Primer on Cash Flow Valuation

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Primer on Cash Flow Valuation
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The greater danger for most of us is not that our
aim is too high and we might miss it, but that it
is too low and we reach it. Michelangelo
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(No Transcript)
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Learning Objectives

• Primary learning objectives To provide students
  with an understanding of
• business valuation using discounted cash flow
  valuation techniques and
• the importance of understanding assumptions
  underlying business valuations
• Secondary learning objectives To provide
  students with an understanding of
• discount rates and risk as applied to business
  valuation
• how to analyze risk
• alternative definitions of cash flow and how and
  when they are applied
• the advantages and disadvantages of the most
  commonly used discounted cash flow methodologies
  
• the sensitivity of terminal values to changes in
  assumptions and
• adjusting firm value for non-operating assets and
  liabilities.

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Required Returns Cost of Equity (ke)

• Capital Asset Pricing Model (adjusted for firm
  size)
• ke Rf ß(Rm Rf) FSP
• Where Rf risk free rate of return
• ß beta (systematic/non-dive
  rsifiable risk)
• Rm expected rate of return on
  equities
• Rm Rf 5.5 (i.e., equity risk
  premium
• historical
  average since
• 1963)
• FSP firm size premium

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Estimates of Size Premium

• Market Value (000,000)
• gt21,589
• 7,150 to 21,589
• 2,933 to 7,150
• 1,556 to 2,933
• 687 to 1,556
• 111 to 687
• lt111

• Percentage Points Added to CAPM Estimate
• 0.0
• 1.3
• 2.4
• 3.3
• 4.4
• 5.2
• 7.2

Source Adapted from estimates provided by
Duff Phelps, LLC.
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Required Returns Cost of Capital

• Weighted Average Cost of Capital (WACC)1,2
• WACC ke x E i (1-t) x D
  kpr x __PR__
• (EDPR)
  (EDPR) (EDPR)
• Where E the market value of equity
• D the market value of debt
• PR the market value of preferred
  stock
• ke cost of equity
• kpr cost of preferred stock
• i the interest rate on debt
• t the firms marginal tax rate

1To estimate WACC, use firms target
debt-to-total capital ratio (TC). 2(D/E)/(1D/E)
(D/E)/(ED)/E (D/E)(E/(ED) D/(ED)
D/TC E/TC 1 D/TC.
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Analyzing Risk

• Risk consists of a non-systematic/diversifiable
  and systematic/non-diversifiable component
• Beta (ß) is a measure of non-diversifiable risk
• Beta quantifies a stocks volatility relative to
  the overall market
• Beta is impacted by the following factors
• Degree of industry cyclicality
• Operating leverage refers to the composition of a
  firms cost structure (fixed plus variable costs)
• Financial leverage refers to the composition of a
  firms capital structure (debt equity)
• Firms with high ratios of fixed to total costs
  and debt to total capital tend to display highly
  volatility and betas

