The document provides an overview of discounted cash flow (DCF) valuation. It discusses the history of DCF dating back to ancient times and its popularity after the 1929 stock market crash. It defines DCF valuation as estimating a company's value based on discounting its predicted future cash flows. The key steps in DCF valuation are estimating future cash flows, determining an appropriate discount rate, and calculating the present value of the future cash flows. DCF valuation requires numerous assumptions about cash flows, growth rates, and discount rates.

1. The Discounted Cash Flow
Valuation

2. DCF History:
DCF calculations have been used in financial
calculations as far back as ancient times. As a
method of asset valuation it has often been
opposed to accounting book value, which is
based on the amount paid for the asset. After the
stock market crash of 1929, DCF analysis gained
popularity for stock valuation. In its more current
economic form, Irving Fisher’s 1930 text “The
Theory of Interest” first discussed DCF as a
viable method of valuation.

3. Discounted Cash Flow (DCF) valuation is:
 Discounted Cash Flow (DCF) valuation is a tool
for estimating the value of a company or its
shares.
 Discounted cash flow (DCF) analysis is a method
of valuing a project (or a Company) using the
concept of time value of money and risk

4. Discounted Cash Flow (DCF) valuation is:
•a method of evaluating an investment opportunity
•by discounting predicted future cash flows generated
by the investment at certain discount rates
•to find out the present value of the investment in
monetary term
Application:
Mostly used in valuating securities (bonds or shares), companies
and
business projects.
Valuation of bonds using DCF is simple and straightforward
while
DCF valuation of shares, companies and business projects is
quite
complex leading several issues for debates exploration.

5. 1. DCF Model (Theory of Interest) by Fisher
(1930):
Where:
PV0 : Present value of cash flows (at time t = 0)
CFt : Cash flow at time t
ki : Discount rate or required rate of return for the
period i
n : Number of periods generating cash flows

6. 2. Value Additivity principle
The summation of present values of cash flows divided from
the same original cash flow will always equal the present
value of the original.
This principle is first demonstrated in MM Proposition I
with tax of Modigliani and Miller (1958) :
Vt = Dt + Et = Vut + VTSt (1)
Where:
Vt : value of the firm at time t
Dt : value of debt at time t
Et : value of equity at time t
Vut : value of unlevered equity at time t (value of the firm when
there is no
leverage, i.e. 100% equity)
VTSt : value of interest tax shield at time t

7. ASSUMPTIONS OF DCF ANALYSIS
According to Ronald W. Hilton
 All cash flows are treated as though they occur at the
end of the year.
 DCF methods treat cash flows associated with
investment projects as though they were known with
certainty, whereas risk adjustments can be made in
an NPV analysis to account—in part—for cash flow
uncertainties.
 Methods assume that all cash inflows are reinvested
in other projects that earn returns for the company.
 DCF analysis assumes a perfect capital market.

8. • Invest in projects that yield a return greater than the
minimum acceptable hurdle rate
• Return on projects should be measured based on:
– cash flows generated: Why cash flows and not
earnings?
– the timing of these cash flows: cash flows that
occur earlier value more than cash flows that occur
later.
– incremental cash flows: use cash flows that are
incremental related to the investment decision.
Discounted Cash Flow (DCF)

9. Why Cash Flows vs Accounting Earnings?
Accounting Earnings
One cannot spend earnings.
Shows revenues when products
and services are sold or provided,
not when they are paid for. Shows
expenses associated with these
revenues, not when expenses are
paid.
Net income includes a number of
non-cash adjustments to
approximate economic activity as
of (or over) a period of time.
Accounting adjustments do not
necessarily reflect the company’s
ability to pay its obligations or
invest for future growth.
Cash Flows
Cash flow reflects the company’s
ability to generate funds in order to
pay its obligations or invest for
future growth
Various Cash Flow measures (i.e. -
Free Cash Flow) adjusts accounting
income to arrive at the funds
available to pay stock and debt
holders. For example, taking out
Dividends provides one way to
compare cash flows across
Companies.

10. Discounted Cash Flow Valuation - DCF
• What is it: In discounted cash flow valuation, the
value of an asset is the present value of the expected
cash flow on the asset.
• Philosophical basis: Every asset has an intrinsic
value that can be estimated, based upon its
characteristics in terms of cash flows, growth and risk.
• Information needed: To use DSF valuation, you need
– To estimate the life of the asset
– To estimate the cash flow during the life of the asset
– To estimate the discount rate to apply to these cash
flows to get present value
• Market inefficiency: Markets are assumed to make
mistakes in pricing assets across time, and are
assumed to correct themselves over time, as new
information comes out about assets.

