EMBA in Management & Finance. Corporate Finance. Eric Jondeau

Transcription

1 EMBA in Management & Finance Corporate Finance

2 EMBA in Management & Finance Lecture 5: Capital Budgeting For the Levered Firm

3 Prospectus Recall that there are three questions in corporate finance. The first regards what long-term investments the firm should make (the capital budgeting question). The second regards the use of debt (the capital structure question). This chapter considers the nexus of these questions. EMBA 3/29

4 Outline 1. Adjusted Present Value Approach 2. Flows to Equity Approach 3. Weighted Average Cost of Capital Method 4. Comparison of the APV, FTE, and WACC Approaches 5. Capital Budgeting when the Discount Rate Must Be Estimated 6. APV Example 7. Beta and Leverage 8. Summary and Conclusions EMBA 4/29

5 1. Adjusted Present Value Approach The value of a project to the firm can be thought of as the value of the project to an unlevered firm (NPV) plus the present value of the financing side effects (NPVF): APV = NPV + NPVF There are four side effects of financing: The Tax Subsidy to Debt The Costs of Issuing New Securities The Costs of Financial Distress Subsidies to Debt Financing EMBA 5/29

6 APV Example Consider a project of the Pearson Company. The timing and size of the incremental after-tax cash flows for an all-equity firm are: $1,000 $125 $250 $375 $ The unlevered cost of equity is r 0 = 10%: NPV $125 $250 $375 $500 = $1, (1.10) (1.10) (1.10) (1.10) 10% NPV 10% = $56.50 The project would be rejected by an all-equity firm: NPV < 0. EMBA 6/29

7 APV Example (continued) Now, imagine that the firm finances the project with $600 of debt at r B = 8%. Pearson s tax rate is 40%, so they have an interest tax shield worth τ C r B B = $600 = $19.20 each year. The net present value of the project under leverage is: APV = NPV + NPV APV APV = $ debt tax shield So, Pearson should accept the project with debt. 4 t= 1 $19.20 t (1.08) = $ = $7.09 EMBA 7/29

8 APV Example (continued) Note that there are two ways to calculate the NPV of the loan. Previously, we calculated the PV of the interest tax shields. Now, let s calculate the actual NPV of the loan: NPV NPV loan loan 4 $ (1 0.4) $600 = $600 t (1.08) (1.08) = $63.59 t= 1 4 APV = NPV + NPVF APV = $ = $7.09 which is the same answer as before. EMBA 8/29

9 2. Flow to Equity Approach Discount the cash flow from the project to the equity holders of the levered firm at the cost of levered equity capital, r S. There are three steps in the FTE Approach: Step One: Calculate the levered cash flows Step Two: Calculate r S. Step Three: Valuation of the levered cash flows at r S. EMBA 9/29

10 Step 1: Levered Cash Flows for Pearson Since the firm is using $600 of debt, the equity holders only have to come up with $400 of the initial $1,000. Thus, CF 0 = $400. Each period, the equity holders must pay interest expense. The after-tax cost of the interest is (1 τ C ) r B B = (1 0.40) 0.08 $600 = $28.80 CF 1 = $ CF 3 = $ CF 2 = $ CF 4 = $ $400 $96.20 $ $ $ EMBA 10/29

11 Step 2: Calculate r S for Pearson B rs = r0 + (1 τ C )( r0 rb ) S To calculate the debt to equity ratio, B/S, start with B/V PV PV 4 $125 $250 $375 $ t (1.10) (1.10) (1.10) (1.10) t= 1 (1.08) = = $ $63.59 = $1, B = $600 when V = $1, so S = $ $600 r S = (1 0.40)( ) = 11.77% $ EMBA 11/29

12 Step 3: Valuation for Pearson Discount the cash flows to equity holders at r S = 11.77% $400 $96.20 $ $ $ PV $96.20 $ $ $ = $ (1.1177) (1.1177) (1.1177) (1.1177) PV = $28.56 EMBA 12/29

13 3. WACC Approach S B rwacc = rs + rb (1 τ C ) S + B S + B To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital. Suppose Pearson s target debt to equity ratio is 1.50 B = 1.50 B = 1.5S S B 1.5S 1.5 S = = = 0.60 = = 0.40 S + B S + 1.5S 2.5 S + B r r WACC WACC = (0.40) (11.77%) + (0.60) (8%) (1 0.40) = 7.58% EMBA 13/29

14 Valuation for Pearson Using WACC To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital NPV $125 $250 $375 $500 = $1, (1.0758) (1.0758) (1.0758) (1.0758) NPV 7.58% = $6.68 EMBA 14/29

15 4. Comparison of the APV, FTE, and WACC Approaches All three approaches attempt the same task: Valuation in the presence of debt financing. Guidelines: Use WACC or FTE if the firm s target debt-to-value ratio applies to the project over the life of the project. Use the APV if the project s level of debt is known over the life of the project. In the real world, the WACC is the most widely used by far. EMBA 15/29