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How Operating Leverage Affects Pretax Profits
Revenue Fixed Costs Variable Costs1 Pretax Profits Revenue Fixed Costs Variable Costs1 Pretax Profits Revenue Fixed Costs Variable Costs1 Pretax Profits Revenue Fixed Costs Variable Costs1 Pretax Profits Comment
400 50 200 150
200 50 100 25
100 50 50 0 Breakeven
50 50 25 (25) Continue Operation
0 50 0 (50) Shutdown Operations
Key Points 1. Once revenue exceeds fixed costs, increases in revenue result in more than proportional increases in profits 2. A firm should operate at a loss as long as revenue variable costs. Why? Because the firm can cover a portion of its fixed costs. Key Points 1. Once revenue exceeds fixed costs, increases in revenue result in more than proportional increases in profits 2. A firm should operate at a loss as long as revenue variable costs. Why? Because the firm can cover a portion of its fixed costs. Key Points 1. Once revenue exceeds fixed costs, increases in revenue result in more than proportional increases in profits 2. A firm should operate at a loss as long as revenue variable costs. Why? Because the firm can cover a portion of its fixed costs. Key Points 1. Once revenue exceeds fixed costs, increases in revenue result in more than proportional increases in profits 2. A firm should operate at a loss as long as revenue variable costs. Why? Because the firm can cover a portion of its fixed costs. Key Points 1. Once revenue exceeds fixed costs, increases in revenue result in more than proportional increases in profits 2. A firm should operate at a loss as long as revenue variable costs. Why? Because the firm can cover a portion of its fixed costs.
1Assumes variable costs equal one-half of revenue. 1Assumes variable costs equal one-half of revenue. 1Assumes variable costs equal one-half of revenue. 1Assumes variable costs equal one-half of revenue. 1Assumes variable costs equal one-half of revenue.
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How Operating Leverage Affects Financial Returns1
Case 1 Case 2 Revenue Increases by 25 Case 3 Revenue Decreases by 25
Revenue 100 125 75
Fixed Variable2 Total Cost of Sales 48 32 80 48 40 88 48 24 72
Earnings Before Taxes3 20 37 3
Tax Liability _at_ 40 8 14.8 1.2
After-Tax Earnings 12 22.2 1.8
Firm Equity 100 100 100
Return on Equity () 12 22.2 1.8
1All figures are in millions of dollars unless otherwise noted. 2In Case 1, variable costs represent 32 of revenue. Assuming this relationship is maintained, variable costs in Cases 2 and 3 are estimated by multiplying total revenue by .32. 3Note that (1-.32) or 68 of the change in revenue between Case 1 and Case 2 and Case 3, respectively, directly impacts earnings before taxes. 1All figures are in millions of dollars unless otherwise noted. 2In Case 1, variable costs represent 32 of revenue. Assuming this relationship is maintained, variable costs in Cases 2 and 3 are estimated by multiplying total revenue by .32. 3Note that (1-.32) or 68 of the change in revenue between Case 1 and Case 2 and Case 3, respectively, directly impacts earnings before taxes. 1All figures are in millions of dollars unless otherwise noted. 2In Case 1, variable costs represent 32 of revenue. Assuming this relationship is maintained, variable costs in Cases 2 and 3 are estimated by multiplying total revenue by .32. 3Note that (1-.32) or 68 of the change in revenue between Case 1 and Case 2 and Case 3, respectively, directly impacts earnings before taxes. 1All figures are in millions of dollars unless otherwise noted. 2In Case 1, variable costs represent 32 of revenue. Assuming this relationship is maintained, variable costs in Cases 2 and 3 are estimated by multiplying total revenue by .32. 3Note that (1-.32) or 68 of the change in revenue between Case 1 and Case 2 and Case 3, respectively, directly impacts earnings before taxes.
Key Point High fixed to total cost ratios
magnify fluctuations in financial returns. Why?
Because of the large percentage of revenue in
excess of fixed costs that flows to pretax
profits.
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How Financial Leverage Affects Financial Returns1
Case 1 No Debt Case 2 25 Debt to Total Capital Case 3 50 Debt to Total Capital
Equity 100 75 50
Debt 0 25 50
Total Capital 100 100 100
Earnings before Interest and Taxes 20 20 20
Interest _at_ 10 0 2.5 5
Income before Taxes 20 17.5 15
Less income Taxes _at_ 40 8 7 6
Net Income 12 10.5 9
After-Tax Return on Equity () 12 14 18
1All figures are in millions of dollars unless otherwise noted. 1All figures are in millions of dollars unless otherwise noted. 1All figures are in millions of dollars unless otherwise noted. 1All figures are in millions of dollars unless otherwise noted.
Key Point High debt to total capital
ratios magnify fluctuations in financial returns.
Why? Because equitys share of
total capital declines faster than net income as
debts share of total capital
increases.
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Leveraged versus Unleveraged Betas

• In the absence of debt, the ß is called the
  unleveraged ßu, which is impacted by the firms
  operating leverage and the cyclicality of the
  industry in which the firm competes
• In the presence of debt, the ß is called the
  leveraged ßl
• If a firms shareholders bear all the risk of
  operating and financial leverage and interest is
  tax deductible, leveraged and unleveraged betas
  can be calculated as follows
• ßl ßu (1 (1-t) (D/E)) and ßu ßl / (1
  (1-t) (D/E))
• where t, D, and E are the tax rate, debt and
  equity, respectively.
• Implications
• --Increasing D/E raises firms breakeven and
  increases shareholder risk that firm will be
  unable to generate future cash flows sufficient
  to pay their minimum required returns.
• --Tax deductibility of interest reduces
  shareholder risk by increasing after-tax cash
  available for shareholders.

