Chapter 18 Valuation and Capital Budgeting for the Levered Firm Dec. 2012

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1 University of Science and Technology Beijing Dongling School of Economics and management Chapter 18 Valuation and Capital Budgeting for the Levered Firm Dec Dr. Xiao Ming USTB 1

2 Key Concepts and Skills Understand the effects of leverage on the value created by a project Be able to apply Adjusted Present Value (APV), the Flows to Equity (FTE) approach, and the WACC method for valuing projects with leverage Dr. Xiao Ming USTB 2

3 Chapter Outline 18.1 Adjusted 18.2 Flows 18.3 Weighted Present Value Approach to Equity Approach Average Cost of Capital Method 18.4 A Comparison of the APV, FTE, and WACC Approaches 18.5 Capital Estimated 18.6 APV 18.7 Beta Budgeting When the Discount Rate Must Be Example and Leverage Dr. Xiao Ming USTB 3

4 18.1 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 Dr. Xiao Ming USTB 4

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 $ The unlevered cost of equity is R 0 = 10%: NPV 10% = $1,000 + $125 (1.10) + $250 (1.10) 2 + $375 (1.10) 3 + $500 (1.10) 4 NPV 10% = $56.50 The project would be rejected by an all-equity firm: NPV < 0. Dr. Xiao Ming USTB 5

6 APV Example 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 $ = $19.20 each year. The net present value of the project under leverage is: APV = NPV + NPV debt tax shield 4 $19.20 APV = $ t t= 1 (1.08) APV = $ = $7.09 So, Pearson should accept the project with debt. Dr. Xiao Ming USTB 6

7 18.2 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 (LCFs) Step Two: Calculate R S. Step Three: Value the levered cash flows at R S. Dr. Xiao Ming USTB 7

8 Step One: Levered Cash Flows Since the firm is using $600 of debt, the equity holders only have to provide $400 of the initial $1,000 investment. 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 ) = $ (1.40) = $28.80 Dr. Xiao Ming USTB 8

9 Step One: Levered Cash Flows CF 3 = $ CF 4 = $ CF 2 = $ CF 1 = $ $400 $96.20 $ $ $ Dr. Xiao Ming USTB 9

10 Step Two: Calculate R S B RS = R0 + ( 1 TC )( R0 RB ) S B To calculate the debt to equity ratio,, start with S PV = $125 (1.10) + $250 (1.10) 2 + $375 (1.10) PV= $ $63.59 = $1, $500 (1.10) t= 1 B = $600 when V = $1, so S = $ (1.08) B V t R S = $ (1.40)(.10.08) = 11.77% $ Dr. Xiao Ming USTB 10

11 Step Three: Valuation Discount the cash flows to equity holders at R S = 11.77% $400 $96.20 $ $ $ NPV NPV $96.20 $ $ $ = $ (1.1177) (1.1177) (1.1177) (1.1177) = $28.56 Dr. Xiao Ming USTB 11

12 18.3 WACC Method R WACC = S S + B R S + S B + B R 1 T B ( C ) 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 Dr. Xiao Ming USTB 12

13 WACC Method S B 1.50 = 1. 5S = B S B 1.5S 1.5 S = = = B S + 1.5S 2.5 S + B = = 0.40 R R WACC WACC = = (0.40) (11.77%) 7.58% + (0.60) (8%) (1.40) Dr. Xiao Ming USTB 13

14 WACC Method To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital NPV $125 $250 $375 = $ 1, (1.0758) (1.0758) (1.0758) $500 (1.0758) 4 NPV 7.58% = $6.68 Dr. Xiao Ming USTB 14

15 18.4 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, by far, the most widely used. Dr. Xiao Ming USTB 15

16 Summary: APV, FTE, and WACC 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 Dr. Xiao Ming USTB 16

17 Summary: APV, FTE, and WACC 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 Dr. Xiao Ming USTB 17

18 18.5 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-scaleenhancing 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. Dr. Xiao Ming USTB 18

19 18.7 Beta and Leverage Recall that an asset beta would be of the form: β Asset = Cov( UCF, Market) σ 2 Market Dr. Xiao Ming USTB 19

20 Beta and Leverage: No Corporate Taxes In a world without corporate taxes, and with riskless corporate debt (b Debt = 0), it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: Equity β = Asset 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 Asset = βdebt + β Asset Asset Equity Dr. Xiao Ming USTB 20

21 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: β Debt Equity Debt + (1 T ) Equity Equity = 1+ (1 TC ) β Unlevered firm Since must be more than 1 for a 1 C levered firm, it follows that β Equity > β Unlevered firm Dr. Xiao Ming USTB 21

22 Beta and Leverage: With Corporate Taxes If the beta of the debt is non-zero, then: β Equity = β Unlevered firm + (1 T )(β β ) C Unlevered firm Debt B S L Dr. Xiao Ming USTB 22

23 Summary The APV formula can be written as: APV The FTE formula can be written as: FTE The NPV = t= UCFt (1 + R ) 1 0 t Additional Initial + effects of investment debt = LCF Initial Amount t t (1 + ) = investment borrowed t 1 RS WACC formula can be written as WACC = t= 1 UCF (1 + R t WACC ) t Initial investment Dr. Xiao Ming USTB 23

24 Summary 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. Dr. Xiao Ming USTB 24

25 Quick Quiz Explain how leverage impacts the value created by a potential project. Identify when it is appropriate to use the APV method? The FTE approach? The WACC approach? Dr. Xiao Ming USTB 25

26 Dr. Xiao Ming USTB 26

Advanced Corporate Finance

Introduction Advanced Corporate Finance Introduction Instructor: Nikunj Kapadia Office: Room 310 C Tel: 545 5643 Email: nkapadia@som.umass.edu Class Room: 108 Course Requirement Prerequisite: FINOPMGT