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### Chap 4.pdf beta

1. 1. Cost of Capital and Leverage. WACC Chapter 4
2. 2. OutlineProject selection for a levered firmBeta and cost of equity of a levered firm Hamada equationWACCProject selection in a diversified firm Mensac case 2
3. 3. What types of capital do firms use?DebtPreferred stockCommon equity Existing shareholders New stock 3
4. 4. Do different investors ask for the same return?Example: A company has the following EBITevery year (see the table next page). kRF=4%,the market risk premium is 6%. If the companyis 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. 5. Example (2) Economy Bad Avg. GoodProb. 0.25 0.50 0.25EBIT 5,000 10,000 15,000Cost 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. 6. Example (3)Probability 0.25 0.5 0.25EBIT \$ 5,000.00 \$ 10,000.00 \$ 15,000.00Interest \$ - \$ - \$ -EBT \$ 5,000.00 \$ 10,000.00 \$ 15,000.00Taxes \$ - \$ - \$ -NI \$ 5,000.00 \$ 10,000.00 \$ 15,000.00EPS \$ 5.00 \$ 10.00 \$ 15.00Average NI \$ 10,000Average EPS \$ 10Standard deviation 3.54Value of equity \$ 100,000Share price \$ 100.00 6
7. 7. Example (4)For the levered firm let us assume that thedebt is risk-free and check, whether this isthe 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. 8. Example (5)The cost of equity of the levered firmbecomescost 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. 9. Beta and cost of equity of a levered firm: Hamada equation (risk-free debt)Because the increased use of debt causes boththe costs of debt and equity to increase, we needto estimate the new cost of equityThe Hamada equation attempts to quantify theincreased cost of equity due to financial leverageIt uses the unlevered beta of a firm, whichrepresents the risk of a firm as if it had no debtHamada equation assumes that the debt is risk-free 9
10. 10. Hamada equation (cont’d) βL = βU [1 + (1 – T)(D/E)]where T is the tax rate; D/E is the debt-equityratio and βU is the beta of equity of an unleveredfirm with the same operating cash flowIn our example βU = 1, D/E = 400/600 = 2/3βL = 1(1+0.67)=1.67kLS = 4% + 1.67 x 6% = 14 %Notice that kLS = kUS [1 + (1 – T)(D/E)]-kRF (1 – T)(D/E) 10
11. 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 Dβ = β 1 + (1 − T ) L S U S − (1 − T ) β D E E 11
12. 12. ExampleThe risk-free rate is 6%, as is the marketrisk premium. The unlevered beta of thefirm 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. 13. Example (2)For riskless debt we have βL = βU[1 + (1 – T)(D/E)] β kL = kRF + (kM – kRF)βL 13
14. 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. 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. 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. 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. 18. Determining levered cost of equity, kLsFind kU directly D k + (1 − t c ) L S kD kS = U E D 1 + (1 − t c )Find average kUs EFind kLs L S U S D U E ( k = k + (1 − tC ) k S − k D ) 18
19. 19. WACC E L DWACC = k S + (1 − tc )k D V V E Dif k D = k f , WACC = k U S + (1 − tc ) V V 19
20. 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. 21. Example: Find WACC 2βL = 0.95× 1+ (1− 0.4) = 1.33 3k = .07 +1.33×.06 = 0.15 = 15% L S 1 .67WACC= ×.15 + (1− .4)× ×.10 1+ .67 1+ .67WACC= 11.4% 21
22. 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. 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 riskof an average project undertaken by thefirm. Therefore, the WACC only representsthe “hurdle rate” for a typical project withaverage risk.Different projects have different risks. Theproject’s WACC should be adjusted toreflect the project’s risk. 23
24. 24. Risk and the Cost of CapitalRate 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. 25. Divisional Cost of CapitalRate 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. 26. What are the types of project risk?Stand-alone riskCorporate riskMarket risk 26
27. 27. How is each type of risk used?Market risk is theoretically best in mostsituations.However, creditors, customers, suppliers,and employees are more affected bycorporate riskTherefore, corporate risk is also relevant 27
28. 28. How to determine the risk-adjusted cost ofcapital 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. 29. Methods for Estimating a Project’s BetaPure play: Find several publicly traded companies exclusively in project’s business Use average of their betas as proxy for project’s betaDifficulties: Sometimes it is hard to findsuch companies 29
30. 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. 31. ExampleFind the division’s market risk and cost ofcapital based on the CAPM, given theseinputs 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. 32. Example (contd.)Levered beta = 1.7, so division has moremarket 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. 33. Mensac case 33