Corporate Finance Financing and Valuation Professor André Farber Solvay Business School 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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) 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 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 + 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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) @ 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 17/04/2017 Vietnam 2004

Weighted Average Cost of Capital After tax WACC for levered company: Market values 17/04/2017 Vietnam 2004

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% 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

MM formula: example Data Base case NPV: -100 + 22.5(1-0.40)/.09 = 50 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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

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 17/04/2017 Vietnam 2004

Miles-Ezzel: example Data Base case NPV = -200 + 281 = +81.11 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 17/04/2017 Vietnam 2004