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# slides20 - 20 Capital structure Key points If we ignore...

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20. Capital structure

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Key points If we ignore taxes and the possibility of bankruptcy: The cash flows generated by the firm are independent of capital structure . The firms’ overall cost of capital and the value of the firm depend only on the size, timimg, and risk of the cash flows ( not on the capital structure). Capital structure only affects how these cash flows are divided up among the providers of capital. In practice, things are more complicated: The tax deductibility of interest payments provides an advantage to debt financing. But debt financing increases default risk . Since bankruptcy is costly, there is a limit to how much debt firms will take on. Each firm has an optimal capital structure which bal- ances these factors against each other. 2
Effect of leverage on cost of equity Ignoring taxes and the risk of bankruptcy... If the total return on assets is independent of how the pie is split between debt and equity, then, given R A , R D , and the debt-equity ratio, we can solve the following equation for R E : R A = D A · R D + E A · R E With a little algebra, we get, R E = R D + EM · ( R A - R D ) where EM = A/E is the equity multiplier. Notes: The top equation should look familiar! In the absence of default risk, R D is the riskfree rate! The second equation looks similar to the CAPM. It also looks similar to the accounting identity ROE = EM x ROA. 3

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Cost of equity for levered firm Or, in slightly different words... Based on the previous results, we can determine the relationship between the cost of equity for a levered firm (partially debt fi- nanced) versus the cost of equity if the firm were all equity financed ( unlevered ): R L = R D + EM · ( R U - R D ) where R L = cost of equity for levered firm R U = cost of equity for unlevered firm EM = equity multiplier = Total assets / equity Note: We are still ignoring taxes and bankruptcy risk. 4
Beta of a levered firm From the preceding expression (and the CAPM), we can also de- termine the relationship between the beta of a levered firm versus the its beta if it were all equity financed (unlevered): β L = EM × β U where β L = beta of levered firm β U = beta of unlevered firm EM = equity multiplier = Total assets / equity Notes: We are still ignoring taxes and bankruptcy risk. Remember, since there is no default risk, R D is the riskfree rate! 5

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Example Suppose a completely equity financed firm has a beta of 1. What will its beta be if it changes its capital structure to a debt/equity ratio of 1? If the unlevered firm has a cost of equity equal to 13% and cost of debt equal to 5%, what are the costs of debt and equity for the levered firm? Verify that the WACC is the same for the levered and unlevered firms. 6
Example — continued To understand more clearly what is going on, it is useful to flesh out the example a little bit: D/E=0 D/E= 1 Assets 7692 7692 Debt 0 3846 Equity 7692 3846 Shares outstanding 200 100 Share price 38.46 38.46 Interest rate 5% 5% Note: Share price = Equity / Shares outstanding.

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slides20 - 20 Capital structure Key points If we ignore...

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