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Cash Flows in Capital Budgeting Three approaches: Free Cash Flow and WACC Adjusted Present Value Cash Flows to Equity

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Effects of Leverage (Debt) Modigliani-Miller (MM) 1958 –Showed that value of a firm (project) is not affected by the use of leverage assuming No transaction costs No taxes No bankruptcy costs Information is available to all In practice, Interests on debt are tax deductible but dividends are not Costs of issuing new securities (stocks and bonds) are high Costs of financial distress are not trivial Information asymmetry exists

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Free (Unlevered) Cash Flows Tax consequence After-tax (AT) value =Before-tax (BT) value*(1–Tax rate) Free Cash Flows = Operating CF – Additions to NWC – Additions to fixed assets Two common approaches to computing Operating CF Operating CF = EBIT + Depreciation – Taxes Operating CF = Net Income + Depreciation + AT interest Net Working Capital (NWC) = Current assets – current liabilities Additions to NWC = Ending NWC – Beginning NWC Additions to fixed assets = Ending Net Fixed Assets (NFA) – Beginning NFA + depreciation –Or simply = the aggregate net asset purchases

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Terminal Value Estimating detailed cash flows forever is unrealistic and impractical Assume a “terminal” value (resale value) –Constant Growth Rate (g) approach* TV T = FCF T-1 *(1+g) / (WACC – g) Assumes terminal value is a growing perpetuity –Use book value –Use book value * market-to-book multiple –Use P/E ratio to estimate equity value + book value of debt –Use EBITDA ratio How important is terminal value?

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Weight Average Cost of Capital (WACC) Approach Use unlevered Cash Flows to the Firm Use WACC as the discount rate

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Adjusted Present Value (APV) Approach APV = NPV + NPVF NPV = the value of the project to an unlevered firm NPVF = the present value of financing side effects There are four major side effects of financing : –The Tax Subsidy to Debt –The Costs of Issuing New Securities –The Costs of Financial Distress –Other Subsidies to Debt Financing Not all side effects exist for all projects The most common one is the tax subsidy of debt Interest tax shield = Interest Expense * Tax Rate

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PV of Interest Tax Shield PV of Interest Tax Shield Interest expense t = Debt t-1 * interest rate Interest tax shield t = Interest expense t * tax rate PV of Interest Tax Shield t = Interest tax shield t / (1 + interest rate) t –Note: discount rate is the before-tax interest rate Example: The firm borrowed $150 (thousands) in t0 Interest Expense in t1 = 3% x 150 = $45 Interest Tax Shield in t1 = $45 x 40% = $1.80 PV of Interest Tax Shield = $1.80/1.03 = $1.7476

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Flow-to-Equity (FTE) Approach Use cash flows to the equity holders of the levered firm as future cash flows Use the cost of levered equity capital, r S, as the discount rate Compute NPV from the perspective of equity holders

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Cash Flows to Equity Holders Revenue= Unit price x units sold - Variable Costs= Unit cost x units sold Gross Profit - Cash Fixed Costs - Depreciation EBIT (Operating Income/Profit) - Interest EBT - Tax Net Income/Profit Cash Flow to Equity Holders = Net Income + Depreciation - (Addition to Fixed Assets – Debt Financing) - Addition to Net Working Capital Net after-tax cash flow to Equity Holders

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Cost of Levered Equity Capital Cost of equity, required return on stock, r S –Should reflect both business and financial risks –Usually computed based on CAPM and beta of the stock (we’ll discuss CAPM later) –Another approach is to start with the unlevered cost of capital, r U –r U reflects all business risk –Modigliani and Miller (1958) Proposition II: Leverage increases equity risk & required return Some of the increase is offset by interest tax shield r s = r U + (B/S L ) (1-T C ) (r U - r B ) r B is the interest rate (cost of debt) r s is the return on levered equity (cost of equity) r U is the return on unlevered cost of capital B is the value of debt S L is the value of levered equity

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A Comparison of the APV, FTE, and WACC Approaches All three approaches attempt the same task –valuation in the presence of debt financing. APVWACCFTE Initial Investment FullFullEquity Portion Cash FlowsUCFUCFLCF Discount Rates r U r WACC r S PV of financing effectsYesNoNo Guidelines: –Use WACC or FTE if the firm’s target debt-to-value ratio is constant –Use the APV if the project’s level of debt is known over the life of the project. In practice, the WACC approach is the most widely used by far.

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Capital Budgeting When the Business Risk Changes Projects with similar business risk –Expansion projects E.g. Kellogg introduces a new cereal –Use existing WACC or r S Projects with significantly different business risk –New business model E.g. Blockbuster entering the mail-order rental market –No exact formula exists for this. Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant.

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Summary The APV formula can be written as: The FTE formula can be written as: The WACC formula can be written as

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Conclusions Use the WACC or FTE if the firm's target debt to value ratio applies to the project over its life. –WACC is the most commonly used by far. –FTE has appeal for a firm deeply in debt. The APV method is used if the level of debt is known over the project’s life. –The APV method is frequently used for special situations like interest subsidies, LBOs, and leases. The risk of the equity of the firm is positively related to the leverage of the firm.

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