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- 1. Chapter Eighteen:Valuation and Capital Budgeting for the Levered Firm
- 2. 18- Recall • Recall 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 discusses the interplay of these questions. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 3. 18- Chapter Outline 18.1 Adjusted Present Value Approach 18.2 Flows to Equity Approach 18.3 Weighted Average Cost of Capital Method 18.4 A Comparison of the APV, FTE, and WACC Approaches 18.5 Capital Budgeting When the Discounting Rate Must Be Estimated 18.6 APV Example 18.7 Beta and Leverage 18.8 Summary and Conclusions McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 4. 18- 18.1 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 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 5. 18- 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 $500 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. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 6. 18- 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: • So, Pearson should accept the project with debt. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 7. 18- APV Example (continued) 2nd method • 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: 600*0.08 = interest • Which is the same answer as before. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 8. 18- 18.2 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. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 9. 18- Step One: Levered Cash Flows for Pearson • Since 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 0 1 2 3 4 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 10. 18- 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 V=B+S • B = $600 when V = $1,007.09 so S = $407.09. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 11. 18- Step Three: Valuation for Pearson • 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 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 12. 18- 18.3 WACC Method for Pearson • 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. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 13. 18- Valuation for Pearson using WACC • To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital = McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 14. 18- 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 the most widely used approach by far. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 15. 18- Summary: APV, FTE, and WACC APV WACC FTE Initial Investment All All Equity Portion Cash Flows U-CF U-CF L-CF 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 – WACC is by far the most common – FTE is a reasonable choice for a highly levered firm McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 16. 18- 18.8 Summary of the Methods 1. The APV formula can be written as: 2. The FTE formula can be written as: 3. The WACC formula can be written as McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 17. 18- 18.5 Capital Budgeting When the Discounting 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 discounting rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 18. 18- 18.5 Capital Budgeting When the Discounting Rate Must Be Estimated: An example • World-Wide Enterprises (WWE) is planning to enter into a new line of business (widget industry) • American Widgets (AW) is a firm in the widget industry. • WWE has a D/E of 1/3, AW has a D/E of 2/3. • Borrowing rate for WWE is10 % Borrowing rate for AW is 8 % • Given: Market risk premium = 8.5 %, Rf = 8%, Tc= 40% • What is the appropriate discount rate for WWE to use for its widget venture? McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 19. 18- 18.5 Capital Budgeting When the Discounting Rate Must Be Estimated: An example • A four step procedure to calculate discount rates: 1. Determining AW’s cost of Equity Capital (rs) 2. Determining AW’s Hypothetical All-Equity Cost of Capital. (r0) 3. Determining rs for WWE’s Widget Venture 4. Determining rWACC for WWE’s Widget Venture. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 20. 18- STEP 1:Determining AW’s cost of Equity Capital (rs) B McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 21. 18- STEP 2 :Determining AW’s Hypothetical All- Equity Cost of Capital. (r0) McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 22. 18- STEP 3 :Determining rs for WWE’s Widget Venture Assuming that the business risk of WWE and AW are the same, NOTE : rs (WWE) < rs (AW) because B/S (WWE) < B/S (AW) McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 23. 18- STEP 4: Determining rWACC for WWE’s Widget Venture. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 24. 18- 18.6 APV Example: • Worldwide Trousers, Inc. is considering a $5 million expansion of their existing business. • The initial expense will be depreciated straight-line over five years to zero salvage value • The pretax salvage value in year 5 will be $500,000. • The project will generate pretax earnings of $1,500,000 per year, and not change the risk level of the firm. • The firm can obtain a five-year $3,000,000 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 $100,000 investment in net working capital. • Calculate the APV. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 25. 18- 18.6 APV Example: Cost Let’s work our way through the four terms in this equation: The cost of the project is not $5,000,000. We must include the round trip in and out of net working capital and the after-tax salvage value. NWC is risk-less, so we discount it at rf. 5m + 100,000 Salvage value should - =- + + have the same risk as + rf + r0 the rest of the firm’s assets, so we use r0. = - McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 26. 18- 18.6 APV Example: PV unlevered project Turning our attention to the second term, = -$ + + + The PV unlevered project is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 27. 18- 18.6 APV Example: PV depreciation tax shield Turning our attention to the third term, APV = –$4,873,561.25 + $3,095,899 + PV depreciation+ PV interest tax shield 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% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 28. 