16 Comparison of the APV, FTE, and WACC Approaches APV WACC FTE Initial Investment All All Equity Portion Cash Flows UCF UCF LCF Discount Rates r 0 r WACC r S PV of financing effects Yes No No Which approach is best? Use APV when the level of debt is constant Use WACC and FTE when the debt ratio is constant WACC is by far the most common FTE is a reasonable choice for a highly levered firm EMBA 16/29

17 5. Capital Budgeting When the Discount Rate Must Be Estimated A scale-enhancing project is one where the project is similar to those of the existing firm. In the real world, executives would make the assumption that the business risk of the non-scale-enhancing project would be about equal to the business risk of firms already in the business. No exact formula exists for this. Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant. EMBA 17/29

18 6. APV Example Worldwide Trousers, Inc. is considering replacing a $5 million piece of equipment. The project will generate pretax savings of $1,500,000 per year, and not change the risk level of the firm. The initial expense will be depreciated straight-line to zero salvage value over 5 years; the pretax salvage value in year 5 will be $500,000. The firm can obtain a 5-year $3,000,000 loan at 12.5% to partially finance the project. If the project were financed with all equity, the cost of capital would be 18%. The corporate tax rate is 34%, and the risk-free rate is 4%. The project will require a $100,000 investment in net working capital. Calculate the APV. EMBA 18/29

19 APV Example: Cost Let s work our way through the four terms in this equation: APV = Cost + PV + PV + PV unlevered depreciation interest project tax shield tax shield The cost of the project is not $5,000,000. We must include the round trip in and out of net working capital and the after-tax salvage value. NWC is riskless, so we discount it at r f. Salvage value should have the same risk as the rest of the firm s assets, so we use r , , 000 (1 0.34) Cost = $5.1m (1 + r ) (1 + r ) = $4,873, f 0 EMBA 19/29

20 APV Example: PV unlevered project Turning our attention to the second term, APV = $4,873, PV + PV + PV unlevered depreciation interest project tax shield tax shield PVunlevered project is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%. PV UCF $1.5 m (1 0.34) t (1 ) (1.18) 5 5 t unlevered = = t project t= 1 + r0 t= 1 = $3, 095,899 EMBA 20/29

21 APV Example: PV depreciation tax shield Turning our attention to the third term, APV = $4,873, $3,095,899 + PV + PV depreciation tax shield interest tax shield PVdepreciation tax shield is the is the present value of the tax savings due to depreciation (D) discounted at the risk free rate: r f = 4% PV = 5 depreciation tax shield t= 1 t= 1 D τ C t f (1 + r ) 5 $1m 0.34 = = t $1,513,619 (1.04) EMBA 21/29

22 APV Example: PV interest tax shield Turning our attention to the last term, APV = $4,873, $3,095,899 + $1,513,619 + PV interest tax shield PVinterest tax shield is the present value of the tax savings due to interest expense discounted at the firm s debt rate: r B = 12.5% PV 5 5 C B interest = = t tax shield t= 1 + rb t= ,500 = = 453, t (1.125) t= 1 τ r $3m $3m t (1 ) (1.125) EMBA 22/29

23 APV Example: Adding It All Up Let s add the four terms in this equation: APV = Cost + PV + PV + PV unlevered depreciation interest project tax shield tax shield APV = $4,873, $3, 095,899 + $1,513, $453, = $189,930 Since the project has a positive APV, it looks like a go. EMBA 23/29

24 7. Beta and Leverage Recall that an asset beta would be of the form: β = Cov( UCF, R ) Asset 2 σ Market Market EMBA 24/29

25 Beta and Leverage: No Corporate Taxes In a world without corporate taxes, and with riskless corporate debt, (β Debt = 0) it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: β Asset Equity = Asset β Equity In a world without corporate taxes, and with risky corporate debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: Debt Equity β = β + β Asset Asset Asset Debt Equity EMBA 25/29

26 Beta and Leverage: With Corporate Taxes In a world with corporate taxes, and riskless debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: Debt β Equity = 1 + (1 τ C ) β Equity Unlevered firm Debt Since 1 + (1 τ C ) must be more than 1 for a Equity levered firm, it follows that β Equity > β Unlevered firm EMBA 26/29

27 Beta and Leverage: With Corporate Taxes If the beta of the debt is non-zero, then: β = β + (1 τ ) ( β β ) Equity Unlevered firm C Unlevered firm Debt B S L EMBA 27/29

28 8. Summary and Conclusions 1. The APV formula can be written as: APV UCFt = + Additional Initial t (1 + r ) effect of debt investment t= The FTE formula can be written as: FTE t= 1 ( Initial Amount ) LCFt = t (1 + r ) investment borrowed S 3. The WACC formula can be written as UCFt NPV Initial WACC = t (1 + r ) investment t= 1 WACC EMBA 28/29

29 Summary and Conclusions 4. Use the WACC or FTE if the firm's target debt to value ratio applies to the project over its life. WACC is the most commonly used by far. FTE has appeal for a firm deeply in debt. 5 The APV method is used if the level of debt is known over the project s life. The APV method is frequently used for special situations like interest subsidies, LBOs, and leases. 6 The beta of the equity of the firm is positively related to the leverage of the firm. EMBA 29/29