1. Project Training
Discounted Cash Flow

2. Learning Objectives – DCF Analysis
 Understand the theoretical basis of a DCF
 Understand the weighted average cost of capital
 Understand the different terminal value approaches:
– Terminal Multiple method
– Perpetuity Growth method
 Derive an implied valuation range
 Application: Construct a DCF & WACC model
[2]

3. What is a Company ultimately worth?
 Cash in the investors’ pockets
[3]

4. Two Key Questions of DCF
 How much cash?
 When investors receive it?
[4]

5. What is a DCF Analysis?
 Intrinsic value of the company
– Theoretical vs. relative value
 Base on unlevered free cash flows (FCFs)
– Independent of capital structure
– Free cash flows available to all capital holders
 Value equals the sum of the present values (PV) of:
(1) Unlevered free cash flows &
(2) Projected terminal value
• Estimated value beyond the forecast period
– PV calculated by on a discount rate
• Typically, weighted average cost of capital (WACC)
[5]

6. Advantages of a DCF Valuation
 Intrinsic value based on projected FCFs
 Flexible, adaptable analysis
– How do changes in projections impact value?
• Growth rates
• Operating margins
• Synergies, expansion plans, etc.
 Objective calculation (through PV)
 Requires scrutiny of key drivers of value
 Always obtainable
[6]

7. Challenges of a DCF Valuation
*DCF results should be presented as a RANGE of estimated values not a single estimate!
 Cash flows from forecasts
– Possible bias (run sensitivities)
– Reliability
 Subjective valuation
– Based on numerous assumptions
 Highly sensitive to changes in:
– FCFs: growth rates & margins assumptions
– Estimated terminal value
– Assumed discount rate (beta, market conditions)
[7]

8. Methodology Steps for a DCF
1. Estimate the Cost of Capital
2. Forecast Free Cash Flows (FCFs)
3. Calculate the Present Values of FCFs
4. Estimate the Terminal Value
5. Derive an Implied Valuation Range
[8]

9. Sources for Forecasting Free Cash Flow
 Use standalone model projections for DCF and FCF projections
– Alternative cases to assess:
• Upside potential
• Downside risk
• Synergies usually treated as separate analysis
 Consider "steady state" forecast horizon
– Cash flows can be "sustained forever" (stable growth)
• Generally viewed NOT to exceed economy's growth rate
[9]

10. "Multi-Stage" Projections
 Forecast horizon potentially can be in stages
– Concept: Slow growth over time to steady-state
 How long does it take to achieve steady state?
– Length varies by industry / situation
• Does the company have a sustainable advantage?
• Growth from single product with protected position?
 Generally speaking: As growth nears stable growth, risk and CAPX needs decline
– Closer to industry average?
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11. Calculating Free Cash Flow
EBITDA
Less: Depreciation and amortization
= EBIT
Less: Taxes (at the marginal tax rate)
= Tax-Effected EBIT or “NOPAT”
Plus: Depreciation and amortization
+/-: Changes in deferred taxes
Less: Capital expenditures Watch your Sources
& Uses of Cash!
+/-: Changes in net working capital
+/-: Changes in other non-cash items
= Unlevered Free Cash Flow
[ 11 ]

