New equity beta and required return for equity capital

Problem 1: 

After reading all about the tax advantages of having a high leverage ratio, the CEO of LevCo is considering a leveraged recapitalization and wants to know the new cost of equity capital subsequent to the recap. The firm currently has $27 million in assets and $12 million in debt and is interested in taking on an additional $9 million in debt. LevCo's closest competitor has a debt-to-equity ratio of 0.5 and an equity beta of 1.25. Ten-year treasuries currently yield 2.3% and the expected return on the S&P 500 is 10.0% per annum. The marginal corporate tax rate is 40%. What will the new equity beta and required return for equity capital for LevCo's shareholders subsequent to the transaction?

Problem 2:

On the evening of Sunday March 16, 2008, with the assistance of the Fed, JP Morgan Chase (JPM) announced that they were acquiring Bear Stearns Cos. (BSC) and were paying $2 for each of BSC's 118,091,000 shares. When the markets closed on the following trading day (St. Patrick's Day), JPM settled out at $40.31 per share. As of the previous Friday, JPM was trading at $36.54 and had 3,396,539,000 shares outstanding. Assume that the investors did not infer that JPM's existing assets or growth opportunities were any more or less valuable due to the Fed's backing of the transaction, there were no expected synergies from the deal, and markets are otherwise efficient. Using the JPM investor reactions to the deal, what was the implied market value of BSC?

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Finance Basics: New equity beta and required return for equity capital
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