Due Date 1159 p.m. EST, Sunday, of Unit 7 Points 100

Due Date: 11:59 p.m. EST, Sunday, of Unit 7
Points: 100
Overview:
Over the course of the last few units, you have been working on
crafting the argument
for your Argument Essay. You will now write an argument
essay that answers one of
these questions.
The essay should answer ONE of these questions:
1. Should climate change be considered a real issue or a hoax?
2. Should the United States have universal health care?
3. Should employers have access to employee’s social media
content?
Each of the above questions relate to one of the issues you have
already written about
in the Unit 4 Assignment: Pro and Con of an Issue. Now, choose
one side of the issue
to develop into an argument essay.
You should answer ONE of the above questions in a well-
thought out and developed

argument essay with:
• A clear introduction that sets up the issue, explains your
topics, and ends with your
thesis statement.
• Body paragraphs focusing on one topic in support of your
argument in each paragraph.
o You need three reliable and academic sources for this
assignment in support of
your argument. You should include evidence that is directly
quoted, paraphrased,
or summarized to support each topic. The evidence should have
appropriate in-
text citations.
o You will typically want to include one piece of evidence in
the body of each
paragraph, as you did in the paragraph and pro/con assignment.
You are not
required to include a source about the counterargument (other
side of your
argument), but you may if you would like.
• Then, end with a conclusion that wraps up your essay’s
argument and leaves the reader

with something to consider about your issue.
ENG110 – College Writing
Argument Essay
• Include a references page for the three sources you used in
your essay.
You can use the ideas from your Pro/Con paragraphs in your
argument essay, but
they should be revised and reworded so that you are not just
resubmitting your
Unit 4 assignment.
Argument Essay and Third Person, Objective Writing
We have probably all had to argue for a position we held. What
makes someone
receptive to your argument? Normally, the audience is more
willing to listen to your
position if you argue for it objectively and avoid unreasonable,
argumentative tactics.
Your argument needs to be logical and fair, giving people the
ability to disagree with
you.
Your argument also should be written in the third person to
show that you can be
objective, meaning you use “He,” “she,” “they,” “people,”
“one” and do not use “I,” “me,”
“we,” “us,” “our,” “you,” and “your.”
Instructions:

• Create an argument essay that answers ONE of the above
questions.
• You should have a well-articulated argument essay with an
introduction, body
paragraphs (with evidence), conclusion, and a references page.
Requirements:
• Please submit a Microsoft Word document or PDF.
• The essay should be three to four pages in length with an
additional APA-style
title and reference pages. The document should follow proper
APA style
formatting (Times New Roman, 12 font suggested) with 1-inch
margins and
double spaced.
• Include three (3) sources in your essay that are reliable and
academic.
o Make sure you have at least three (3) in-text citations where
you have
directly quoted, paraphrased, or summarized material from the
sources.

You will need corresponding references for each of these
sources that
match the in-text citations.
• You need an introduction and conclusion for this essay.
Remember the
introduction sets up the essay and ends with the thesis
statement. The
conclusion sums up the essay and restates the thesis in a
different way. The
introduction and conclusion should not be exact replicas of each
other.
• Your body paragraphs should each focus on one topic that
supports your
argument.
• Your writing should be free of punctuation, spelling, and
grammar errors and
contain appropriate word choice for an academic setting with
clear sentence
structure.
Be sure to read the criteria by which your work will be
evaluated before you write

and again after you write.
Evaluation Rubric for the Argument Essay Assignment
CRITERIA Novice
Needs
Improvement
Proficient Exemplary
(0–11 points) (12–15 points) (16–17 points) (18–20 points)
Introduction and
Conclusion
Introduction and/or
the conclusion are
not present.
Introduction/
conclusion are
very hard to
understand and
significantly
missing details.
Introduction and
conclusion are
attempted. The
introduction and
conclusion may be
lacking details to
properly set up and
then wrap up the