12. What is the Terminal Value?
 Value of the business beyond the projections
– Used due to the impractical nature of extended forecast period (i.e., 20 or 30
years)
Projections ?
Yr 0 Value -  Yr N Value - ???
 Two methods:
1. Exit Multiple
• Assumes the business is worth (or "sold") a multiple of an operating statistic
at the end of the projections
2. Perpetuity Growth
• Assumes growth of FCFs at constant rate in perpetuity
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13. Exit Multiple Method
 Value the business as a multiple of a relevant operating statistic
– "Worth/sold for 8.0x EBITDA at the end of year N”
 Choosing the appropriate Exit Multiple:
– Multiple of EBITDA, EBIT, etc.
– Reasonable multiple from comparables, usually current
• Is the current multiple sustainable?
• Public Comparables: "worth" a multiple at end of Year N
• Acquisition Comparables: "sold" for a multiple at end of Year N
– Do not double count synergies for a potential M&A target if using a separate DCF
valuation of synergies
– Be wary of cyclical industries
• Examine ranges and rolling average of EBITDA multiples
– Valued on pre-tax basis (to investors)
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14. Perpetuity Growth Method
 Assumes the business grows at a constant rate in perpetuity
 Consider using "normalized" cash flow in final year
– Sustaining capital investment (i.e., Depreciation ~ CapEx)
– Steady state working capital needs
– Consider no deferred taxes
 Perpetuity growth formula:
Where:
FCFn x (1 + g) FCF = normalized free cash flow in period N
Terminal Value =
g = nominal perpetual growth rate
(r - g)
r = discount rate or WACC
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15. Which Method to Use - When and Why?
 Perpetuity Growth Rate:
– Academically proven approach
 Exit Multiple: more often used in practice
– Inherent difficulty in estimating when the company achieves "steady state",
perpetual growth rate growth
– Multiples commonly used for valuation
– Major considerations:
• How do you choose the appropriate multiple?
• Introduces relative value with intrinsic value approach
 Perpetuity Growth Rate is commonly used by practitioners for:
– Synergies
– Mature industries
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16. Equivalent Perpetuity Growth Rate
 Helpful reality check to analyze the results calculated by
Exit Multiple Method:
[EBITDAN x Multiple x Discount Rate) – FCFN]
Equivalent Perpetuity Growth Rate 1 =
[FCFN x EBITDAN X Multiple)]
 Resulting “equivalent g” should be within a reasonable comfort level
1 Quick, less complex short-cut approximation: Estimated Perpetuity Growth Rate  Discount Rate – [FCFN+1 /(EBITDAN x Multiple)]
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17. Equivalent Exit Multiple
 Helpful reality check to analyze the results calculated by Perpetuity Growth Rate
Method:
FCFN X (1 + g)
Equivalent EBITDA Multiple =
EBITDAN (r – g)
 Resulting "equivalent multiple" should be within a reasonable comfort level
– Compare with the comparables
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18. Calculate the Enterprise Value
+
PV of PV of
Free Cash Flows Terminal Value
(Discounted @ WACC) (Discounted @ WACC)
= Enterprise Value
(Firm Value)
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19. Calculate the Equity Value
Enterprise Debt, Preferred Stock Equity
Value – and Min. Interests + Cash = Value1
 Which balance sheet do you?
(1) Latest available (2) PV date – projected balance sheet
Equity Value
Diluted Shares = Equity Value Per Share
 Typically, use latest available share and option information
– Ideally, consistent timing with balance sheet items
 Footnote and use reasonable assumptions
1 For certain companies, it may be appropriate to include equity investments, NOLs or non-operating assets. Such assets not reflected in the cash flows would
raise the equity value
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20. Terminal Value as % of Enterprise Value
 Calculate the PV of the Terminal Value as % of Enterprise Value
 Another reality check
– How much of the firm's DCF value is derived from value generated beyond
the projected FCF's?
 Comfort level depends on:
• Company and industry
• Situation
• Forecast horizon
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21. The Final DCF Analysis
 Compare DCF result with current stock price
 Derive a reasonable, defensible range
– Range of discount rates
– Range of exit multiples / perpetuity growth rates
 Weigh DCF results more heavily when comparables analyses are not as applicable
– No "pure play" public comps or acquisition comps
 Common to see various scenarios ("cases")
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22. Basis of Mid-Period Convention
 Acquisition occurs on December 31, 20X0 Key: Periods 1-5 Cash Flows
 Fiscal year end of December 31
 Assumes mid-year cash flows
 Discount rate of 10%
Discount back Discount back Discount back Discount back Discount back
0.5 years 1.5 years 2.5 years 3.5 years 4.5 years
12/31/20X0 12/31/20X1 12/31/20X2 12/31/20X3 12/31/20X4 12/31/20X5
Basis for the “mid-period convention”:
Valuation date:  Cash flows are generated more or less continuously
DURING the period, not at the end of the period.
 Mid-period convention moves each cash flow from the
END of the period to the MIDDLE of the same period.
 Q: What is the impact of the valuation?
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23. Terminal Values & Mid-Period Convention
 Perpetuity growth method:
– "FCFN" means FCF during period "N" is received at "N - 0.5" with the mid-period
convention
• Continuous flow consistent with other forecasted free cash flow periods
– Discount back "N - 0.5" periods
– Use MID-PERIOD FCFN X (1 + g)
(r – g) X (1 + r)
Terminal Value for
Perpetuity growth method
 Exit multiple method:
– Assumption: Business sold or valued at the end of period "N"
– Discount back "N“
– Common to use end-period
EBITDAN X Multiple
(1 + r)N
Terminal Value for
Exit multiple method
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24. Equivalent Multiples and Growth Rates
 To equate implied multiples and growth rates when using the mid-period
convention, grow the perpetuity growth rate method by 1/2 a period
FCFN X (1+r) 0.5
EBITDA X Multiple = (r – g)
Equivalent Perpetuity Growth Rate ((EBITDAN X Multiple X Discount Rate) – FCFN X (1 + r)0.5)
(using mid-period convention) = (EBITDAN X + (FCFN X (1 + r)0.5)
Equivalent Perpetuity Growth Rate FCFN X (1 + g) X (1 + r)0.5)
(using mid-period convention) = EBITDAN X + (r - g)
[ 24 ]

