Discount Rate (WACC)
Calculate the Value of the Corporation
Calculate Intrinsic Stock Value
=
Value of Corporation MINUS Value of Debt
MINUS Value of Preferred Stock.
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
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.
Free Cash Flow to Firm
Model – Example
Step 1:
FCFF
Calculate the free cash flow amount:
= 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!
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.
Relative Valuation
Techniques
The relative value concept is based on making
comparisons in order to determine value. Relative
Valuation measures include:
1.
2.
3.
Price / Earnings Ratio
Price / Book Ratio
Price / Sales Ratio
Earnings Multiplier
Approach - The P/E Ratio
The P/E ratio is simply the number of times investors
value earnings as expressed in stock’s price.
Companies with higher P/E ratio as compared to a
benchmark are considered over valued & Vice Versa.
However, sometimes investors realize that the P/E
ratio should be higher for companies whose earnings
are expected to grow rapidly, which then, does not
necessarily indicate overvaluation!
The P/E Ratio FOR A
Constant Growth
Company- Determinants
P0
= D1 / (K – G)
Dividing both sides of Equation by Expected Earnings:
P0/E1
= (D1/E1) / (K – G)
P/E Ratio & Interest rates
The P/E ratio reflects investors optimism &
pessimism. As the required rate of Return increases,
other things being equal, the P/E ratio increases.
As interest rates increase, bonds become More
attractive compared to Stocks on a current return
basis.
Hence, As interest rates rise, P/E ratio should decline
& Vice Versa.
P/E Ratio- Example
Making Valuations through comparisons
P/E = Price to Earnings ratio
So, if comparable stocks are trading at x15.
&
Earnings for a stock are equal to: $3
What should be the stock price? 45
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.
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.
Price/Book Value
Price to Book Value is calculated as the ratio of price
to stockholder’s Equity as measured on the Balance
Sheet.
If the Value of the Ratio is 1, the Market price is equal
to the accounting Value & Vice Versa.
Companies with higher P/BV ratio as compared to a
benchmark are considered over valued & Vice Versa.
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.
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)
Market value per share = $1,875/25
= $1,875.
= $75.
Price/Book Value - Example
Making Valuations through comparisons
P/BV = Price to Book Value (S.Equity) ratio
So, if comparable stocks are trading at x10.
& BV for a stock is equal to: $5
What should be the stock price?
50
PRICE/Sales Ratio
The PSR is calculated by dividing a company’s current
stock Price by its revenue per share.
One rule of thumb for PSR is to say that PSR os 1 is
average for all companies, & therefore those with a
PSR considerably less than 1 are undervalued.
Companies with higher P/S ratio as compared to a
benchmark are considered over valued & Vice Versa.
PRICE/Sales Ratio
Making Valuations through comparisons
P/S = Price to Sales ratio
So, if comparable stocks are trading at x1.
& Sales per share for a stock is equal to: $5
What should be the stock price?
5
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
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
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?
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%
Thank you for your
time & Patience 
Assignment # 9 (6 Questions)
Q1:
ABC Co. recently had FCFE of $120 Million. Company
had 50,000 Bonds outstanding trading @ par with a Coupon
Rate of 8%. Capital Expenditure & Change in Working
Capital during the year were 15 Million & 5Million,
respectively. Company had Depreciation & Amortization
charges of 2 Million & 0.5 Million, Respectively. XYZ Co. has
a tax rate of 35% with Cost of equity of 12% & WACC
equivalent to 10%. No debt outstanding was paid during
the year. Although, company issued new bonds worth of 1
million. Company has 500,000 shares of preferred stock
outstanding with a par of $120 & dividend rate of 5%.
Company is expected to grow at a constant rate of 5%
forever. With the given information, calculate Value of the
firm & intrinsic value per share using FCFF Model assuming
1 million Common Stock shares outstanding.
Assignment # 9 (6 Questions)
Q2:
ABC Co. recently had EBIT of $100 Million.
Company had 20,000 Bonds outstanding trading @ par
with a Coupon Rate of 7%. Capital Expenditure &
Change in Working Capital during the year were 5
Million & 1Million, respectively. Company had
Depreciation & Amortization charges of 2.5 Million &
1.5 Million, Respectively. XYZ Co. has a tax rate of
35% with Cost of equity of 12% & WACC equivalent
to 9%. Company is expected to grow at a constant
rate of 7% forever. With the given information,
calculate Value of the firm & intrinsic value per share
using FCFF Model assuming 1.5 million shares of
common stock outstanding.
Assignment # 9 (6 Questions)
Q3:An analyst has collected the following information about
XYZ Co.:

Projected NI for the next year $200 million.

Projected depreciation expense for the next year $10
million.

Projected capital expenditures for the next year $65 million.

Projected increase in operating working capital next year
$30 million.

Interest Expense for the year was $2.5 million & Company
paid back 20 Million of its debt outstanding but also issued
$4 million of new debt.

Cost of equity 12%.

Number of shares outstanding today 20 million.
Assignment # 9 (6 Questions)
Q3:
A.
B.
The company’s free cash flow to firm is expected to
grow at 15% for first two years, then @ 10% for
year 3 & year 4 & then it will grow @ 5% forever.
What is the stock’s intrinsic value today using FCFF
Model?
The company’s free cash flow to Equity is expected to
grow at 10% for first two years, then @ 8% for year
3 & then it will grow @ 5% forever. What is the
stock’s intrinsic value today using FCFE Model?
Assignment # 9 (6 Questions)
Q4:
The analyst has estimated the company’s free cash
flows for the following years:
Year
Free Cash Flow
1
$3,000
2
4,000
3
5,000
The analyst estimates that after three years (t = 3) the
company’s free cash flow will grow at a constant rate of 6
percent per year. The analyst estimates that the company’s
weighted average cost of capital is 10 percent. The
company’s debt and preferred stock has a total market value
of $25,000 and there are 1,000 outstanding shares of
common stock. What is the (per-share) intrinsic value of the
company’s common stock?
Assignment # 9 (6 Questions)
Q5:
Lamonica Motors just reported earnings per share
of $2.00. The stock has a price earnings ratio of 40,
so the stock’s current price is $80 per share. Analysts
expect that one year from now the company will have
an EPS of $2.40, and it will pay its first dividend of
$1.00 per share. The stock has a required return of 10
percent. What price earnings ratio must the stock
have one year from now so that investors realize their
expected return?
Assignment # 9 (6 Questions)
Q6:
Dean Brothers Inc. recently reported net income
of $1,500,000. The company has 300,000 shares of
common stock, and it currently trades at $60 a share.
The company continues to expand and anticipates
that one year from now its net income will be
$2,500,000. Over the next year the company also
anticipates issuing an additional 100,000 shares of
stock, so that one year from now the company will
have 400,000 shares of common stock. Assuming the
company’s price/earnings ratio remains at its current
level, what will be the company’s stock price one year
from now?