essay. The
introduction/
conclusion are not
related.
Introduction and
conclusion nicely
set up and wrap up
the essay. The
introduction/
conclusion could
relate better.
Introduction and
conclusion effectively
set up and wrap up
the essay. The
introduction/
conclusion relate well
to each other.
Organization and
Structure
Many details are
not in a logical or
expected order.
The paper does
not use
paragraphs and
does not focus on
the assigned
argument issue.
Writing may have

some discernible
organization, but
some details are not
in a logical or
expected order. The
paper uses
paragraphs
ineffectively and
lacks focus on the
assigned argument
issue.
Writing is
organized, and
details are placed
in a logical order.
Paragraphs are
mostly used
effectively and
generally focus well
on the assignment
argument issue.
Writing is effective,
purposeful, and well-
organized.
Paragraphs are used
effectively and focus
well on the assigned
argument issue.
Argument Fails to develop
argument(s). No
clear thesis to

highlight the
argument.
Some argument(s)
are developed but
may be missing one
or need further
elaboration. Thesis
attempts to highlight
the argument,
though clarification
is needed.
Develops most
argument(s).
Thesis highlights
the argument with
only minor need for
clarification.
Fully develops
argument(s) fairly.
Thesis highlights the
argument well.
Resources and
Citations
No reliable and
academic
resources used.
Resources do not
relate to the
argument and/or
are not properly

1 reliable and
academic resource
used. Resources
generally relate to
the argument but
may not be properly
formatted in the
assignment.
2 reliable and
academic
resources
used. Resources
relate to the
argument, and for
the most part, are
3 reliable and
academic resources
used. Resources
effectively relate to
the argument and are
properly formatted in
the assignment.
CRITERIA Novice
Needs
Improvement
Proficient Exemplary
formatted in the

assignment.
properly formatted
in the assignment.
(0–5 points) (6–7 points) (8 points) (9–10 points)
Paper Length Significantly less
than 1 page or
significantly more
than 4 pages.
Only 1–2 pages in
length.
Only 2–3 pages in
length.
3–4 pages in length.
Clear and
Professional
Writing and APA
Format
Writing is hard to
understand
because of errors
in grammar,
spelling, and
punctuation. Word
choice is
inappropriate for

an academic
setting. Sentence
structure is often
unclear. Paper
rarely or does not
use the third-
person
perspective and
an objective tone.
APA format is not
followed.
Writing is sometimes
difficult to
understand because
of several errors in
grammar,
punctuation, and
spelling. Word
choice is sometimes
inappropriate for an
academic setting.
Sentence structure
is sometimes
unclear. Paper
inconsistently uses a
third-person
perspective and
objective tone. APA
format is sometimes
followed.
Writing is easy to
understand despite
minor errors in

punctuation,
spelling, and
grammar.
Appropriate word
choice is used for
an academic
setting. Sentence
structure is mostly
clear. Paper mostly
uses a third-person
perspective and
objective tone. APA
format is mostly
followed.
Writing is free of
almost all
punctuation, spelling,
and grammar errors.
Appropriate word
choice is used for an
academic setting.
Sentence structure is
clear. Paper is written
in the third-person
perspective with an
objective tone. APA
format is followed.
Corporate Valuation and Stock Valuation
CHAPTER 7
© 2020 Cengage Learning. All Rights Reserved. May not be

copied, scanned, or duplicated, in whole or in part, except for
use as permitted in a license distributed with a certain product
or service or otherwise on a password-protected website for
classroom use.
Topics in Chapter
Features of common stock
Valuing common stock
Dividend growth model
Free cash flow valuation model
Market multiples
Preferred stock
classroom use.
Corporate Valuation and Stock Valuation
classroom use.
Common Stock: Owners, Directors, and Managers
Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Since managers are “agents” of shareholders, their goal should
be: Maximize stock price.

classroom use.
Classified Stock
Classified stock has special provisions for each class, usually
involving voting rights and dividend rights.
Usually named Class A, Class B, etc.
New shares in IPO sometimes have voting restrictions but full
dividend rights.
Founders’ shares usually have voting rights but dividend
restrictions.
Standard & Poor’s no longer allows new additions to its indices
to have classified stock.
classroom use.
Tracking Stock
The dividends of tracking stock are tied to a particular division,
rather than the company as a whole.
Investors can separately value the divisions.
Its easier to compensate division managers with the tracking
stock.
But tracking stock usually has no voting rights, and the
financial disclosure for the division is not as regulated as for
the company.
Very few companies have tracking stock.

