Alpha corporation has just paid its annual dividend and is looking forward to another successful year ahead. the company had free cash flow for the year just ended of $1 billion, all of which it just paid out to its shareholders as a dividend. right now, shareholders do not believe that alpha has any growth opportunities, so they expect the annual cash flow and dividend stream to remain unchanged for the foreseeable future. alpha has 100 million shares outstanding and a market capitalization of $10 billion. the company is entirely equity-financed. the capital market is efficient. a) alpha’s ceo now proposes that the company skip its dividend one year from now and instead invest the entire amount of the coming year’s $1 billion free cash flow in a project that management believes will generate a perpetual annual rate of return of 21%. the ceo further asserts that the new project has similar risk to the company’s assets in place. if the company were to announce immediately its plans for the investment one year from now (financed by skipping next year’s dividend) what do you think will happen to alpha’s stock price? b) some of alpha’s board members are worried that shareholders are expecting a dividend next year and that announcing plans to skip next year’s dividend will lower the stock price today. suppose alpha were to announce instead that it plans to pay its usual dividend one year from now and that it has no plans for any new investment at t = 1. what will happen to the stock price today? c) suppose alpha settles on a compromise: alpha announces today that it will invest in the new project one year from now, but it will simultaneously issue enough new shares at that time to enable it to pay the usual $10 dividend per share to its existing shareholders. what do you think will happen to alpha’s share price one year from now under this plan? what do you think will happen to alpha’s stock price today? which of the three plans do you think alpha’s shareholders would prefer?