A company with $2$ million shares outstanding has announced a

rights offer to raise $$10$ million. The stock currently sells for $$50$ per share.

$1.$ What are the minimum and maximum possible subscription prices?

Now, assume the subscription price is set at $$40$ per share.

$2.$ How many shares must be sold?

$3.$ How many rights will it take to buy one share?

$4.$ What is the ex$-$rights price?

$5.$ What is the value of a right?

$6.$ Show how a shareholder with $5,000$ shares before the offering and no desire

$($or money$)$ to buy additional shares is not harmed by the rights offer.

$7.$ Show how a shareholder with $5,000$ shares before the offering who

exercises the rights is not harmed by the rights offer.

$($Only solve for questions $3-7)$