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Estimating a Firms Beta

• Regress percent change in firms share price plus
  dividends against percent change in a broadly
  defined stock index plus dividends for last 3-5
  years.
• However, this assumes the historical relationship
  between risk and return will hold in the future
• If we have reason to believe this is not true,
  the bottoms-up approach may be appropriate.
• In the bottoms-up approach, we use a sample of
  similar firms1
• Step 1 Select sample of firms with similar
  cyclicality and operating leverage (i.e., usually
  in the same industry)
• Step 2 Calculate average unlevered beta for
  firms in the sample to eliminate the effects of
  their current capital structures on their betas
• ßu ßl / (1 (1-t) (D/E))
• Step 3 Relever average unlevered beta using the
  (D/E) ratio and marginal tax rate tof the firm
  whose beta you are trying to estimate (i.e.,
  target firm)
• ßl ßu (1 (1-t) (D/E))

1This assumes the firms future risk/reward
relationship is more likely to mirror that of the
average firm in the industry adjusted for
financial leverage.
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Estimating Abbot Labs Levered Beta
Step 1 Select sample of firms having similar cyclicality and operating leverage Step 1 Select sample of firms having similar cyclicality and operating leverage Step 1 Select sample of firms having similar cyclicality and operating leverage Step 2 Compute average of firms unlevered betas Step 3 Relever average unlevered beta using targets debt/equity ratio
Firm Levered Beta1 Debt / Equity1 Unlevered Beta2 Abbot Labs Relevered Beta3
Abbot Labs .2900 .2662 .2501 NA
Johnson Johnson .6000 .0762 .5738 NA
Merck .6600 .3204 .5536 NA
Pfizer .6800 .3044 .5750 NA
Average .4881 .4209
1Yahoo Finance (1/29/2011). Beta estimates are based on historical relationship between the firms share price and a broadly defined stock index. 2ßu ßl / (1 (1-t) (D/E)), where ßu and ßl are unlevered and levered betas marginal tax rate is .4. Abbot Labs (ßu ) .2900 / (1 (1 - .4).2662)) .2501 Johnson Johnson (ßu ) .6000 / (1 (1 - .4).0762)) ..5738 Merck (ßu) .6600 / (1 (1 - .4).3204)) .5536 Pfizer (ßu) .6800 / (1 (1 - .4).3044)) .5750 3ßl ßu (1 (1-t) (D/E)) using the target firms (Abbot Labs) debt/equity ratio and marginal tax rate. Abbot Labs relevered beta .4881 (1 (1 - .4).2662)) .4209 1Yahoo Finance (1/29/2011). Beta estimates are based on historical relationship between the firms share price and a broadly defined stock index. 2ßu ßl / (1 (1-t) (D/E)), where ßu and ßl are unlevered and levered betas marginal tax rate is .4. Abbot Labs (ßu ) .2900 / (1 (1 - .4).2662)) .2501 Johnson Johnson (ßu ) .6000 / (1 (1 - .4).0762)) ..5738 Merck (ßu) .6600 / (1 (1 - .4).3204)) .5536 Pfizer (ßu) .6800 / (1 (1 - .4).3044)) .5750 3ßl ßu (1 (1-t) (D/E)) using the target firms (Abbot Labs) debt/equity ratio and marginal tax rate. Abbot Labs relevered beta .4881 (1 (1 - .4).2662)) .4209 1Yahoo Finance (1/29/2011). Beta estimates are based on historical relationship between the firms share price and a broadly defined stock index. 2ßu ßl / (1 (1-t) (D/E)), where ßu and ßl are unlevered and levered betas marginal tax rate is .4. Abbot Labs (ßu ) .2900 / (1 (1 - .4).2662)) .2501 Johnson Johnson (ßu ) .6000 / (1 (1 - .4).0762)) ..5738 Merck (ßu) .6600 / (1 (1 - .4).3204)) .5536 Pfizer (ßu) .6800 / (1 (1 - .4).3044)) .5750 3ßl ßu (1 (1-t) (D/E)) using the target firms (Abbot Labs) debt/equity ratio and marginal tax rate. Abbot Labs relevered beta .4881 (1 (1 - .4).2662)) .4209 1Yahoo Finance (1/29/2011). Beta estimates are based on historical relationship between the firms share price and a broadly defined stock index. 2ßu ßl / (1 (1-t) (D/E)), where ßu and ßl are unlevered and levered betas marginal tax rate is .4. Abbot Labs (ßu ) .2900 / (1 (1 - .4).2662)) .2501 Johnson Johnson (ßu ) .6000 / (1 (1 - .4).0762)) ..5738 Merck (ßu) .6600 / (1 (1 - .4).3204)) .5536 Pfizer (ßu) .6800 / (1 (1 - .4).3044)) .5750 3ßl ßu (1 (1-t) (D/E)) using the target firms (Abbot Labs) debt/equity ratio and marginal tax rate. Abbot Labs relevered beta .4881 (1 (1 - .4).2662)) .4209 1Yahoo Finance (1/29/2011). Beta estimates are based on historical relationship between the firms share price and a broadly defined stock index. 2ßu ßl / (1 (1-t) (D/E)), where ßu and ßl are unlevered and levered betas marginal tax rate is .4. Abbot Labs (ßu ) .2900 / (1 (1 - .4).2662)) .2501 Johnson Johnson (ßu ) .6000 / (1 (1 - .4).0762)) ..5738 Merck (ßu) .6600 / (1 (1 - .4).3204)) .5536 Pfizer (ßu) .6800 / (1 (1 - .4).3044)) .5750 3ßl ßu (1 (1-t) (D/E)) using the target firms (Abbot Labs) debt/equity ratio and marginal tax rate. Abbot Labs relevered beta .4881 (1 (1 - .4).2662)) .4209
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Valuation Cash Flow

