Chap 4.pdf beta
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The document discusses the cost of capital and leverage for firms, including the weighted average cost of capital (WACC), beta and cost of equity calculations for levered firms using the Hamada equation, and how to determine the cost of capital for new projects, divisions, or companies based on their specific risk levels. Examples are provided to illustrate how to calculate WACC, levered beta, and cost of equity for firms and divisions with different capital structures and risk profiles.
![Hamada equation (cont’d)
βL = βU [1 + (1 – T)(D/E)]
where T is the tax rate; D/E is the debt-equity
ratio and βU is the beta of equity of an unlevered
firm with the same operating cash flow
In our example βU = 1, D/E = 400/600 = 2/3
βL = 1(1+0.67)=1.67
kLS = 4% + 1.67 x 6% = 14 %
Notice that
kLS = kUS [1 + (1 – T)(D/E)]-kRF (1 – T)(D/E)
10](https://image.slidesharecdn.com/chap4-pdfbeta-121113070345-phpapp01/85/Chap-4-pdf-beta-10-320.jpg)
![Example (2)
For riskless debt we have
βL = βU[1 + (1 – T)(D/E)]
β
kL = kRF + (kM – kRF)βL
13](https://image.slidesharecdn.com/chap4-pdfbeta-121113070345-phpapp01/85/Chap-4-pdf-beta-13-320.jpg)
![Example (3)
For riskless debt we have
βL = βU[1 + (1 – T)(D/E)]
βL = 1.0[1 + (1 – 0.4)( 250/ 1,750)]
β
kL = kRF + (kM – kRF)βL
kL = 6.0% + (6.0%)1.0857
14](https://image.slidesharecdn.com/chap4-pdfbeta-121113070345-phpapp01/85/Chap-4-pdf-beta-14-320.jpg)
![Example (4)
For riskless debt we have
βL = βU[1 + (1 – T)(D/E)]
βL = 1.0[1 + (0.6)(0.1429)]= 1.0857
β
kL = kRF + (kM – kRF)βL
kL = 6.0% + (6.0%)1.0857 = 12.51%
15](https://image.slidesharecdn.com/chap4-pdfbeta-121113070345-phpapp01/85/Chap-4-pdf-beta-15-320.jpg)
![Example (5)
For risky debt we have
β
kD = kRF + (kM – kRF)βD=6%+(6%)0.2 =7.2%
βL = βU[1 + (1 – T)(D/E)]-(1 – T)(D/E)βD
β
βL = 1.0[1 + (0.6)(0.1429)]- (0.6)(0.1429)0.2
= 1.0857-0.0171 = 1.0686
kL = kU + (1 – T)(D/E)(kU - kD)
kL = 12% + (0.6)(0.1429)(4.8%) = 12.411%
16](https://image.slidesharecdn.com/chap4-pdfbeta-121113070345-phpapp01/85/Chap-4-pdf-beta-16-320.jpg)
Chap 4.pdf beta
- 1. Cost of Capital and Leverage. WACC Chapter 4
- 2. Outline Project selection for a levered firm Beta and cost of equity of a levered firm Hamada equation WACC Project selection in a diversified firm Mensac case 2
- 3. What types of capital do firms use? Debt Preferred stock Common equity Existing shareholders New stock 3
- 4. Do different investors ask for the same return? Example: A company has the following EBIT every year (see the table next page). kRF=4%, the market risk premium is 6%. If the company is all-equity financed, its beta is 1 • What is the cost of equity in this case? What is the company value? If there are 1,000 shares outstanding, what is the share price? • If company wants to issue 40,000 of debt to buy back some shares, what is the cost of debt and the new cost of equity assuming no taxes? 4
- 5. Example (2) Economy Bad Avg. Good Prob. 0.25 0.50 0.25 EBIT 5,000 10,000 15,000 Cost of equity is • 4%+6%x1=10% The company value is • (0.25x5,000 + 0.5x10,000 + 0.25x15,000)/.1 =100,000 The share price is 100 5
