http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/basics.html
DISCOUNTED CASHFLOW MODELS: WHAT THEY ARE AND HOW
TO CHOOSE THE RIGHT ONE..
THE FUNDAMENTAL CHOICES FOR DCF VALUATION

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Cashflows to Discount
o Dividends
o Free Cash Flows to Equity
o Free Cash Flows to Firm
Expected Growth
o Stable Growth
o Two Stages of Growth: High Growth -> Stable Growth
o Three Stages of Growth: High Growth -> Transition Period -> Stable
Growth
Discount Rate
o Cost of Equity
o Cost of Capital
Base Year Numbers
o Current Earnings / Cash Flows
o Normalized Earnings / Cash Flows
WHICH CASH FLOW TO DISCOUNT...


The Discount Rate should be consistent with the cash flow being discounted
o Cash Flow to Equity -> Cost of Equity
o Cash Flow to Firm -> Cost of Capital
Should you discount Cash Flow to Equity or Cash Flow to Firm?
o Use Equity Valuation
 (a) for firms which have stable leverage, whether high or not, and
 (b) if equity (stock) is being valued
o Use Firm Valuation
 (a) for firms which have high leverage, and expect to lower the
leverage over time, because
 debt payments do not have to be factored in
 the discount rate (cost of capital) does not change
dramatically over time.
 (b) for firms for which you have partial information on leverage
(eg: interest expenses are missing..)
 (c) in all other cases, where you are more interested in valuing the
firm than the equity. (Value Consulting?)

Given that you discount cash flow to equity, should you discount dividends or
Free Cash Flow to Equity?
o Use the Dividend Discount Model
 (a) For firms which pay dividends (and repurchase stock) which
are close to the Free Cash Flow to Equity (over a extended period)
 (b)For firms where FCFE are difficult to estimate (Example: Banks
and Financial Service companies)
o Use the FCFE Model
 (a) For firms which pay dividends which are significantly higher or
lower than the Free Cash Flow to Equity. (What is significant? ...
As a rule of thumb, if dividends are less than 75% of FCFE or
dividends are greater than FCFE)
 (b) For firms where dividends are not available (Example: Private
Companies, IPOs)
WHAT IS THE RIGHT GROWTH PATTERN...

The Choices
THE PRESENT VALUE FORMULAE
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
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For Stable Firm:
For two stage growth:
For three stage growth:
Definitions of Terms
V0= Value of Equity (if cash flows to equity are discounted) or Firm (if cash flows to
firm are discounted)
CFt = Cash Flow in period t; Dividends or FCFE if valuing equity or FCFF if valuing
firm.
r = Cost of Equity (if discounting Dividends or FCFE) or Cost of Capital (if discounting
FCFF)
g = Expected growth rate in Cash Flow being discounted
ga= Expected growth in Cash Flow being discounted in first stage of three stage growth
model
gn= Expected growth in Cash Flow being discounted in stable period
n = Length of the high growth period in two-stage model
n1 = Length of the first high growth period in three-stage model
n2 - n1 = Transition period in three-stage model
WHICH MODEL SHOULD I USE?

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Use the growth model only if cash flows are positive
Use the stable growth model, if
o the firm is growing at a rate which is below or close (within 1-2% ) to the
growth rate of the economy
Use the two-stage growth model if
o the firm is growing at a moderate rate (... within 8% of the stable growth
rate)
Use the three-stage growth model if
o the firm is growing at a high rate (... more than 8% higher than the stable
growth rate)
SUMMARIZING THE MODEL CHOICES
Stable Growth
Model
Dividend Discount
Model
 Growth rate in
firmís earnings
is stable. (g of
firmeconomy+1%)
 Dividends are
FCFE Model

Growth rate in
firmís earnings
is stable.
(gfirmeconomy+1%
)
FCFF Model

Growth rate in
firmís earnings
is stable.
(gfirmeconomy+1%
)

close to FCFE
(or) FCFE is
difficult to
compute.
Leverage is
stable
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
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
Two-Stage
Model
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
Three-Stage
Model

Growth rate in
firmís earnings
is moderate.
Dividends are
close to FCFE
(or) FCFE is
difficult to
compute.
Leverage is
stable
Growth rate in
firmís earnings
is high.
Dividends are
close to FCFE
(or) FCFE is
difficult to
compute.
Leverage is
stable
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Dividends are
very different
from FCFE (or)
Dividends not
available
(Private firm)
Leverage is
stable
Growth rate in
firmís earnings
is moderate.
Dividends are
very different
from FCFE (or)
Dividends not
available
(Private firm)
Leverage is
stable
Growth rate in
firmís earnings
is high.
Dividends are
very different
from FCFE (or)
Dividends not
available
(Private firm)
Leverage is
stable

Leverage is
high and
expected to
change over
time (unstable).

