Primer on Cash Flow
Valuation
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
Exhibit 1: Course Layout: Mergers,
Acquisitions, and Other
Restructuring Activities
Part I: M&A
Environment
Part II: M&A Process
Part III: M&A
Valuation and
Modeling
Part IV: Deal
Structuring and
Financing
Part V: Alternative
Business and
Restructuring
Strategies
Ch. 1: Motivations for
M&A
Ch. 4: Business and
Acquisition Plans
Ch. 7: Discounted
Cash Flow Valuation
Ch. 11: Payment and
Legal Considerations
Ch. 15: Business
Alliances
Ch. 2: Regulatory
Considerations
Ch. 5: Search through
Closing Activities
Ch. 8: Relative
Valuation
Methodologies
Ch. 12: Accounting &
Tax Considerations
Ch. 16: Divestitures,
Spin-Offs, Split-Offs,
and Equity Carve-Outs
Ch. 3: Takeover
Tactics, Defenses, and
Corporate Governance
Ch. 6: M&A
Postclosing Integration
Ch. 9: Financial
Modeling Techniques
Ch. 13: Financing the
Deal
Ch. 17: Bankruptcy
and Liquidation
Ch. 10: Private
Company Valuation
Ch. 14: Valuing
Highly Leveraged
Transactions
Ch. 18: Cross-Border
Transactions
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.
Required Returns:
Cost of Equity (ke)
Capital Asset Pricing Model (adjusted for firm size):
ke = Rf + ß(Rm – Rf) + FSP
Where Rf
ß
Rm
Rm – Rf
FSP
= risk free rate of return
= beta (systematic/non-diversifiable risk)
= expected rate of return on equities
= 5.5% (i.e., equity risk premium
historical average since
1963)
= firm size premium
Estimates of Size Premium
Market Value (000,000)
>$21,589
$7,150 to $21,589
$2,933 to $7,150
$1,556 to $2,933
$687 to $1,556
$111 to $687
<$111
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.
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__
(E+D+PR)
(E+D+PR)
(E+D+PR)
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 firm’s marginal tax rate
1To
estimate WACC, use firm’s target debt-to-total capital ratio (TC).
= [(D/E)/(E+D)/E] = [(D/E)(E/(E+D)] = D/(E+D) = D/TC; E/TC = 1 – D/TC.
2(D/E)/(1+D/E)
Analyzing Risk
•
•
•
•
•
Risk consists of a nonsystematic/diversifiable and
systematic/non-diversifiable component
Beta (ß) is a measure of non-diversifiable
risk
Beta quantifies a stock’s 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 firm’s cost structure
(fixed plus variable costs)
– Financial leverage refers to the
composition of a firm’s 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
How Operating Leverage Affects 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.
1Assumes
variable costs equal one-half of revenue.
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 @ 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.
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.
2In
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.
How Financial Leverage Affects
Financial Returns1
Case 1: No Debt
Case 2: 25% Debt to
Total Capital
Case 3: 50% Debt to
Total Capital
100
75
50
0
25
50
Total Capital
100
100
100
Earnings before Interest and
Taxes
20
20
20
Interest @ 10%
0
2.5
5
Income before Taxes
20
17.5
15
Less income Taxes @ 40%
8
7
6
Net Income
12
10.5
9
After-Tax Return on Equity (%)
12
14
18
Equity
Debt
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 equity’s share of total capital declines faster than net income as debt’s
share of total capital increases.
Leveraged versus Unleveraged Betas
•
•
•
In the absence of debt, the ß is called the unleveraged ßu, which is impacted
by the firm’s 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 firm’s 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 firm’s 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.
Estimating a Firm’s Beta
• Regress percent change in firm’s share price plus dividends against
percent change in a broadly defined stock index plus dividends for last 35 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 firms:1
– 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 t*of the firm whose beta you are trying to estimate
(i.e., target firm)
ßl = ßu (1 + (1-t*) (D/E)*)
1This
assumes the firm’s future risk/reward relationship is more likely to mirror that of the average
firm in the industry adjusted for financial leverage.
Estimating Abbot Labs’ Levered Beta
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 target’s
debt/equity ratio
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
Firm
1Yahoo
Finance (1/29/2011). Beta estimates are based on historical relationship between the firm’s share
price and a broadly defined stock index.
2ß = ß / (1 + (1-t) (D/E)), where ß and ß are unlevered and levered betas; marginal tax rate is .4.
u
l
u
l
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
3ß = ß (1 + (1-t) (D/E)) using the target firm’s (Abbot Labs) debt/equity ratio and marginal tax rate.
l
u
Abbot Labs’ relevered beta = .4881 (1 + (1 - .4).2662)) = .4209
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 noncash 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
Cash-Based Versus GAAP Accounting:
An 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 cashbased accounting which indicates the period in which cash inflows and outflows
actually occurs.
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 – Δ 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.
cash in excess of normal operating requirements.
3Cash from operating activities.
4Cash from investing activities.
5Cash from financing activities.
2Excludes
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 – Δ Net Working Capital2)3 – Gross Capital
Expenditures4
1PV
of enterprise cash flows is the enterprise value of the firm
cash in excess of normal operating requirements.
3Cash from operating activities.
4Cash from investing activities.
2Excludes
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
Total Cash Flow
(10)
18
8
Discussion Questions
1. How does the size of the firm affect its
perceived risk? Be specific?
2. 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?
Commonly Used Discounted Cash Flow
Valuation Methods
• Zero Growth
Model
• Constant Growth
Model
• Variable Growth
Model
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
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
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.
FCFF1=FCFF0(1+g)
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.
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
Variable (Supernormal) Growth Model
• Cash flow exhibits both a high and a stable growth
period.
• High growth period: The firm’s 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).
Variable Growth Model Cont’d.
n
P0,FCFF = Σ FCFF0 x (1+gt)t +
t=1 (1+ WACC)t
Pn
(1+WACC)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 > 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 > gm)
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 year’s cash flow is $4 million. The
firm’s 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.
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
Solving Variable Growth Model Example
Using A Growing Annuity
P0,FCFF =
High Growth Period
(Growth Annuity)
PV of FCFF
Growing at
x
Constant Rate
Fraction of
PV Growing
N Periods
+
+
Terminal Period
(Constant Growth Model)
PV of Terminal
Period FCFF
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
= $148.15
Determining Growth Rates
• Key premise: A firm’s 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 firm’s growth rate that is
expected to last forever. Generally equal to or less than
the industry or overall economy’s growth rate. For
multinational firms, the growth rate is the world
economy’s rate of growth.
• Length of the high growth period: The greater the current
growth rate of a firm’s cash flow relative to the stable
growth rate, the longer the high growth period.
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.
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 firm’s 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 firm’s debt is $10 million, what is the present
value of the firm (enterprise value)?
Adjusting Firm Value
• Generally, the value of the firm’s equity is the sum of the present
value of the firm’s operating assets and liabilities plus terminal value
(i.e., enterprise value) less market value of firm’s 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
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?
Adjusting Firm Value Example Cont’d.
Enterprise Value
Plus: Non-Operating Assets
Excess Cash Balances
PV of Licenses
$104
$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
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.