McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Corporate Finance Ross  Westerfield  Jaffe Seventh Edition 17 Chapter Seventeen Capital Budgeting for the Levered Firm

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Prospectus Recall two of the key questions in corporate finance. –What long-term investments should the firm make? The capital budgeting question –How much debt and equity should the firm have? The capital structure question This chapter considers the nexus of these questions.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Chapter Outline 17.1 Adjusted Present Value Approach 17.2 Flows to Equity Approach 17.3 Weighted Average Cost of Capital Method 17.4 A Comparison of the APV, FTE, and WACC Approaches 17.5 Capital Budgeting: When the Discount Rate Must Be Estimated 17.6 APV Example 17.7 Beta and Leverage 17.8 Summary and Conclusions

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Adjusted Present Value Approach APV = NPV + NPVF 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): 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

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example –$1,000$125 $250 $375 $500 The unlevered cost of equity is r 0 = 10%: The project would be rejected by an all-equity firm: NPV < 0. Consider a project of the Pearson Company. The timing and size of the incremental after-tax cash flows for an all-equity firm are:

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example The project would be rejected by an all-equity firm: NPV < 0. CF2 CF1 F2 F1 CF0 1 $125 1 –$56.50 –$1,000 $250 I NPV 10 CF4 CF3 F4 F3 1 $375 1 $500

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved 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 T C Br B =.40×$600×.08 = $19.20 each year.  The net present value of the project under leverage is: APV = NPV + NPV debt tax shield  So, Pearson should accept the project with debt.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved 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:  Which is the same answer as before. APV = NPV + NPVF

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Two Ways to Find the NPV of the loan: NPV of the loan: CF2 CF1 F2 F1 CF0 3 –$28.80 = 1 $63.59 $600 –$ I NPV 8 PV of the interest tax shields. CF1 F1 CF0 4 $63.59 $0 I NPV 8 $19.20 =.40×$600×.08 $600×.08×(1–.40)

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Flows 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: Value the levered cash flows at r S.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Step One: 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 B×r B ×(1 – T C ) = $600×.08×(1 –.40) = $ –$400 $ CF 2 = $250 – $ CF 3 = $375 – –$ CF 4 = $500 – – 600 CF 1 = $125 – $96.20

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Step Two: Calculate r S for Pearson B = $600 when V = $1, so S = $ P V = $ $63.59 = $1, B S B V To calculate the debt to equity ratio,, start with

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Step Three: Valuation for Pearson Discount the cash flows to equity holders at r S = 11.77% –$400$96.20$221.20$346.20–$128.80

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Step Three: Complete Valuation CF2 CF1 CF0 $96.20 $28.56 –$400 $ I NPV 11.77% CF4 CF3 $ –$ Discount the cash flows to equity holders at r S = 11.77% –$400$96.20$221.20$346.20–$128.80

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved WACC Method for Pearson 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

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved 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 7.58% = $6.68

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Valuation for Pearson using WACC CF2 CF1 CF0 $125 $6.68 –$1,000 $250 I NPV 7.58% CF4 CF3 $375 $500 Discount the unlevered cash flows at the weighted average cost of capital –$1,000$125$250$375$500

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved A 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.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Summary: APV, FTE, and WACC APVWACCFTE Initial Investment AllAllEquity Portion Cash FlowsUCFUCFLCF Discount Rates r 0 r WACC r S PV of financing effectsYesNoNo 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

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved 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.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Beta and Leverage Recall that an asset beta would be of the form:

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Beta and Leverage: No Corp.Taxes In a world without corporate taxes, and with riskless corporate debt, (  Debt = 0 ) it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:  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:

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Beta and Leverage: with Corp. 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:  Since must be more than 1 for a levered firm, it follows that  Equity >  Unlevered firm.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Beta and Leverage: with Corp. Taxes If the beta of the debt is non-zero, then:

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Summary and Conclusions 1.The APV formula can be written as: 2.The FTE formula can be written as: 3.The WACC formula can be written as

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Summary and Conclusions 4Use 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. 5The 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. 6The beta of the equity of the firm is positively related to the leverage of the firm.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example: Worldwide Trousers, Inc. is considering replacing a $5 million piece of equipment. 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 project will generate pretax savings of $1,500,000 per year, and not change the risk level of the firm. 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.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example: Cost 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. Let’s work our way through the four terms in this equation: 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 0. + PV depreciation tax shield + PV interest tax shield PV unlevered project APV = –Cost +

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example: PV unlevered project is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%. Turning our attention to the second term, + PV depreciation tax shield + PV interest tax shield PV unlevered project APV = –$4,873, PV unlevered project

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example: PV depreciation tax shield is the is the present value of the tax savings due to depreciation discounted at the risk free rate: r f = 4% Turning our attention to the third term, PV depreciation tax shield + PV depreciation tax shield + PV interest tax shield $3,095,899 APV = –$4,873, PV depreciation tax shield

