The following information is used for Parts A, B, and C.

Rearden Metal has earnings per share of $2. It has 10 million shares outstanding and is trading at $20 per share. Rearden Metal is planning to acquire Associated Steel, which has earnings per share of $1.25, 4 million shares outstanding, and a price per share of $15. Both companies have no debt in their capital structure.

1. Assuming that Rearden Metal seeks an independent valuation from an external financial analyst. The analyst estimates that Rearden Metal will increase its revenue with a net cash flow of $500,000 per annum in perpetuity after acquiring Associated Steel. The cost of capital of Rearden Metal is 20% per annum. Rearden Metal will pay for Associated Steel by issuing new shares.

1. If the exchange ratio is 0.5, what is the earning per share (EPS) of the combined firm after the takeover?
2. If Rearden would like to achieve an EPS of $2 in the combined firm after the takeover, what is the exchange ratio?