Growth rate in
firmís earnings
is moderate.
Leverage is
high and
expected to
change over
time (unstable).



Growth rate in
firmís earnings
is high.
Leverage is
high and
expected to
change over
time (unstable).
GROWTH AND FIRM CHARACTERISTICS
Dividend Discount
FCFE Discount Model FCFF Discount Model
Model
 Pay no or low
 Have high
 Have high
dividends
capital
capital
High growth firms
 Earn high
expenditures
expenditures
generally
returns on
relative to
relative to
projects
depreciation.
depreciation.
(ROA)
 Earn high
 Earn high


Have low
leverage (D/E)
Have high risk
(high betas)

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
Stable growth firms
generally


Pay large
dividends
relative to
earnings (high
payout)
Earn moderate
returns on
projects (ROA
is closer to
market or
industry
average)
Have higher
leverage
Have average
risk (betas are
closer to one.)



returns on
projects
Have low
leverage
Have high risk
narrow the
difference
between cap ex
and
depreciation.
(Sometimes
they offset
each other)
Earn moderate
returns on
projects (ROA
is closer to
market or
industry
average)
Have higher
leverage
Have average
risk (betas are
closer to one.)






returns on
projects
Have low
leverage
Have high risk
narrow the
difference
between cap ex
and
depreciation.
(Sometimes
they offset
each other)
Earn moderate
returns on
projects (ROA
is closer to
market or
industry
average)
Have higher
leverage
Have average
risk (betas are
closer to one.)
SHOULD I NORMALIZE EARNINGS?