• Valuation cash flows represent actual cash flows
  available to reward both shareholders and lenders
• Cash flow statements include cash inflows and
  outflows from
• operating,
• investing, and
• financing activities
• GAAP cash flows are adjusted for non-cash inflows
  and outflows to calculate valuation cash flow.
  Examples include the following
• Adding depreciation back to net income
• Deducting gains from and adding losses to net
  income resulting from asset sales
• Valuation cash flows include free cash flows to
  equity investors or equity cash flow and free
  cash flows to the firm or enterprise cash flow

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Cash-Based Versus GAAP AccountingAn Example

• Assume
• A firm has annual revenue of 10 million each
  year for the next five years,
• It buys a piece of equipment for 10 million in
  the first year, and
• The equipment is fully expensed in the first
  year. All other costs are ignored.
• Cash-Based Accounting Yr. 1 Yr.
  2 Yr.3 Yr.4 Yr. 5
• Revenue 10 10
  10 10 10
• Cost (10)
• Pretax profit 0 10
  10 10 10
• Profit is (10) million in the
  first year and a positive 10 million in each
  successive year.
• GAAP Accounting
• Cost (2)
  (2) (2) (2) (2)
• Pretax profit 8 8
  8 8 8
• To smooth profitability and better align costs
  incurred with the period in which the
• revenues were actually generated,
  assume the equipment was depreciated equally
• over 5years or 2 million per
  year. Profitability would be 8 million annually.
• Key Point The timing of cash flows
  impacts valuation. Valuation cash flow uses cash-
• based accounting
  which indicates the period in which cash inflows
  and outflows
• actually occurs.

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Calculating Free Cash Flow to Equity Investors
or Equity Cash Flow (FCFE)

• FCFE (equity cash flow)1 represents cash flow
  available for paying dividends or repurchasing
  common equity, after taxes, debt repayments, new
  debt and preferred stock issues, and all
  reinvestment requirements.
• FCFE (Net Income Depreciation ? Net Working
  Capital2)3 Gross Capital Expenditures4 (New
  Preferred Equity Issues Preferred Dividends
  New Debt Issues Principal Repayments)5
• 1PV of equity cash flows is the equity value of
  the firm.
• 2Excludes cash in excess of normal operating
  requirements.
• 3Cash from operating activities.
• 4Cash from investing activities.
• 5Cash from financing activities.

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Calculating Free Cash Flow to the Firm or
Enterprise Cash Flow (FCFF)

• FCFF (enterprise cash flow)1 is cash flow
  available to repay lenders and/or pay common and
  preferred dividends and repurchase equity, after
  taxes and reinvestment requirements but before
  debt repayments.
• FCFF (Earnings before interest taxes (1-tax
  rate) Depreciation ? Net Working Capital2)3
  Gross Capital Expenditures4
• 1PV of enterprise cash flows is the enterprise
  value of the firm
• 2Excludes cash in excess of normal operating
  requirements.
• 3Cash from operating activities.
• 4Cash from investing activities.

