1. Last Study Topics Understanding of Statements Qualification of Statements Numerical

2. Today’s Study Topics Numericals Company and Project Costs of Capital Measuring the Cost of Equity

3. Continue b. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? – The correlation between the bond portfolio and the index fund is +.1. – rp = x1r1 + x2r2 – rp = (0.5 × 0.09) + (0.5 × 0.14) = 0.115 = 11.5%

4. Continue σ P 2 = x 1 2 σ 1 2 + 2x 1 x 2 σ 1 σ 2 ρ 12 + x 2 2 σ 2 2 σ P 2 = (0.5) 2 (0.10) 2 + 2(0.5)(0.5)(0.10)(0.16)(0.10) + (0.5) 2 (0.16) 2 σ P 2 = 0.0097 σ P = 0.985 = 9.85%

5. Understanding Therefore, he can do even better by investing equal amounts in the corporate bond portfolio and the index fund. His expected return increases to 11.5% and the standard deviation of his portfolio decreases to 9.85%.

6. Explain “There may be some truth in these CAPM and APT theories, but last year some stocks did much better than these theories predicted, and other stocks did much worse.” Is this a valid criticism? – No. Every stock has unique risk in addition to market risk. The unique risk reflects uncertain events that are unrelated to the return on the market portfolio. The Capital Asset Pricing Model does not predict these events.

7. Explain a. The APT factors cannot reflect diversifiable risks. – True. By definition, the factors represent macro- economic risks that cannot be eliminated by diversification. b. The market rate of return cannot be an APT factor. – False. The APT does not specify the factors.

8. Continue c. Each APT factor must have a positive risk premium associated with it; otherwise the model is inconsistent. – True. Investors will not take on non-diversifiable risk unless it entails a positive risk premium.

9. Continue d. There is no theory that specifically identifies the APT factors. – True. Different researchers have proposed and empirically investigated different factors, but there is no widely accepted theory as to what these factors should be.

10. Continue e. The APT model could be true but not very useful, for example, if the relevant factors change unpredictably. – True. To be useful, we must be able to estimate the relevant parameters. – If this is impossible, for whatever reason, the model itself will be of theoretical interest only.

11. APT Model – Consider the following simplified APT model: Factor Risk Exposures FACTOREXPECTED RISK PREMIUM Market6.4% Interest rate-0.6% Yield Spread5.1% MARKETINTEREST RATEYIELD SPREAD STOCK(b 1 )(b 2 )(b 3 ) P1.0-2.0-0.2 P21.20.3 P3.3.51.0

12. Continue a. Calculate the expected return for the following stocks. Assume r f = 5%. – For Stock P ⇒ r = (1.0)×(6.4%) + (-2.0)×(-0.6%) + (-0.2)×(5.1%) = 6.58% – For Stock P2 ⇒ r = (1.2)×(6.4%) + (0)×(-0.6%) + (0.3)×(5.1%) = 9.21% – For Stock P3 ⇒ r = (0.3)×(6.4%) + (0.5)×(-0.6%) + (1.0)×(5.1%) = 6.72%

13. Continue b. What are the factor risk exposures for the portfolio? – Factor risk exposures: b 1 (Market) = (1/3)×(1.0) + (1/3)×(1.2) + (1/3)×(0.3) = 0.83 b 2 (Interest rate) = (1/3)×(-2.0) +(1/3)×(0) + (1/3)×(0.5) = -0.50 b 3 (Yield spread) = (1/3)×(-0.2) + (1/3)×(0.3) + (1/3)×(1.0) = 0.37

14. Continue b. What is the portfolio’s expected return? r P = (0.83)×(6.4%) + (-0.50)×(-0.6%) + (0.37)×(5.1%) = 7.5%

15. Three Factors Model The following table shows the sensitivity of four stocks to the three Fama–French factors in the five years to 2001. Estimate the expected return on each stock assuming that the interest rate is 3.5%, the expected risk premium on the market is 8.8%, the expected risk premium on the size factor is 3.1%, and the expected risk premium on the book-to- market factor is 4.4%.

