Consider an unlevered firm. The expected annual earnings $($before

taxes$)$ of the firm are $$10$ million in perpetuity. The expected return on the firm$$s

equity is currently $10\%.$ The corporate tax rate is $25\%.$ The company has currently

$1,500,000$ shares outstanding. The firm plans to carry out a recapitalization,

according to which it will take out a perpetual loan of $$20$ million at an interest rate

of $5\%,$ and it will use the proceedings from this loan to purchase back shares.

a What is the value of the company and the share price before the

recapitalization plan is announced?

b What is the value of the company and the share price after the

recapitalization plan is announced $($but before the loan is taken out$)?$

c How many shares will be company repurchase? What is the value of the

equity and the share price after the repurchase?