solvay business school – université libre de bruxelles 12/07/2015vietnam 20041 corporate finance...

04/19/23 Vietnam 2004 1Solvay Business School – Université Libre de Bruxelles

Corporate FinanceFinancing and Valuation

Professor André Farber

Solvay Business School


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


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


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


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


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


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)


Subsidized loan

• To understand the procedure, let’s start with a very simple setting:

• 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


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: -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

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


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


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

)1(11C

TT Tr

CB

)]²1(1[)1(11

2C

T

C

TT Tr

C

Tr

CB

T

tt

C

t

Tr

CB

10 )]1(1[


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 1,133

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 NPVsubsidy = + 250APV = + 842


Weighted Average Cost of Capital

• After tax WACC for levered company:

V

DTr

V

ErWACC CDE )1(

Market values


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%

1084.125

50)35.1(08.

125

75146. WACC


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

01084.

355.15.12 NPV


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:

VV

DT

r

TEBITV C

A

C

)1(

WACC

TEBIT

LTr

TEBITV C

CA

C )1(

)1(

)1(

)1( LTrWACC CA

Cost of capital all equity

Debt, a constant

Present value of future cash flows after taxes – including the tax shield


MM formula: example

DataInvestment 100Pre-tax CF 22.50rA 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 taxesD = 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 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


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%

E

DTrrrr CDAAE )1)((

V

DTr

V

ErWACC CDE )1(

Same value as with MM formula


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

V

Dr

V

Err DE

E

Drrrr DE )(

V

D

V

Edebtequityasset

E

Ddebtassetassetequity )(


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

D

ADCA r

rrLTrWACC

1

1


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) = 145.42

No rebalancing

solvay business school – université libre de bruxelles 12/07/2015vietnam 20041 corporate finance...

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