If you are able to buy 100 shares of each firm's stock, what is your profit?

For which of the two IPO's would you expect to be rationed given that other investors have better information, and hence know how to distinguish between the two issues?

What profit do you expect in reality?

What is the average underpricing?

What is your expected profit if the undervalued stock is undervalued by $0.50, everything else being  the same?

What is in this case the average underpricing?

Why do we have a winner's curse in this situation?

What is the expected profit if the undervalued stock is undervalued by $1.50, everything else bing the same?

What is the average underpricing now?

Does it make sense to underprice by this much if the goal of the firm is a) to get you interested in the IPO, and b) to minimize its losses.

If Pitt-Panther sets the subscription price at $20 per share, how many shares must be sold?

How many rights are required in order to buy one share?

What is the ex-rights price?

What is the value of a right?

Suppose you own 100 shares, but intend  to sell the rights, instead of exercising the rights and buy new shares. Is this a good decision?

What if you decide to exercise your rights, does this affect your total value?

If the rights are trading at $10 per right, how will this affect you if you own 100 shares and what would you recommend to someone who does not own shares?

How about if they trade at $13 per right?

What would be the minimum current share price (including the right) for you to be interested in buying rights at $13 each?

P_in = Price including rights
P_ex = Price excluding rights

(1) Without any rationing, your profit would be ($1*100) - ($0.50*100) = $50

(2) You'd expect the underpriced issue to be rationed, since informed investors will subscribe to this one, but they won't subscribe to the overpriced one.

(3) With rationing (and being an uninformed investor) we expect our profits to equal: ($1*50) -  ($0.50*100) = $0

(4) One IPO is overpriced by 5% ($0.50 on a $10 price) and the other is underpriced by 10% ($1 on a $10 stock), hence, on average we have [10% - 5%] / 2 = 2.5% underpricing.

(5)  The underpriced stock will still be rationed: ($0.50*50) - ($0.50*100) = -$25
 
(6) [5%-5%] / 2 = 0%

(7)  Without any underpricing, uninformed investors would incur a loss if they participate in IPO's. They will either get all the shares they ordered, but the shares will be overvalued, or, they will receive less or no shares in case the shares are undervalued.

(8) ($1.50*50) - ($0.50*100) = $25

(9) [15% - 5%] / 2 = 5%  => more underpricing on average results in more gains for uninformed (and informed) investors.

(10) No, by underpricing by 2.5% or slightly more the uninformed investors are already willing to participate because on average they will not be punished for not being informed. Underpricing by more would create larger losses for the firm.

Solutions to the Rights Offering Problem:

(1)  $10 million / $20 = 500,000

(2)  2 million / 500,000 = 4 rights are required to buy one new share

(3)  4 shares at $80 = $320
       1 share at $20 = $  20
        total is 5 shares, worth $340, or $68 per share.

(4) The price including the right is $80, the price excluding the right (since you just exercised that right) is $68, therefore, the value of the right is $12  (Think about the bargain that you are offered; you can buy a share in the firm (excluding the right) for $20, while we know that the real value of a share without a right is $68. That is $48 profit. You need, however 4 shares to realize this profit, or $12 each.)

(5) Does not matter. If you do not sell, you have a value of 100 shares at $80 is $8,000. If you sell your rights, you will have 100 shares worth $68, plus you can sell 100 rights at $12 each, your total is still $8,000.

(6) No. You will have 125 shares now (100 plus the additional 25 you buy in the rights offering) valued at $68 each, or $8,500 in total. This is the same as having 100 shares at $80 each, and buying 25 more shares at $20 each.

(7) If rights are trading at $10 each, you prefer to exercise the rights, because than we know the rights have a $12 value. You are not willing to sell something for $10 that is worth $12. If you sell, you make a loss of 100 ? $2 = $200.

 If you could buy right s for $10 each, you want to buy as many as possible.  If you buy 4 rights for $40 and an additional share in the rights
offering, you now have share worth $68, but you paid just $60.

 In other words, at a price of $10, nobody wants to sell rights, and everyone would want to buy as many as possible. This is not a sustainable situation: the rights have to trade at $12 each given the current stock price of $80.

(8) In this case you want to sell your rights. You make a dollar profit on each right you can sell. However, nobody wants to buy rights for $13. If you buy for rights for $52 plus an additional share for $20, you paid $72 for a share that is worth only $68. Again, the right can only trade at $12 given the current stock price of $80.

(9) First note that the higher the current stock price (which is now equal to $80), the more attractive it becomes to be offered to buy shares for $20. In other words, the higher the stock price, the more you would be willing to pay for a right.

If we know that a right is trading at $13, it means that the difference in the price with and without rights of the stock is $13, or, P_in - P_ex = $13, or  P_ex = P_in - $13.

We also know that if we buy four (4) shares, at P_in, we can buy one more share for $20. Therefore, we can have 5 shares for the total price of (4 * P_in) + $20.

The average price, excluding the rights, is thus: P_ex = [(4 * P_in )+ $20] / 5  => substituting for P_ex:

P_in - $13 = [(4 * P_in) + $20] / 5  => P_in = $85

Which makes sense, because if you can buy shares for $20, it becomes more attractive is the real stock price is higher. In other words, the value of the right, which allows you to benefit from the firm's bargain price, has become more valuable.