Why normalize earnings?
o The firm may have had an exceptionally good or bad year (which is not
expected to be sustainable)
o The firm is in financial trouble, and its current earnings are below normal
or negative.
What types of firms can I normalize earnings for?
o The firms used to be financially healthy, and the current problems are
viewed as temporary.
o The firm is a small upstart firm in an established industry, where the
average firm is profitable.
HOW DO I NORMALIZE EARNINGS?
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If the firm is in trouble because of a recession, and its size has not changed
significantly over time,
Use average earnings over an extended time period for the firm
Normalized Earnings = Average Earnings from past period (5 or 10 years)
If the firm is in trouble because of a recession, and its size has changed
significantly over time,
Use average Return on Equity over an extended time period for the firm
Normalized Earnings = Current Book Value of Equity * Average Return on Equity
(Firm)
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If the firm is in trouble because of firm-specific factors, and the rest of the
industry is healthy,
Use average Return on Equity for comparable firms
Normalized Earnings = Current Book Value of Equity * Average Return on Equity
(Comparables)
Source unknown:
Calculating Discounted Cash Flow
The three key questions in company valuation can all be answered using discounted cash
flow methods.
Take a Closer Look
New Tech's Valuation Process.
The discounted cash flow valuation used by New Tech was conducted by its financial
advisor.
Value:
How much is a company worth today, based on what it will earn in the future?
The company's predicted cash flows (or earnings) are discounted to give a present
value.
Rate of return:
What is an investor's expected rate of return, given the amount invested and the
company's financial projections? Investors will calculate their rate of return by:
discounting the cash flow and the value they will take out of the company; and
comparing this amount to what they invested at the beginning.
Equity share:
How much equity will the investor receive for the investment? Dividing the
investment by the value of the company will give the percentage of ownership
shares the investor will get. But first you need to know the value.
1. How Much is This Company Worth Today?
Let's say investors are considering an investment in your company and plan to take their
money out in five years. To them, your company is worth today what it can earn during
the five years, plus their share of the value of the company at the end of the five years.
This is like saying, the value of a five-year 10% Canada savings bond is the interest it
will earn each year plus the principal amount paid back at the end of the term. The
interest is equivalent to cash flows, and the principal is equivalent to the value of the
company at the end of the year. The big difference is that the cash flows and the value at
the end of the term are known for certain with a savings bond, but for investments in
active businesses, these are unknowns. The discounted cash flow method applies
adjustments or "discounts" to account for those unknowns.
Using this method, the value is the total of the cash flows, adjusted or discounted, plus
the value remaining (or residual value), also discounted.
discounted cash flow value = discounted cash flows + discounted residual value
A Simplified Example
A company is projected to have fluctuating cash flows (e.g. losses of $200,000 in the first
two years, a gain of $300,000 in the third, etc.) that total $1 million over five years. How
much is it worth today?
a) Discount the cash flows.
The cash flows are discounted at a rate acceptable to the investor - say 20% (see chart).
This leaves a present value of $0.4 million. In other words, the calculation indicates that
getting $1 million in five years is the same as having $0.4 million today, using a discount
rate of 20%. (This rate is used to calculate a discount factor for each year; the first year's
cash flows are only discounted for one year, by about 80%; but the fifth year's cash flow
must be discounted for five years, so it's discounted by much more, about 40%.)
Year
1
Year
2
Year
3
Year
4
Year
5
Projected cash
flows (000s)
-$100
-$100
$300
$400
$500
$1,000
Discounted
cash
flows (@ 20%)
-$83
-$69
$174
$192
$200
$414
Total
b) Find the residual value of the company and discount it.
The company's value at the end of the five years is calculated as being $10 million. This
"residual value" is then adjusted by a discount factor (based on the 20% rate the investor
finds acceptable), leaving a value of $4 million. You can think of the "residual" as an
estimate of how much someone would pay to buy the whole company at the end of the
investment period.
c) Add the discounted cash flow and the discounted residual value.
The cash flow value and the residual value are then added together. The estimated value
of the firm using the discounted cash flow model is $0.4 million + $4 million or $4.4
million.
Projected
Cash
flows
$1
million
Residual
value
$10
million
Discounted cash
flow value
Discounted to
Notes:
present value
$0.4 million
Discounted at 20% over
five years.
$4.0 million
Capitalized and
discounted based on 20%
discount rate over five
years.
$4.4 million
Estimated fair market
value today.
This example is very simplified. For a more detailed explanation, see Calculating New
Tech's Discounted Cash Flow Value, based on our case example company. Further
discussion can be found in the Valuation Methods tool.
2. Investors' Rate of Return
Investors want to calculate their rate of return. To do that they must compare the amount
of the investment to the amount they will earn at the end of the investment period. But
how can they know what they will earn in the future? Again, they must use the
discounted cash flow projections to estimate the future value of their investment.
A Simplified Example
If investors had invested $500,000 and received 35% of the company's shares, how much
will their return be at the end of the investment?
a) Take estimated cash flow for the final year.
The cash flow in the final year is used as a basis to decide the value of the company.
Imagine that the company is projecting earnings of $500,000 in the final year.
b) Estimate the value or sale price of the company based on the cash flow.
How much will someone pay for this company in five years? Perhaps companies will be
selling for 5 times or 10 times their earnings. Investors must decide what they think the
market will be like and choose a multiple to multiply the cash flow by to convert it to a
value for the company. Let's say the investors choose 8 times earnings. Then the value of
the company when the investors will exit should be 8 times $500,000 or $4 million.
c) The value of the investors' share is calculated.
If the investors have purchased 35% of the shares of the company, they can expect to take
away $1.4 million when the business is sold.
d) The investors determine their rate of return.
The investors' original investment of $500,000 is then compared to the return of $1.4
million. The return is the equivalent of a return of 23% compound interest for five years
(see the table below).
Projected final year's cash flow
$500,000
Multiplied by 8 to find estimated selling
price of the company
$4
million
Divided by 35% to represent the
investor's share
$1.4
million
Calculated as a rate of return on original
investment of $500,000 (compounding
the interest)
23%
3. How Much of the Company do the Investors Get?
The valuation information you get from discounted cash flow also allows you to consider
the percentage of shares the investors receive in return for their investment. In the
example above, the investors' share was assumed to be 35%. At that proportion, and
given a value of $4 million at the end of the investment period, the investors would make
$1.4 million, or 23% on the initial $500,000 investment.
If the investors feel that isn't an adequate return, then one way to increase the return is to
give them a greater equity share for the same investment. So, for example, if their
$500,000 investment bought them 45% of the company, instead of 35%, they would get
45% percent of the $4 million exit value — or $1.8 million. And that is equivalent to a
29% return on their investment.
Investors' share
35%
share
45%
share
Exit value of company
$4
million
$4
million
Divided by investors % share
$1.4
million
$1.8
million
23%
29%
Calculated as a rate of return on
original investment of $500,000
(compounding the interest)
Value, Return and Exit Strategy
The way the values and rates of return are calculated depend on the specific exit strategy
used. In the next section, the implications of different exit strategies on exit values are
discussed.