Ross7eCh17Capital Budgeting for the Levered Firm(公司理财,罗斯,第七版)

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CHAPTER

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Capital Budgeting for the Levered FirmMcGraw-Hill/Irwin Corporate Finance, 7/e

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ProspectusRecall 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.

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Chapter Outline17.1 Adjusted Present Value Approach17.2 Flows to Equity Approach 17.3 Weighted Average Cost of Capital Method

17.4 A Comparison of the APV, FTE, and WACC Approaches17.5 Capital Budgeting When the Discount Rate Must Be Estimated 17.6 APV Example 17.7 Beta and Leverage 17.8 Summary and ConclusionsMcGraw-Hill/Irwin Corporate Finance, 7/e

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17.1 Adjusted Present Value Approach

APV = NPV + NPVFThe 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 FinancingMcGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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APV ExampleConsider 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

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The unlevered cost of equity is r0 = 10%:

NPV10% NPV10%McGraw-Hill/Irwin Corporate Finance, 7/e

$125 $250 $375 $500 $1,000 2 3 (1.10) (1.10) (1.10) (1.10) 4 $56.50

The project would be rejected by an all-equity firm: NPV < 0.© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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APV ExampleThe project would be rejected by an all-equity firm: NPV < 0.CF0CF1 F1 CF2 F2 CF3 I NPVMcGraw-Hill/Irwin Corporate Finance, 7/e

–$1,000$125 1 $250 1 $375 1

10–$56.50

F3 CF4 F4

$5001

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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 ( 1 . 08 ) t 1 APV $56.50 63.59 $7.09So, Pearson should accept the project with debt.McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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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: 4 $600 .08 (1 .4) $600 NPVloan $600 t 4 ( 1 . 08 ) ( 1 . 08 ) t 1

NPVloan $63.59APV = NPV + NPVF

APV $56.50 63.59 $7.09Which is the same answer as before.McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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Two Ways to Find the NPV of the loan:NPV of the loan:CF0 CF1 $600 –$28.80 = $600×.08×(1–.40)CF1 3 F1 –$628.80 I 1 NPV 8 $63.59© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

PV of the interest tax shields.CF0 $0

F1CF2

$19.20 = .40×$600×.0 4 8 $63.59

F2 INPVMcGraw-Hill/Irwin Corporate Finance, 7/e

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17.2 Flows to Equity ApproachDiscount 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.

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Step One: Levered Cash Flows for PearsonSince the firm is using $600 of debt, the equity holders only have to come up with $400 of the initial $1,000. Thus, CF0 = –$400 Each period, the equity holders must pay interest expense. The after-tax cost of the interest is B×rB×(1 – TC) = $600×.08×(1 – .40) = $28.80 CF3 = $375 – 28.80 CF4 = $500 – 28.80 – 600 CF2 = $250 – 28.80

CF1 = $125 – 28.80–$400 $96.20 $221.20 $346.20 –$128.80

0McGraw-Hill/Irwin Corporate Finance, 7/e

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Step Two: Calculate rS for PearsonB rS r0 (1 TC )( r0 rB ) S B B To calculate the debt to equity ratio, , start with S V4 $125 $250 $375 $500 19.20 PV 2 3 4 t (1.10) (1.10) (1.10) (1.10) ( 1 . 08 ) t 1

P V = $943.50 + $63.59 = $1,007.09 B = $600 when V = $1,007.09 so S = $407.09.

$600 rS .10 (1 .40)(.10 .08) 11.77% $407.09McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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Step Three: Valuation for PearsonDiscount the cash flows to equity holders at rS = 11.77%–$400 0 $96.20 1 $221.20 2 $346.20 3 –$128.80 4

$96.20 $221.20 $346.20 $128.80 PV $400 2 3 (1.1177) (1.1177) (1.1177) (1.1177) 4 PV $28.56McGraw-Hill/Irwin Corporate Finance, 7/e

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Step Three: Valuation for PearsonDiscount the cash flows to equity holders at rS = 11.77%–$400 0 $96.20 1 $221.20 2 CF0 CF1 I NPVMcGraw-Hill/Irwin Corporate Finance, 7/e

$346.20 3

–$128.80 4 –$400 $96.20 $221.20

11.77%$28.56

CF2

CF3CF4

$346.20–$128.20

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17.3 WACC Method for PearsonS B rW ACC rS rB

(1 TC ) 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 1.5S B 1.50 S S B 1.5S 1.5 1 0.60 0.40 0.60 S B S B S 1.5S 2.5 rW ACC (0.40) (11.77%) (0.60) (8%) (1 .40)rW ACC 7.58%© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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Valuation for Pearson using WACCTo find the value of the project, discount the unlevered cash flows at the weighted average cost of capitalNPV $1,000 $125 $250 $375 $500 (1.0758) (1.0758) 2 (1.0758)3 (1.0758) 4NPV7.58% = $6.68

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Valuation for Pearson using WACCDiscount the unlevered cash flows at the weighted average cost of capital –$1,000 $125 $250 $375 $500 0 1 2 3 CF0 CF1 I NPVMcGraw-Hill/Irwin Corporate Finance, 7/e

4 –$1,000 $125 $250 $375 $500

7.58%$6.68

CF2 CF3 CF4

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17.4 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 Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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Summary: APV, FTE, and WACCAPVInitial Investment Cash Flows Discount Rates PV of financing effects All UCF r0 Yes

WACC FTEAll UCF rWACC No Equity Portion LCF rS No

Which approach is best? Use APV when the level of debt is constant Use WACC and FTE when the debt ratio is constantWACC is by far the most common FTE is a reasonable choice for a highly levered firmMcGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.

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