Rose International is currently an all-equity firm and has just announced plans to expand its current business. In order to fund this expansion, Rose will need to raise $100 million in new capital. After the expansion, Rose is expected to produce earnings before interest and taxes of $50 million per year in perpetuity. Rose has already announced the planned expansion but has not yet determined how best to fund the expansion. Rose currently has 16 million shares outstanding and following the expansion announcement, these shares are trading at $25 per share. Rose has the ability to borrow at a rate of 5% or to issue new equity at $25 per share.
a)If Rose finances their expansion by issuing new stock, what will Rose's cost of equity capital be?(5 marks)
b)If Rose finances their expansion by issuing $100 million in debt at 5%, what will Rose's cost of equity capital be?(5 marks)
c)Show mathematically that the stock price of Rose does not depend on whether they issue new stock or borrow to fund their expansion. Explain your answer.