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## Valuation and Capital Budgeting RWJ Chp 17

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**Adjusted Present Value Approach**• 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**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: -RM1,000 RM125 RM250 RM375 RM500 0 1 2 3 4 The unlevered cost of equity is r0 = 10%: The project would be rejected by an all-equity firm: NPV < 0.**APV Example (continued)**• Now, imagine that the firm finances the project with RM600 of debt at rB = 8%. • Pearson’s tax rate is 40%, so they have an interest tax shield worth TCBrB = 0.40 × RM600 × 0.08 = RM19.20 each year.**The net present value of the project under leverage is:**PV of All-Equity project • So, Pearson should accept the project with debt.**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:**PV of After-tax**payments PV of loan repayments • Which is the same answer as before.**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.**Step One: Levered Cash Flows for Pearson**• Since the firm is using RM600 of debt, the equity holders only have to come up with RM400 of the initial RM1,000. • Thus, CF0 = -RM400 • Each period, the equity holders must pay interest expense. • The after-tax cost of the interest is B×rB×(1-TC) = RM600×.08×(1-.40) = RM28.80**CF4 = RM500 -28.80 -600**CF3 = RM375 -28.80 CF2 = RM250 -28.80 CF1 = RM125-28.80 RM96.20 RM221.20 RM346.20 -RM128.80 0 1 2 3 4 -RM400**Step Two: Calculate rS for Pearson**• To calculate the debt to equity ratio, B/S, start with the debt to value ratio. Note that the value of the project is**B = RM600 when V = RM1,007.09**so S = RM407.09.**Step Three: Valuation for Pearson**• Discount the cash flows to equity holders at rs = 11.77%**-RM400 RM96.20 RM221.20 RM346.20**-RM128.80 0 1 2 3 4**To find the value of the project, discount the unlevered**cash flows at the weighted average cost of capital. • Suppose Pearson Inc. target debt to equity ratio is 1.50**Valuation for Pearson using WACC**• To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital**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.**Summary: APV, FTE, and WACC**APV WACC FTE Initial Investment All All Equity Portion Cash Flows UCF UCF LCF Discount Rates r0 rWACC rS PV of financing effects Yes No No Which approach is best? • Use APV when the level of debt is constant • Use WACC and FTE when the debt ratio is constant**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.**APV Example:**Worldwide Trousers, Inc. is considering a RM5 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 RM500,000. • The project will generate pretax earnings of RM1,500,000 per year, and not change the risk level of the firm. • The firm can obtain a 5-year RM3,000,000 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 RM100,000 investment in net working capital. Calculate the APV.**APV Example: Cost**Let’s work our way through the four terms in this equation:**Cost of the project**• The cost of the project is not RM5,000,000. • We must include the round trip in and out of net working capital and the after-tax salvage value. • NWC is riskless, so we discount it at rf. Salvage value should have the same risk as the rest of the firm’s assets, so we use r0.**PV unlevered project**The PV unlevered project is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%.**PV depreciation tax shield**The PV depreciation tax shield is the present value of the tax savings due to depreciation discounted at the risk free rate , at rf = 4% Project: RM5 mil Lifespan: 5 years Salvage Value: 0 Capital Allowance: RM1 mil**APV Example: PV interest tax shield**The PV interest tax shield is the present value of the tax savings due to interest expense discounted at the firms debt rate, at rD = 12.5%**APV Example: Adding it all up**Let’s add the four terms in this equation: Since the project has a positive APV, it looks like a go.**Beta and Leverage**• Recall that an asset beta would be of the form:**Beta and Leverage: No Corp.Taxes**• In a world without corporate taxes, and with riskless corporate debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:**Beta and Leverage: No Corp.Taxes**• 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:**Since must be more than 1 for a**levered firm, it follows that 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:**Beta and Leverage: with Corp. Taxes**• If the beta of the debt is non-zero, then:**Summary and Conclusions**• The APV formula can be written as: • The FTE formula can be written as: • The WACC formula can be written as**Summary and Conclusions**• Use the WACC or FTE if the firm's target debt to value ratio applies to the project over its life. • The APV method is used if the level of debt is known over the project’s life. • The beta of the equity of the firm is positively related to the leverage of the firm.