25. What are Synergies?
 Financial benefits arising from a merger
 3 main areas to consider:
1. Net incremental revenues (net of costs to achieve)
2. Cost savings
3. Merger outlays (severance, additional CapEx)
 Sources of synergy projections
– Management
– Research
– Estimates from comparable acquisitions
(e.g., "5.0% of Target sales")
[ 25 ]

26. How Do You Value Synergies?
 DCF valuation of the synergies
– Project the synergy cash flows
– Terminal value via perpetuity growth rate method
 Value on an independent basis from the standalone DCF
– Create a "DCF with synergies" value
• Standalone DCF value + synergies DCF value
 Do NOT double count the control premium in the standalone DCF terminal value
[ 26 ]

27. Some Synergy DCF Considerations
1. Progression of the phase in
– Achieving full potential does not happen in one year
2. Percentage realization
– Common to see 50% & 100% realization cases
3. Tax-effect the operating income impact
– At the marginal rate
4. Factor in costs to achieve the synergies
– Cash merger outlays
5. Consider 0% or very low perpetuity growth rate
– Competitive pressures
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28. Weighted Average Cost of Capital
 Discount rate used to calculate the PV of future cash flows
 Required rate of return for both equity and debt investors
 Return commensurate with risk of the investment (i.e., target company or project,
not the acquirer in an M&A transaction)
E D
WACC = Ke x + Kd x (1 - T) x
D+E D+E
Where:
Ke = cost of equity (from CAPM)
Kd = cost of debt (current cost of borrowing from average yield to maturity)
E = market value of equity
D = market value of debt
T = marginal tax rate
Note: Interest expense is tax deductible, so the true cost of borrowing is the after-tax interest expense.
[ 28 ]

