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Capital Budgeting with Risk Discount Rates, Expected Returns, and a Project‟s Internal Rate of Return-- some clarification The Capital Asset Pricing Model, and the SML in particular give us an estimate of the normal rate of return that is expected on assets with varying amounts of (beta) risk. The expected return we get from the SML should be used as the discount rate in valuing investment opportunities and proposed projects. This discount rate is also referred to as the cost of capital for the project, or the hurdle rate. Once we have forecasted the cash flows from a proposed project or investment, we can compute the project‟s Internal Rate of Return. IRR and NPV Typically, a project will have a positive NPV if the IRR exceeds the project‟s cost of capital or hurdle rate. That is, the NPV is positive if the IRR plots above the Security Market Line on a risk/return graph. Project A would have a positive NPV, while Project B would have a negative NPV Expected Return *IRRA SML project cost of capital Rf *IRRB Project Beta Beta Two Complexities in Choosing Discount Rates for Projects or Divisions. If the firm has no debt in the capital structure and the project being evaluated has the same (Beta) risk as the firm‟s existing projects, then the expected return on the firm‟s equity is the appropriate discount rate for the project. If the project beta differs from the firm beta then use the project beta. How can this be estimated? If the firm has debt in the capital structure, adjustments are required. Interest is tax deductible. Either allow for in cash flows or alter discount rate to reflect. Financial leverage increases equity betas relative to the firm‟s beta • Is an equity-beta or firm-beta estimated by regression techniques using stock return data? Project vs. Firm Risk (Unlevered Firm) Expected Return project cost SML of capital firm cost of capital Rf Beta Firm Project Beta Beta The Weighted Average Cost Of Capital (WACC) • When a firm has both debt and equity in its capital structure, the most frequent recommendation is to work with the weighted average cost of capital (WACC): S B (13.5) WACC rS rB (1 TC ) SB SB • where – S is the market value of the firm‟s stock – B is the market value of the firm‟s debt – rS is the required rate of return on the firm‟s stock – rB is the required before tax rate of return on the firm‟s debt – TC is the firm‟s marginal tax rate The costs of debt and equity. The before tax cost of debt can be calculated as the yield to maturity on the firm‟s existing debt. Can also be found from yields on companies with comparable financial risk. The after tax cost of debt is the before tax cost of debt multiplied by (1-Tc), where Tc is the firm‟s effective marginal tax rate. • The cost of equity can be calculated using the Security Market Line (SML) from the CAPM. rS= Rf+ b (E[RM]- Rf) • This can be using the firm‟s own beta, or that of another firm that comprises a good surrogate for the project. WACC Example Gamma airlines is financed with 60% debt and 40% equity. Currently the YTM on Gamma bonds is 9%, and Gamma has estimated its cost of equity to be 14.5%. Gamma‟s corporate tax rate is 40%. What is Gamma‟s WACC? WACC = .40(14.5%) + .60(9%)(1-.40) = 9.04%. Issues: What if the risk of the project at hand differs from that of Gamma‟s past projects? What if risk of this project is similar to that of Delta Airlines‟ projects, and the 14.5% cost of equity figure was actually obtained for Delta. However, Delta‟s capital structure differs from Gamma‟s. Betas and Leverage We noted earlier that the beta of a portfolio is the average of the component betas. Also, we can think of the firm‟s assets as a portfolio of the debt and equity claims. From these insights it follows (see pgs 565-566) that: S B(1 TC ) See Assets S B(1 T ) Debt Equity S B(1 T ) (13.3) for C C no tax case • Where S is the market value of the stock (equity), B is the market value of debt (borrowings), and Tc is the tax rate. Adjusting beta for different capital structures In this analysis it is often assumed that the debt has a zero beta (a big simplification). Then: (13.4) S bAssets bEquity S B(1 TC ) Example: Gamma airlines‟ equity beta is observed to be 1.31. It‟s equity is worth 25.0 million while its debt is worth 15.0 million and its tax rate is 40%. What is the beta of the underlying assets? 25 bAssets 131 0.96 . 25 15(1.4) Points to Note Regarding Betas and Leverage If the firm uses no debt (B=0) the equity beta and the asset beta are equal. If the firm uses debt, the equity beta is increased relative to the asset beta: b Equity 1 B (1 TC ) b Assets S implies: (1) equity holders will require a higher rate of return, (2) when surrogate firms are used to estimate beta, allowances for differing capital structures will be required. Why does Beta increase with financial leverage? Leverage Increases the volatility of the equity cash flow: Numerical Illustration: Outcome Good Bad % Ch. EBI 125 100 -20% Interest 50 50 0% Income 75 50 -33.3% Aside on Leverage and Risk A stock/margin example Suppose you buy XOM at $70 per share with no leverage (margin). If stock price rises 10% to $77, your return is 10% Now,suppose you buy XOM at $70 with 50% margin (you pay $35 and borrow $35 at 5%). If stock price is $77: • You payback 35*1.05=36.75, and keep difference, 40.25. Your return is 15% (40.25/35-1) Stock/margin continued But this is a double-edged sword… Suppose you buy XOM at $70 per share with no