Risk and the cost of capital 9 Risk and the cost of capital McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

9-1 company and project costs of capital Firm Value Sum of value of assets

Figure 9.1 company cost of capital A company’s cost of capital can be compared to CAPM required return Required return Project beta 0.5 Company cost of capital 5.5 0.2 SML

9-1 company and project costs of capital Company Cost of Capital

9-1 company and project costs of capital Weighted Average Cost of Capital Traditional measure of capital structure, risk and return

9-2 measuring the cost of equity Capital Structure (CS) Mix of debt and equity within a company Expand CAPM to include CS r = rf + β(rm − rf) requity = rf + β(rm − rf)

9-2 measuring the cost of equity Estimating Beta SML shows relationship between return and risk CAPM uses beta as proxy for risk Other methods can also determine slope of SML and beta Regression analysis can be used to find beta

Figure 9.2a citigroup Return Weekly Data 2010-2011   beta = 1.83 alpha = -0.31 R-squared = 0.64 Correlation = 0.80 Annualized std dev of market = 19.52 Annualized std dev of stock = 44.55 Variance of stock = 1984.83 Std error of beta 0.14

Figure 9.2B citigroup Return Wkly Data 2008-2009   beta = 3.32 alpha = 0.24 R-squared = 0.49 Correlation = 0.70 Annualized std dev of market = 30.11 Annualized std dev of stock = 142.95 Variance of stock = 20436.08 Std error of beta 0.34

Figure 9.2c disney Return Wkly Data 2010-2011 beta = 0.33 alpha = 0.02   beta = 0.33 alpha = 0.02 R-squared = 0.22 Correlation = 0.47 Annualized std dev of market = 19.52 Annualized std dev of stock = 13.68 Variance of stock = 187.13 Std error of beta 0.06

Figure 9.2D disney Return Wkly Data 2008-2009 beta = 0.41 alpha = 0.17   beta = 0.41 alpha = 0.17 R-squared = 0.19 Correlation = 0.44 Annualized std dev of market = 30.11 Annualized std dev of stock = 28.08 Variance of stock = 788.62 Std error of beta 0.08

Figure 9.2e campbell’s Return Wkly Data 2010-2011   beta = 0.33 alpha = 0.02 R-squared = 0.22 Correlation = 0.47 Annualized std dev of market = 13.68 Annualized std dev of stock = 19.52 Variance of stock = 381.22 Std error of beta 0.06

Figure 9.2f campbell’s Return, % Wkly Data 2008-2009   beta = 0.41 alpha = 0.17 R-squared = 0.19 Correlation = 0.44 Annualized std dev of market = 28.08 Annualized std dev of stock = 30.11 Variance of stock = 906.55 Std error of beta 0.08

Table 9.1 estimates of betas Standard Error Canadian Pacific 1.27 .10 CSX 1.41 .08 Kansas City Southern 1.68 .12 Genesee & Wyoming 1.25 Norfolk Southern 1.42 .09 Rail America 1.15 .14 Union Pacific 1.21 .07 Industry portfolio 1.34 .06

9-2 measuring the cost of equity Beta Stability % IN SAME % WITHIN ONE RISK CLASS CLASS CLASS 5 YEARS LATER 5 YEARS LATER 10 (High betas) 35 69 9 18 54 8 16 45 7 13 41 6 14 39 5 14 42 4 13 40 3 16 45 2 21 61 1 (Low betas) 40 62 Source: Sharpe and Cooper (1972)

9-2 measuring the cost of equity 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 asset Assets = debt + equity

9-2 measuring the cost of equity Expected Returns and Betas Prior to Refinancing Expected return (%) Bdebt Bassets Bequity Rdebt = 8 Rassets = 12.2 Requity = 15

9-2 measuring the cost of equity Company cost of capital (COC) is based on average beta of assets Average beta of assets is based on the % of funds in each asset Example 1/3 new ventures β = 2.0 1/3 expand existing business β = 1.3 1/3 plant efficiency β = 0.6 AVG β of assets = 1.3

9-2 measuring the cost of equity Company Cost of Capital

9-3 analyzing project risk

9-3 analyzing project risk Allowing for Possible Bad Outcomes Example Project Z will produce one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at 10% company COC:

9-3 analyzing project risk Allowing for Possible Bad Outcomes Example, continued Company’s engineers are behind schedule developing technology for project. There is a small chance that it will not work. Most likely outcome still $1 million, but some chance that project Z will generate zero cash flow next year:

9-3 analyzing project risk Allowing for Possible Bad Outcomes Example, continued If technological uncertainty introduces a 10% chance of zero cash flow, unbiased forecast could drop to $900,000:

Table 9.2 cash flow forecasts

9-4 certainty equivalents—another way to adjust for risk Risk, Discounted Cash Flow (DCF), and Certainty Equivalents (CEQ)

Figure 9.3 two ways to calculate present value

9-4 certainty equivalents—another way to adjust for risk Example Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?

9-4 certainty equivalents—another way to adjust for risk Example, continued Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?

9-4 certainty equivalents—another way to adjust for risk Example, continued Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta? Assume cash flows change, but are risk-free. What is new PV?

9-4 certainty equivalents—another way to adjust for risk Example, continued 94.6 is risk-free, is certainty equivalent of 100

9-4 certainty equivalents—another way to adjust for risk Example, continued Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?

9-4 certainty equivalents—another way to adjust for risk Example, continued Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta? Assume cash flows change, but are risk-free. What is new PV? Difference between 100 and certainty equivalent (94.6) is 5.4% This % can be considered annual premium on risky cash flow

9-4 certainty equivalents—another way to adjust for risk Example, continued Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta? Assume cash flows change, but are risk-free. What is new PV?