16. Continue Factor Sensitivities FACTORCOCA-COLAEXXON MOBILEPFIZERREEBOK Market.82.50.661.17 Size-0.29.04-.56.73 Book-to- Market.24.27-.071.14 r Coca-Cola = 3.5% + (0.82 × 8.8%) + (-0.29 × 3.1%) + (0.24 × 4.4%) = 10.87% r EXXON = 3.5% + (0.50 × 8.8%) + (0.04 × 3.1%) + (0.27 × 4.4%) = 9.21%

17. Continue r PFizer = 3.5% + (0.66 × 8.8%) + (-0.56 × 3.1%) + (-0.07 × 4.4%) = 7.26% r Reebok = 3.5% + (1.17 × 8.8%) + (0.73 × 3.1%) + (1.14 × 4.4%) = 21.08%

18. Summary Qualification of Statements. Examples. – CAPM – APT – Three Factors Model

19. Principles of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Chapter 9 McGraw Hill/Irwin Capital Budgeting and Risk

20. Today’s Study Topics Company and Project Costs of Capital Measuring the Cost of Equity Capital Structure and COC Discount Rates for Intl. Projects Estimating Discount Rates Risk and DCF

21. Introduction LONG BEFORE THE development of modern theories linking risk and expected return, smart financial managers adjusted for risk in capital budgeting. How they should treat the element of risk with respect to each and every projects of different class?

22. Continue Various rules of thumb are often used to make these risk adjustments. – For example, many companies estimate the rate of return required by investors in their securities and then use this company cost of capital to discount the cash flows on new projects.

23. COMPANY AND PROJECT COSTS OF CAPITAL The company cost of capital is defined as the expected return on a portfolio of all the company’s existing securities. It is used to discount the cash flows on projects that have similar risk to that of the firm as a whole.

24. Continue We estimated that investors require a return of 9.2% from Pfizer common stock. If Pfizer is contemplating an expansion of the firm’s existing business, it would make sense to discount the forecasted cash flows at 9.2 %. The company cost of capital is not the correct discount rate if the new projects are more or less risky than the firm’s existing business..

25. Company Cost of Capital A firm’s value can be stated as the sum of the value of its various assets. Each project should in principle be evaluated at its own opportunity cost of capital. For a firm composed of assets A and B, the firm value is;

26. Continue Here PV(A) and PV(B) are valued just as if they were mini-firms in which stockholders could invest directly. Investors would value A by discounting its forecasted cash flows at a rate reflecting the risk of A. They would value B by discounting at a rate reflecting the risk of B. – The two discount rates will, in general, be different.

27. Continue This means that Pfizer should accept any project that more than compensates for the project’s beta. In other words, Pfizer should accept any project lying above the upward-sloping line that links expected return to risk in Figure 1. – If the project has a high risk, Pfizer needs a higher prospective return than if the project has a low risk.

28. Company Cost of Capital A company’s cost of capital can be compared to the CAPM required return Required return Project Beta 1.26 Company Cost of Capital 13 5.5 0 SML

29. Understanding In terms of Figure1, the rule tells Pfizer to accept any project above the horizontal cost of capital line, that is, any project offering a return of more than 9.2%. – The company cost of capital rule, which is to accept any project regardless of its risk as long as it offers a higher return than the company’s cost of capital.

30. Understanding – It is clearly silly to suggest that Pfizer should demand the same rate of return from a very safe project as from a very risky one. – If Pfizer used the company cost of capital rule, it would reject many good low-risk projects and accept many poor high-risk projects. Many firms require different returns from different categories of investment.

31. Understanding For example, discount rates might be set as follows:

32. Perfect Pitch and the Cost of Capital The true cost of capital depends on project risk, not on the company undertaking the project. – So why is so much time spent estimating the company cost of capital? First, many (maybe, most) projects can be treated as average risk, that is, no more or less risky than the average of the company’s other assets. – For these projects the company cost of capital is the right discount rate.

