# Weighted Average Cost of Capital - UCSB's Department of Economics

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.

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. Capital Budgeting for the Levered Firm Adjusted Present Value

Flows to Equity Weighted Average Cost of Capital APV Example Adjusted-Present-Value (APV) NPV for an unlevered firm

NPVF = net present value of financing APV = NPV + NPVF 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 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

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) Weighted-Average-Cost-ofCapital Discount rate: rWACC

PVUCF: PV of Unlevered Cash Flows Value = PVUCF - Initial investment for entire project Summary: APV, FTE, and WACC APV WACC

FTE Initial Investment Cash Flows Discount Rates All UCF r0 All UCF

rWACC Equity Portion LCF 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. 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 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 APV recap Value = 475 + 29.918 = 504.918

Debt = - 126.2295 Equity = 378.6885 Debt/Equity = 1/3 Debt/(Debt + Equity) = 1/4 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

FTE (continued) Cost Borrowing Cost to equity 475 - 126.2295 348.7705 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 FTE valuation

NPV = - 348.7705 + 84.06885/.22 = 29.918 Same as in APV method. Now, same thing with WACC. Find rWACC rWACC = (S/(S+B))rS+(B/(B+S))(1-TC)rB

=(3/4)(.222) + (1/4)(.66)(.1) = .183 WACC method continued NPV = - 475 + 92.4/.183 = 29.918 All methods give the same thing. 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 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.

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

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 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 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 Review item Complete the following statement and explain briefly: nothing matters in

finance except __________ and _________. 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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