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Quantitative Problems Chapter 11

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Quantitative Problems Chapter 11
Ebay, Inc. went public in September of 1998. The following information on shares outstanding was listed in the final prospectus filed with the SEC1.
In the IPO, the Ebay issued 3,500,000 new shares. The initial price to the public was $18.00 per share. The final first-day closing price was $44.88.
1. If the investment bankers retained $1.26 per share as fees, what was the net proceeds to Ebay? What was the market capitalization of new shares of Ebay?
Solution: Net Proceeds to Ebay  (18.00  1.26)  3,500,000  $58,590,000.00
Market Cap  44.88  3,500,000  157,080,000
2. Two common statistics in IPOs are underpricing and money left on the table. Underpricing is defined as percentage change between the …show more content…

Solution: Price  3.90  25  $97.50
13. For 2003, Microsoft, Inc. reported earnings per share around $0.75. If Microsoft is in an industry with a ratio ranging from 30 to 40, what is a reasonable price range for Microsoft?
Solution: Microsoft’s price should be between $0.75  30 to $0.75  40, or $22.50 to $30.00.
14. Consider the following security information for 4 securities making up an index:
Security
Price
Shares
Outstanding

time  0 time  1

1
8
13
20 million
2
22
25
50 million
3
35
30
120 million
4
50
55
75 million
What is the change in the value of the index from time  0 to time  1 if the index is calculated using a value-weighted arithmetic mean?
Solution: For a value-weighted arithmetic mean, the change is calculated as follows:
First, the market value at time  0 is calculated as:
Security
Price
Shares
Outstanding
Market
Value

time  0 time  1

1
8
13
20 million
$160
2
22
25
50 million
$1,100
3
35
30
120 million
$4,200
4
50
55
75 million
$3,750

$9,210
The change is then calculated as:

Index1  Index0  1.0027
15. An index had an average (geometric) mean return over 20 years of 3.8861%. If the beginning index value was 100, what was the final index value after 20 years?
Answer: The actual return over the 20 years is (1.038861)20  2.143625
So, the final index value is 214.3625
16. $1/(1  0.51)  $20/(1  0.15)  $18.26
17. 23  $3.5 

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