33. Continue Second, the company cost of capital is a useful starting point for setting discount rates for unusually risky or safe projects. – It is easier to add to, or subtract from, the company cost of capital than to estimate each project’s cost of capital from scratch. Anyone who can carry a tune gets relative pitches right.

34. Business People are used to, but not about absolute risk or required rates of return. Therefore, they set a companywide cost of capital as a benchmark. This is not the right hurdle rate for everything the company does. – But adjustments can be made for more or less risky ventures.

35. MEASURING THE COST OF EQUITY Suppose that you are considering an across- the-board expansion by your firm. Such an investment would have about the same degree of risk as the existing business. Therefore you should discount the projected flows at the company cost of capital. Companies generally start by estimating the return that investors require from the company’s common stock.

36. Continue Used the capital asset pricing model to do the working. This states; – Expected stock return =r f + Beta(r m – r f ) An obvious way to measure the beta (B) of a stock is to look at how its price has responded in the past to market movements.

37. Measuring Betas The SML shows the relationship between return and risk. CAPM uses Beta as a proxy for risk. Other methods can be employed to determine the slope of the SML and thus Beta. Regression analysis can be used to find Beta.

38. Dell Computer Stock Calculated monthly returns from Dell Computer stock in the period, after it went public in 1988, is given on the next slide. Also plotted returns against the market returns for the same month, is given too. We have fitted a line through the points. – The slope of this line is an estimate of beta.

39. Measuring Betas Dell Computer Slope determined from plotting the line of best fit. Price data – Aug 88- Jan 95 Market return (%) Dell return (%) R 2 =.11 B = 1.62

40. Measuring Betas Dell Computer Slope determined from plotting the line of best fit. Price data – Feb 95 – Jul 01 Market return (%) Dell return (%) R 2 =.27 B = 2.02

41. Other Stocks The next diagram shows a similar plot for the returns on General Motors stock, and the Third shows a plot for Exxon Mobil. In each case we have fitted a line through the points. The slope of this line is an estimate of beta. – It tells us how much on average the stock price changed for each additional 1% change in the market index.

42. Measuring Betas General Motors Slope determined from plotting the line of best fit. Price data – Aug 88- Jan 95 Market return (%) GM return (%) R 2 =.13 B = 0.80

43. Measuring Betas General Motors Slope determined from plotting the line of best fit. Price data – Feb 95 – Jul 01 Market return (%) GM return (%) R 2 =.25 B = 1.00

44. Measuring Betas Exxon Mobil Slope determined from plotting the line of best fit. Price data – Aug 88- Jan 95 Market return (%) Exxon Mobil return (%) R 2 =.28 B = 0.52

45. Measuring Betas Exxon Mobil Slope determined from plotting the line of best fit. Price data – Feb 95 – Jul 01 Market return (%) Exxon Mobil return (%) R 2 =.16 B = 0.42

46. Understanding Diagrams show plots for the three stocks during the subsequent period, February 1995 to July 2001. Although the slopes varied from the first period to the second, there is little doubt that Exxon Mobil’s beta is much less than Dell’s or that GM’s beta falls somewhere between the two. – If you had used the past beta of each stock to predict its future beta, you wouldn’t have been too far off.

47. Understanding Only a small portion of each stock’s total risk comes from movements in the market. The rest is unique risk, which shows up in the scatter of points around the fitted lines in Diagrams. – R-squared (R 2 ) measures the proportion of the total variance in the stock’s returns that can be explained by market movements.

48. Table 1 Estimated betas and costs of (equity) capital for a sample of large railroad companies and for a portfolio of these companies. The precision of the portfolio beta is much better than that of the betas of the individual companies—note the lower standard error for the portfolio.

