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 IV: Deal Structuring and

Financing

Part II: M&A ProcessPart I: M&A Environment

Ch. 11: Payment and Legal Considerations

Ch. 7: Discounted Cash Flow Valuation

Ch. 9: Financial Modeling Techniques

Ch. 6: M&A Postclosing Integration

Ch. 4: Business and Acquisition Plans

Ch. 5: Search through Closing Activities

Part V: Alternative Business and Restructuring

Strategies

Ch. 12: Accounting & Tax Considerations

Ch. 15: Business Alliances

Ch. 16: Divestitures, Spin-Offs, Split-Offs,

and Equity Carve-Outs

Ch. 17: Bankruptcy and Liquidation

Ch. 2: Regulatory Considerations

Ch. 1: Motivations for M&A

Part III: M&A Valuation and

Modeling

Ch. 3: Takeover Tactics, Defenses, and Corporate Governance

Ch. 13: Financing the Deal

Ch. 8: Relative Valuation

Methodologies

Ch. 18: Cross-Border Transactions

Ch. 14: Valuing Highly Leveraged

Transactions

Ch. 10: Private Company Valuation

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 = risk free rate of return ß = beta (systematic/non-diversifiable 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

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).2(D/E)/(1+D/E) = [(D/E)/(E+D)/E] = [(D/E)(E/(E+D)] = D/(E+D) = D/TC; E/TC = 1 – D/TC.

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 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.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.

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 @ 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

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 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 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

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 .42091Yahoo Finance (1/29/2011). Beta estimates are based on historical relationship between the firm’s 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)) = .57503ßl = ßu (1 + (1-t) (D/E)) using the target firm’s (Abbot Labs) debt/equity ratio and marginal tax rate. 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 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

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 8To 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.

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.2Excludes cash in excess of normal operating requirements.3Cash from operating activities.4Cash from investing activities.5Cash from financing activities.

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 firm2Excludes cash in excess of normal operating requirements.3Cash from operating activities.4Cash from investing activities.

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

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 + Pn

t=1 (1+ WACC)t (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 + 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

= $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 $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

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.