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• P=Div/ke=1/0.10=\$10\n\nScenario 1: Ex: ke=10%; ROE=15%; b=50%; g=ROExb; Div0=\$0.50; P0=\$10; g=0.15x0.5=7.5%\n\nP1=Div1/(k-g)=0.5x(1.075)/(0.10-0.075)=\$21.50\n\nScenario 2: Ex: ke=10%; ROE=5%; b=50%; g=ROExb; Div0=\$0.50; P0=\$10; g=0.05*0.5=2.5%\n\nP1=0.5*(1.025)/(0.1-0.025)=\$6.83\n
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• ### Chapter 13

1. 1. Chapter 13: Risk, Return, and Capital Budgeting
2. 2. 13- Chapter Outline 13.1 The Cost of Equity Capital 13.2 Estimation of Beta 13.3 Determinants of Beta 13.4 Extensions of the Basic Model 13.5 Estimating Bombardier’s Cost of Capital 13.6 Reducing the Cost of Capital 13.7 Summary and Conclusions McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
3. 3. 13- What’s the Big Idea? • In ACTSC 371, capital budgeting focused on the appropriate size and timing of cash flows. • This chapter discusses the appropriate discount rate when cash flows are risky. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
4. 4. 13- 13.1 The Cost of Equity Capital personal ke Shareholder Firm with invests in excess cash Pay cash dividend financial asset A firm with excess cash can either pay a dividend or make a capital investment company ROE Shareholder’s Invest in project Terminal Value Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
5. 5. 13- How Does the Company Decide? • If a company has projects that are positive NPV (ie the projects’ ROEs are greater than the investors’ personal expected rate of return (ke) ROE > Ke then the company should invest the funds. (retain and invest the funds) • If the Company does not have projects for which the ROE is greater than the investors’ ke, then it should dividend it out. ROE < Ke • The investor can get a better return than the company in the 2nd situation. • g =ROE × b (ROE x retention ratio), so the g will increase to compensate for the investor not having the funds in hand if the ROE > ke McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
6. 6. 13- ROE=Corporate ke; ke=personal We will look at this more later, but.... Initially, McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
7. 7. 13- This was Simplified.... •We used a constant growth Gordon DDM model here for illustration purposes. •We would often use a multi-stages DDM or other DCF model to value the stock. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
8. 8. 13- The Cost of Equity • From the firm’s perspective, the expected return is the Cost of Equity Capital : • To estimate a firm’s cost of equity capital, we need to know three things: 1. The risk-free rate, RF 2. The market risk premium, 3. The company beta, McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
9. 9. 13- 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? McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
10. 10. 13- Example (continued) Suppose Stansfield Enterprises is evaluating the following non-mutually exclusive projects. Each costs \$100 and lasts one year. Project Project β Project’s IRR NPV at Estimated Cash 30% Flows Next Year A 2.5 \$150 50% \$15.38 B 2.5 \$130 30% \$0 C 2.5 \$110 10% -\$15.38 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
11. 11. 13- Using the SML to Estimate the Risk- Adjusted Discount Rate for Projects Good Project IRR A projects 30% B C Bad projects 5% Firm’s risk (beta) 2.5 An all-equity firm should accept an (investment type) project whose IRR exceeds the cost of equity capital and reject (investment type) projects whose IRRs fall short of the cost of capital. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
12. 12. 13- 13.2 Estimation of Beta: Measuring Market Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P/TSX index, is used to represent the market. – We talk a lot in terms of how the market cannot be identified. – This is an idealized view of the world. Beta - Sensitivity of a stock’s return to the return on the market portfolio.  May be calculated two common ways. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
13. 13. 13- 13.2 Estimation of Beta • Theoretically, the calculation of beta is straightforward: • Problems 1. Betas may vary over time. 2. The sample size may be inadequate. 3. Betas are influenced by changing financial leverage and business risk. • Solutions – Problems 1 and 2 (above) can be moderated by more sophisticated statistical techniques. – Problem 3 can be lessened by adjusting for changes in business and financial risk. – Look at average beta estimates of comparable firms in the industry. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
14. 14. 13- 13.2 Estimation of Beta • As mentioned… Beta, merely being the above calculation, is open to fluctuations in the market. (or a regression of some kind) • It is important to look at the date so as to look forward to what we anticipate to happen, not just what we have seen in the past. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
15. 15. 13- Beta Aside McGraw-Hill Ryerson 15 © 2005 McGraw–Hill Ryerson Limited
16. 16. 13- Beta Aside • Estimates of beta based on many years of data may be of little relevance because of business risks that are currently being encountered. McGraw-Hill Ryerson 15 © 2005 McGraw–Hill Ryerson Limited
17. 17. 13- Beta Aside • Estimates of beta based on many years of data may be of little relevance because of business risks that are currently being encountered. • Typically, 1 or 5 years of data (month end closes =60 data points) McGraw-Hill Ryerson 15 © 2005 McGraw–Hill Ryerson Limited