- 6. Example (3) Probability 0.25 0.5 0.25 EBIT $ 5,000.00 $ 10,000.00 $ 15,000.00 Interest $ - $ - $ - EBT $ 5,000.00 $ 10,000.00 $ 15,000.00 Taxes $ - $ - $ - NI $ 5,000.00 $ 10,000.00 $ 15,000.00 EPS $ 5.00 $ 10.00 $ 15.00 Average NI $ 10,000 Average EPS $ 10 Standard deviation 3.54 Value of equity $ 100,000 Share price $ 100.00 6
- 7. Example (4) For the levered firm let us assume that the debt is risk-free and check, whether this is the case or not: Debt $ 40,000 Interest rate 4% Number of shares 600 Probability 0.25 0.5 0.25 EBIT $ 5,000.00 $ 10,000.00 $ 15,000.00 Interest $ 1,600.00 $ 1,600.00 $ 1,600.00 EBT $ 3,400.00 $ 8,400.00 $ 13,400.00 Taxes $ - $ - $ - NI $ 3,400.00 $ 8,400.00 $ 13,400.00 EPS $ 5.67 $ 14.00 $ 22.33 Average NI $ 8,400 Average EPS $ 14.00 Standard deviation 5.89 7
- 8. Example (5) The cost of equity of the levered firm becomes cost of equity kLS = EPS/Share price = 14/100 = 14% Why? Return to shareholders is riskier now (look at EPS volatility) It should be higher 8
- 9. Beta and cost of equity of a levered firm: Hamada equation (risk-free debt) Because the increased use of debt causes both the costs of debt and equity to increase, we need to estimate the new cost of equity The Hamada equation attempts to quantify the increased cost of equity due to financial leverage It uses the unlevered beta of a firm, which represents the risk of a firm as if it had no debt Hamada equation assumes that the debt is risk- free 9
- 10. Hamada equation (cont’d) βL = βU [1 + (1 – T)(D/E)] where T is the tax rate; D/E is the debt-equity ratio and βU is the beta of equity of an unlevered firm with the same operating cash flow In our example βU = 1, D/E = 400/600 = 2/3 βL = 1(1+0.67)=1.67 kLS = 4% + 1.67 x 6% = 14 % Notice that kLS = kUS [1 + (1 – T)(D/E)]-kRF (1 – T)(D/E) 10
- 11. Beta and cost of equity of a levered firm: risky debt If debt is risky, the cost of equity of a levered firm is found using the following equation: L S U S D U k = k + (1 − T ) k S − k D E ( ) where kD is the cost of risky debt. Similarly, for beta we can write D D β = β 1 + (1 − T ) L S U S − (1 − T ) β D E E 11
- 12. Example The risk-free rate is 6%, as is the market risk premium. The unlevered beta of the firm is 1.0. The total assets are 2,000,000 • Find the cost of equity of a levered firm if it has 250,000 of a risk-free debt • The same if the beta of debt is 0.2 12
- 13. Example (2) For riskless debt we have βL = βU[1 + (1 – T)(D/E)] β kL = kRF + (kM – kRF)βL 13
- 14. Example (3) For riskless debt we have βL = βU[1 + (1 – T)(D/E)] βL = 1.0[1 + (1 – 0.4)( 250/ 1,750)] β kL = kRF + (kM – kRF)βL kL = 6.0% + (6.0%)1.0857 14
- 15. Example (4) For riskless debt we have βL = βU[1 + (1 – T)(D/E)] βL = 1.0[1 + (0.6)(0.1429)]= 1.0857 β kL = kRF + (kM – kRF)βL kL = 6.0% + (6.0%)1.0857 = 12.51% 15
- 16. Example (5) For risky debt we have β kD = kRF + (kM – kRF)βD=6%+(6%)0.2 =7.2% βL = βU[1 + (1 – T)(D/E)]-(1 – T)(D/E)βD β βL = 1.0[1 + (0.6)(0.1429)]- (0.6)(0.1429)0.2 = 1.0857-0.0171 = 1.0686 kL = kU + (1 – T)(D/E)(kU - kD) kL = 12% + (0.6)(0.1429)(4.8%) = 12.411% 16
- 17. How to determine the cost of equity for a new company? Identify the peer companies For each peer, find its unlevered β and cost of equity using their cost of debt and D/E ratio • Try using market values of debt and equity Find the average unlevered β and kSU Find β and kSL for your company, using its cost of debt and D/E ratio 17