classroom use.
Different Approaches for Valuing Common Stock
Free cash flow model
Constant growth
Nonconstant growth
Dividend growth model
Constant growth
Nonconstant growth
Using the multiples of comparable firms
classroom use.
The Free Cash Flow Valuation Model: FCF and WACC
Free cash flow (FCF) is:
The cash flow available for distribution to all of a company’s
investors.
Generated by a company’s operations.
The weighted average cost of capital (WACC) is:
The overall rate of return required by all of the company’s
investors.
classroom use.
Value of Operations (Vop)

The PV of expected future FCF, discounted at the WACC, is the
value of a company’s operations (Vop):
classroom use.
Sources of Value
Value of operations
Nonoperating assets
Short-term investments and other marketable securities
Ownership of non-controlling interest in another company
Value of nonoperating assets usually is very close to figure that
is reported on balance sheets.
classroom use.
Claims on Corporate Value
Debtholders have first claim.
Preferred stockholders have the next claim.
Any remaining value belongs to stockholders.
classroom use.

Total Corporate Value: Sources and Claims
classroom use.
Value of operations= PV of FCF discounted
at WACC
Conceptually correct, but how do you find the present value of
an infinite stream?
classroom use.
Suppose FCFs are expected to grow at a constant rate, gL,
starting at t=1, and continue forever. What happens to FCF?
What is the value of operations if FCFs grow at a constant rate?
See next slide.
classroom use.
Value of operations in terms of FCF1 and gL:

We can multiply and divide by (1+gL), for a reason that will
soon be clear, as shown on the next slide.
classroom use.
Rewritten value of operations:
We can group , as shown on the next slide.
classroom use.
Value of operations with grouped terms:
We can group the terms, as shown on the next slide.
classroom use.
Value of operations if FCF grows
at a constant rate:

What happens toif t gets large? It depends on the size of gL
relative to WACC. See next slide.
classroom use.
What happens to as t gets large?
If gL < WACC: Then < 1.
If gL ≥ WACC: Then ≥ 1.
What happens to the value of operations if gL ≥ WACC? See
next slide.
classroom use.
What happens to the value of operations
if gL ≥ WACC?
Vop = (Big) + (Bigger) + (Even Bigger) + …+ (Really big!)
= Infinity! So g can’t be greater than or equal to WACC!
classroom use.
What happens to the value of operations

if gL ≤ WACC?
Vop = (Small) + (Smaller) + (Even smaller) + …+ FCF0
(Really small!) = ?
All the terms get smaller and smaller, but what happens to the
sum? See next slide
classroom use.
What is the sum of an infinite number of factors that get smaller
at a geometric rate?
Consider this example. The first row is t. The second row is a
number that is less than 1 that is compounded to the power of t.
The third row is the cumulative sum.t1234 . . .
∞(1/2)t1/21/41/81/161/∞ ≈ 0Σ(1/2)t1/23/47/815/16≈ 1
This sum converges to 1. Similarly, converges (although not to
1). See next slide.
classroom use.
Constant Growth Formula for Value of Operations: gL begins at
Time 1
If FCF are expected to grow at a constant rate of gL from Time
1 and afterwards, and gL<WACC:
This is the PV of all FCF from Time 1 through infinity, when

discounted at WACC.
classroom use.
Constant Growth Formula for Value of Operations: gL begins at
Time 0
If FCF are expected to grow at a constant rate of gL from Time
0 and afterwards, and gL<WACC:
This is still the PV of all FCF from Time 1 through infinity,
when discounted at WACC.
classroom use.
Data for FCF Valuation
FCF0 = $24 million
WACC = 11%
FCF is expected to grow at a constant rate of gL = 5%
Short-term investments = $100 million
Debt = $200 million
Preferred stock = $50 million
Number of shares =n = 10 million
use as permitted in a license distributed with a certai n product