29. Weighted Average Cost of Capital
 Discount rate used to calculate the PV of future cash flows
 Required rate of return for both equity and debt investors
 Return commensurate with risk of the investment (i.e., target company or project,
not the acquirer in an M&A transaction)
E D
WACC = Ke x + Kd x (1 - T) x
D+E D+E
Where:
Ke = cost of equity (from CAPM)
Kd = cost of debt (current cost of borrowing from average yield to maturity)
E = market value of equity
D = market value of debt
T = marginal tax rate
Note: Interest expense is tax deductible, so the true cost of borrowing is the after-tax interest expense.
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30. Issues with the Capital Structure
 "E" = market value of equity
– Private company: estimate from comparables
 "D" = market value of debt
– Book value used as common, practical proxy
• Market quotes not readily available for all debt
• Price movements usually based on interest rate changes since issuance (and
changes in credit profile)
– Be extremely careful with:
• Recent substantial changes in risk-free rate
• Changes in company's credit profile
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31. Issues with the Capital Structure (Cont.)
 Adjust debt for operating leases?
– Yes: if material source of financing / capital
 Use "net debt" or "total debt?"
– Both are common and generally acceptable
– Be consistent and justify your rationale!
• Are there industry specific approaches?
 Other considerations to examine:
– Historical vs. current capital structure
– Possible future financing sources
– Company's vs. industry average capital structure
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32. Determining the Cost of Debt
 Ideally, observable in market
– Yield to maturity from long-term bond (10 years)
– Normally quoted as “Spread” over risk-free rate
 Estimate Kd when no publicly traded debt
– Obtain quote from capital markets
• Based on risk / credit profile
• Quote usually based on "spread" over risk-free benchmark
– Based on comparables
– Examine debt footnote
• Interest rate on recent issuance? Average cost of debt?
 Tax effect at the marginal rate
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33. Overview of the Cost of Equity
 Cost of Equity (Ke) = an investor's expected rate of return including dividends &
capital appreciation
 Greater risks require higher expected returns
– Equity investors have a residual claim on assets
– Subordinate claim to debt holders and preferred stockholders
 Ke often reflects perceived risk of an investment
– Utilities: low risk, low expected return
– Biotech: high risk, high expected return
 Ke difficult to estimate
– Not readily observable in the market
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34. Capital Asset Pricing Model (CAPM)
 Tool used to estimate required equity returns
– Equity investors expect higher return to taking higher risk
 Two types of risk:
1. Systematic risk: market risk
• Unavoidable risk
– Common to all risky securities
• Warrants a “risk premium” above a risk-free rate of return
• Beta measures the amount of an asset’s market risk
2. Unsystematic risk: specific to a company
• Avoidable risk through diversification
• Warrants no “risk premium”
[ 34 ]

35. The CAPM Formula
 CAPM formula:
Where:
Ke = required return on equity
Rf = risk free rate
Ke = rf + [B x (rm – rf)]
B = Beta of the company
Rm – rf = “market risk premium” or the expected
return on market minus the risk-free rate
 Risk-free rate (rf)
– Typically, estimated by 10-year US Treasury
 Beta (B) - popular sources:
1) Barra's predicted betas (from FactSet)
2) Bloomberg (historical betas)
3) Average calculation from comparable companies
 Market risk premium (rm - rf)
– Common source: long-term horizon equity risk premium from Ibbotson Associates' SBBI:
Valuation Edition Yearbook
[ 35 ]

36. Risk – Free Rate: Long-Term Rate
 Rate of return on a "riskless" investment
– US Treasury securities best characterizes a "riskless" security
 Use the long-term rate that best matches the time frame of most investment or
acquisition decisions
– Extension beyond forecast period accounts for terminal value
 In practice, use the market's risk-free benchmark
– Currently, the US Treasury 10 year note
– May want to look at a longer horizon
• 20 year rate derived from 30 year bond with 20 years until maturity
[ 36 ]

37. What is an Equity Beta?
 An equity beta measures a the degree to which a company's equity returns vary
with the return of the overall market
– Beta of 1.0 = risky as overall market
• Expected returns will equal overall market returns
 Ideally, beta value should be an expected value;
– Cost of equity is an expected return :
• Barra supplies predicted betas (available via FactSet) ,
– Common to use historical betas
 Private company - Use an industry average beta
(a) Beta equals the covariance of the security and the market divided by the variance of the market.
[ 37 ]

