Raven Hog is a startup that develops a machine for producing thingamajigs. Since its founding a couple of years ago, the firm has borrowed a total of $6,000,000 from Virtue Bank Corp. It is currently estimated that Raven Hog's development project will succeed with 0.5 probability in which case the firm's assets would be worth $10,000,000. If the project does not succeed, the firm will be worthless. Now Raven Hog can invest in improving its technology. This investment would cost $1,500,000 and increase the success probability to 0.7.

a) Show that Raven Hog suffers from debt overhang.

b) Show that Raven Hog can solve the debt overhang issue by recapitalizing. Specifically, the recapitalization would include lowering the debt face value in exchange for a firm commitment to undertake the additional investment. Both equity-holders and debtholders must approve the recapitalization. What range of debt face values solves the debt overhang?