49. Summary

50. The Expected Return on Union Pacific Corporation’s Common Stock Suppose that in mid-2001 you had been asked to estimate the company cost of capital of Union Pacific Corporation. Table 1 provides two clues about the true beta of Union Pacific’s stock: – The direct estimate of.40 and the average estimate for the industry of.50. Use the industry average of.50

51. Continue In mid-2001 the risk-free rate of interest r f was about 3.5%. 8% for the risk premium on the market, You would have concluded that the expected return on Union Pacific’s stock was about 7.5%. – Expected stock return= r f +Beta(r m – r f ) = 3.5 +.5(8.0) = 7.5%

52. CAPITAL STRUCTURE AND THE COMPANY COST OF CAPITAL we need to look at the relationship between the cost of capital and the mix of debt and equity used to finance the company. Think again of what the company cost of capital is and what it is used for. We define it as the opportunity cost of capital for the firm’s existing assets; – we use it to value new assets that have the same risk as the old ones.

53. Company Cost of Capital simple approach Company Cost of Capital (COC) is based on the average beta of the assets. The average Beta of the assets is based on the % of funds in each assets. – Example – 1/3 New Ventures B=2.0 – 1/3 Expand existing business B=1.3 – 1/3 Plant efficiency B=0.6 AVG Beta of assets = 1.3

54. Capital Structure Capital Structure - The mix of debt & equity within a company Expand CAPM to include Capital Structure R = r f + B ( r m - r f ) Becomes; R equity = r f + B ( r m - r f )

55. Union Pacific Corp. Example

56. Understanding If the firm is contemplating investment in a project that has the same risk as the firm’s existing business, the opportunity cost of capital for this project is the same as the firm’s cost of capital; in other words, it is 12.75%. – What would happen if the firm issued an additional 10 of debt and used the cash to repurchase 10 of its equity?

57. Union Pacific Corp. Example

58. Understanding The change in financial structure does not affect the amount or risk of the cash flows on the total package of debt and equity. Therefore, if investors required a return of 12.75% on the total package before the refinancing, they must require a 12.75% return on the firm’s assets afterward.

59. Solve for Equity Since the company has more debt than before, the debt holders are likely to demand a higher interest rate. We will suppose that the expected return on the debt rises to 7.875%. – Now you can write down the basic equation for the return on assets and solve for return on Equity. i.e.

60. Continue Return on equity = 16% – Increasing the amount of debt increased debt holder risk and led to a rise in the return that debt holders required (r debt rose from 7.5 to 7.875%). – The higher leverage also made the equity riskier and increased the return that shareholders required (r equity rose from 15 to 16 %).

61. Continue The weighted average return on debt and equity remained at 12.75%. What happen to cost of capital and return on equity, – If Co. has paid all of its debt and replace it with equity?

62. How Changing Capital Structure Affects Beta The stockholders and debtholders both receive a share of the firm’s cash flows, and both bear part of the risk. – For example, if the firm’s assets turn out to be worthless, there will be no cash to pay stockholders or debtholders. But debtholders usually bear much less risk than stockholders. Debt betas of large blue- chip firms are typically in the range of.1 to.3.

63. Continue The firm’s asset beta is equal to the beta of a portfolio of all the firm’s debt and its equity. The beta of this hypothetical portfolio is just a weighted average of the debt and equity betas:

64. Continue If the debt before the refinancing has a beta of.1 and the equity has a beta of 1.1, then; – Beta assets =.8

65. Continue What happens after the refinancing? The risk of the total package is unaffected, but both the debt and the equity are now more risky. – Suppose that the debt beta increases to 0.2. – Beta Equity = 1.2

66. Understanding Financial leverage does not affect the risk or the expected return on the firm’s assets, but it does push up the risk of the common stock. Shareholders demand a correspondingly higher return because of this financial risk. Figure on the next slide shows the expected return and beta of the firm’s assets. – It also shows how expected return and risk are shared between the debtholders and equity holders before the refinancing.

67. Capital Structure & COC Expected return (%) B debt B assets B equity R rdebt =7.5 R assets =12.75 R equity =15 Expected Returns and Betas prior to refinancing

68. Understanding After the refinancing. – Both debt and equity are now more risky, and therefore investors demand a higher return. – But equity accounts for a smaller proportion of firm value than before. – As a result, the weighted average of both the expected return and beta on the two components is unchanged.