classroom use.
Find Value of Operations
classroom use.
Total Value of Company (VTotal)
classroom use.
Estimated Intrinsic Value of Equity
(VEquity)Voperations$420.00+ ST
Inv.100.00VTotal$520.00−Debt200.00− Preferred
Stk.50.00VEquity$270.00
classroom use.
Estimated Intrinsic Stock Price per Share,
(1 of 2)Voperations`$420.00+ ST
Inv.100.00VTotal$520.00−Debt200.00− Preferred

classroom use.
Expansion Plan: Nonconstant Growth
Finance expansion financed by owners.
Projected free cash flows (FCF):
Year 1 FCF = −$10 million.
Year 2 FCF = $20 million.
Year 3 FCF = $35 million
FCF grows at constant rate of 5% after year 3.
No change in WACC, marketable securities, debt, preferred
stock, or number of shares of stock.
classroom use.
Estimating the Value of Operations
Free cash flows are forecast for three years in this example, so
the forecast horizon is three years.
Growth in free cash flows is not constant during the forecast, so
we can’t use the constant growth formula to find the value of
operations at time 0.

classroom use.
Time Line of FCFYear012345…
tFCF−$10$20$35FCF3(1+gL)FCF4(1+gL)FCFt(1+gL)
Free cash flows are forecast for three years in this example, so
the forecast horizon is three years.
Growth in free cash flows is not constant during the forecast, so
we can’t use the constant growth formula to find the value of
operations at time 0.
classroom use.
Horizon ValueYear012345…
tFCFFCF3(1+gL)FCF4(1+gL)FCFt(1+gL)HV3← ↵ ← ↵ ← ↵
Horizon value is also called terminal value, or continuing value.
classroom use.
Horizon Value Application
(FCF3 = $35, WACC = 11%, gL = 5%)
This is the value of FCF from Year 4 and beyond discounted
back to Year 3.

classroom use.
Value of Operations at t=0: PV of FCF1 through FCF3 plus PV
of HV3Year012345… tFCFFCF1FCF2FCF3PV of FCF in
explicit forecast← ↵ ← ↵ ←
↵ FCF3(1+gL)FCF4(1+gL)FCFt(1+gL)+HV3← ↵ ← ↵ ← ↵ PV
of HV← ↵ ← ↵ ← ↵ = Value of operations Time 0
PV of HV is the PV of FCF beyond the explicit forecast. So PV
of HV plus PV of FCF in explicit forecast is the PV of all future
FCFs.
classroom use.
Application: Current Value of Operations (Nonconstant g in
FCF until after Year 3; gL = 5%; WACC = 11%)
classroom use.
Estimated Intrinsic Stock Price per Share,
(2 of 2) Voperations$480.67 + ST Inv. 100.00
VTotal$580.67 −Debt200.00− Preferred Stk.
50.00VEquity$330.67 ÷ n 10 $33.07

classroom use.
How much of the value of operations is based on cash flows
from Year 4 and beyond?
The horizon value is the value of all FCF from Year 4 and
beyond, discounted back to Year 3.
The present value of HV3 is the present value of all FCF from
Year 4 and beyond.
The PV of HV3 is the percent of total value due to long-term
cash flows.
classroom use.
Value of Operations and Present Value of Horizon Value
Value of operations: Vop = $480.67
Horizon value: HV3 = $612.5
PV of HV3 = $612.5/(1 + 0.11)3
= $447.855
classroom use.
Percent of Value Due to Long-Term Cash Flows
In this example, 93% of value is due to cash flows 4 or more

years into the future.
For the average company, this percentage is around 80%.
classroom use.
Long-term versus Short-term Focus
Why focus on quarterly earnings if most value is from longer-
term cash flows?
Changes in quarterly earnings can signal changes future in cash
flows. This would affect the current stock price.
Managers often have bonuses tied to quarterly earnings, so they
have incentive to manage earnings.
classroom use.
Forecasting Free Cash Flows: A Simple Approach
Forecast sales to grow at chosen growth rates.
Forecast net operating profit after taxes (NOPAT) and total net
operating capital (OpCap) as a percent of sales.
classroom use.
Current Situation (in millions)
Most recent data:

Sales of $2,000
Total net operating capital, OpCap = $1,120
Operating profitability ratio
OP = NOPAT/Sales = 4.5%
Capital requirement ratio
CR = OpCap/Sales = 56%.
The target weighted average cost of capital (WACC) is 9%.
classroom use.
Initial Operating Assumptions for the No Change Scenario
Operating ratios remain unchanged from values in most recent
year.
Sales will grow by 10%, 8%, 5%, and 5% for the next four
years.
The long-term growth rate in sales is 5%.
The target weighted average cost of capital (WACC) is 9%.
classroom use.
AssumptionsActualForecastInputs01234WACC9.0%Sales$2,000
OpCap$1,120Sales growth
rate10%8%5%5%NOPAT/Sales4.5%4.5%4.5%4.5%4.5%OpCAP
/Sales56.0%56.0%56.0%56.0%56.0%

classroom use.
Examples of Forecasting Items
Sales1 = $2,000(1+0.10) = $2,200
NOPAT1 = $2,200(0.045) = $99
OpCap1 = $2,200(0.56) = $1,232
FCFt = NOPATt − (OpCapt − OpCapt-1)
ROICt = NOPATt/OpCapt
classroom use.
Forecasted FCF: No changes in operating ratiosScenario:
No
ChangeActualForecast01234Sales$2,000$2,200$2,376$2,495$2,
620NOPAT$99$107$112$117.879OpCap$1,120$1,232$1,331$1,
397.088$1,466.942FCF −$13$8.36$45.738$48.025Growth in
FCF-164%447.1%5.0%ROIC8.0%8.0%8.0%8.0%8.0%
FCF is negative in Year 1.
ROIC of 8% is less than WACC of 9%--not good!
Note: There is no rounding in intermediate calculations.
classroom use.
Estimated Intrinsic Value (1 of 2)

classroom use.
Estimated Intrinsic Value (2 of 2)Scenario: No ChangeHorizon
Value:HV4 =$1,260.65Value of Operations:Present value of
HV$893.08+ Present value of FCF$64.45Value of operations
≈$958
classroom use.
The Value of Operations versus the Total Net Operating Capital
The ROIC (8%) is too low compared to the WACC (9%).
The capital is not earning enough to meet investors’ required
return, so:
Horizon value ($958) is less than the total net operating capital
at the horizon ($1,467).
Current value of operations ($958) is less than the current total
net operating capital ($1,120).
ROIC must be greater than WACC/(1+gL) for horizon value to
be greater than the total net operating capital at the horizon.
classroom use.
Value Drivers
The ROIC (8%) is too low compared to the WACC (9%).

The capital is not earning enough to meet investors’ required
return, so:
Horizon value ($958) is less than the total net operating capital
at the horizon ($1,467).
Current value of operations ($958) is less than the current total
net operating capital ($1,120).
ROIC must be greater than WACC/(1+gL) for horizon value to
be greater than the total net operating capital at the horizon.
classroom use.
Impact of Higher Growth RatesNo ChangeImprove
Growthg0,110%11%g1,28%9%g2,35%6%g3,45%6%gL5%6%OP
4.5%4.5%CR56.0%56.0%ROIC8.0%8.0%Vop,0$958$933WACC
9.00%9.00%
Higher growth causes Vop,0 to fall.
ROIC must be greater than WACC/(1+WACC) for growth to add
value.
WACC/(1+WACC) = 8.26%
classroom use.
Impact of Higher Operating ProfitabilityNo ChangeImprove
OPg0,110%10%g1,28%8%g2,35%5%g3,45%5%gL5%5%OP4.5
%5.5%CR56.0%56.0%ROIC8.0%9.8%Vop,0$958$1,523WACC9
.00%9.00%
Higher operating profitability increases the ROIC.
ROIC of 9.8% > 8.26%

