17-1 CHAPTER 17 Capital Budgeting for the Levered Firm McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-2 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 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-3 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 Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-4 17.1 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 Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-5 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 $500 The unlevered cost of equity is r0 = 10%: NPV10% NPV10% $125 $250 $375 $500 $1,000 (1.10) (1.10) (1.10) (1.10) $56.50 The project would be rejected by an all-equity firm: NPV < McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-6 APV Example The project would be rejected by an all-equity firm: NPV < I NPV McGraw-Hill/Irwin Corporate Finance, 7/e 10 –$56.50 CF0 –$1,000 CF1 $125 F1 CF2 $250 F2 CF3 $375 F3 CF4 $500 F4 © 2005 The McGraw-Hill Companies, Inc All Rights 17-7 APV Example (continued) Now, imagine that the firm finances the project with $600 of debt at rB = 8% Pearson’s tax rate is 40%, so they have an interest tax shield worth TCBrB = 40×$600×.08 = $19.20 each year The net present value of the project under leverage is: APV = NPV + NPV debt tax shield $19.20 APV $56.50 t ( 08 ) t 1 APV $56.50 63.59 $7.09 So, Pearson should accept the project with debt McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-8 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: $600 .08 (1 4) $600 NPVloan $600 t ( 08 ) ( 08 ) t 1 NPVloan $63.59 APV = NPV + NPVF APV $56.50 63.59 $7.09 Which is the same answer as before McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-9 Two Ways to Find the NPV of the loan: NPV of the loan: CF0 CF1 F1 CF2 F2 I NPV McGraw-Hill/Irwin Corporate Finance, 7/e PV of the interest tax shields $600 CF0 –$28.80 = $600×.08×(1–.40) CF1 F1 –$628.80 I NPV $0 $19.20 = 40ì$600ì.08 $63.59 $63.59 â 2005 The McGraw-Hill Companies, Inc All Rights 10 17.2 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, rS There are three steps in the FTE Approach: Step One: Calculate the levered cash flows Step Two: Calculate rS Step Three: Valuation of the levered cash flows at rS McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 34 Hamilos Worldwide Using WACC a) Using the WACC methodology, comment on the desirability of this project S D rWACC rs rD (1 TC ) V V rs r0 D (r0 rD )(1 TC ) E rs 18% (18% 12.5%)(1 0.30) rWACC 23.775% 12.5% (1 30) 5 rWACC 14.76% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 35 Hamilos Worldwide Using WACC a) Using the WACC methodology, comment on the desirability of this project NPVWACC $5,100,000 $500,000 (1 0.30) 1,000,000 (1.1476) t t 1 $100,000 $500,000 (1 30) (1.1476) $322,677.06 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 36 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 implies a debt-to-value ratio of 3/5: D E D E E D DE EE McGraw-Hill/Irwin Corporate Finance, 7/e E 3 2 5 E © 2005 The McGraw-Hill Companies, Inc All Rights 37 Hamilos Worldwide Using APV So, let’s find PV unlevered and borrow 3/5 of that value project STEP ONE: PV unlevered = PV unlevered + PV depreciation + PV interest – PV flotation project McGraw-Hill/Irwin Corporate Finance, 7/e project tax shield tax shield costs © 2005 The McGraw-Hill Companies, Inc All Rights 38 Hamilos Worldwide Using APV PV levered = PV unlevered + PV depreciation + PV interest – PV flotation project project PV unlevered = project tax shield t=1 tax shield UCFt (1 + r0)t PV depreciation = tax shield McGraw-Hill/Irwin Corporate Finance, 7/e costs t=1 D×TC (1 + rf)t © 2005 The McGraw-Hill Companies, Inc All Rights 39 Hamilos Worldwide Using APV PV levered = PV unlevered + PV depreciation + PV interest – PV flotation project project tax shield D = × PV unlevered tax shield TC×rD×D = t t = (1 + rD) PV interest = tax shield McGraw-Hill/Irwin Corporate Finance, 