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Weighted Average Cost of Capital

This guide explores the Weighted Average Cost of Capital (WACC), Adjusted Present Value (APV), and Flow-to-Equity (FTE) methodologies in capital budgeting for levered firms. It explains why managers might invest despite poor firm performance, illustrating how they can pull out of bankruptcy by leveraging equity gains, while debt quite often suffers. Key aspects include understanding the NPV calculations for unlevered and levered firms, and comparing the effectiveness of these approaches based on the firm's capital structure. Essential concepts are summarized with numerical examples for clarity.

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Weighted Average Cost of Capital

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  1. Weighted Average Cost of Capital And equivalent approaches

  2. Exam quickie • 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. Reading note • Skip sections 17.5 through 17.8. • Pages 444-451.

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

  7. 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

  8. 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

  9. 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)

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

  11. 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.

  12. 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

  13. APV • Physical asset of project is discounted at .2. • NPV = 92.4/.2 - 475 = 462 - 475 = -13 • Bond financing of 126.2295 • rB = .1 • NPVF = TC x B = 42.918 • APV = -13 + 42.918 = 29.918

  14. APV recap • Value = 475 + 29.918 = 504.198 • Debt = - 126.2295 • Equity = 378.6985 • Debt/Equity = 1/3 • Debt/(Debt + Equity) = 1/4

  15. 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

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

  17. FTE: Required return on equity • rS =r0 +(B/S)(1-TC)(r0-rB) • B/S = 1/3 • rS = .2 +(1/3)(.66)(.2-.1) = .22...

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

  19. Find rWACC • rWACC = (S/(S+B))rS+(B/(B+S))(1-TC)rB • =(3/4)(.22…) + (1/4)(.66)(.1) • = .1831666...

  20. WACC method continued • NPV = • -475 + 92.4/.183166… • = 29.918. • All methods give the same thing.

  21. 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

  22. 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.

  23. 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)

  24. 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

  25. 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

  26. Exam quickie • 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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