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12/03/02 16:23 1
Corporate Financial PolicyFinancing and Valuation
Professor André FarberSolvay Business School
2001-2002
12/03/02 16:23 2
References
Brealey Myers (2000) Chap 19 Financing and ValuationWorth reading: Appendix to Chapter 19 available on BM website: www.mhhe.com/business/finance/bmRoss Westerfield Jaffee (1999) Chap 17 Valuation and Capital Budget for the Levered FirmLuehrman Using APV: A Better Tool for Valuing Operations Harvard Business Review May-June 1997
12/03/02 16:23 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 financingdecision 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
12/03/02 16:23 4
The Adjusted Present Value Rule
• The most straightforward. Permits the user to see the sources of valuein 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
12/03/02 16:23 5
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• Issue cost = 526• APV = + 170 - 526 = - 356
12/03/02 16:23 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 Shield1 5,000 400 852 1602 4,148 332 920 1333 3,227 258 994 1034 2,223 179 1,074 725 1,160 93 1,160 37
• PV(Tax Shield) = 422• APV = 170 + 422 = 592
12/03/02 16:23 7
APV calculation with subsidized borrowing
• Suppose now that you have an opportunity to borrow at 5% when themarket 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 alsoapplicable for the analysis of leasing contracts.See B&M Chap 25
12/03/02 16:23 8
Subsidized loan
• 1 period, certainty– Cash flows after taxes: C0 = -100 C1 = + 105– Corporate tax rate: 40%, rA=rD=8%– Base case: NPV0= -100 + 105/1.08 = -2.78 <0
• Debt financing at market rate (8%)• PV(Tax Shield) = (0.40)(8) / 1.08 = 2.96• APV = - 2.78 + 2.96 = 0.18 >0
12/03/02 16:23 9
NPV of subsidized loan
• You can borrow 100 at 5% (below market borrowing rate - 8%). Whatis the NPV of this interest subsidy?Net cash flow with subsidy at time t =1 : -105 + 0.40 ×5 = -103
• How much could I borrow without subsidy for the same future net cashflow?Solve: B + 8% B - 0.40 × 8% ×B = 103
Solution:
NPVsubsidy = +100 - 98.28 = 1.72
28.98048.1
103)40.01%(81
103==
−+=B
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
12/03/02 16:23 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 - 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
12/03/02 16:23 11
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 flow• Bt : remaining balance at the end of year t
• For final year T:
• 1 year before:
• At time 0:
11 )1( −− −+= TCTT BTrBC ))1(1(1C
TT Tr
CB
−+=⇒ −
2121 )1()( −−−− −+−= TCTTT BTrBBC2
12
))1(1())1(1( C
T
C
TT
Tr
CTr
CB
−++
−+=⇒ −
−
Final reimbursement Interest after taxes
Interest after taxesFinal reimbursement
∑−+
==
T
t tC
t
Tr
CB
10
))1(1(
NPVsubsidy = D - B0
12/03/02 16:23 12
Back to initial example
DataMarket rate 8%Amount borrowed 5,000Borrowing rate 5%Maturity 5 yearsTax rate 40%Annuity 1,155
Net Cash Flows CalculationYear 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 1,1133
B0 = PV(NetCashFlows) @ 4.80% = 4,750NPVsubsidy = 5,000 - 4,750 = + 250
APV calculation:NPV base case NPV0 = + 170PV Tax Shield without subsidy PV(TaxShield) = + 422NPV Subsidy NPBsubsidy = + 250
APV = + 842
12/03/02 16:23 13
Weighted Average Cost of Capital
• After tax WACC for levered company
VDrT
VErWACC DCE ××−+×= )1(
Market values
12/03/02 16:23 14
WACC - Sangria Corporation
Balance Sheet (Book Value, millions)Assets 100 Debt 50
Equity 50Total 100 Total 100
Balance Sheet (Market Value, millions)Assets 125 Debt 50
Equity 75Total 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%
1084.1255008.)35.1(
12575146. =××−+×=WACC
12/03/02 16:23 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 = 2.085 (1 - 0.35) = 1.355
01084.355.15.12 =+−=NPV
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 ofcompany
12/03/02 16:23 16
WACC - Modigliani-Miller formula
• Assumptions:1. Perpetuity2. Debt constant
)1(VDTrWACC CA −=
Proof:
uA
cu VINPV
rTEBIT
V +−=⇒−
= 0)1(
WACCTEBIT
VDTr
TEBITLT
VV
VVDTVDTV
rDrT
VV
C
cA
c
c
u
cucuD
Dcu
)1(
)1(
)1(1
−=
−
−=
−=⇒
××+=+=+=
Cost of capitalall equity
Present value of future cashflows after taxes - takingthe tax shield into account
12/03/02 16:23 17
MM formula: example
DataInvestment 100Pre-tax CF 22.50rA 9%rD 5%TC 40%
Base case NPV 5009.
)40.1(5.221000 =−
+−=NPV
Financing:Borrow 50% of PV of future cash flows after taxesD = 0.50 V
Using MM formula: WACC = 9%(1-0.40 × 0.50) = 7.2% 50.87072.
)40.01(5.22100 =−
+−=APV
Same as APV introduced previously? To see this, first calculate D. As: V = VU + TC D = 150 + 0.40 Dand: D = 0.50 VV = 150 + 0.40 × 0.50×V ⇒ V = 187.5 ⇒ D = 93.50
⇒ APV =NPV0 + TC D = 50 + 0.40 × 93.50 = 87.50
12/03/02 16:23 18
Back to the standard WACC formula
Step 1: calculate rE using: EDTrrrr cDAAE )1)(( −−+=
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 formulaVDrT
VErWACC DCE ××−+×= )1(
WACC = 11.4% x 0.50 + 5% x (1 – 0.40) x 0.50 = 7.2%
12/03/02 16:23 19
Adjusting WACC for debt ratio or business risk
• Step 1: unlever the WACC
• Step 2: Estimate cost of debt at newdebt ratio and calculate cost ofequity
• Step 3: Recalculate WACC at newfinancing weights
• Or
• Step 1: Unlever beta of equity
• Step 2: Relever beta of equity andcalculate cost of equity
• Step 3: Recalculate WACC at newfinancing weights
VDr
VErr DE +=
EDrrrr DE )( −+=
VD
VE
debtequityasset βββ +=
ED
assetequityassetequity )( ββββ −+=
12/03/02 16:23 20
Miles-Ezzel: another WACC formula
• Assumptions:Any set of cash flowsDebt ratio L = Dt/Vt constantwhere Vt = PV of remaining after-tax cash flow
D
ADCA r
rrLTrWACC
++
−=11
12/03/02 16:23 21
Miles-Ezzel: example
DataInvestment 200Pre-tax CFYear 1 160Year 2 300Year 3 100rA 10%rD 5%TC 40%L 50%
Base case NPV = -200 + 281 = +81.11
Using Miles-Ezzel formulaWACC = 10% - 0,50 x 0,40 x 5% x 1,10/1,05 = 8,95%APV = -200 + 286.15 = 86.15Initial debt: D0 = 0.50 V0 = (0.50)(286.15)=143.07Debt 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 = 90.84Debt: D = 0.50 V = (0.50)(290.84) = 145.42No rebalancing