Weighted Average Cost of Capital
And equivalent approaches
Exam quickie
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
Reading note
Skip sections 17.5 through 17.8. Pages 444-451.
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 Bond financing of 126.2295 rB = .1
NPVF = TC x B = 42.918
APV = -13 + 42.918 = 29.918
APV recap
Value = 475 + 29.918 = 504.198 Debt = - 126.2295 Equity = 378.6985 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) = .22...
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)(.22…) + (1/4)(.66)(.1) = .1831666...
WACC method continued
NPV = -475 + 92.4/.183166… = 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
Exam quickie
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.