CHAPTER

1. CHAPTER 17 Capital Budgeting forthe Levered Firm

2. Prospectus • 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 considers the nexus of these questions.

3. Chapter Outline 17.1 Adjusted Present Value Approach 17.2 Flows to Equity Approach 17.3 Weighted Average Cost of Capital Method 17.4 A Comparison of the APV, FTE, and WACC Approaches 17.5 Capital Budgeting When the Discount Rate Must Be Estimated 17.6 APV Example 17.7 Beta and Leverage 17.8 Summary and Conclusions

4. 17.1 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

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 $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.

6. APV Example CF0 –$1,000 CF1 $125 The project would be rejected by an all-equity firm: NPV < 0. F1 1 CF2 $250 F2 1 CF3 $375 F3 1 I 10 CF4 $500 NPV –$56.50 1 F4

7. 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: APV = NPV + NPV debt tax shield So, Pearson should accept the project with debt.

8. 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: APV = NPV + NPVF Which is the same answer as before.

9. CF0 $600 CF0 $0 CF1 –$28.80 = CF1 $19.20 = .40×$600×.08 F1 3 F1 4 CF2 –$628.80 I 8 F2 1 NPV $63.59 I 8 NPV $63.59 Two Ways to Find the NPV of the loan: PV of the interest tax shields. NPV of the loan: $600×.08×(1–.40)

10. 17.2 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.

11. CF4 = $500 –28.80 –600 CF3 = $375 –28.80 CF2 = $250 –28.80 CF1 = $125 –28.80 $96.20 $221.20 $346.20 –$128.80 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 –$400 0 1 2 3 4

12. B B To calculate the debt to equity ratio, , start with S V Step Two: Calculate rS for Pearson PV = $943.50 + $63.59 = $1,007.09 B = $600 when V = $1,007.09 so S = $407.09.

13. –$400 $96.20 $221.20 $346.20 –$128.80 0 1 2 3 4 Step Three: Valuation for Pearson • Discount the cash flows to equity holders at rS = 11.77%

14. –$400 $96.20 $221.20 $346.20 –$128.80 0 1 2 3 4 Step Three: Valuation for Pearson • Discount the cash flows to equity holders at rS = 11.77% CF0 –$400 CF1 $96.20 CF2 $221.20 I 11.77% CF3 $346.20 NPV $28.56 CF4 –$128.20

15. 17.3 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’s target debt to equity ratio is 1.50

16. Valuation for Pearson using WACC • To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital NPV7.58% = $6.68

17. Valuation for Pearson using WACC • Discount the unlevered cash flows at the weighted average cost of capital –$1,000 $125 $250 $375 $500 0 1 2 3 4 CF0 –$1,000 CF1 $125 CF2 $250 I 7.58% CF3 $375 NPV $6.68 CF4 $500

18. 17.4 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 by far.

19. 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 • WACC is by far the most common • FTE is a reasonable choice for a highly levered firm

20. 17.5 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.

21. 17.6 APV Example: Worldwide Trousers, Inc. is considering replacing a $5 million piece of equipment. The initial expense will be depreciated straight-line to zero salvage value over 5 years; the pretax salvage value in year 5 will be $500,000. The project will generate pretax savings of $1,500,000 per year, and not change the risk level of the firm. The firm can obtain a 5-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.

22. APV = –Cost + PVunlevered + PVdepreciation + PVinterest project tax shield tax shield 17.6 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 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.

23. APV = –$4,873,561.25 + PVunlevered PVunlevered + PVdepreciation + PVinterest project project tax shield tax shield 17.6 APV Example: PV unlevered project Turning our attention to the second term, is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%.

24. APV = –$4,873,561.25 + PVdepreciation PVdepreciation tax shield tax shield + PVdepreciation + PVinterest $3,095,899 tax shield tax shield 17.6 APV Example: PV depreciation tax shield Turning our attention to the third term, is the is the present value of the tax savings due to depreciation discounted at the risk free rate: rf = 4%

25. APV = –$4,873,561.25 + PVinterest tax shield + $1,513,619 + PVinterest $3,095,899 tax shield 17.6 APV Example: PV interest tax shield Turning our attention to the last term, is the present value of the tax savings due to interest expense discounted at the firm’s debt rate: rD = 12.5%

26. APV = –Cost + PVunlevered + PVdepreciation + PVinterest project tax shield tax shield 17.6 APV Example: Adding it all up Let’s add the four terms in this equation: 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.

27. 17.7 Beta and Leverage • Recall that an asset beta would be of the form:

28. 17.7 Beta and Leverage: No Corp.Taxes • In a world without corporate taxes, and with riskless corporate debt, (bDebt = 0) it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: 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:

29. Since must be more than 1 for a levered firm, it follows that bEquity > bUnlevered firm. 17.7 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:

30. 17.7 Beta and Leverage:with Corp. Taxes • If the beta of the debt is non-zero, then:

31. 17.8 Summary and Conclusions • The APV formula can be written as: • The FTE formula can be written as: • The WACC formula can be written as

32. 17.8 Summary and Conclusions • 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. • 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. • The beta of the equity of the firm is positively related to the leverage of the firm.