- 18. Determining levered cost of equity, kLs Find kU directly D k + (1 − t c ) L S kD kS = U E D 1 + (1 − t c ) Find average kUs E Find kLs L S U S D U E ( k = k + (1 − tC ) k S − k D ) 18
- 19. WACC E L D WACC = k S + (1 − tc )k D V V E D if k D = k f , WACC = k U S + (1 − tc ) V V 19
- 20. Example: Find WACC, given these inputs: Target D/E ratio = 66.7 % kD = 10% kRF = 7% Tax rate = 40% Market risk premium = 6% Industry Beta = 0.95 20
- 21. Example: Find WACC 2 βL = 0.95× 1+ (1− 0.4) = 1.33 3 k = .07 +1.33×.06 = 0.15 = 15% L S 1 .67 WACC= ×.15 + (1− .4)× ×.10 1+ .67 1+ .67 WACC= 11.4% 21
- 22. WACC Estimates for Some Large U. S. Corporations, Nov. 1999 Company WACC Intel 12.9% General Electric 11.9 Motorola 11.3 Coca-Cola 11.2 Walt Disney 10.0 AT&T 9.8 Wal-Mart 9.8 Exxon 8.8 H. J. Heinz 8.5 BellSouth 8.2 22
- 23. Should the company use the composite (company average) WACC as the hurdle rate for each of its projects? NO! The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk. Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk. 23
- 24. Risk and the Cost of Capital Rate of Return (%) Acceptance Region W ACC 12.0 H 10.5 A Rejection Region 10.0 9.5 B 8.0 L Risk 0 Risk L Risk A Risk H 24
- 25. Divisional Cost of Capital Rate of Return (%) WACC 13.0 Division H’s WACC Composite WACC 11.0 for Firm A Project H 10.0 9.0 Project L 7.0 Division L’s WACC Risk 0 RiskL Risk H RiskAverage 25
- 26. What are the types of project risk? Stand-alone risk Corporate risk Market risk 26
- 27. How is each type of risk used? Market risk is theoretically best in most situations. However, creditors, customers, suppliers, and employees are more affected by corporate risk Therefore, corporate risk is also relevant 27
- 28. How to determine the risk-adjusted cost of capital for a particular project or division? By making subjective adjustments to the firm’s composite WACC Not very scientific! By attempting to estimate what the cost of capital would be if the project/division were a stand-alone firm with the same capital structure. This requires estimating the project’s beta 28
- 29. Methods for Estimating a Project’s Beta Pure play: Find several publicly traded companies exclusively in project’s business Use average of their betas as proxy for project’s beta Difficulties: Sometimes it is hard to find such companies 29
- 30. Methods for Estimating a Project’s Beta Using Accounting beta (won’t use in the class) • Estimate the project’s beta by running regression between project’s ROA and market ROA (S&P index) Problems: • Accounting betas are not perfectly correlated with market betas (correlation is about 0.5–0.6) • Normally can’t get data on new projects’ ROAs before the capital budgeting decision has been made 30
- 31. Example Find the division’s market risk and cost of capital based on the CAPM, given these inputs Target debt/value ratio = 40% (D/E = 66.7%) kD = 10% kRF = 7% Tax rate = 40% betaDivision = 1.7 Market risk premium = 6%. 31
- 32. Example (contd.) Levered beta = 1.7, so division has more market risk than the company on average (1.33). Division’s required return on equity: ks = kRF + (kM – kRF)βDiv. = 7% + (6%)1.7 = 17.2% WACCDiv. = wdkd(1 – T) + wcks = 0.4(10%)(0.6) + 0.6(17.2%) = 12.72% 32
- 33. Mensac case 33