11. Valuing a company using a DCF model
Steps:
1. Understand the business of the company you are valuing
2. Find Inputs:
a) Calculate the Discount Rate
– Weighted Average Cost of Capital (WACC)
b) Build Future (Pro forma) Cash Flow and find the PV of these cash
flow
– Free Cash Flow (FCF)
c) Calculate Terminal Value
– EBITDA Multiple
3. Analyze Outputs:
a) Enterprise value (EV)
b) Equity (share price)
c) Perform Sensitivity Analysis
• There are many correct answers and many variations on methods
and which numbers to use (academics vs. practitioners).

12. Relevant & Irrelevant Cash Flows
Relevant Cash Flow
 Flows that will be incurred as
a direct result of the project
(incremental cash flows)
 Tax benefits (tax shield on
depreciation)
 Opportunity Cost
Irrelevant Cash Flow
 Flows that do not change as a
results of the project
 Flows that have already occurred
(sunk costs)
 Flows that would be incurred
regardless of the project
activities (replace equipment)
 Non-cash items (depreciation)

13. Depreciation / Amortization / Capital
•While depreciation reduces taxable income and
taxes, it does not reduce cash flows.
•It is a non-cash expense; therefore, it needs to be
added back.
•There is a cash flow benefit associated with
depreciation – the tax benefit. In general, the tax
benefit from depreciation can be written as:
Tax Benefit = Depreciation * Tax Rate
•Capital expenditures (CAPEX) are not treated as
accounting expenses, but they do cause cash
outflows.

14. Working Capital
•The cash available for day-to-day operations of an
organization. Strictly speaking, one borrows cash
(and not working capital) to be able to buy assets or
to pay for obligations.
•Intuitively, money invested in inventory or in
accounts receivable cannot be used elsewhere.
Therefore, it represents a drain on cash flows.

15. To get from accounting earnings to cash flows:
Free Cash Flow =Before Tax Profit (BTP) or EBIT
- Taxes
+ Add back Depreciation/Amortization
+/- Change in Working Capital
- Capital Expenditures

16. Fundamentals of any Discounted Cash Flow Valuation
 Expected cashflow in each period
 Divided by the appropriate discount factor that reflects the
riskiness of the estimated cashflows
 Example: How much is an infinite stream of ISK 15 million/year
worth?
Assuming a 10% discount rate:
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Expected
cashflow
Discount rate
Year

18. Structure of a DCF model
Year 2011 2012 2013 2014 2015 2016 ……..
Period 0 1 2 3 4 5 ……..
FCF C1 C2 C3 C4 C5 ……..
……..
Terminal
value
(TV)
PV (CF) C1/
(1+r)1
C1/
(1+r)1
C1/
(1+r)1
C1/
(1+r)1
(C1+TV)
/(1+r)1
Sum of
PV(CF)
EV
Input: Cash Flow
Output: Value (Enterprise Value)
EV of the company as of the
end of year 2011
Company
enters
steady
state
Year 1 to 5: Capture changes and volatility in the
business (cash flow)
Industry standard:
5 to 10 yr horizon

19. DCF Example
Lemonade Stand Business
Year 0 Year 1 Year 2 Year 3
Initial Cost (50,000)
Taxes (34%) (25,500) (28,560) (34,000)
Operating Income 75,000 84,000 100,000
Income $49,500 $55,440 $66,000
Plus: Depreciation 3,750 4,200 5,000
Minus: working capital 1,500 1,000 1,600
Minus: CapEx 3,000 4,040 4,400
Free Cash Flow ($50,000) $48,750 $54,600 $65,000
Discount Rate 10%
Discounted Values ($50,000) $44,318 $45,123 $48,835
Present Value $88,277

20. What Rate Should We Use to
Discount Cash Flows?

21. Determining Discount Rates
The discount rate should be determined in accordance with the
following factors:
 Riskiness of the business or project—The higher the risk, the
higher the required rate of return.
 Size of the company—Studies indicate that returns are also
related inversely to the size of the entity. That is, a larger
company will provide lower rates of return than a smaller
company of otherwise similar nature.
 Time horizon—Generally, yield curves are upward sloping (longer
term instruments command a higher interest rate); therefore, cash
flows to be received over longer periods may require a slight
premium in interest, or discount, rate.