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example: PV interest tax shield is the present value of the tax savings due to interest expense discounted at the firm’s debt rate: r D = 12.5% Turning our attention to the last term, PV interest tax shield + $1,513,619 + PV interest tax shield $3,095,899 APV = –$4,873,

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved APV Example: Adding it all up Since the project has a positive APV, it looks like a go. Let’s add the four terms in this equation: APV = –$4,873, $3,095,899 + $1,513,619 + $453, APV = $189,930 + PV depreciation tax shield + PV interest tax shield PV unlevered project APV = –Cost +

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Example: Hamilos Worldwide Hamilos Worldwide is considering a $5 million expansion of their existing business. The initial expense will be depreciated straight-line over 5 years to zero salvage value; the pretax salvage value in year 5 will be $500,000. The project will generate pretax gross earnings of $1,500,000 per year, and not change the risk level of the firm. Hamilos can obtain a 5-year 12.5% loan to partially finance the project. Flotation costs are 1% of the proceeds. If undertaken, this project should maintain a target D/E ratio of If the project were financed with all equity, the cost of capital would be 18%. The corporate tax rate is 30%, and the risk-free rate is 6%. The project will require a $100,000 investment in net working capital.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using WACC a)Using the WACC methodology, comment on the desirability of this project.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using WACC a)Using the WACC methodology, comment on the desirability of this project.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV b)Using the APV methodology, comment on the desirability of this project. First some preliminaries: The firm wants to finance the project such that the debt-equity ratio = 1.5. This is equivalent to a debt-to-value ratio of 3:5

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV So, let’s find STEP ONE: + PV depreciation tax shield + PV interest tax shield PV unlevered project = PV unlevered project – PV flotation costs PV unlevered project and borrow 3/5 of that value.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV PV unlevered project  t = 1 5 UCF t (1 + r 0 ) t = PV depreciation = tax shield  t = 1 5 D×TCD×TC (1 + r f ) t + PV depreciation tax shield + PV interest tax shield PV levered project = PV unlevered project – PV flotation costs

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV Recall that the dollar amount of debt depends on the PV levered project + PV depreciation tax shield + PV interest tax shield PV levered project = PV unlevered project – PV flotation costs PV interest tax shield  t = 1 5 = TC×rD×TC×rD× (1 + r D ) t × PV unlevered project 3 5 PV interest tax shield  t = 1 5 = TC×rD×DTC×rD×D (1 + r D ) t D =D = 3 5 × PV unlevered project

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV + PV depreciation tax shield + PV interest tax shield PV levered project = PV unlevered project – PV flotation costs D =D = 3 5 × PV unlevered project We need to borrow D * such that: Our pre-tax flotation costs are one percent of D * D * ×(1 –.01) = 3 5 × PV unlevered project D * = PV unlevered × × 0.01×D * = PV unlevered project × ×

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved A digression on flotation costs Please note: flotation costs are deductible. So the present value of the after-tax flotation costs are PV flotation costs = PV unlevered project ××– (1 – T C ) ×

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV + PV depreciation tax shield PV levered project = PV unlevered project  t = 1 5 UCF t (1 + r 0 ) t =  t = 1 5 D×TCD×TC (1 + r f ) t + + PV interest tax shield  t = TC×rD×TC×rD× (1 + r D ) t × PV unlevered project 3 5 – PV flotation costs PV unlevered project ××– (1 – T C ) ×

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV + PV depreciation tax shield PV levered project = PV unlevered project + PV interest tax shield – PV flotation costs

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV + PV depreciation tax shield PV levered project = PV unlevered project = $3,283, PV levered project PV levered project – × × PV levered project PV levered project = $4,547, PV levered project $4,547, = 1 – = $4,547, = $4,920, $1,263, PV interest tax shield × PV levered project – PV flotation costs PV levered project – ×

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using APV

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using FTE c)Using the FTE methodology, comment on the desirability of this project. Since the bondholders are financing $2,952,338.20, the shareholders only have to pony up $2,147,661 = $5,100,000 – $2,952,338 Thus the year-zero levered cash flow is $2,047, after-tax flotation costs = –$2,147,662 –$20, LCF 0 = –$2,168,536.92

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Hamilos Worldwide Using FTE The LCF for years 1 through 4 is $1,091, = = [$1.5m – $1m –.125×$2,952, ] ×(1 –.30) + $1,000,000 The LCF for year 5 is –$1,410, = $1,091, – $2,952, $100,000 + $500,000(1 –.30) The NPV at r s = % is –$18, LCF 0 = –$2,168,536.92

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Summary Hamilos Worldwide Using WACC NPV = –$322, Using APV NPV = $48, Using FTE NPV = –$18, Should we accept or reject the project? If the dollar amount of debt is known over the project’s life, (in this example the amount of debt would be $2,952,338.20) then the APV method is appropriate and the firm would accept the project. Otherwise, the firm should reject the project.