Corporate Finance Financing and Valuation

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Corporate FinanceFinancing and Valuation

• Professor André Farber
• Solvay Business School

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References

• Brealey Myers (2000) Chap 19 Financing and
  Valuation
• Worth reading Appendix to Chapter 19 available
  on BM website www.mhhe.com/business/finance/bm
• Ross Westerfield Jaffee (1999) Chap 17 Valuation
  and Capital Budget for the Levered Firm
• Luehrman Using APV A Better Tool for Valuing
  Operations Harvard Business Review May-June 1997

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Interactions between capital budgeting and
financing

• The NPV for a project could be affected by its
  financing.
• (1) Transactions costs
• (2) Interest tax shield
• There are two ways to proceed
• The APV Approach
• Compute a base case NPV, and add to it the NPV of
  the financing decision ensuing from project
  acceptance
• APV Base-case NPV NPV(FinancingDecision)
• The Adjusted Cost of Capital Approach
• Adjust the discount rate to account for the
  financing decision

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The Adjusted Present Value Rule

• The most straightforward. Permits the user to see
  the sources of value in the project, if it's
  accepted
• Procedure
• (1) Compute the base-case NPV using a discount
  rate that employs all equity financing (rA),
  applied to the project's cash flows
• (2) Then, adjust for the effects of financing
  which arise from
• Flotation costs
• Tax Shields on Debt Issued
• Effects of Financing Subsidies
• APV NPV NPVF

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APV - Example

• Data
• Cost of investment 10,000
• Incremental earnings 1,800 / year
• Duration 10 years
• Discount rate rA 12
• NPV -10,000 1,800 x a10 170
• (1) Stock issue
• Issue cost 5 from gross proceed
• Size of issue 10,526 ( 10,000 / (1-5))
• Issue cost 526
• APV 170 - 526 - 356

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APV calculation with borrowing

• Suppose now that 5,000 are borrowed to finance
  partly the project
• Cost of borrowing 8
• Constant annuity 1,252/year for 5 years
• Corporate tax rate 40
• Year Balance Interest Principal Tax Shield
• 1 5,000 400 852 160
• 2 4,148 332 920 133
• 3 3,227 258 994 103
• 4 2,223 179 1,074 72
• 5 1,160 93 1,160 37
• PV(Tax Shield) 422
• APV 170 422 592

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APV calculation with subsidized borrowing

• Suppose now that you have an opportunity to
  borrow at 5 when the market rate is 8.
• What is the NPV stemming from this lower
  borrowing cost?
• (1) Compute after taxes cash flows from borrowing
• (2) Discount at cost of debt after taxes
• (3) Subtract from amount borrowed
• The approach developed in this section is also
  applicable for the analysis of leasing contracts
  (See BM Chap 25)

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Subsidized loan

• To understand the procedure, lets start with a
  very simple setting
• 1 period, certainty
• Cash flows after taxes C0 -100 C1 105
• Corporate tax rate 40, rArD8
• Base case NPV0 -100 105/1.08 -2.78 lt0
• Debt financing at market rate (8)
• PV(Tax Shield) (0.40)(8) / 1.08 2.96
• APV - 2.78 2.96 0.18 gt0

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NPV of subsidized loan

• You can borrow 100 at 5 (below market borrowing
  rate -8). What is the NPV of this interest
  subsidy?
• Net cash flow with subsidy at time t1 -105
  0.40 5 -103
• How much could I borrow without subsidy for the
  same future net cash flow?
• Solve B 8 B - 0.40 8 B 103
• Solution
• NPVsubsidy 100 98.28 1.72

Net cash flow
After-tax interest rate
PV(Interest Saving)(8 5)/1.048 2.86
PV(?TaxShield)0.40(5 8)/1.048 -1.14

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APV calculation

• NPV base case NPV0 - 2.78
• PV(Tax Shield) no subsidy PV(TaxShield) 2.96
• NPV interest subsidy NPVsubsidy 1.72
• Adjusted NPV APV 1.90
• Check After tax cash flows
• t 0 t 1
• Project - 100 105
• Subsidized loan 100 - 103
• Net cash flow 0 2
• How much could borrow today against this future
  cash flow?
• X 8 X - (0.40)(8) X 2 ? X 2/1.048 1.90

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A formal proof

• Ct net cash flow for subsidized loan
• r market rate
• D amount borrowed with interest subsidy
• B0 amount borrowed without interest subsidy to
  produce identical future net cash flows
• Bt remaining balance at the end of year t
• For final year T CT BT-1 r(1-TC) BT-1
• (final reimbursement interest after taxes)
• 1 year before CT-1 (BT-2 - BT-1) r(1-TC)
  BT-2
• (partial reimbursement interest after taxes)
• At time 0
• NPVsubsidy D B0