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Comparing Free Cash Flow to the Firm and to
Equity
Free Cash Flow to the Firm Free Cash Flow to Equity
Cash from Operating Activities 40 40
Cash from Investing Activities (22) (22)
Cash from Financing Activities (10)
Total Cash Flow 18 8
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Discussion Questions

• How does the size of the firm affect its
  perceived risk? Be specific?
• How would you estimate the beta for a publicly
  traded firm? For a private firm?
• 3. Explain the difference between equity and
  enterprise cash flow?
• 4. What is the appropriate discount rate to use
  with equity cash flow? Why? With enterprise cash
  flow? Why?

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Commonly Used Discounted Cash Flow Valuation
Methods

• Zero Growth Model
• Constant Growth Model
• Variable Growth Model

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Zero Growth Model

• Free cash flow is constant in perpetuity.
• P0 FCFF0 / WACC, where FCFF0 is free cash
• flow to the firm and WACC is the weighted
  
• average the cost of capital
• P0 FCFE0 / ke where FCFE0 is free cash flow
• to equity investors and ke is the cost of
  
• equity

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Zero Growth Model Example

• What is the value of a firm, whose annual FCFF0
  of 1 million is expected to remain constant in
  perpetuity and whose weighted average cost of
  capital is 12.
• P0 1 / .12 8.3 million

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Constant Growth Model

• Cash flow next year (i.e., FCFF1, the first year
  of the
• forecast period) is expected to grow at a
  constant rate.
• FCFF1FCFF0(1g)
• P0 FCFF1 / (WACC-g), where g is the expected
  rate of
• growth of FCFF1.
• P0 FCFE1 / (ke g), where g is the expected
  rate of
• growth of FCFE1.

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Constant Growth Model Example

• Estimate the value of a firm (P0) whose cost of
  equity is 15 and whose cash flow in the prior
  year is projected to grow 20 in the current year
  and then at a constant 10 annual rate
  thereafter. Cash flow in the prior year is 2
  million.
• P0 (2 x 1.2)(1.1) / (.15 - .10) 52.8 million

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Variable (Supernormal) Growth Model

• Cash flow exhibits both a high and a stable
  growth period.
• High growth period The firms growth rate
  exceeds a rate that can be sustained long-term.
• Stable growth period The firm is expected to
  grow at a rate that can be sustained indefinitely
  (e.g., industry average growth rate).
• Discount rates Reflecting the slower growth rate
  during the stable growth period, the discount
  rate during the stable period should be lower
  than doing the high growth period (e.g., industry
  average discount rate).

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Variable Growth Model Contd.
n
P0,FCFF S FCFF0 x (1gt)t
Pn t1 (1
WACC)t (1WACC)n
Where Pn FCFFn x (1 gm)
(WACCm gm) FCFF0 free cash
flow to the firm in year 0 WACC
weighted average cost of capital through year n
WACCm Weighted average cost of capital
beyond year n (Note
WACC gt WACCm) Pn value of the firm at
the end of year n (terminal value) gt
growth rate through year n gm
stabilized or long-term industry average growth
rate beyond year n (Note gt gt
gm)
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Variable Growth Model Example

• Estimate the value of a firm (P0) whose cash flow
  is projected to grow at a compound annual average
  rate of 35 for the next five years and then
  assume a more normal 5 annual growth rate. The
  current years cash flow is 4 million. The
  firms weighted average cost of capital during
  the high growth period is 18 and then drops to
  the industry average rate of 12 beyond the fifth
  year.