leverage (margin). If stock price falls 10% to $63, your return is -10% Now, suppose you buy XOM at $70 with 50% margin (you pay $35 and borrow $35 at 5%). If stock price is $63: • You payback 35*1.05=36.75, and keep difference, 26.25. Your return is -25% (26.25/35-1) Stock/margin example illustrated Margin Example Buy stock at Price = $70, r=5% Return Return 1 Price Margin=0 Margin=.5 0.8 50 -0.28571 -0.62143 55 -0.21429 -0.47857 0.6 60 -0.14286 -0.33571 65 -0.07143 -0.19286 0.4 70 0 -0.05 0.2 return Margin=0 75 0.071429 0.092857 80 0.142857 0.235714 0 Margin=.5 85 0.214286 0.378571 -0.2 90 0.285714 0.521429 95 0.357143 0.664286 -0.4 100 0.428571 0.807143 -0.6 -0.8 50 60 70 80 90 100 stock price Back to Notes How to use the tools developed here to select discount rates for capital budgeting. The cost of capital for each project (or division) should reflect the systematic risk of that project and the capital structure of the firm (or division) taking the project. So, Select a publicly traded company that is comparable in terms of the risk of the underlying business. Obtain the unlevered (asset) beta of the comparable. Obtain the corresponding project equity beta for your firm, reflecting your firm‟s capital structure. Obtain the cost of equity and cost of debt for this project at your firm. Calculate the WACC for the project and perform NPV analysis. How to use the tools, continued… Why is this so hard? Because your comparable need not have the same capital structure as your own firm. What we‟re going to do is start with a levered comparable, figure out the beta of the equivalent unlevered firm, and then find the corresponding equity beta for your project at your capital structure Then, figure out the WACC and solve NPV... It‟s just ugly. Example: BK Industries BK Industries is a conglomerate company with operations in marine power, pleasure boating, defense, and fishing tackle. BK‟s equity beta is 1.0. BK has and will maintain a debt/equity ratio of 1.0. Can we use the company cost of capital to value an investment in text editing? Latec Inc. is a firm that makes only text editing systems. Latec‟s equity beta is 1.35. Latec has a debt to equity ratio of 0.75, and a marginal tax rate of 45%. Delevered Betas with debt/equity ratios The formulas for obtaining asset betas from equity betas and vice versa provided earlier required dollars values for debt (B) and equity (S). What if you are only given the leverage ratio, L = B/S? The formulas are restated as: 1 bAssets bEquity 1 L(1 TC ) bEquity bAssets (1 L(1 TC )) Step 1: Delever Latec‟s Beta to obtain the Beta of text-editing assets: Latec has L =0.75, TC = .45, and an equity beta of 1.35. 1 bAssets 135 0.955 . 1 0.75(1 0.45) Step 2: Relever the asset Beta to reflect BK‟s capital structure: Recalling that BK will keep its debt/equity ratio equal to one, we can get: bEquity 0.9551 1(1.45) 148 . •This is the beta for a BK equity position in a text editing asset. •Why is this equity beta greater than Latec‟s? BK Industries, Cont. Assume that the risk free rate is 8% and that BK‟s cost of debt is also 8%. The market risk premium is 7%. The required return on BK‟s equity is: rS RF bEquity ( RM RF ) 8% 148 * 7% 18.36% . The weighted average cost of capital for the text editing venture (using the fact that B/S = 1 here) is: S B WACC rS rB (1 TC ) SB SB = (0.5) *18 .36 % (0.5) * 8%(1 0.45 ) 11 .38 % Finally, we can evaluate the NPV of the text editing venture using the WACC that reflects the risk associated with this particular business. Using the cash flow estimates obtained earlier: 3.980 5.419 6.685 5.990 22.465 NPV 26.0 (1.1138 ) (1.1138 ) 2 (1.1138 ) 3 (1.1138 ) 4 (1.1138 ) 5 $3.778 Million • The NPV is positive, so proceed with the text editing business. • Notice that the selected discount rate of 11.38% reflects: The risk (beta) of text editing businesses, not BK‟s existing businesses. BK‟s capital structure, not that of the surrogate firm. Why the firm (or division‟s) capital structure? In the long run, each individual project is funded from a “pool” of capital. That pool includes both debt and equity. If we evaluated projects based on the specific financing used then those that were debt financed would tend to look better than those that are equity financed. But are they really better projects? Some practical observations (useful on cases and in real applications) Leverage is some times measured as, the debt to equity ratio (which we denoted L) the debt to total capital (equity + debt) ratio, which is the weighting on debt (W). You can convert these measures as • L = W/(1-W) • W = L/(1+L) The debt and equity numbers used should, in principle, be based on market values. • In practice, the market value of equity is typically used, along with the book value of debt. Summary: Risk, Return, and Discount Rates Some risk can be diversified, some cannot. „Beta‟ coefficients provide a measure of non- diversifiable risk. We expect that non-diversifiable risk will earn a risk premium in equilibrium but that diversifiable risk will not. The CAPM (and particularly the SML) is a simple model capturing important insights regarding risk and diversification. Discount rates for projects should reflect the systematic risk of the project (not necessarily that of the firm) and the capital structure of the firm or division (not necessarily the financing of the project).

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posted: | 5/22/2011 |

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