The higher ROIC causes a big increase in Vop,0.
classroom use.
Impact of Lower Capital RequirementsNo ChangeImprove
CRg0,110%10%g1,28%8%g2,35%5%g3,45%5%gL5%5%OP4.5
%4.5%CR56.0%51.0%ROIC8.0%8.8%Vop,0$958$1,191WACC9
.00%9.00%
Lower capital requirements increases the ROIC.
ROIC of 8.8% > 8.26%
The higher ROIC causes an increase in Vop,0.
classroom use.
Impact of Simultaneous Improvements in OP and CRNo
ChangeImprove OP and
CRg0,110%10%g1,28%8%g2,35%5%g3,45%5%gL5%5%OP4.5
%5.5%CR56.0%51.0%ROIC8.0%10.8%Vop,0$958$1,756WACC
9.00%9.00%
The ROIC is much higher due to the improvements in
operations.
classroom use.

Impact of Simultaneous Improvements in Growth, OP, and
CRNo ChangeImprove
Allg0,110%11%g1,28%9%g2,35%6%g3,45%6%gL5%6%OP4.5
%5.5%CR56.0%51.0%ROIC8.0%10.8%Vop,0$958$2,008WACC
9.00%9.00%
operations.
With a higher ROIC, growth adds substantial value.
classroom use.
Summary: Value of operations for previous combinations of
ROIC and
gLROICROICROICROICROIC8.0%8.8%9.8%10.8%gL5%$958$
1,191$1,523$1,756gL6%$933$1,247$1,694$2,008
operations.
With a higher ROIC, growth adds substantial value.
classroom use.
Are volatile stock prices consistent with rational pricing?
The previous slide shows that small changes in ROIC and
growth cause large changes in value.
Similarly, small changes in the cost of capital (WACC), perhaps
due to changes in risk or interest rates, cause large changes in
value.
As new information arrives, investors continually update their

estimates of operating profitability, capital requirements,
growth, risk, and interest rates.
If stock prices aren’t volatile, then this means there isn’t a good
flow of information.
classroom use.
Value of dividend-paying stock = PV of dividends discounted at
required return
Conceptually correct, but how do you find the present value of
an infinite stream?
classroom use.
Suppose dividends are expected to grow at a constant rate, gL,
forever.
D1 = D0(1 + gL)1
D2 = D0(1 + gL)2
Dt = D0(1 + gL)t
What is the present value of a constant growth Dt when
discounted at the stock’s required return, rs? See next slide.

classroom use.
Present Value of a Constant Growth Dividend
What happens to as t gets bigger?
If gL<rs: Then < 1.
So the bracket approaches zero as t gets large.
classroom use.
Constant Dividend Growth Model (gL<rs)
If gL is constant and less than rs, then converges to:
classroom use.
What happens if gL > rs?
So gL must be less than rs for the constant growth model to be
applicable!!

classroom use.
Required rate of return: beta = 1.2, rRF = 7%,
and RPM = 5%.
Use the SML to calculate rs:
classroom use.
Estimated Intrinsic Stock Value:
D0 = $2.00, rs = 13%, gL = 6%
classroom use.
Expected Stock Price in 1 Year
classroom use.

Expected Dividend Yield and Capital
Gains Yield (Year 1)
classroom use.
Total Year 1 Return
Total return = Dividend yield + Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = gL.
classroom use.
Rearrange model to rate of return form:
classroom use.

Nonconstant Growth Stock
Nonconstant growth of 30% for Year 0 to Year 1, 25% for Year
1 to Year 2, 15% for Year 2 to Year 3, and then long-run
constant gL = 6%.
Can no longer use constant growth model.
However, growth becomes constant after 3 years.
classroom use.
Steps to Estimate Current Stock Value
Forecast dividends for nonconstant period, which ends at
horizon date after which growth is constant at gL.
Find horizon value, which is PV of dividends beyond horizon
date discounted back to horizon date
Horizon value = =
classroom use.
Steps to Estimate Current Stock Price (Continued)
Find PV of each dividend in the forecast period.
Find PV of horizon value.
Sum PV of dividends and PV of horizon value.
Result is estimated current stock value.