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Variable Growth Model Example Solution

• PV1-5 4 x 1.35 4 x (1.35)2 4 x (1.35)3
  
• (1.18) (1.18)2
  (1.18)3
• 4 x (1.35)4 4 x (1.35)5
• (1.18)4 (1.18)5
• 30.5
• PV5 ((4 x (1.35)5 x 1.05)) / (.12 - .05)
  117.65
• (1.18)5
• P0 PV1-5 PV5 30.50 117.65 148.15

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Solving Variable Growth Model Example Using A
Growing Annuity

• P0,FCFF High Growth Period
  Terminal Period
• (Growth Annuity)
  (Constant Growth
  Model)
• PV of FCFF Fraction of
  PV of Terminal
  
• Growing at x PV Growing
  Period FCFF
• Constant Rate N Periods
• P0,FCFF FCFF0(1 g) x 1 (1 g)/(1
  WACC)n FCFFn x (1 g)/(WACC - g)
  
• (WACC g)
  (1 WACC)n
  
• 4.00 (1.35) x 1 (1.35/1.18)5
  (4.00 x 1.355 x 1.05/(.12 - .05)
• (.18 - .35)
  1.185
  
• -.91.8 x -.96 117.65
• 30.50 117.65

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Determining Growth Rates

• Key premise A firms value can be approximated
  by the sum of the high growth plus a stable
  growth period.
• Key risks Sensitivity of terminal values to
  choice of assumptions about stable growth rate
  and discount rates used in both the terminal and
  annual cash flow periods.
• Stable growth rate The firms growth rate that
  is expected to last forever. Generally equal to
  or less than the industry or overall economys
  growth rate. For multinational firms, the growth
  rate is the world economys rate of growth.
• Length of the high growth period The greater the
  current growth rate of a firms cash flow
  relative to the stable growth rate, the longer
  the high growth period.

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Choosing the Correct Tax Rate(Marginal or
Effective)

• Effective rates are those a firm is actually
  paying after allowable deductions (e.g.,
  investment tax credits) and deferrals (e.g.,
  accelerated depreciation)
• Marginal tax rates are those paid on the last
  dollar of income earned
• Zero and Constant Growth Models In calculating
  valuation cash flows, use marginal tax rates1
• Variable Growth Model In calculating valuation
  cash flows,
• Use effective rates to calculate annual cash
  flows when effective rates are less than marginal
  rates and
• Use marginal rates in calculating terminal period
  cash flows.1
• 1The use of effective tax rates during the
  terminal or an indefinite growth period implies
  the firm will defer
• the payment of taxes indefinitely.

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Practice Exercise

• Free cash flow to equity last year was 4
  million. It grew by 20 in the current year it
  is expected to grow at a 15 rate annually for
  the next five years, and then assume a more
  normal 4 growth rate thereafter. The firms cost
  of equity is 10 during the high growth period
  and then drops to 8 during the normal growth
  period. What is the present value of the firm to
  equity investors (equity value)? If the market
  value of the firms debt is 10 million, what is
  the present value of the firm (enterprise value)?

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Adjusting Firm Value

• Generally, the value of the firms equity is the
  sum of the present value of the firms operating
  assets and liabilities plus terminal value (i.e.,
  enterprise value) less market value of firms
  long-term debt.
• However, value may be under or overstated if not
  adjusted for present value of non-operating
  assets and liabilities assumed by the acquirer.
• PVFCFE PVFCFF (incl. terminal value) PVD
  PVNOA PVNOL
• where PVFCFE PV of free cash flow to
  equity investors
• PVFCFF PV of free cash flow to
  the firm (i.e., enterprise
• value)
• PVD PV of debt
• PVNOA PV of non-operating
  assets
• PVNOL PV of non-operating
  liabilities

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Adjusting Firm Value Example

• A target firm has the following characteristics
• An estimated enterprise value of 104 million
• Long-term debt whose market value is 15 million
• 3 million in excess cash balances
• Estimated PV of currently unused licenses of 4
  million
• Estimated PV of future litigation costs of 2.5
  million
• 2 million common shares outstanding
• What is the value of the target firm per common
  share?

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Adjusting Firm Value Example Contd.
Enterprise Value 104
Plus Non-Operating Assets Excess Cash Balances PV of Licenses 3 4
Less Non-Operating Liabilities PV of Potential Litigation 2.5
Less Long-Term Debt 15
Equals Equity Value 93.5
Equity Value Per Share 46.75
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Things to Remember

• Zero growth model Cash flow is expected to
  remain constant in perpetuity.
• Constant growth model Cash flow is expected to
  grow at a constant rate.
• Variable (supernormal) growth model Cash flow
  exhibits both a high and a stable growth period.
• Total present value represents the sum of the
  discounted value of the cash flows over both
  periods.
• The terminal value frequently accounts for most
  of the total present value calculation and is
  highly sensitive to the choice of growth and
  discount rates.