18. 18. 13- Beta Aside • Estimates of beta based on many years of data may be of little relevance because of business risks that are currently being encountered. • Typically, 1 or 5 years of data (month end closes =60 data points) • Some corrections may have to be considered because of thin trading or other market inefficiencies McGraw-Hill Ryerson 15 © 2005 McGraw–Hill Ryerson Limited
19. 19. 13- Stability of Beta • Most analysts argue that betas are generally stable for firms remaining in the same industry. • That’s not to say that a firm’s beta can’t change. – Changes in product line – Changes in technology – Deregulation – Changes in financial leverage McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
20. 20. 13- Some have argued... • That the beta of a company tend towards 1 (the beta of the market) – This is because the beta starts as non-one because the company may have started as a niche player of project company and then eventually diversifies. Marker Beta = 1 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
21. 21. 13- Betas Get Adjusted • BMO and other companies use averages and other methods that include leading and lagging beta values – Ex: estimate beta for the past, coincident and future 60 months. • Average then in some manner. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
22. 22. 13- Using an Industry Beta • It is frequently argued that one can better estimate a firm’s beta by involving the whole industry. – If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta. – If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta. • Don’t forget about adjustments for financial leverage. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
23. 23. 13- 13.3 Determinants of Beta • Business Risk – Cyclicity of Revenues – Operating Leverage • Financial Risk – Financial Leverage McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
24. 24. 13- Cyclicality of Revenues • Highly cyclical stocks have high betas. – Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle. – Transportation firms and utilities are less dependent upon the business cycle. (Investment Trust candidates) • Note that cyclicality is not the same as variability— stocks with high standard deviations need not have high betas. – Movie studios have revenues that are variable, depending upon whether they produce “hits” or “flops ,” but their revenues are not especially dependent upon the business cycle. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
25. 25. 13- There is a difference between... More volatile returns and a more pronounced movement of returns relative to the market. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
26. 26. 13- Operating Leverage • The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs. • Operating leverage increases as fixed costs rise and variable costs fall. • Operating leverage magnifies the effect of cyclicity on beta. (assuming a relationship between the stock and market exists) • The degree of operating leverage is given by: McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
27. 27. 13- Operating Leverage Total Δ EBIT \$ costs Fixed costs Δ Volume Fixed costs Volume Operating leverage increases as fixed costs rise and variable costs fall. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
28. 28. 13- From an Analyst Perspective Investopedia explains Operating Leverage The higher the degree of operating leverage, the greater the potential danger from forecasting risk. Higher DOL ➔ Greater potential risk That is, if a relatively small error is made in forecasting sales, it can be magnified into large errors in cash flow projections. The opposite is true for businesses that are less leveraged. A business that sells millions of products a year, with each contributing slightly to paying for fixed costs, is not as dependent on each individual sale McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
29. 29. 13- Financial leverage arises when a firm decides to finance a majority of its assets by taking on debt. •Firms do this when they are unable to raise enough capital by issuing shares in the market to meet their business needs. •When a firm takes on debt, it becomes a liability on which it must pay interest. •Equity issued is not debt but the equity holder expects dividend or that the shares will increase in value (capital gain) McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
30. 30. 13- Financial Leverage and Beta • Operating leverage refers to the sensitivity to the firm’s fixed costs of production. • Financial leverage is the sensitivity of a firm’s fixed costs of financing. • The relationship between the betas of the firm’s debt, equity, and assets is given by: • Financial leverage always increases the equity beta relative to the asset beta. (Think “portfolio”) Increase Debt, Increase Be McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
31. 31. 13- Financial Leverage and Beta: Example Consider Grand Sport, Inc., which is currently all-equity and has a beta of 0.90. The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity. Since the firm will remain in the same industry, its asset beta should remain 0.90. However, assuming a zero beta for its debt, its equity beta would become twice as large:  Debt   1 âEquity  Equity  = 0.90 × 1 + 1  = 1.80 = âAsset × 1 +      McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
32. 32. 13- Preferred Shares • Often put into the debt component • Or, there may be a separate beta for the preferred shares, thus there would be different weighting coefficients for the three components. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
