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-of-Capital

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 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 constantUse 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 475 Borrowing - 126.2295 Cost to equity 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 (can’t 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 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

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.