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Weighted Average Cost of Capital

Weighted Average Cost of Capital. And equivalent approaches. Review item. A corporation is near bankruptcy. Why do the managers invest in bad risks?. Answer on bad risks. Managers represent equity … at least they are supposed to.

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Weighted Average Cost of Capital

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  1. Weighted Average Cost of Capital And equivalent approaches

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

  3. 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.

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

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

  6. Unlevered NPV • Unlevered cash flows = CF from operations - Capital Spending - Added NWC - corporate taxes for unlevered firm. • Discount rate: r0 • PVUCF: PV of unlevered cash flows • NPV = PVUCF - Initial investment

  7. 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

  8. Flow-to-Equity (FTE) • LCF = UCF - (1 - TC) x rB x B • PVLCF = Present value of LCF • FTE = PVLCF - Portion of initial investment from equity • Required return on levered equity (rS) • rS = r0 + B/SL x (1 - TC) x (r0 - rB)

  9. Weighted-Average-Cost-of-Capital • Discount rate: rWACC • PVUCF: PV of Unlevered Cash Flows • Value = PVUCF - Initial investment for entire project

  10. Summary: APV, FTE, and WACC APV WACC FTE Initial Investment All All Equity Portion Cash Flows UCF UCF LCF Discount Rates r0 rWACC rS PV of financing Yes No No Which is best? • Use WACC and FTE when the debt ratio is constant • Use APV when the level of debt is known.

  11. Example p. 437: Project • Cash inflows 500 • Cash costs 360 • Operating income 140 • Corporate tax 47.6 • Unlevered cash flow 92.4 • Cost of project 475

  12. 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) • rB = .1 • NPVF = TC x B = 42.918 • APV = -13 + 42.918 = 29.918

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

  14. Flow to Equity • Cash inflows 500 • Cash costs - 360 • Interest - 12.62295 • Income after interest 127.37705 • Corporate tax - 43.3082 • Levered cash flow 84.06885

  15. FTE (continued) • Cost 475 • Borrowing - 126.2295 • Cost to equity 348.7705

  16. FTE: Required return on equity • rS =r0 +(B/S)(1-TC)(r0-rB) • B/S = 1/3 • rS = .2 +(1/3)(.66)(.2-.1) = .222

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

  18. Find rWACC • rWACC = (S/(S+B))rS+(B/(B+S))(1-TC)rB • =(3/4)(.222) + (1/4)(.66)(.1) • = .183

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

  20. 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

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

  22. 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)

  23. Example continued. Do it again • Another project, same as before. • Retain debt-equity ratio. • rWACC = (S/(B+S))rS + (B/(B+S))rB(1-TC) • rWACC = .30555555rS +.694444 rB (.66) • rS=r0 +(B/S)(1-TC)(r0-rB) • rWACC= .15277777

  24. Value, using rWACC • 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

  25. Cash flows to equity • Cost to equity = 0 • CF’s = (10-3)*.66 = 6.6-3*.66=.462 • rS = r0 + (B/S)*(r0 –rB))(1- TC ) • rS = .35 • NPV = 4.62/.35 = 13.2

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

  27. 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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