33. 33. 13- Both firms have total assets of \$100 m Nodett is all equity financed; Somdett has \$40 m in debt. ROE=1.08/60x100=1.8% ? If debt = 0, then 0.6x5=3 McGraw-Hill Ryerson 32 © 2005 McGraw–Hill Ryerson Limited
34. 34. 13- 13.4 Extensions of the Basic Model • The Firm versus the Project • The Cost of Capital with Debt McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
35. 35. 13- The Firm versus the Project • Any project’s cost of capital depends on the use to which the capital is being put—not the source. • Therefore, it depends on the risk of the project and not the risk of the company. • In other words, you may be able to borrow cheaply and then put that cheap cash into a really risky project. Bad idea! McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
36. 36. 13- Capital Budgeting & Project Risk Project IRR The SML can tell us why: Incorrectly accepted negative NPV projects Hurdle rate Incorrectly rejected rf positive NPV projects Firm’s risk (beta) βFIRM A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
37. 37. 13- Capital Budgeting & Project Risk Suppose the Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%, the market risk premium is 10%, and the firm’s beta is 1.3. 17% = 4% + 1.3 × [14% – 4%] This is a breakdown of the company’s investment projects: 1/3 Automotive retailer β = 2.0 1/3 Computer Hard Drive Mfr. β = 1.3 1/3 Electric Utility β = 0.6 average β of assets = 1.3 When evaluating a new electrical generation investment, which cost of capital should be used? McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
38. 38. 13- Capital Budgeting & Project Risk Project IRR 24% Investments in hard drives or auto retailing 17% should have higher 10% discount rates. Firm’s risk (beta) 0.6 1.3 2.0 r = 4% + 0.6×(14% – 4% ) = 10% 10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
39. 39. 13- The Cost of Capital with Debt • The Weighted Average Cost of Capital is given by: WACC  S   B  rWACC =  × rS +   × rB × (1 − TC ) S +B S +B • It is because interest expense is tax-deductible that we multiply the last term by (1- TC) • Tax shield McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
40. 40. 13- WACC Spreadsheet Errata • I implied that if you simply graph D/E versus WACC, you will get a minimum point • Also, that the D/E that is the minimum will be the ‘optimum’ capital structure • The latter is true but the former is a but off • Debt cost (kd) will change over time. • As more debt is added, then the cost of the debt goes up; ke also changes • This will cause a minimum point with an optimum capital structure McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
41. 41. 13- Market Market Market Debt/Value Equity/Value Debt/Equity Debt B-T Cost of Ratio (wd) Ratio (wc) Ratio (D/S) Rating Debt (rd) 0 1 0.00 A 7.00% 0.2 0.8 0.25 BBB 8.00% 0.4 0.6 0.67 BB 10.00% 0.6 0.4 1.50 C 12.00% 0.8 0.2 4.00 D 15.00% Inputs provided in the problem: Risk-free rate 5% Market risk premium 6% Unlevered beta 1.2 Tax rate 40% Debt/Value Equity/Value Debt/Equity A-T Cost of Leveraged Cost of Ratio (wd) Ratio (wc) Ratio (D/S) Debt (rd) Beta Equity WACC 0.0 1.0 0.00 4.20% 1.20 12.20% 12.20% 0.2 0.8 0.25 4.80% 1.38 13.28% 11.58% 0.4 0.6 0.67 6.00% 1.68 15.08% 11.45% 0.6 0.4 1.50 7.20% 2.28 18.68% 11.79% 0.8 0.2 4.00 9.00% 4.08 29.48% 13.10% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
42. 42. 13- McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
43. 43. 13- 13.5 Estimating Bombardier’s Cost of Capital • We aim at estimating Bombardier’s cost of capital, as of January 31, 2004. • First, we estimate the cost of equity and the cost of debt. – We estimate an equity beta to estimate the cost of equity. – We can often estimate the cost of debt by observing the YTM of the firm’s debt. • Second, we determine the WACC by weighting these two costs appropriately. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
44. 44. 13- 13.5 Estimating Bombardier’s Cost of Capital • Bombardier’s beta is 1.48; the (current) risk-free rate is 4.61%, and the (historical) market risk premium is 3.84%. • Thus the cost of equity capital is We could have worked up ke with APT of a build-up McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
45. 45. 13- 13.5 Estimating Bombardier’s Cost of Capital • The yield on the company’s 6.4% 22 December 2006 bond is 5.4%. • Since this is a short bond, we add 1.2% to obtain a 6.6% cost of issuing long-term debt. Where did this come from? [horizon risk] • The firm is in the 33.6% marginal tax rate. • Thus the cost of debt is McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
46. 46. 13- 13.5 Estimating Bombardier’s Cost of Capital • To calculate the cost of capital, we need to estimate the value weights for equity and debt: • We simplify, and combine preferred stock with common stock: S=504+2032+8403 B=8074 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
47. 47. 13- McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
48. 48. 13- 13.5 Estimating Bombardier’s Cost of Capital • Bombardier’s WACC as of January 31, 2004, is given by:  S   B  rWACC =  × rS +   × rB × (1 − TC ) S+B S +B 7.78-percent is Bombardier’s cost of capital. It should be used to discount any project where one believes that the project’s risk is equal to the risk of the firm as a whole, and the project has the same leverage as the firm as a whole. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
49. 49. 13- This is a point in time estimate... •As we have seen, WACC is a moving target, as it is impacted by capital structure (increasing leverage) •Beta is impacted by leverage •kd and ke are both impacted by debt level (capital structure) •WACC is used to discount CFs where there will be debt included. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
