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**CHAPTER 18: CAPITAL BUDGETING WITH LEVERAGE**

Topics 18.1 – 18.6 Valuation 18.7 Beta and Leverage Core Question: How to determine the NPV of a project if it is financed with debt?

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Background In chapter 8, there was a four step procedure for evaluating corporate investment decisions: Forecast cash flows assess project risk estimate opportunity cost of capital compute NPV This procedure treats each project like an independent firm that is all-equity financed If financing decisions did not matter, this is all that is required. But if they do matter, there are three basic approaches Adjusted present value (APV) Flow to equity (FTE) Weighted average cost of capital (WACC)

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**18.1 APV Approach APV = NPVU + NPVF NPVU (NPV of unlevered firm)**

project value under all-equity financing PV of unlevered cash flows (UCF) discount rate: r0 NPVF (net present value of financing side effects) PV of tax shields to debt costs of issuing new securities costs of financial distress subsidies to debt financing

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APV Example A project costs $60,000 and generates expected pre-tax operating cash flows of $10,000 per year in perpetuity. The corporate tax rate is 40% and the cost of capital under all-equity financing is 12%. Should the firm make this investment under all-equity financing? What is there is debt, and the debt-value ratio is 0.06?

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18.2 FTE Approach Estimate levered cash flows = cash flow to equityholders of levered firm (LCF) Calculate discount rate rS Compute PV of LCF---Use 1 & 2 4. PV of the project: PV of LCF subtract equity contribution (equity contribution = initial investment - amount borrowed) it is possible for the equity contribution to be negative—this means that the amount borrowed exceeds the initial cost of the investment in such cases, the excess can be thought of as a dividend paid out to equity holders

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FTE Example Consider the same example as for APV above, assuming that the rate of interest on debt is rB = 6%

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**Discount unlevered cash flows (UCF) at rWACC where**

Compute PV of UCF, subtract initial investment The unlevered cash flows (UCF) are the same as used in the APV approach for calculating the present value of future cash flows under all-equity financing This method was discussed previously in Chapter 13

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WACC Example Continue with the same example from APV and FTE.

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**Comparison of Approaches**

In the simple example above in a perpetual no-growth setting, all three approaches (APV, FTE, WACC) gave the same answer In theory, this should always be the case, but in practice it is usually far simpler to use one method than either of the others

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WACC Consider the following example. A project costs $80,000 today and generates expected pre-tax operating cash flows of $50,000 per year for four years. The corporate tax rate is 40%, the (levered) cost of equity (rS ) is 20%, the cost of debt is 8%, and the equity-value ratio is 60% WACC approach: rWACC = .60(.20) + .40(.08)(1 − .4) = .1392 NPV = −$80,000 + $50,000(1 − .4) × A.13924 = $7,554.92

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What about APV Since the debt-value ratio is 40% and the PV of the future cash flows is $87,554.92, the amount to be borrowed is .4($87,554.92) = $35,021.97 The discount rate under all-equity financing can be calculated as follows. Since the effects of debt are to be incorporated later, use the weighted average cost of capital but assume that there are no corporate taxes, i.e. the value of the project under all-equity financing would be NPVU = −$80,000 + $50,000(1 − .4) × A = $5,304.00 If the debt of $35, is assumed to be perpetual, then NPVF = .4($35,021.97) = $14,008.79 APV = $5, $14, = $19,312.79

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What about APV cont’d What if the debt is assumed to be repaid at the end of the project (i.e. after four years)? The amount of interest paid per year is .08($35,021.97) = $2,801.76 then NPVF = $2,801.76(.4) × A.084 = $3,711.91 APV = $5, $3, = $9,015.91

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**What About APV? (Cont’d)**

The basic problem here is that the assumptions underlying WACC and APV (so far) are inconsistent In particular, WACC assumes that the debt-value ratio is constant over time, whereas (so far) in APV the assumption has been that debt is constant over time This was consistent in the perpetual case since value is constant over time in that context In general, in order to maintain a constant debt-value ratio, the amount of debt must change throughout the project life Define a project’s debt capacity d as the amount of debt needed to maintain the firm’s target debt-value ratio over the life of the project (note that d varies over time) Then calculate NPVF assuming that the firm borrows an amount that is equal to its debt capacity d

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What About FTE? We need to calculate levered cash flows, assuming the same borrowing pattern as for APV, and then discount at rS = 20%: This gives

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**General rule: Comparison Use APV when debt level is constant**

Use WACC and FTE when firm’s debt ratio is constant

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**More on APV and Discount rate**

Note that the discount rate of r0 specified for APV above applies to the unlevered cash flows, not the debt tax shield The appropriate discount rate for the debt tax shield under APV depends on the debt policy of the firm: if debt level is constant (e.g. as in perpetuity case), use rB if debt level varies with project value (e.g. non-perpetual case), use r0

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**18.6 More APV examples: Issuing Costs**

An investment project costs $3 million and generates pretax operating cash flows of $825,000 per year for 10 years. The corporate tax rate is 40% and r0 is 10%. (1) What is the all-equity NPV? ($41,561)

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Example cont’d Financing alternative #1: the firm has no cash and will finance the project with $3 million of new equity, issue costs are 7% of the gross proceeds and are tax deductible. What is APV Answer: ($-93,923)

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Example cont’d Financing alternative #2: the firm has $1.5 million in cash on hand and can borrow the remaining $1.5 million for 6 years at 8% interest (annual coupon payment). The bond will be issued at par. (Assume no issuing costs of debt.) (Answer: 263,460)

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**Example cont’d (A more complicated version of last slide)**

Financing alternative #2: the firm has $1.5 million in cash on hand and can obtain the remaining $1.5 million through a 6 years, 8% coupon (annual coupon payment) bond issued at par. The issuing costs for the bond is 1% of the amount raised. (Assume that issuing costs for debt are tax-deductible but amortized over the life of the bond.) APV = NPV + NPV(Floatation costs) + NPV(Loan) Amount raised: Discount rate: NPV(Floatation costs) floatation costs = Amortized over 6 years, annual tax deduction is Annual tax shield = NPV(Floatation costs) or Net floatation costs

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Cont’d 2. NPV (Loan) = Amount borrowed – PV (after-tax interest payments) – PV (principal repayment) = PV(interest tax shield) or PV(interest tax shields) 3. APV = 41, , ,141 =255,220

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**Financing alternative #3: Subsidized financing **

Example cont’d Financing alternative #3: Subsidized financing The firm has $1.5 million in cash on hand and can borrow the remaining $1.5 million for 6 years from the government at a special interest rate of 5% with no floatation costs (gov’t takes care of it.) Note that if the firm does not use gov’t loan, it has to borrow from the open market at 8%.

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18.7 Beta and Leverage To use APV, you have to know r0, the cost of unlevered equity. If the firm already has debt, you cannot simply use historical stock return data to compute beta, even if the project’s risk is identical to that of the existing firm. The following formula can be derived: Risky Corporate Debt: where is the beta computed using historical returns and is the corresponding beta for an identical (but unlevered) firm Risk-free Corporate Debt: Usually assume

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Example A firm has a debt-equity ratio of 0.5. Based on historical stock return data, the firm’s equity is The firm faces a corporate tax rate of 40%. The risk free rate of interest is 5% and the expected market risk premium is 6%. Determine r0 assuming the the firm’s debt has (i) zero systematic risk, and (ii) βB of 0.10.

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**Assigned Problems: # 18.1, 4, 7, 8, 9(change the company name to NEC), 12, 14, 16, 17**

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