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Weighted Average Cost of Capital And equivalent approaches

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Review item A corporation is near bankruptcy. Why do the managers invest in bad risks?

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Answer on bad risks Managers represent equity … at least they are supposed to. Risk gives them a chance to pull out of bankruptcy. Equity gets the gain. A bad outcome leaves them still bankrupt. Debt suffers the loss.

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Capital Budgeting for the Levered Firm Adjusted Present Value Flows to Equity Weighted Average Cost of Capital APV Example

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Adjusted-Present-Value (APV) NPV for an unlevered firm NPVF = net present value of financing APV = NPV + NPVF

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Unlevered NPV Unlevered cash flows = CF from operations - Capital Spending - Added NWC - corporate taxes for unlevered firm. Discount rate: r 0 PV UCF : PV of unlevered cash flows NPV = PV UCF - Initial investment

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Net present value of financing side effects PV of Tax Subsidy to Debt Costs of Issuing New Securities The Costs of Financial Distress Subsidies to Debt Financing

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Flow-to-Equity (FTE) LCF = UCF - (1 - T C ) x r B x B PV LCF = Present value of LCF FTE = PV LCF - Portion of initial investment from equity Required return on levered equity (r S ) r S = r 0 + B/S L x (1 - T C ) x (r 0 - r B )

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Weighted-Average-Cost-of- Capital Discount rate: r WACC PV UCF : PV of Unlevered Cash Flows Value = PV UCF - Initial investment for entire project

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Summary: APV, FTE, and WACC APVWACCFTE Initial Investment AllAllEquity Portion Cash FlowsUCFUCFLCF Discount Rates r 0 r WACC r S PV of financing YesNoNo Which is best? Use WACC and FTE when the debt ratio is constant Use APV when the level of debt is known.

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Example p. 437: Project Cash inflows500 Cash costs360 Operating income140 Corporate tax 47.6 Unlevered cash flow 92.4 Cost of project 475

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APV Physical asset of project is discounted at.2. NPV = 92.4/.2 - 475 = 462 - 475 = -13 Borrowing 126.2295 (from B/S = 1/3) r B =.1 NPVF = T C x B = 42.918 APV = -13 + 42.918 = 29.918

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APV recap Value = 475 + 29.918 = 504.918 Debt = - 126.2295 Equity = 378.6885 Debt/Equity = 1/3 Debt/(Debt + Equity) = 1/4

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Flow to Equity Cash inflows500 Cash costs - 360 Interest- 12.62295 Income after interest127.37705 Corporate tax- 43.3082 Levered cash flow 84.06885

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FTE (continued) Cost 475 Borrowing -126.2295 Cost to equity348.7705

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FTE: Required return on equity r S =r 0 +(B/S)(1-T C )(r 0 -r B ) B/S = 1/3 r S =.2 +(1/3)(.66)(.2-.1) =.222

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FTE valuation NPV = - 348.7705 + 84.06885/.22… = 29.918 Same as in APV method. Now, same thing with WACC.

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Find r WACC r WACC = (S/(S+B))r S +(B/(B+S))(1-T C )r B =(3/4)(.222) + (1/4)(.66)(.1) =.183

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WACC method continued NPV = - 475 + 92.4/.183 = 29.918 All methods give the same thing.

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Example: Start-up, all debt financed. Cost of project = 30 CF of project 10 before tax, 6.6 after. Discount rate for an all equity firm.2. NPV = 6.6/.2 - 30 = 3

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More APV example Tax shield from borrowing 30 at r B =.1 =.1(30).34 = 1.02. Discounted value = NPVF = 10.2. APV = 3 + 10.2 = 13.2.

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Leverage of the start-up Not 100%. Value is 30 + 13.2. B = 30, S = 13.2 S/(B+S) =.305555555 (can’t expect a round number here)

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Example continued. Do it again Another project, same as before. Retain debt-equity ratio. r WACC = (S/(B+S))r S + (B/(B+S))r B (1-T C ) r WACC =.30555555r S +.694444 r B (.66) r S =r 0 +(B/S)(1-T C )(r 0 -r B ) r WACC =.15277777

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Value, using r WACC NPV = -30 + 6.6/.1527777 =13.2 Lesson: WACC works when the debt equity ratio is established before the project and retained thereafter. APV works when the project changes the debt equity ratio

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Cash flows to equity Cost to equity = 0 CF’s = (10-3)*.66 = 6.6-3*.66=.462 r S = r 0 + (B/S)*(r 0 – r B) )(1- T C ) r S =.35 NPV = 4.62/.35 = 13.2

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Review item Complete the following statement and explain briefly: nothing matters in finance except __________ and _________.

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Answer: taxes and bankruptcy Explanation. Because of homemade leverage, capital structure doesn’t matter in the absence of taxes and bankruptcy. Taxes matter because debt generates tax shields. Bankruptcy matters because financial distress damages the assets of the firm.

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