Risk and the cost of capital 9 Risk and the cost of capital

9-1 company and project costs of capital Firm Value Sum of value of assets Value additive property is an important concept that has many applications. A firm’s value is the sum of the value of its various 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 The company cost of capital is not the appropriate discount rate for all its projects. If you consider each project as a mini-firm, the value of that mini-firm depends on its beta. The discount rate depends on the project’s discount rate. The required rate of return depends on the project and not on the company that is undertaking it.

9-1 company and project costs of capital Company Cost of Capital This is possibly the most important slide in the chapter. Take time to explain the difference between accounting terminology and finance terminology. While we use the same format for firm value, the meanings are distinctly different. Instead of asset we use value. And in place of debt and equity we use market values, not book values. Note the cost of capital for debt and equity is different. Each variable in the COC equation must be explained in detail or students will not follow the rest of the material.

9-1 company and project costs of capital Weighted Average Cost of Capital Traditional measure of capital structure, risk and return There is much less to cover here, other than to show the WACC formula as the result of the prior exercise.

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 The SML can be used to determine the required rate of return on a project. Regression analysis is used for estimating beta. Generally, monthly returns (60 months) for the firm and the market are used for the estimation.

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 Regression analysis can be used to estimate the beta of a firm. Total return data for the firm is used. A broadly based value-weighted index is used for market return. Generally 5-year (60 months) monthly data is used. Market return is plotted on the x-axis and the company returns on the y-axis. Slope of the fitted line is the beta estimate. A financial calculator can be used to estimate beta. The graph shows the beta estimate for Citigroup. The following five slides repeat the same exercise for three different stocks.

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 Citigroup beta, part two.

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 Disney beta

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 Disney beta, part two.

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 Campbell’s beta.

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 Campbell’s beta, part two.

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 Beta estimates have standard errors. Standard error can be used to construct a range of values for beta within which true beta lies.

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 Betas are also calculated for specific assets. Explain how a firm is the weighted sum of its parts.

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 Here beta of debt is usually low. Beta of equity is usually much higher. The beta of assets is somewhere in between. Company cost of capital can be thought of as the opportunity cost of capital for the firm’s existing assets. Beta of debt is generally low. Beta of equity is generally much higher. Beta of assets would lie between the two depending on the capital structure (bD < bA < bE).

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 Company cost of capital is calculated using the weighted-average beta of the assets. New ventures are high-risk projects. Expansion of the existing business has an average risk and improving plant efficiency is a low-risk project. An example of average beta of a firm based on three different types of projects is provided.

9-2 measuring the cost of equity Company Cost of Capital Expansion in the existing business would have the same risk as the company. The company cost of capital is appropriate for such projects. But for other types of projects, an adjustment should be made to reflect the relative risk of the project. This frame provides an example of different discount rates being used for different types of projects. In other words, most firms require different returns for different categories of investment. For example, speculative ventures = 30%; new products = 20%; expansion of existing business = 15% (company cost of capital); and cost improvement = 10%.

9-3 analyzing project risk This frame provides the formula for estimating the beta of revenues and the formula for calculating the beta of assets. Asset betas are useful when you cannot calculate the equity beta. Asset betas can also be thought of as related to revenues and costs. Beta of fixed cost is zero. This is an alternative way of looking at asset betas. High fixed costs generally imply high operating leverage. High operating leverage implies a high asset beta. Companies with high operating leverage do have high betas according to empirical evidence.

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: The next four slides are taken directly from the book and illustrate the Project Z example. It will be necessary to read the text and draw data directly from the book. These slides do not stand alone.

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: Continuation of the Project Z example.

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: Continuation of the Project Z example.

Table 9.2 cash flow forecasts Continuation of the Project Z example.

9-4 certainty equivalents—another way to adjust for risk Risk, Discounted Cash Flow (DCF), and Certainty Equivalents (CEQ) This frame shows an alternative way of taking risk into consideration. Instead of using higher discount rates for high-risk projects, we can use certainty equivalent cash flows and risk-free rate to arrive at the same present value. Use the risk-adjusted discount rate for discounting risky cash flows. This is the general method for calculating the present value of risky cash flows. Certainty equivalent cash flows are equivalent risk-free cash flows. These are discounted using the risk-free rate. The present value is the same as before.

Figure 9.3 two ways to calculate present value The figure from the book that shows the two methods for calculating PV is presented. Explain the concept of a “haircut” and how it reduces cash flows as an alternative method for accounting for risk. This may be preferred in cases where cash-flow estimates are more certain than discount rates.

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? A numerical example of a risky cash flow is given. Use CAPM to calculate the risk-adjusted discount rate for risky cash flows. Using a single discount rate may not be appropriate for all situations.

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? This slide shows the calculation for the PV of the risky cash flows using the risk-adjusted discount rate.

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? Now let us calculate the certainty equivalent cash flows. Certainty equivalent cash flows, when discounted at the risk-free rate, should provide the same PV. The table provides the example of certainty equivalent cash flows. Note that these are different from risky cash flows. Year 1 CEQ = [100/1.12](1.06) = $94.6; Year 2 CEQ = [100/(1.12^2)](1.06^2) = $89.6; Year 3 CEQ = [100/(1.12^3)](1.06^3) = $84.8.

9-4 certainty equivalents—another way to adjust for risk Example, continued 94.6 is risk-free, is certainty equivalent of 100 Present value is obtained by discounting risky cash flows using risk-adjusted discount rate. The certainty equivalent cash flows are discounted at the risk-free rate to get the same PV. Here the relationship between risky cash flows and equivalent risk-free cash flows is explored.