Question

A company goes public by using an auction. The bids are contained in the table below. The firm wants to sell 11 million shares.

Price ($)	Number of Shares (millions)
25	3.5
24	3.0
23	2.5
22	5.0
21	7.5
20	5.5

Assume that the auction is conducted as a dirty auction, and the clearing price is $22. Describe which bidders would receive shares, the price they would pay, and how much of their orders would be filled. Enter your answers for the number of receive shares in millions. For example, an answer of 1.234 million should be entered as 1.234, not 1,234,000. Round the monetary values to the nearest dollar and answers for the number of receive shares to three decimal places. If the investor wouldn't receive shares, enter "0" in both columns.

Bid Price ($)	The Auction Price	Number of Receive Shares (millions)
25	$
24	$
23	$
22	$
21	$
20	$

Answer 1

In a dirty auction or a dutch auction, the price of the bid is lowered to the price where all the offering can be sold

Total Number of shares = 11 million

Number of bids at $25 = 3.5 million
Balance shares = 11 - 3.5 = 7.5 million

Number of bids at $24 = 3 million
Balance shares = 7.5 - 3 = 4.5 million

Number of bids at $23 = 2.5 million
Balance shares = 4.5 - 2.5 = $2 million

Number of bids at $22 = 5 million
Balance shares = 2 - 2 = 0 m

Hence, the auction price is $22

Bid Price ($)	Auction Price	Number of shares received (million)
25	22	3.5
24	22	3
23	22	2.5
22	22	2
21	22	0
20	22	0