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Back to initial example
Data Market rate 8 Amount borrowed
5,000 Borrowing rate 5 Maturity 5 years Tax
rate 40 Annuity 1,155
Net Cash Flows Calculation Year Balance
Interest Repayment TaxShield Net CF 1
5,000 250 905
100 1,055 2 4,095 205
950 82
1,073 3 3,145 157 998
63 1,092 4
2,147 107 1,048 43
1,112 5 1,100 55
1,100 22 1,133
B0 PV(NetCashFlows) _at_ 4.80 4,750 NPVsubsidy
5,000 - 4,750 250
APV calculation NPV base case NPV0
170 PV Tax Shield without subsidy PV(TaxShield)
422 NPV Subsidy NPVsubsidy 250 APV
842
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Weighted Average Cost of Capital

• After tax WACC for levered company

Market values
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WACC -Sangria Corporation
Balance Sheet (Book Value, millions) Assets 100
Debt 50 Equity 50 Total 100 Total 100
Balance Sheet (Market Value, millions) Assets
125 Debt 50 Equity 75 Total 125 Total 125
Cost of equity 14.6 Cost of debt (pretax)
8 Tax rate 35
Equity ratio E/V 75/125 60 Debt ratio
D/V 50/125 40
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Using WACC

• WACC is used to discount free cash flows
  (unlevered)
• Example Sangria Corp. considers investing 12.5m
  in a machine.
• Expected pre-tax cash flow 2.085m (a
  perpetuity)
• After-tax cash flow 2.085 (1 - 0.35) 1.355
• Beware of two traps
• (1) Risk of project might be different from
  average risk of company
• (2) Financing of project might be different from
  average financing of company

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WACC - Modigliani-Miller formula

• Assumptions
• 1. Perpetuity
• 2. Debt constant
• With L D / V

• Proof
• Market value of unlevered firm
• VU EBIT (1-TC)/rA
• Market value of levered firm V VU TC D
• Define LD/V
• Solve for V

Cost of capital all equity
Debt, a constant
Present value of future cash flows after taxes
including the tax shield
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MM formula example
Data Investment 100 Pre-tax CF 22.50 rA 9 rD
5 TC 40
Base case NPV -100 22.5(1-0.40)/.09 50
Financing Borrow 50 of PV of future cash flows
after taxes D 0.50 V
Using MM formula WACC 9(1-0.40 0.50) 7.2
NPV -100 22.5(1-0.40)/.072 87.50
Same as APV introduced previously? To see this,
first calculate D. As V VU TC D 150 0.40
D and D 0.50 V V 150 0.40 0.50 V ? V
187.5 ? D 93.50 ? APV NPV0 TC D 50 0.40
93.50 87.50
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Using the standard WACC formula

• Step 1 calculate rE using
• As D/V 0.50, D/E 1
• rE 9 (9 - 5)(1-0.40)(0.50/(1-0.50))
  11.4
• Step 2 use standard WACC formula
• WACC 11.4 x 0.50 5 x (1 0.40) x 0.50
  7.2

Same value as with MM formula
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Adjusting WACC for debt ratio or business risk

• Step 1 unlever the WACC
• Step 2 Estimate cost of debt at new debt ratio
  and calculate cost of equity
• Step 3 Recalculate WACC at new financing weights

• Or
• Step 1 Unlever beta of equity
• Step 2 Relever beta of equity and calculate cost
  of equity
• Step 3 Recalculate WACC at new financing weights

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Miles-Ezzel WACC formula with debt variable

• Assumptions
• Any set of cash flows
• Debt ratio L Dt/Vt constant
• where Vt PV of remaining after-tax cash flow

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Miles-Ezzel example
Data Investment 200 Pre-tax CF Year 1 160 Year
2 300 Year 3 100 rA 10 rD 5 TC 40 L
50
Base case NPV -200 281 81.11
Using Miles-Ezzel formula WACC 10 - 0.50 x
0.40 x 5 x 1.10/1.05 8.95 APV -200 286.15
86.15 Initial debt D0 0.50 V0
(0.50)(286.15)143.07 Debt rebalanced each
year Year Vt Dt 0 286.15 143.07 1
215.75 107.88 2 55.07 27.07
Using MM formula WACC 10(1-0.40 x 0.50)
8 APV -200 290.84 90.84 Debt D 0.50 V
(0.50)(290.84) 145.42 No rebalancing