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# Valuation and capital budgeting for the levered firm

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• Note, the example in the text assumes a perpetual project, so the PV of the tax shield is calculated assuming a perpetuity. The approach in this slide is comparable, but for a finite life project.
• This example assumes an interest only loan.
• This assumes we know the value created by the project. A more straightforward assumption is to assume that the ratio is 600/400, based on the amount provided by each source to fund the project. With these values, R S =11.80%.
• Note that the chapter examples work out nicely with the perpetuity assumption, in that each approach provides the same value. With a finite life project, the values will deviate based on assumptions made, for example, the repayment of the \$600.
• ### Transcript

• 1. Valuation and Capital Budgeting for the Levered Firm 18-1
• 2. 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 18-2
• 3. APV ExampleConsider a project of the Pearson Company. The timing and sizeof the incremental after-tax cash flows for an all-equity firm are: –\$1,000 \$125 \$250 \$375 \$500 0 1 2 3 4 The unlevered cost of equity is R0 = 10%: \$125 \$250 \$375 \$500 NPV10% = −\$1,000 + + + + (1.10) (1.10) (1.10) (1.10) 4 2 3 NPV10% = −\$56.50The project would be rejected by an all-equity firm: NPV < 0. 18-3
• 4. APV Example• 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 4 \$19.20 APV = −\$56.50 + ∑ t =1 (1.08) t APV = −\$56.50 + 63.59 = \$7.09• So, Pearson should accept the project with debt. 18-4
• 5. 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, RS.• There are three steps in the FTE Approach: – Step One: Calculate the levered cash flows (LCFs) – Step Two: Value the levered cash flows at RS. 18-5
• 6. 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, 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 18-6
• 7. Step One: Levered Cash Flows CF3 = \$375 – 28.80 CF4 = \$500 – 28.80 – 600 CF2 = \$250 – 28.80CF1 = \$125 – 28.80 –\$400 \$96.20 \$221.20 \$346.20 –\$128.80 0 1 2 3 4 18-7
• 8. Step Two: Calculate RS 4 \$125 \$250 \$375 \$500 19.20APV : PV = + 2 + 3 + 4 +∑ (1.10) (1.10) (1.10) (1.10) t =1 (1.08) t P V = \$943.50 + \$63.59 = \$1,007.09B = \$600 when V = \$1,007.09 so S = \$407.09. RS = 11.77% 18-8
• 9. Step Three: Valuation• Discount the cash flows to equity holders at RS = 11.77% –\$400 \$96.20 \$221.20 \$346.20 –\$128.80 0 1 2 3 4 \$96.20 \$221.20 \$346.20 \$128.80FTE : NPV = −\$400 + + + − (1.1177) (1.1177) (1.1177) (1.1177) 4 2 3NPV = \$28.56 18-9
• 10. 18.3 WACC Method S B RWACC = 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 18-10
• 11. WACC Method B ∴1.5S = B 1.50 = S B 1 .5 S 1 .5 S = = = 0.60 = 1 − 0.60 = 0.40S + B S + 1 .5 S 2 .5 S+B RWACC = (0.40) × (11.77%) + (0.60) × (8%) × (1 − .40) RWACC = 7.58% 18-11
• 12. WACC Method• To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital \$125 \$250 \$375 \$500 NPV = −\$1,000 + + + + (1.0758) (1.0758) 2 (1.0758)3 (1.0758) 4 NPV7.58% = \$6.68 18-12
• 13. 18.4 A Comparison of the APV, FTE, andWACC 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. 18-13
• 14. Summary: APV, FTE, and WACC APV WACC FTEInitial Investment All All Equity PortionCash Flows UCF UCF LCFDiscount Rates R0 RWACC RSPV of financingeffects Yes No No 18-14
• 15. Summary: APV, FTE, and WACCWhich 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 18-15
• 16. 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-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. 18-16
• 17. 18.7 Beta and Leverage• Recall that an asset beta would be of the form: Cov (UCF , Market ) β Asset = σ2 Market 18-17
• 18. Beta and Leverage: No Corporate Taxes• In a world without corporate taxes, and with riskless corporate debt (βDebt = 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 = × β Equity Asset • 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 = × β Debt + × β Equity Asset Asset 18-18
• 19. 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 +  Equity × (1 − TC ) β Unlevered firm      • Since 1 + Debt × (1 − TC )  must be more than 1 for a  Equity    levered firm, it follows that βEquity > βUnlevered firm 18-19
• 20. Beta and Leverage: With Corporate Taxes• If the beta of the debt is non-zero, then: B β Equity = β Unlevered firm + (1 − TC )(β Unlevered firm − β Debt ) × SL 18-20
• 21. Summary1. The APV formula can be written as: Additional ∞ UCFt Initial APV = ∑ + effects of − t =1 (1 + R0 ) t investment debt4. The FTE formula can be written as: ∞ LCFt  Initial Amount  FTE = ∑ −  investment − borrowed   t =1 (1 + RS )  t 7. The WACC formula can be written as ∞ UCFt Initial NPVWACC =∑ − t =1 (1 + RWACC ) t investment 18-21
• 22. Summary2 Use the WACC or FTE if the firms 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.3 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.4 The beta of the equity of the firm is positively related to the leverage of the firm. 18-22