7/e costs Recall that the dollar amount of debt depends on the PV levered project PV interest tax shield project t=1 TC×rD× × PV unlevered project (1 + rD)t © 2005 The McGraw-Hill Companies, Inc All Rights 40 Hamilos Worldwide Using APV PV levered = PV unlevered + PV depreciation + PV interest – PV flotation project project D = × PV unlevered tax shield tax shield costs We need to borrow D* such that: project * D ×(1 – 01) = × PV unlevered project * × × PV unlevered D = 0.99 project Our pre-tax flotation costs are one percent of D* 0.01 * 0.01×D = × × PV unlevered 0.99 project McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 41 A digression on floatation costs Oh by the way, flotation costs are deductible So the present value of the after-tax flotation costs are PV flotation costs McGraw-Hill/Irwin Corporate Finance, 7/e 0.01 × × PV unlevered = – (1 – TC) ì 0.99 project â 2005 The McGraw-Hill Companies, Inc All Rights 42 Hamilos Worldwide Using APV PV levered = PV unlevered + PV depreciation + PV interest – PV flotation project project = t=1 tax shield UCFt (1 + r0)t + t=1 + t=1 tax shield costs D×TC (1 + rf)t TC×rD× × PV unlevered project (1 + rD)t 0.01 – (1 – TC) × × × PV unlevered 0.99 project McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 43 Hamilos Worldwide Using APV PV = PV unlevered + PV depreciation + PV interest – PV flotation levered project PVlevered project project 5 UCFt D TC t t ( r ) ( r ) t 1 t 1 t 1 o f tax shield TC rD PVlevered project (1 rD ) t tax shield costs 0.01 (1 TC ) PVlevered 99 project PVlevered project 1,500,000 (.70) $1,000,000 .30 t (1.18) (1.06) t t 1 t 1 0.30 0.125 PVlevered project t McGraw-Hill/Irwin Corporate Finance, 7/e (1.125) t 0.01 (.70) PVlevered 99 project © 2005 The McGraw-Hill Companies, Inc All Rights 44 Hamilos Worldwide Using APV PV levered = PV unlevered + PV depreciation + PV interest – PV flotation project project tax shield tax shield costs PVlevered= $3,283,529.57 + $1,263,709.14 + project 0.08011× PVlevered – 0.00424 × PVlevered project project PVlevered – 0.08011× PVlevered + 0.00424× PVlevered = $4,547,238.71 project PVlevered = project project project $4,547,238.71 $4,547,238.71 = – 0.08011 + 0.00424 McGraw-Hill/Irwin Corporate Finance, 7/e 0.92413 = $4,920,563.66 © 2005 The McGraw-Hill Companies, Inc All Rights 45 Hamilos Worldwide Using APV APV $100,000 500,000 (1 30) $5,100,000 $4,920,563.66 5 (1.06) (1.18) APV 48,277.71 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 46 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 $2,047,661.80 = $5,100,000 – $2,952,338 Thus the year-zero levered cash flow is $2,047,661.80 + after-tax flotation costs 01 LCF0 $2,147,662 (1 30) $4,920,563.66 99 = –$2,147,662 –$20,875.11 LCF0 = –$2,168,536.92 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 47 Hamilos Worldwide Using FTE LCF0 = –$2,168,536.92 The LCF for years one through is $1,091,670.41 = = [$1.5m – $1m – 125×$2,952,338.20 ] ×(1 – 30) + $1,000,000 The LCF for year is –$1,410,667.79 = $1,091,670.41 – $2,952,338.20 + $100,000 + $500,000(1 – 30) The NPV at rs = 23.775% is –$18,759.67 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 48 Summary Hamilos Worldwide Using WACC NPV = –$322,677.06 Using APV NPV = $48,277.71 Using FTE NPV = –$18,759.67 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 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights ... McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-6 APV Example The project would be rejected by an all-equity firm: NPV < I NPV McGraw-Hill/Irwin Corporate Finance, ... McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 17-9 Two Ways to Find the NPV of the loan: NPV of the loan: CF0 CF1 F1 CF2 F2 I NPV McGraw-Hill/Irwin Corporate Finance, ... McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 27 17.7 Beta and Leverage Recall that an asset beta would be of the form: β Asset McGraw-Hill/Irwin Corporate Finance,