18- 18.6 APV Example: PV interest tax shield Turning our attention to the last term, APV = –$4,873,561.25 + $3,095,899 + $1,513,619 + 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% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 29. 18- 18.6 APV Example: Adding it all up Let’s add the four terms in this equation: APV = –Cost + PV unlevered + PV depreciation + PV interest project tax shield tax shield APV = –$4,873,561.25 + $3,095,899 + $1,513,619 + $453,972.46 APV = $189,930 Since the project has a positive APV, it looks like a go. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 30. 18- 18.7 Beta and Leverage • Recall that an asset beta would be of the form: B McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 31. 18- 18.7 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: B BEquity • 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: B ×BDebt + BEquity McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 32. 18- 18.7 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: B B • Since must be more than 1 for a levered firm, it follows that B B McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 33. 18- 18.7 Beta and Leverage: with Corp. Taxes • If the beta of the debt is non-zero, then: B B B B McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 34. 18- 18.8 Summary and Conclusions 1. The APV formula can be written as: 2. The FTE formula can be written as: 3. The WACC formula can be written as McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 35. 18- 18.8 Summary and Conclusions (cont.) 4. 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. 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. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 36. 18- All you need to know about CCA (for this course) • Depreciation is not tax deductible. • Instead, you may deduct Capital Cost Allowance (CCA) from your taxes. • Assets are placed in a “CCA pool”, with a given CCA rate. The assets are then “depreciated” at the CCA rate on a declining balance calculation. • Once an asset is sold, it is removed from the pool, and thus the taxpayer can no longer enjoy the CCA deduction on that amount. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 37. 18- All you need to know about CCA (for this course) • Assume we purchase a machine for $1 million. Assume it is in a CCA class with a rate of 10%. What are the annual CCA deductions available? McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 38. 18- All you need to know about CCA (for this course) • Assume we purchase a machine for $1 million. Assume it is in a CCA class with a rate of 10%. What are the annual CCA deductions available? Year UCC Start CCA UCC End 1 1,000,000 100,000 900,000 2 900,000 90,000 810,000 3 810,000 81,000 729,000 4 729,000 72,900 656,100 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 39. 18- All you need to know about CCA (for this course) • Assume we purchase a machine for $1 million. Assume it is in a CCA class with a rate of 10%. What are the annual CCA deductions available? Year UCC Start CCA UCC End 1 1,000,000 100,000 900,000 2 900,000 90,000 810,000 3 810,000 81,000 729,000 4 729,000 72,900 656,100 This is actually wrong. The rules assume that the purchase occurred in the middle of the year; hence, the first year’s deduction is half the usual amount. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 40. 18- All you need to know about CCA (for this course) • So the correct amounts must adjust for this “half- year rule” McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 41. 18- All you need to know about CCA (for this course) • So the correct amounts must adjust for this “half- year rule” Year UCC Start CCA UCC End 1 500,000 50,000 450,000 2 950,000 95,000 855,555 3 855,000 85,500 769,500 4 769,500 76,950 692.550 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 42. 18- All you need to know about CCA (for this course) • So the correct amounts must adjust for this “half- year rule” Year UCC Start CCA UCC End 1 500,000 50,000 450,000 2 950,000 95,000 855,555 3 855,000 85,500 769,500 4 769,500 76,950 692.550 50% x $1 m = 500k added to the class in yr 1 (remainder added in year 2) McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 43. 18- All you need to know about CCA (for this course) • The present value of these deductions is given by the PVCCATS formula: PV of annuity growing at –d, with PV of annuity growing first payment CdT at –d, with first payment SdT, starting at time n McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 44. 18- Special details on sales of assets • What happens when an asset is sold? – If there are no other assets in the pool, the class is “closed”. • If the sale price is greater than the UCC, there is a “recapture” which is fully taxable. • If the sale price is less than the UCC, there is a “terminal loss” which is fully deductible. • If the sale price is greater than the purchase price, there is recapture up to the original cost, then a capital gain (taxed at a 50% inclusion rate) above that. – If other assets remain in the class, the sale value is deducted from the class, reducing the UCC at that time. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 45. 18- CCA on Real Estate • Rental real estate is usually in class 1, with a CCA rate of 4%. (Note only the building is in class 1. Land is not depreciable, and thus is ineligible for CCA) • CCA cannot be taken on real estate in order to create a tax loss, thus the maximum CCA deduction is limited to the taxable income otherwise available. – How might you get around this rule? (Don’t forget GAAR) McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
- 46. 18- CCA on Real estate • Given that investors expect the value of the real estate to increase, they often forgo the CCA deduction knowing that the deduction, if taken, would trigger a large recapture tax at the time of sale. Is this wise? – Assume I purchase a $1 million apartment building. Assume 75% of the price is attributable to the building, the rest is land. Assume the following: • Tax rate 40%; CCA rate 4% and the full deduction is available. This is the only building I own • We expect the building to be sold at a profit in about 10 years. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited

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