Pandora Box Company Incorporated makes a rights issue at a subscription price of $$5$ a share. One new share can be purchased for every five shares held. Before the issue there were $25$ million shares outstanding and the share price was $$10.$

a$)$ What is the total amount of new money raised? Note: Do not round intermediate calculations. Enter your answer in millions.

b$)$ What is the expected stock price after the rights are issued? Note: Enter your answer rounded to $4$ decimal places.

c$)$ By what percentage would the total value of the company need to fall before shareholders would be unwilling to take up their rights? Note: Do not round intermediate calculations. Enter your answer as a positive percent rounded to $2$ decimal places.

d$)$ Suppose that you initially own $200$ shares plus $$200$ in the bank. If you take up your rights issue, what will be your total wealth after the issue is completed? Note: Do not round intermediate calculations. Enter your answer rounded to nearest whole dollar.

e$)$ Suppose that the company now decides to issue the new stock at $$4$ instead of $$5$ a share. How many new shares would it have needed to raise the same sum of money? Note: Enter your answer in millions rounded to $1$ decimal place.

f$)$ What is the expected stock price under this new arrangement after the rights are issued? Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.