50. 50. 13- Build up Methodology © 2009 Valuation Products and Services, LLC McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
51. 51. 13- 13.6 Reducing the Cost of Capital • What is Liquidity? • Liquidity, Expected Returns, and the Cost of Capital • Liquidity and Adverse Selection • What the Corporation Can Do McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
52. 52. 13- What is Liquidity? • The idea that the expected return on a stock and the firm’s cost of capital are positively related to risk is fundamental. • Recently a number of academics have argued that the expected return on a stock and the firm’s cost of capital are negatively related to the liquidity of the firm’s shares as well. • The trading costs of holding a firm’s shares include brokerage fees, the bid-ask spread, and market impact costs. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
53. 53. 13- Less liquidity equals... • Larger bid/ask spreads • Larger ke in the minds of the investors (to compensate for the risk of not being able to sell the stock quickly) • Lower stock prices McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
54. 54. 13- Liquidity, Expected Returns, and the Cost of Capital • The cost of trading an illiquid stock reduces the total return that an investor receives. • Investors thus will demand a high expected return when investing in stocks with high trading costs. • This high expected return implies a high cost of capital to the firm. High costs because in IPO they get less funds. • Illiquid stocks get an ‘illiquidity premium’; reflects risk in holding the stock. • The premium is fine for a long-term investor, not a short term. • Lower liquidity is reflected in the discount rate and thus drops the price. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
55. 55. 13- Liquidity and the Cost of Capital Cost of Capital Liquidity An increase in liquidity, i.e., a reduction in trading costs, lowers a firm’s cost of capital. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
56. 56. 13- Liquidity and Adverse Selection • There are a number of factors that determine the liquidity of a stock. • One of these factors is adverse selection. • This refers to the notion that traders with better information can take advantage of specialists and other traders who have less information. • The greater the heterogeneity of information, the wider the bid-ask spreads, and the higher the required return on equity. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
57. 57. 13- What the Corporation Can Do • The corporation has an incentive to lower trading costs since this would result in a lower cost of capital. • A stock split would increase the liquidity of the shares. (more market for a lower cost share) • A stock split would also reduce the adverse selection costs thereby lowering bid-ask spreads. (the lower cost share more accessible to all) • This idea is a new one and empirical evidence is not yet in. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
58. 58. 13- What the Corporation Can Do • Companies can also facilitate stock purchases through the Internet. • Direct stock purchase plans and dividend reinvestment plans (DRIPS) handled on-line allow small investors the opportunity to buy securities cheaply. • The companies can also disclose more information, especially to security analysts, to narrow the gap between informed and uninformed traders. This should reduce spreads. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
59. 59. 13- Another Way….Dutch Auction McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
60. 60. 13- Another Way….Dutch Auction • Ex: Google McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
61. 61. 13- Another Way….Dutch Auction • Ex: Google McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
62. 62. 13- Another Way….Dutch Auction • Ex: Google • Reduces IPO expenses McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
63. 63. 13- Another Way….Dutch Auction • Ex: Google • Reduces IPO expenses • Called an Open IPO McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
64. 64. 13- Another Way….Dutch Auction • Ex: Google • Reduces IPO expenses • Called an Open IPO • Bids are submitted for a certain number of shares. McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
65. 65. 13- Another Way….Dutch Auction • Ex: Google • Reduces IPO expenses • Called an Open IPO • Bids are submitted for a certain number of shares. • No ‘book’ is built. McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
66. 66. 13- Another Way….Dutch Auction • Ex: Google • Reduces IPO expenses • Called an Open IPO • Bids are submitted for a certain number of shares. • No ‘book’ is built. • Shares are allocated to the winning bidders until the issue is sold out. McGraw-Hill Ryerson 59 © 2005 McGraw–Hill Ryerson Limited
67. 67. 13- 13.7 Summary and Conclusions • The expected return on any capital budgeting project should be at least as great as the expected return on a financial asset of comparable risk. Otherwise the shareholders would prefer the firm to pay a dividend. • The expected return on any asset is dependent upon β. • A project’s required return depends on the project’s β. • A project’s β can be estimated by considering comparable industries or the cyclicality of project revenues and the project’s operating leverage. • If the firm uses debt, the discount rate to use is the rWACC. • In order to calculate rWACC, the cost of equity and the cost of debt applicable to a project must be estimated. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited