1. Corporate Finance Financing and Valuation
Professor André Farber
Solvay Business School
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Vietnam 2004

2. References Brealey Myers (2000) Chap 19 Financing and Valuation
Worth reading: Appendix to Chapter 19 available on BM website:
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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Vietnam 2004

3. 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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Vietnam 2004

4. 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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Vietnam 2004

5. APV - Example Data Cost of investment 10,000
Incremental earnings 1,800 / year
Duration years
Discount rate rA 12%
NPV = -10, ,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 = = - 356
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Vietnam 2004

6. 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,
2 4,
3 3,
4 2, ,
5 1, ,
PV(Tax Shield) = 422
APV = = 592
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Vietnam 2004

7. 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 B&M Chap 25)
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Vietnam 2004

8. Subsidized loan
To understand the procedure, let’s start with a very simple setting:
1 period, certainty
Cash flows after taxes: C0 = C1 = + 105
Corporate tax rate: 40%, rA=rD=8%
Base case: NPV0= /1.08 = <0
Debt financing at market rate (8%)
PV(Tax Shield) = (0.40)(8) / 1.08 = 2.96
APV = = 0.18 >0
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Vietnam 2004

9. 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 t=1: × 5 = -103
How much could I borrow without subsidy for the same future net cash flow?
Solve: B + 8% B × 8% × B = 103
Solution:
NPVsubsidy = +100 – = 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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10. 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
Subsidized loan
Net cash flow
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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Vietnam 2004

11. 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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12. 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
, ,055
, ,073
, ,092
, , ,112
, , ,133
B0 = 4.80% = 4,750
NPVsubsidy = 5, ,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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13. Weighted Average Cost of Capital
After tax WACC for levered company:
Market values
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14. WACC -Sangria Corporation
Balance Sheet (Book Value, millions)
Assets Debt 50
Equity 50
Total Total 100
Balance Sheet (Market Value, millions)
Assets Debt 50
Equity 75
Total 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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15. 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 = ( ) = 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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Vietnam 2004

16. 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: L≡D/V
Solve for V:
Debt, a constant
Cost of capital all equity
Present value of future cash flows after taxes – including the tax shield
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Vietnam 2004

17. MM formula: example Data Base case NPV: -100 + 22.5(1-0.40)/.09 = 50
Investment 100
Pre-tax CF
rA 9%
rD 5%
TC 40%
Base case NPV: (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%( × 0.50) = 7.2%
NPV = (1-0.40)/.072 = 87.50
Same as APV introduced previously? To see this, first calculate D.
As: V =VU + TC D = D
and: D = 0.50 V
V = ×0.50× V → V = → D = 93.50
→ APV = NPV0 + TC D = × = 87.50
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Vietnam 2004

18. 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 % x (1– 0.40) x = 7.2%
Same value as with MM formula
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Vietnam 2004

19. 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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Vietnam 2004

20. 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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Vietnam 2004

21. Miles-Ezzel: example Data Base case NPV = -200 + 281 = +81.11
Investment 200
Pre-tax CF
Year
Year
Year
rA 10%
rD 5%
TC 40%
L 50%
Base case NPV = =
Using Miles-Ezzel formula
WACC = 10% x 0.40 x 5% x 1.10/1.05 = 8.95%
APV = = 86.15
Initial debt: D0 = 0.50 V0 = (0.50)(286.15)=143.07
Debt rebalanced each year:
Year Vt Dt
Using MM formula:
WACC = 10%( x 0.50) = 8%
APV = = 90.84
Debt: D = 0.50 V = (0.50)(290.84) =
No rebalancing
17/04/2017
Vietnam 2004