33. Example: Hamilos Worldwide Hamilos Worldwide is considering a $5 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 $500,000. The project will generate pretax gross earnings of $1,500,000 per year, and not change the risk level of the firm. Hamilos can obtain a 5-year 12.5% loan to partially finance the project. Flotation costs are 1% of the proceeds. If undertaken, this project should maintain a target D/E ratio of 1.50. If the project were financed with all equity, the cost of capital would be 18%. The corporate tax rate is 30%, and the risk-free rate is 6%. The project will require a $100,000 investment in net working capital.

34. Hamilos Worldwide Using WACC • Using the WACC methodology, comment on the desirability of this project.

35. Hamilos Worldwide Using WACC • Using the WACC methodology, comment on the desirability of this project.

36. Hamilos Worldwide Using APV • Using the APV methodology, comment on the desirability of this project. First some preliminaries: The firm wants to finance the project such that the debt-equity ratio = 1.5. This implies a debt-to-value ratio of 3/5:

37. = PVunlevered project PVunlevered PVunlevered + PVdepreciation + PVinterest – PVflotation project project tax shield tax shield costs Hamilos Worldwide Using APV So, let’s find and borrow 3/5 of that value. STEP ONE:

38. 5 UCFt S 5 D×TC S = (1 + r0)t (1 + rf)t t = 1 t = 1 = PVunlevered project PVunlevered PV levered PVdepreciation = + PVdepreciation – PVflotation + PVinterest project project tax shield tax shield costs tax shield Hamilos Worldwide Using APV

39. 3 × PVunlevered D= 5 project Recall that the dollar amount of debt depends on the PV levered. 5 TC×rD×D S PVinterest = (1 + rD)t tax shield t = 1 3 ×PVunlevered project TC×rD× 5 5 S project = (1 + rD)t t = 1 PVinterest tax shield = PVunlevered project PV levered + PVdepreciation – PVflotation + PVinterest project tax shield costs tax shield Hamilos Worldwide Using APV

40. 3 × PVunlevered D= PV unlevered 5 project project 0.01 1 3 × PV unlevered D*×(1 – .01)= 0.99 0.99 5 3 3 project 5 5 PV unlevered × × D* = project = PVunlevered 0.01×D*= × × project PV levered + PVdepreciation – PVflotation + PVinterest project tax shield costs tax shield Hamilos Worldwide Using APV We need to borrowD* such that: Our pre-tax flotation costs are one percent of D*

41. 0.01 0.99 3 PV flotation PV unlevered × – (1 –TC) × × = 5 costs project A digression on floatation costs Oh by the way, flotation costs are deductible. So the present value of the after-tax flotation costs are

42. 5 D×TC 5 UCFt S S + = 0.01 (1 + rf)t (1 + r0)t t = 1 t = 1 0.99 3 3 5 ×PVunlevered TC×rD× 5 5 S project + (1 + rD)t t = 1 = PVunlevered PV unlevered × – (1 –TC) × × project project PV levered + PVdepreciation + PVinterest – PVflotation project tax shield tax shield costs Hamilos Worldwide Using APV

43. = PVunlevered project PV levered + PVdepreciation + PVinterest – PVflotation project tax shield tax shield costs Hamilos Worldwide Using APV

44. PVlevered PVlevered PVlevered PVlevered PVlevered PVlevered PVlevered project project project project project project project –0.08011× + 0.00424× = $4,547,238.71 $4,547,238.71 $4,547,238.71 = = = PVunlevered 1 –0.08011 + 0.00424 0.92413 project PV levered + PVdepreciation –PVflotation + PVinterest project tax shield costs tax shield Hamilos Worldwide Using APV = $3,283,529.57 + $1,263,709.14 + 0.08011× – 0.00424 × = $4,920,563.66

45. Hamilos Worldwide Using APV

46. Hamilos Worldwide Using FTE • Using the FTE methodology, comment on the desirability of this project. Since the bondholders are financing $2,952,338.20, the shareholders only have to pony up $2,047,661.80 = $5,100,000 – $2,952,338 Thus the year-zero levered cash flow is $2,047,661.80 + after-tax flotation costs = –$2,147,662 –$20,875.11 LCF0 = –$2,168,536.92

47. Hamilos Worldwide Using FTE LCF0 = –$2,168,536.92 The LCF for years one through 4 is $1,091,670.41 = = [$1.5m – $1m – .125×$2,952,338.20 ] ×(1 – .30) + $1,000,000 The LCF for year 5 is –$1,410,667.79 = $1,091,670.41 – $2,952,338.20 + $100,000 + $500,000(1 – .30) The NPV at rs = 23.775% is –$18,759.67

48. Summary Hamilos Worldwide • Using WACC NPV = –$322,677.06 • Using APV NPV = $48,277.71 • Using FTE NPV = –$18,759.67 • Should we accept or reject the project? • If the dollar amount of debt is known over the project’s life, (in this example the amount of debt would be $2,952,338.20) then the APV method is appropriate and the firm would accept the project. • Otherwise, the firm should reject the project.