classroom use.
Example of Estimating Current Stock Value (D0 = $2.00, rs =
13%)
classroom use.
Expected Dividend Yield and Capital
Gains Yield (t = 0)
classroom use.
Expected Dividend Yield and Capital Gains Yield (after t = 3)
During nonconstant growth, dividend yield and capital gains
yield are not constant.
If current growth is greater than g, current capital gains yield is
greater than g.
After t = 3, gL = constant = 6%, so the
capital gains yield = 6%.
Because rs = 13%, after t = 3 dividend
yield = 13% – 6% = 7%.

classroom use.
Using Stock Price Multiples to Estimate
Stock Price
Analysts often use the P/E multiple (the price per share divided
by the earnings per share).
Example:
Estimate the average P/E ratio of comparable firms. This is the
P/E multiple.
Multiply this average P/E ratio by the expected earnings of the
company to estimate its stock price.
classroom use.
Using Entity Multiples
The entity value (V) is:
the market value of equity (# shares of stock multiplied by the
price per share)
plus the value of debt.
Pick a measure, such as EBITDA, Sales, Customers, Eyeballs,
etc.
Calculate the average entity ratio for a sample of comparable
firms. For example,
V/EBITDA
V/Customers

classroom use.
Using Entity Multiples (Continued)
Find the entity value of the firm in question. For example,
Multiply the firm’s sales by the V/Sales multiple.
Multiply the firm’s # of customers by the V/Customers ratio
The result is the firm’s total value.
Subtract the firm’s debt to get the total value of its equity.
Divide by the number of shares to calculate the price per share.
classroom use.
Problems with Market Multiple Methods
It is often hard to find comparable firms.
The average ratio for the sample of comparable firms often has
a wide range.
For example, the average P/E ratio might be 20, but the range
could be from 10 to 50. How do you know whether your firm
should be compared to the low, average, or high performers?
classroom use.
Comparing the FCF Model and Dividend
Growth Model
Can apply FCF model in more situations:
Privately held companies
Divisions of companies
Companies that pay zero (or very low) dividends

FCF model requires forecasted financial statements to estimate
FCF
Takes more effort than just forecasting dividends, but…
Provides more insights into value drivers.
classroom use.
Preferred Stock
Hybrid security.
Similar to bonds in that preferred stockholders receive a fixed
dividend which must be paid before dividends can be paid on
common stock.
However, unlike bonds, preferred stock dividends can be
omitted without fear of pushing the firm into bankruptcy.
classroom use.
Value of Preferred Stock
(Dividend = $2.10; rps = 7%)
classroom use.

(
)
t
op
t
t 1
FCF
V
1WACC
¥
=
=
+
å
(
)
(
)
(
)
(
)
12
op
12
3
3
FCFFCF
V
1WACC1WACC
FCF
FCF
...
1WACC1WACC
¥

¥
=+
++
++
++
(
)
(
)
(
)
1
21L
2
31
tL
L
t1
1
FCFFCF1g
FCFFCF1g
FCFFCF1g
-
=+
=+
=+
(
)
(
)
(
)
(
)
(
)

(
)
(
)
1
2L
1
op
12
2t-1
1L1L
3t
FCF1g
FCF
V
1WACC1WACC
FCF1gFCF1g
......
1WACC1WACC
+
=++
++
++
++
++
(
)
(
)
(
)
(
)
(
)
(

)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
1
1L1LL
op
12
LL
2t-1
1LL1LL
3t
LL
FCF1gFCF1g1g
V
1WACC1g1WACC1g
FCF1g1gFCF1g1g
......
1WACC1g1WACC1g
+++
=+

++++
++++
++++
++++
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
12
LL
11
op
12
LL
3t
LL

11
3t
LL
1+g1+g
FCFFCF
V=+
1+g1+g
1+WACC1+WACC
1+g1+g
FCFFCF
++...++...
1+g1+g
1+WACC1+WACC
éùéù
êúêú
ëûëû
éùéù
êúêú
ëûëû
12
LL
3
11
op
LL
1
L
1
L
t
L
L
FCFFCF
V=
1g1g
FC