38. Issues to Consider Regarding Betas*
Predicted Beta Vs. Historical Beta
 Based on a multi-factor forecast model (i.e. Barra  Used is past performance is an effective predictor of
betas) future performance (i.e., the company’s performance is
 May be used for dynamic companies relatively stable)
Industry Average Beta Vs. Individual Beta
 Provides Multiple data points, especially for  Used for well established companies with leverage in a
companies with: relative range to the industry average
– Short operational histories
– Limited market exposure
– Restructured operations
– Leverage significantly different than industry
average
Adjusted Beta Vs. Unadjusted Beta
 Beta of most stocks converges to 1.00 over time  Calculated according to strict mathematical definition
 May understate relative volatiility (if beta > 1.00)  May overstate relative volatility (if beta > 1.00)
[ 38 ]

39. Unlevering and Relevering Equity Betas
 Unlever beta to neutralize impact leverage:
Where:
BL BU = unlevered beta (“asset beta”)
BU = BL = levered beta (“equity beta”)
D
1+ X (1 - T) T = marginal tax rate
E D = market value of debt 1
E = market value of equity
 Relever a beta at a targeted capital structure:
– Company's current capital structure
– Industry average capital structure
– Projected capital structure
D
BL = B U [1 + x (1 - T)]
E
1 The value of preferred stock and minority interest may be included in the value of debt for purposes of unlevering /relevering beta, but should not be tax-effected.
[ 39 ]

40. Mechanics of Unlevering & Relevering
 Common approach:
1. Enter the levered betas for the comparable companies
2. Unlever at each company's D/E ratio
3. Calculate the average unlevered "beta
4. RELEVER the average unlevered beta (or an appropriate beta)
• Use a range appropriate for the Target company
 D/E: use "net debt" or "total debt?"
– Both are common and generally acceptable
– Be consistent and justify your rationale!
• Are there industry specific approaches?
[ 40 ]

41. Exercise: Unlevering Betas
 Assumption – Company A:
BL
T = 38.0%
D= $475 MM
E= $788 MM
 Q1: Calculate the unlevered beta of Company A:
[ 41 ]

42. Exercise: Relevering Betas
 Assumptions – Comparable Companies:
Company B u = 1.01 Company D u = 0.87
Company C u = 0.95 Company E u = 1.13
 Q2: Calculate the average unlevered beta of the comparable companies:
 Q3: Calculate the implied levered beta for Company A (use the average
unlevered beta above, Company A's debt to equity ratio and tax rate):
[ 42 ]

43. What is "Market Risk Premium?"
 Total return of stocks over the risk-free rate
– Estimation of reward for bearing equity risk
 Popular sources:
– Long-term equity risk premium from Ibbotson Associates' SBBI Valuation
Edition Yearbook
• Based on historical market returns vs. risk-free rate
– Forward-looking models estimating expected equity market returns
 Estimates vary from ~4% – 7%
[ 43 ]

44. Small-Cap Adjustments to CAPM
 Small stocks tend to be riskier than large stocks
– Historically, small stocks tend to have:
• Higher returns & larger betas
 Higher betas do not account entirely for the higher returns of small companies
– Higher returns tend to be in excess of CAPM
 CAPM modified for firm size:
SP = appropriate size premium based on
Ke = rf + [B x (rm – rf)] + SP
the firm’s market capitalization
Common source: Ibbotson Associates’
SBBI Valuation Edition
[ 44 ]

45. Exercise: Calculating WACC
 Assumptions – Company A:
L = 1.36(from prior exercise) Market risk premium = 7.2%
T = 38.0% Kd = 8.0%
D = $475 MM rf = 4.00%
E = $788 MM Size premium = 1.70%
 Q1: Calculate the Ke of Company A:
 Q2: Calculate the WACC of Company A:
[ 45 ]

46. International Issues with Cost of Capital
 Risks will vary from country to country
 Calculating cost of capital internationally more challenging
– Limited data
– Lack of integrated markets
– Emerging markets even more difficult!
 Possible to obtain country specific assumptions, especially with developed
countries
– Equity risk premium & betas
– Risk-free rate (such as UK Treasury 10-year bond)
 Seek specialists and internal resources!
[ 46 ]