69. Capital Structure & COC Expected return (%) B debt B assets B equity R rdebt =7.875 R assets =12.7 5 R equity =16 Expected Returns and Betas prior to refinancing

70. Capital Structure and Discount Rates The company cost of capital is the opportunity cost of capital for the firm’s assets. That’s why we write it as r assets. If a firm encounters a project that has the same beta as the firm’s overall assets, then r assets is the right discount rate for the project cash flows.

71. Continue When the firm uses debt financing, the company cost of capital is not the same as r equity the expected rate of return on the firm’s stock; r equity is higher because of financial risk. – When the firm changes its mix of debt and equity securities, the risk and expected returns of these securities change; however, the asset beta and the company cost of capital do not change.

72. Continue When companies discount an average-risk project, they do not use the company cost of capital as we have computed it. They use the after-tax cost of debt to compute the after-tax weighted-average cost of capital or WACC.

73. DISCOUNT RATES FOR INTERNATIONAL PROJECTS Foreign Investments Are Not Always Riskier; Table 2 shows estimated betas for the Egyptian market and for markets in Poland, Thailand, and Venezuela. The standard deviations of returns in these markets were two or three times more than the U.S. market, but only Thailand had a beta greater than 1.

74. International Risk Source: The Brattle Group, Inc.  Ratio - Ratio of standard deviations, country index vs. S&P composite index

75. Continue The reason is low correlation. – For example, the standard deviation of the Egyptian market was 3.1 times that of the Standard and Poor’s index, but the correlation coefficient was only.18. – The beta was 3.1 x 0.18 =.55.

76. Understanding Table doesn’t prove that investment abroad is always safer than at home. But it should remind you always to distinguish between diversifiable and market risk. The opportunity cost of capital should depend on market risk.

77. DISCOUNT RATES FOR INTERNATIONAL PROJECTS Foreign Investment; Suppose that the Swiss pharmaceutical company, Roche, is considering an investment in a new plant near Basel in Switzerland. Since the project is risky, the company requires a higher return than the Swiss franc interest rate. – First measures the risk of the investment by estimating Roche’s beta and the beta of other Swiss pharmaceutical companies in that country.

78. Continue Beta of 1.1 and that the expected risk premium on the Swiss market index is 6%. Then Roche needs to discount the Swiss franc cash flows from its project at 1.1 x 6 = 6.6%. – calculates these betas relative to the Swiss market index. What if the project chooses to be in other country than Swiss? What would be the possible affect on the discount rate under this circumstances?

79. Understanding Risk cannot be considered in isolation; it depends on the other securities in the investor’s portfolio. Beta measures risk relative to the investor’s portfolio. For example, you can now buy funds that specialize in investment in emerging capital markets such as Vietnam, Peru, or Hungary.

80. Continue As investors increase their holdings of overseas stocks, it becomes less appropriate to measure risk relative to the domestic market and more important to measure the risk of any investment relative to the portfolios that they actually hold.

81. SETTING DISCOUNT RATES WHEN YOU CAN’T CALCULATE BETA What should a manager do if the asset has no such convenient price record? What if the proposed investment is not close enough to business as usual to justify using a company cost of capital? – These cases clearly call for judgment.

82. Continue For managers making that kind of judgment, we offer two pieces of advice. – 1. Avoid fudge factors. Don’t give in to the temptation to add fudge factors to the discount rate to offset things that could go wrong with the proposed investment. Adjust cash-flow forecasts first.

83. Example Project Z will produce just one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at a 10% company cost of capital. – P.V = = $909,100

84. Continue The most likely outcome is $1 million, But you also see some chance that project Z will generate zero cash flow next year. Also, new worry is the ‘Technology’. – There is some discount rate (10% plus a fudge factor) that will give the right value, but we don’t know what that adjusted discount rate is?

85. Continue For many projects, the most likely cash flow is also the unbiased forecast. If there are three possible outcomes with the probabilities shown below, the unbiased forecast is $1 million.

