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Unformatted text preview: Problem 1) D/E=1 We start by computing the return on equity as: Then we can compute the WACC as: Then the CAPM gives us the debt beta and asset beta: The debt equity ratio is D/E=1. We can also start by working out the debt and equity betas as 0.25, and then compute the asset beta as: Then use the asset beta to work out the cost of capital as: r E =22% r D =12% r A =17% beta E =1.5 beta D =0.25 beta A =0.875 r f =10% r M =18% r E = r f +beta E *(r M-r f ) = 10%+1.5*(18%-10%) = 22% WACC = D/V*r D +E/V*r E = 0.5*12%+0.5*22% = 17% Debt: 10%+beta D *8% = 12%, hence beta D = 0.25 Assets: 10%+beta A *8% = 17%, hence beta A = 0.875 beta A =D/V*beta D +D/V*beta E =0.5*0.25+0.5*1.5=1.75/2=0.875 r A =r f +beta A *(r M-r f )=10%+0.875*8%=17% Problem 2) Before D/V 10% 0.8 5% 5% 13% MCAP 360 After D/V 60% 6% Part 1 The debt beta is zero because debt is riskless. Hence, we can compute the asset beta as: The market risk premium is 13%-5%=8%. Then the cost of capital is: 10.76% Part 2 Equity is 90% of the company's value and is 360, hence the total value of the company is 400 million. The total amount of new debt oustanding is 60%, or 0.6*400=240 million. Hence the company has to issue 200 million of debt to pay a dividend of 200 million. Part 3 The debt beta after the financing is: 1.61 Then the required return on the equity is: 17.90% Part 4 The wealth of the shareholders has not changed at all. Before the refinancing they owned shares worth 360 million, after the refinancing they own shares worth 160 million (the remaining equity) and cash worth 200 million, hence 360 million in total. Part 5 The shareholders owning the position described in part 4 have a beta for this position of: beta = (160/360)*1.6125+(200/360)*0 = 0.72 This is lower than before, because the shareholders have not invested in the risky debt. In order to rebalance their portfolio they need to invest x dollars in the stock market so that; beta = (160/360)*1.6125+(x/360)*1 = 0.8, or: x = 360*(0.8-(160/360)*1.6125) = 30 Hence, investing 30 million (out of the 200 million in dividend) in the stock market is sufficient to restore the original portfolio risk.the original portfolio risk....
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This document was uploaded on 06/09/2010.
- Fall '09