1. Chapter 15 Required Returns and the Cost of Capital

2. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 1 Chapter Objectives Estimate values for the costs of debt and preference shares. Calculate the WACC. Apply the dividend growth model approach and the SML approach to determine the cost of equity. Discuss alternative approaches to estimating a required rate. Discuss the effects of flotation costs on WACC and the NPV of a project.

3. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 2 The Cost of Capital Vocabulary - the following all mean the same thing:  required return  appropriate discount rate  cost of capital Cost of Capital is the required rate of return on the various types of financing. The overall cost of capital is a weighted average of the individual required rates of return (costs).

4. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 3 The Cost of Capital When we say a firm has a “ cost of capital ” of, for example, 12%, we are saying:  The firm can only have a positive NPV on a project it return exceeds 12%.  The firm must earn 12% just to compensate investors for the use of their capital in a project.  The use of capital in a project must earn 12% or more, not that it will necessarily cost 12% to borrow funds for the project. Thus cost of capital depends primarily on the USE of funds, not the SOURCE of funds.

5. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 4 The assumption is made that firm ’ s capital structure is fixed - a firm ’ s cost of capital then reflects both cost of debt and cost of equity. Type of Financing Mkt ValWeight Long-Term Debt $ 35M 35% Preferred Stock$ 15M 15% Common Stock Equity $ 50M 50% $ 100M 100% Market Value of Long-Term Financing

6. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 5 Cost of Debt Cost of Debt is the required rate of return on investment of the lenders of a company. 012 n M III P )1(1 )1( )1()1( 1 k k I k M k I k M P n n n i in    ×        

7. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 6 Subtract Taxes from the interest of the bond and recalculate yield figures. A B Invest. 1000 1000 EBIT 200 200 -IE 0 50 EBT 200 150 50× （ 1-33% ） -Taxes （ T=33% ） 66 - 49.5 =16.5 万 Net Income 134 100.5 Adjustment to Cost of Debt Interest 33.5 16.549.5 Income tax

8. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 7 Adjustment to Cost of Debt )1()1( 1 k I（1-T）I（1-T） k M P n i in       Subtract Taxes from the interest of the bond and recalculate yield figures.

9. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 8 Flotation Costs The cost of implementing any financing decision must be incorporated into the cash flows of the project being evaluated. Only the incremental costs of financing should be included. Such as underwriting, legal, listing, and printing fees. Subtract Flotation Costs from the price of the security and recalculate yield figures. )1()1( 1 k I（1-T）I（1-T） k M P -F n i in      

10. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 9 Cost of Preferred Stock is the required rate of return on investment of the preferred shareholders of the company. Cost of Preferred Stock 012 n DDD P … P -F )1( 1 k D n i i      k D

11. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 10 Example Assume that Basket Wonders (BW) has preferred stock outstanding with par value of $100, dividend per share of $6.30, and a current market value of $70 per share.  k P = $6.30 / $70 k P = 9% Determination of the Cost of Preferred Stock

12. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 11 Dividend Discount Model Dividend Discount Model Capital-Asset Pricing Model Capital-Asset Pricing Model Before-Tax Cost of Debt plus Risk Premium Before-Tax Cost of Debt plus Risk Premium Cost of Equity Approaches

13. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 12 cost of equity capital The cost of equity capital, k e, is the discount rate that equates the present value of all expected future dividends with the current market price of the stock. D 1 D 2 D (1+k e ) 1 (1+k e ) 2 (1+k e ) +... ++ P 0 =   Dividend Discount Model

14. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 13 constant dividend growth assumption The constant dividend growth assumption reduces the model to: k e = ( D 1 / P 0 ) + g Assumes that dividends will grow at the constant rate “ g ” forever. “ g ” depends on historical average. Constant Growth Model

15. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 14 Example Assume that Basket Wonders (BW) has common stock outstanding with a current market value of $64.80 per share, current dividend of $3 per share, and a dividend growth rate of 8% forever.  k e = ( D 1 / P 0 ) + g k e = ($3(1.08) / $64.80) +.08 k e.1313% k e =.05 +.08 =.13 or 13% Determination of the Cost of Equity Capital

16. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 15 D 0 (1+g 1 ) t D a (1+g 2 ) t-a (1+k e ) t P 0 = growth phases assumption leads to the following formula (assume 3 growth phases): The growth phases assumption leads to the following formula (assume 3 growth phases):    t=1 a t=a+1 b t=b+1  D b (1+g 3 ) t-b (1+k e ) t +  Growth Phases Model

17. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 16 The cost of equity capital, k e, is equated to the required rate of return in market equilibrium. The risk-return relationship is described by the Security Market Line (SML). k e = R j = R f + (R m - R f )  j Capital Asset Pricing Model

18. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 17 Example Assume that Basket Wonders (BW) has a company beta of 1.25. Research by Julie Miller suggests that the risk- free rate is 4% and the expected return on the market is 11.2%.  k e = R f + (R m - R f )  j = 4% + (11.2% - 4%)1.25 k e 13% k e = 4% + 9% = 13% Determination of the Cost of Equity (CAPM)

19. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 18 The cost of equity capital, k e, is the sum of the before-tax cost of debt and a risk premium in expected return for common stock over debt. k e = k d + Risk Premium*  Risk premium is not the same as CAPM risk premium. Before-Tax Cost of Debt Plus Risk Premium

20. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 19 Example Assume that Basket Wonders (BW) typically adds a 3% premium to the before-tax cost of debt.  k e = k d + Risk Premium = 10% + 3% k e 13% k e = 13% Determination of the Cost of Equity (k d + R.P.)

21. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 20 WACC Weighted Average Cost of Capital (WACC) - The expected rate of return on a portfolio of all the firm’s securities. Company cost of capital = Weighted average of debt and equity returns.

22. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 21 WACC Three Steps to Calculating Cost of Capital: 1. Calculate the value of each security as a proportion of the firm’s market value. 2. Determine the required rate of return on each security. 3. Calculate a weighted average of these required returns.

23. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 22 Weighted Average Cost of Capital (WACC) 1 kiwikiwi kwkw n i    K w ——WACC ； K i —— The after-tax cost of the ith method of financing ； W i —— The weight given to the ith method of financing 。

24. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 23 A measure of business performance. It is another way of measuring that firms are earning returns on their invested capital that exceed their cost of capital. Specific measure developed by Stern Stewart & Company in late 1980s. It is a firm ’ s net operating profit after tax (NOPAT) minus a dollar-amount cost of capital charge for the capital employed. Economic Value Added

25. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 24 Since a cost is charged for equity capital also, a positive EVA generally indicates shareholder value is being created. Based on Economic NOT Accounting Profit. Economic Value Added EVA = NOPAT – [ Cost of Capital x Capital Employed ] = EBIT(1-T) – K w C

26. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 25 Use of CAPM in Project Selection  Initially assume all-equity financing.  Determine project beta.  Calculate the expected return.  Adjust for capital structure of firm.  Compare cost to IRR of project. Determining Project-Specific Required Rates of Return

27. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 26 Difficulty in Determining the Expected Return Determining the SML  Locate a proxy for the project (much easier if asset is traded).  Plot the Characteristic Line relationship between the market portfolio and the proxy asset excess returns.  Estimate beta and create the SML.

28. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 27 Project Acceptance and/or Rejection SML X X X X X X X O O O O O O O SYSTEMATIC RISK (Beta) EXPECTED RATE OF RETURN RfRf Accept Reject

29. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 28 Example Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100-percent equity financed. Assume a risk-free rate of 5-percent and a market risk premium of 10-percent. What is the appropriate discount rate for an expansion of this firm? %105.2%5  R%30  R

30. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 29 Example (continued) Suppose Stansfield Enterprises is evaluating the following non-mutually exclusive projects. Each costs $100 and lasts one year. Project Project  Project’s Estimated Cash Flows Next Year IRRNPV at 30% A2.5$15050%$15.38 B2.5$13030%$0 C2.5$11010%-$15.38

31. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 30 Using the SML to Estimate the Risk- Adjusted Discount Rate for Projects An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall short of the cost of capital. Project IRR Firm’s risk (beta) 5% Good project Bad project 30% 2.5 A B C

32. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 31 1. Calculate the required return for Project k (all- equity financed). R k = R f + (R m - R f )  k 2. Adjust for capital structure of the firm (financing weights). Weighted Average Required Return = [ k i ][% of Debt] + [ R k ][% of Equity] Determining Project-Specific Required Rate of Return

33. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 32 Example Assume a computer networking project is being considered with an IRR of 19%. Examination of firms in the networking industry allows us to estimate an all-equity beta of 1.5. Our firm is financed with 70% Equity and 30% Debt at k i =6%. The expected return on the market is 11.2% and the risk-free rate is 4%. Project-Specific Required Rate of Return Example

34. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 33  k e = R f + (R m - R f )  j = 4% + (11.2% - 4%)1.5 k e 14.8% k e = 4% + 10.8% = 14.8% WACC =.30(6%) +.70(14.8%) = 1.8% + 10.36%= 12.16% IRR = 19% > WACC = 12.16% Do You Accept the Project?

35. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 34 Determining Group-Specific Required Rates of Return Use of CAPM in Project Selection:  Initially assume all-equity financing.  Determine group beta.  Calculate the expected return.  Adjust for capital structure of group.  Compare cost to IRR of group project.

36. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 35 Comparing Group-Specific Required Rates of Return Group-Specific Required Returns Company Cost of Capital Systematic Risk (Beta) Expected Rate of Return

37. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 36 Amount of non-equity financing relative to the proxy firm. Adjust project beta if necessary. Standard problems in the use of CAPM. Potential insolvency is a total-risk problem rather than just systematic risk (CAPM). Qualifications to Using Group- Specific Rates

38. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 37 Adjusted Present Value (APV) is the sum of the discounted value of a project ’ s operating cash flows plus the value of any tax-shield benefits of interest associated with the project ’ s financing minus any flotation costs. Adjusted Present Value APV = Unlevered Project Value + Value of Project Financing

39. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 38 Adjusted Present Value 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

40. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 39 Example Assume Basket Wonders is considering a new $425,000 automated basket weaving machine that will save $100,000 per year for the next 6 years. The required rate on unlevered equity is 11%. BW can borrow $180,000 at 7% with $10,000 after-tax flotation costs. Principal is repaid at $30,000 per year (+ interest). The firm is in the 40% tax bracket. NPV and APV Example

41. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 40 to an all-equity-financed firm  What is the NPV to an all-equity-financed firm? NPV = $100,000[PVIFA 11%,6 ] - $425,000 NPV = $423,054 - $425,000 NPV = -$1,946 Basket Wonders NPV Solution

42. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 41  What is the APV? First, determine the interest expense. Int Yr 1($180,000)(7%) = $12,600 Int Yr 2( 150,000)(7%) = 10,500 Int Yr 3( 120,000)(7%) = 8,400 Int Yr 4( 90,000)(7%) = 6,300 Int Yr 5( 60,000)(7%) = 4,200 Int Yr 6( 30,000)(7%) = 2,100 Basket Wonders APV Solution

43. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 42  Second, calculate the tax-shield benefits. TSB Yr 1($12,600)(40%) = $5,040 TSB Yr 2( 10,500)(40%) = 4,200 TSB Yr 3( 8,400)(40%) = 3,360 TSB Yr 4( 6,300)(40%) = 2,520 TSB Yr 5( 4,200)(40%) = 1,680 TSB Yr 6( 2,100)(40%) = 840 Basket Wonders APV Solution

44. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 43  Third, find the PV of the tax-shield benefits. TSB Yr 1($5,040)(.901) = $4,541 TSB Yr 2( 4,200)(.812) = 3,410 TSB Yr 3( 3,360)(.731) = 2,456 TSB Yr 4( 2,520)(.659) = 1,661 TSB Yr 5( 1,680)(.593) = 996 TSB Yr 6( 840)(.535) = 449 PV = $13,513 Basket Wonders APV Solution

45. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 44  What is the APV? APV = NPV + PV of TS - Flotation Cost APV = -$1,946 + $13,513 - $10,000 APV = $1,567 Basket Wonders NPV Solution

46. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 45 APV Example 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.

47. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 46 APV Example: Cost 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.  Let’s work our way through the four terms in this equation: NWC is riskless, so we discount it at r f. Salvage value should have the same risk as the rest of the firm’s assets, so we use r 0. + PV depreciation tax shield + PV interest tax shield PV unlevered project APV = –Cost +

48. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 47 APV Example: PV unlevered project  Turning our attention to the second term, +PV depreciation tax shield +PV interest tax shield PV unlevered project APV = –$4,873,561.25+ is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%. PV unlevered project

49. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 48 APV Example: PV depreciation tax shield  Turning our attention to the third term, is the present value of the tax savings due to depreciation discounted at the risk free rate: r f = 4% PV depreciation tax shield +PV depreciation tax shield +PV interest tax shield $3,095,899 APV = –$4,873,561.25+ PV depreciation tax shield

50. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 49 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: r D = 12.5% PV interest tax shield $3,095,899 + $1,513,619 + PV interest tax shield APV = –$4,873,561.25+

51. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 50 APV Example: Adding it all up Since the project has a positive APV, it looks like a go.  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 + PV depreciation tax shield + PV interest tax shield PV unlevered project APV = –Cost +

52. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 51 A Comparison of the APV and WACC Approaches Two approaches attempt the same task:valuation in the presence of debt financing. Guidelines:  Use WACC 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.

53. Copyright  2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e by Van Horne and Wachowicz. Slides prepared by Wu Xiaolan 52 Summary: APV and WACC APVWACC Initial Investment AllAll Cash FlowsUCFUCF Discount Rates r 0 r WACC PV of financing effectsYesNo Which approach is best? Use APV when the level of debt is constant Use WACC when the debt ratio is constant  WACC is by far the most common