Weighted Average Cost of Capital

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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 r0
• PVUCF PV of unlevered cash flows
• NPV PVUCF - 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 - 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)

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Weighted-Average-Cost-of-Capital

• Discount rate rWACC
• PVUCF PV of Unlevered Cash Flows
• Value PVUCF - Initial investment for entire
  project

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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.

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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

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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)
• rB .1
• NPVF TC 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 inflows 500
• Cash costs - 360
• Interest - 12.62295
• Income after interest 127.37705
• Corporate tax - 43.3082
• Levered cash flow 84.06885

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FTE (continued)

• Cost 475
• Borrowing - 126.2295
• Cost to equity 348.7705

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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

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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 rWACC

• rWACC (S/(SB))rS(B/(BS))(1-TC)rB
• (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 rB.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/(BS) .305555555
• (cant expect a round number here)

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Example continued. Do it again

• Another project, same as before.
• Retain debt-equity ratio.
• rWACC (S/(BS))rS (B/(BS))rB(1-TC)
• rWACC .30555555rS .694444 rB (.66)
• rSr0 (B/S)(1-TC)(r0-rB)
• rWACC .15277777

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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

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Cash flows to equity

• Cost to equity 0
• CFs (10-3).66 6.6-3.66.462
• rS r0 (B/S)(r0 rB))(1- TC )
• rS .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 doesnt 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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