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**Capital budgeting and valuation with leverage**

Chapter 18

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**outline Focus on constant debt to equity ratio**

Present WACC valuation method WACC/APV link Project based WACC Levering up and WACC

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**Capital budgeting procedure**

Remember the steps we follow Estimate the incremental cash flows generated by the project Discount the free cash flow based on the project’s cost of capital to determine the NPV How to estimate the appropriate cost of capital? How does the financing decision affect the free cash flows and the project’s cost of capital?

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**Some simplifying assumptions**

To lay out the method of valuation we require three simplifying assumptions The project has average risk (same as the firm’s) The firm’s debt-to-equity ratio is fixed over time Corporate taxes are the only imperfection We will simplify some assumptions later on

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**rwacc = E/(E+D) rE + D/(E+D) rD(1-τc)**

The WACC method To calculate project value Calculate project’s (unlevered) FCFs see chapter 7 Discount using WACC rwacc = E/(E+D) rE + D/(E+D) rD(1-τc) VL = PV(FCF’s, rwacc)

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**Deriving the WACC method**

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**Deriving the WACC method**

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**Using WACC an Example Example page 577**

Avco, Inc. is a manufacturer of custom packaging products and is considering a new line of packaging (RFX) that includes an embedded radio-frequency identification tag. This improved technology will become absolute after 4 years. In the meanwhile it is expected to increase sales by $60 million per year. Manufacturing costs and operating expenses are expected to be $25 million and $9 million respectively per year.

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**Using WACC an Example Example continued**

Developing the product will require upfront R&D and marketing expenses of $6.67 million together with an investment of $24 million in equipment. The equipment will be obsolete in four years and will depreciate via straight-line method over that period. Avco bills its customers in advance, and it expects no net working capital requirements for the project. Avco’s tax rate is 40%.

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**First step: predicting FCF’s**

This implies the following steam of expected future cash flows

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Calculating WACC The market risk of RFX is expected to be similar to that for the company’s other lines of business. We will use WACC to discount the cash flows generated from the project We need information on the Avco’s capital structure This can be found in the firm’s balance sheet

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The data we need

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NPV calculation

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**Using the APV method when D/E ratio is fixed**

See chapter 15 for the case of fixed $D Alternative method of valuation First, calculate the unlevered value VU by discounting FCF’s using rU. With constant D/E ratio we can estimate rU by: Second, calculate the value of the interest tax shield. With constant D/E ratio we discount the tax shield with rate rU APV: VL = APV = VU + PV(int. tax shield) rU = (D/(E+D))rD + (E/(D+E))rE

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**Deriving the unlevered cost of capital**

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**Deriving the unlevered cost of capital**

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**The unlevered value of the project**

The RFX project has initial investment of $28 million and 4 annual FCF’s of $18 million We discount FCF’s using Avco’s unlevered cost of capital (with target leverage ratio)

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The WACC/APV link

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**Financing the project with fixed D/E ratio**

The value of leveraged project (in $millions): To maintain the ratio D/E=1 time 1 2 3 4 VLt 61.24 47.42 32.64 16.86 time 1 2 3 4 Debt 30.62 23.71 16.32 8.43 Equity

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**Finding expected interest payments**

Given debt levels (in $millions): We calculate interest payments and tax shield with tax rate of 40% and interest of 6% time 1 2 3 4 Debt 30.62 23.71 16.32 8.43 time 1 2 3 4 interest 1.84 1.42 0.97 0.505 Tax shield 0.73 0.57 0.39 0.20

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**Discounting interest tax shield**

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One more example Example – Avco is considering an acquisition of another firm in the same industry. Expected FCF’s will increase by $3.8 t=1, and will grow at annual rate of 3% from then on. The purchase price is $80 million will be financed with $50 million in new debt initially. Avco maintain a constant D/E ratio for the acquisition.

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**Valuation the acquisition using APV**

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Valuation using WACC

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**Project-based cost of capital**

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**Project-based cost of capital how to find WACC of project?**

Up to now we assumed that the project is in the same line of business as the rest of the firm and that it is financed while maintaining the same capital structure This allowed us to assume that the cost of capital of the project equals the firm’s WACC Sometimes these assumptions do not apply Consider GE GE Commercial Finance, GE Aviation, GE Healthcare, GE Energy, NBC Universal, among others

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**Project-based cost of capital**

Comparable firms Firm project rU (comp. firms) = rU (project)

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**Project-based cost of capital**

Calculating WACC for project Identify comparable firms in the same industry of the project (comparable risk) Calculate average unleveraged cost of capital of comparable firms Use this as the project’s unleveraged cost of capital Given debt cost of capital you can calculate the project equity cost of capital Then, given tax rate and firm’s capital structure you can calculate WACC for the project

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**Project-based cost of capital**

Numerical example Suppose now that Avco launches a new plastics manufacturing division with different market risk than its main packaging business WACC of Avco is no longer relevant to us Instead, we estimate the unlevered cost of capital (rU) of other plastic manufacturers Remember this represents the underlying risk of the firm’s assets before we account for leverage effects

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**Step one: calculate unlevered cost of capital for comparable firms**

You identify two single-division plastics firms that have similar business risk

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**Step two: calculate equity cost of capital for project**

Back to our project Remember, our project will be financed with debt and equity and therefore we will benefit from the interest tax shield Suppose Avco maintains its capital structure (equal mix of debt and equity) when adopting the project, and that it will continue to borrow at 6% Then, Avco’s equity cost of capital is

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**Step 3: calculate WACC for project**

Once we have the equity cost of capital, the debt cost of capital, and marginal tax rate we can compute the project’s WACC

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**Changing Capital Structure and**

WACC

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Levering up and WACC What happens to WACC when the firm increases leverage? Example page 592 Consider a firm with debt-to-equity ratio of 25%, debt cost of capital of 6.67%, equity cost of capital of 12%, and tax rate of 40% Its current WACC is,

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**rWACC (new) = 0.5 x 12% + 0.5 x 6.67% x (0.6) = 9%**

Levering up and WACC Example continued Now suppose that the firm changes its debt-to-equity ratio to 50% What is wrong with the calculation: rWACC (new) = 0.5 x 12% x 6.67% x (0.6) = 9%

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**Levering up and WACC Two things can happen when levering up**

First with higher leverage payments to equity holders bear more risk Second with higher leverage the required rate of return on the firm’s debt by investors might increase Suppose that now debt holders require 7.34% instead of 6.67% To recalculate the firm’s WACC lets go back and calculate the firm’s unlevered cost of capital

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Levering up and WACC

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Assigned problems Problems page 2, 5,14

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Valuation and Capital Budgeting for the Levered Firm

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