22. •Debt/equity ratio—The leverage of the company drives the
mix of debt and equity rates in the overall cost of capital
equation. This is a factor that can be of considerable
importance, since rates of return on debt and equity within
a company can vary considerably.
•Real or nominal basis—Market rates of interest or return
are on a nominal basis. If the cash flow projections are
done on a real basis (non-inflation adjusted), then the
discount rate must be converted to real terms.
• Income tax considerations—If the cash flows under
consideration are on an after-tax basis, then the discount
rate should be calculated using an after-tax cost of debt in
the cost of capital equation.

23. Weighted Average Cost of Capital Definition
•Weighted Average Cost of Capital (WACC) is
•the minimum rate of return that must be realized
•in order to satisfy investors: both debt holders and
shareholders.
Project
Returns >
Cost of
Equity +
Cost of
Debt

24. Calculating WACC
Cost of Capital has two components:
Cost of equity (rk)
After tax Cost of debt (rd)
These are multiplied by the relative weight of
their market values to arrive at an average cost:
WACC = rk * (E/(D+E)) + rd * (D/(D+E))
E = market value of equity
D = market value of debt

25. Advantages of DCF valuation
• Since DCF valuation, done right, is based upon an
asset’s fundamentals, it should be less exposed to
market moods and perceptions.
• If good investors buy businesses, rather than stocks,
discounted cash flow valuation is the right way to think
about what you are getting when you buy asset.
• DCF valuation forces you to think about the underlying
characteristics of the firm, and understand its business.
If nothing else, it brings you face to face with the
assumptions you are making when you pay a given price
for an asset.

26. Advantages of DCF valuation
 Can offer a more accurate picture of
fundamental valuation drivers
 Can evaluate different scenarios
 Uses cash flows, not earnings or
accounting measures
 Useful as a sanity check of over/under valued

27. Disadvantages of DCF valuation
• Since it is an attempt to estimate intrinsic value, it
requires far more inputs and information than other
valuation approaches.
• These inputs and information are not only difficult to
estimate, but can be manipulated by analyst to provide
the conclusion he or she wants.
• In an intrinsic valuation model, there is no guarantee
that anything will emerge as under or over valued.
Thus, it is possible in a DCF valuation model, to find
every stock in a market to be over valued . This can be
a problem for
– Equity research analysts, whose job it is to follow sectors and
make recommendations on the most under and over valued
stocks
– Equity portfolio managers, who have to be fully (or close to
fully) invested in equities.

28. Disadvantages of DCF valuation
 Highly sensitive to discount rate
 Highly sensitive to terminal growth rate
 Discount rate changes over time
 Difficult to apply for early stage companies
without cash flows

29. DCF
Strengths:
• Captures the time value of money and opportunity cost
• Scientific
• Widely used
• Based on cash flow
• Weaknesses:
• Almost always results in overvaluation. Why?
• Can we ever predict the future?
• “Forecasts may tell you a great deal about the forecaster; they
tell you nothing about the future.” Warren Buffett
• Based on many assumptions
• Which assumptions are the most critical?
• 5 years vs. 10 years estimation

30. 6 Steps to Build a DCF
 1. Calculate a free cash flow:
 2. Discounting a single cash flow:
– PV = CF1 / (1+r)
 3. Discounting a single cash flow in “n” years from now:
– PV = CFn / (1+r)n
 4. Multiple cash flows in future:
– PV = CF1 / (1+r) + CF2 / (1+r)2 + CF3 / (1+r)3 + …
 5. Growing Perpetuity: TV
– PV = CF / (r-g) (1st CF at end of year 1, then grow at g)
 6. Deduct Net Debt from Enterprise Value to calculate
Equity Value:
– Enterprise Value - Net Debt = Equity Value

31. Cashflow to Firm
EBIT (1-t)
- (Cap Ex - Depr)
- Change in WC
= FCFF
Expected Growth
Reinvestment Rate
* Return on Capital
FCFF1 FCFF2 FCFF3 FCFF4 FCFF5
Forever
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value= FCFF n+1/(r-gn)
FCFFn
.........
Cost of Equity Cost of Debt
(Riskfree Rate
+ Default Spread) (1-t)
Weights
Based on Market Value
Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))
Value of Operating Assets
+ Cash & Non-op Assets
= Value of Firm
- Value of Debt
= Value of Equity
Riskfree Rate :
- No default risk
- No reinvestment risk
- In same currency and
in same terms (real or
nominal as cash flows
+
Beta
- Measures market risk X
Risk Premium
- Premium for average
risk investment
Type of
Business
Operating
Leverage
Financial
Leverage
Base Equity
Premium
Country Risk
Premium
VALUING A FIRM

32. Thanks