1g1g
1WACC1WACC
1
FFCF
.
g1g
1WAC
....
C1
.
1g1
WAC
g
C
éùéù
+
êúêú
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ëûëû
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++
ëûë
++
éùéù
êúêú
++
ëûëû
++
éùéù
êúêú
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ëûëû
û
[

]
[
]
[
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[
]
1
11
op
LL
11
L
2
3
L
Bigger than 1Bigger than 1
Bigger than 1Bigger than
FCFFCF
V=
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1
FCFFCF
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1g1g
¥
éùéù
+
êúêú
++
ëûëû
éùéù
+++
êúêú
++
ëûëû

[
]
[
]
[
]
[
]
11
op
L
1
L
11
LL
2
3
Less than 1Less th
FCFFCF
V=
1g1g
FCFFCF
...
1g
an 1
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g
h
1
a
¥
éùéù
+
êúêú
++
ëûëû

éùéù
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ëûëû
(
)
1
op,0
FCF
V
WACCgL
=
-
(
)
(
)
0L
op,0
FCF1g
V
WACCgL
+
=
-
(
)
(
)
(
)
(
)
0L
op

L
op
FCF1g
V
WACCg
$2410.05
V$420
0.110.05
+
=
-
+
==
-
Total
operations
V
$420.00
STInv.100.00
V$520.00
+
(
)
(
)
t
op at time t
FCF1g
HVV
WACCg
+
==
-
(
)

(
)
(
)
(
)
3
3op,3
3
FCF1g
HVV
WACCg
$3510.05
HV$612.50
0.000.05
+
==
-
+
==
-
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(

)
(
)
4L
4
L
4
4
44
3
124
1234
12
FCF(1g)
$48.025(10.05)
HV$1,260.65
WACCg)0.090.05
HV
$1,260.65
PV of HV$893.08
1WACC10.09
FCF
FCFFCFFCF
PV of FCF
1WACC1WACC1WACC1WACC
-$13$8.36$45.73
PV of FCF
10.0910.09
+
+
===
--
===
++
=+++
++++

=++
++
(
)
(
)
34
8$48.025
10.0910.09
PV of FCF$64.45
+
++
=
(
)
(
)
(
)
(
)
3
12
0
123
ssss
D
DDD
ˆ
P...
1r1r1r1r
¥
¥
=+++
++++
(

)
0L
1
0
sLsL
D1g
D
ˆ
P
rgrg
+
==
--
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
12
0L0L0L
0
12
sss
t
L

Ls,0
t
s
D1gD1gD1g
ˆ
P...
1r1r1r
1g
ˆ
If grthen1, and P
1r
¥
¥
+++
=+++
+++
+
>>=¥
+
(
)
(
)
(
)
sRFMFirm
rrRPb
7%5%1.2
13%
=+
=+
=
(
)
(
)

(
)
10L
0L
1
0
sLsL
0
$2.12
$30.29
DD1g
$2.001.06
D1g
D
ˆ
P
rgrg
$2.12
ˆ
P
0.130.06
=+
==
+
==
--
==
-
t
t
sL
D1
ˆ
In general: P
rg
+

=
-
(
)
(
)
10L
1
0
sL
DD1g
$2.121.06$2.2472
D
ˆ
P
rg
$2.2472
0.130
$32.
0
10
.6
=+
==
=
-
==
-
1
0
10
0
D
$2.12
Dividend yield
P$30.29

ˆ
PP
$32.10$30.29
CG y
7.0
ield
P$30.29
6.0%
%
===
-
-
==
=
11
0s
s0
DD
ˆ
ˆ
P to rg.
rgP
==+
-
s
ˆ
Then, r$2.12/$30.290.06
0.070.0613%
=+
=+=
1
0
At t0:
D
$2.60
Dividend yield5.6%

P$46.66
CG Yield13.0%5.6%7.4%
=
===
=-=
ps
ps
Dividend$2.10
V$30
r7%
===

Due Date 1159 p.m. EST, Sunday, of Unit 7 Points 100

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