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: r 0  PV UCF : PV of unlevered cash flows  NPV = PV UCF - 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 - 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 )

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

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.

Example p. 437: Project  Cash inflows500  Cash costs360  Operating income140  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/ = = -13  Borrowing (from B/S = 1/3)  r B =.1  NPVF = T C x B =  APV = =

APV recap  Value = =  Debt =  Equity =  Debt/Equity = 1/3  Debt/(Debt + Equity) = 1/4

Flow to Equity  Cash inflows500  Cash costs  Interest  Income after interest  Corporate tax  Levered cash flow

FTE (continued)  Cost 475  Borrowing  Cost to equity

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

FTE valuation  NPV =  /.22…  =  Same as in APV method.  Now, same thing with WACC.

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

WACC method continued  NPV =  /.183  =  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/ = 3

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

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

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 = r S r B (.66)  r S =r 0 +(B/S)(1-T C )(r 0 -r B )  r WACC =

Value, using r WACC  NPV = /  =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  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

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 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.