86. Continue This might describe the initial prospects of project Z. But if technological uncertainty introduces a 10 percent chance of a zero cash flow, the unbiased forecast could drop to $900,000:

87. Continue Now, recalculate the PV, – PV = = $818,000

88. Continue – 2. Think about the determinants of asset betas. Often the characteristics of high and low-beta assets can be observed when the beta itself cannot be. Cyclicality, Many people intuitively associate risk with the variability of book, or accounting, earnings. But much of this variability reflects unique or diversifiable risk.

89. Continue What really counts is the strength of the relationship between the firm’s earnings and the aggregate earnings on all real assets. We can measure this either by the accounting beta or by the cash-flow beta. – Firms with high accounting or cash-flow betas should also have high stock betas—and the prediction is correct.

90. Continue This means that cyclical firms—firms whose revenues and earnings are strongly dependent on the state of the business cycle—tend to be high-beta firms. – Thus you should demand a higher rate of return from investments whose performance is strongly tied to the performance of the economy.

91. Continue Operating Leverage, We have already seen that financial leverage increases the beta of an investor’s portfolio. Those who receive the fixed costs are like debt holders in the project; they simply get a fixed payment. – Those who receive the net cash flows from the asset are like holders of common stock; they get whatever is left after payment of the fixed costs.

92. Asset Betas How the asset’s beta is related to the betas of the values of revenue and costs?

93. Asset Betas The betas of the revenues and variable costs should be approximately the same, because they respond to the same underlying variable, the rate of output. Therefore, we can substitute Beta variable cost and solve for the asset beta. Remember that Beta fixed cost = 0.

94. Continue Thus, given the cyclicality of revenues (reflected in Beta revenue ), the asset beta is proportional to the ratio of the present value of fixed costs to the present value of the project.

95. Continue Other things being equal, the alternative with the higher ratio of fixed costs to project value will have the higher project beta. – Empirical tests confirm that companies with high operating leverage actually do have high betas.

96. ANOTHER LOOK AT RISK AND DISCOUNTED CASH FLOW In practical capital budgeting, a single discount rate is usually applied to all future cash flows. – Among other things, the use of a constant discount rate assumes that project risk does not change. This can’t be strictly true, for the risks to which companies are exposed are constantly shifting. It involves converting the expected cash flows to certainty equivalents.

97. Continue We will first explain what certainty equivalents are. Then we will use this knowledge to examine when it is reasonable to assume constant risk. – You are considering construction of an office building that you plan to sell after one year for $400,000. – Since that cash flow is uncertain, you discount at a risk-adjusted discount rate of 12% rather than the 7% risk-free rate of interest.

98. Continue This gives a present value of – PV = 400,000/1.12 = $357,143 Suppose a real estate company offers to fix the price at which it will buy the building from you at the end of the year, – PV = Certain Cash Flow / 1.07 = $357,143 Certain Cash Flow=$382,143

99. Understanding A certain cash flow of $382,143 has exactly the same present value as an expected but uncertain cash flow of $400,000. – The cash flow of $382,143 is therefore known as the certainty-equivalent cash flow. Compensation for uncertainty in-terms of returns is equal to; = $400,000-$357,143 = $42,857 To get rid of the risk, take a cut in the return of; = $400,000 - $382,143 = $17,857

100. Continue Method 1: Discount the risky cash flow at a risk-adjusted discount rate r that is greater than r f. – The risk-adjusted discount rate adjusts for both time and risk. Method 2: Find the certainty-equivalent cash flow and discount at the risk-free interest rate r f.

101. Risk,DCF and CEQ This is called the certainty equivalent of C1 denoted by CEQ 1. Since CEQ 1 is the value equivalent of a safe cash flow, it is discounted at the risk-free rate.

102. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?

103. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?

104. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?

105. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? Now assume that the cash flows change, but are RISK FREE. What is the new PV?

106. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

107. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.

108. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? DEDUCTION FOR RISK

109. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? The difference between the 100 and the certainty equivalent (94.6) is 5.4%…this % can be considered the annual premium on a risky cash flow

110. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

111. Summary