Let's walk through each part of the problem step by step.

Part 1: Total Proceeds for Keros' IPO

The total proceeds are calculated by multiplying the number of shares sold in the IPO by the IPO offer price.

$\text{Total Proceeds} = \text{Number of Shares} \times \text{IPO Offer Price}$

• Number of Shares = 6,000,000
• IPO Offer Price = $15.79

$\text{Total Proceeds} = 6,000,000 \times 15.79 = 94,740,000$

Total proceeds = $94,740,000

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Part 2: Underwriting Fee

The underwriting discount is 6.1%. To find the underwriting fee, multiply the total proceeds by the underwriting discount.

$\text{Underwriting Fee} = \text{Total Proceeds} \times \text{Underwriting Discount}$

• Underwriting Discount = 6.1% = 0.061

$\text{Underwriting Fee} = 94,740,000 \times 0.061 = 5,783,140$

Underwriting Fee = $5,783,140

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Part 3: Net Proceeds for Keros' IPO

Net proceeds are calculated by subtracting the underwriting fee from the total proceeds.

$\text{Net Proceeds} = \text{Total Proceeds} - \text{Underwriting Fee}$

$\text{Net Proceeds} = 94,740,000 - 5,783,140 = 88,956,860$

Net Proceeds = $88,956,860

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Part 4: Market Capitalization

Market capitalization is calculated by multiplying the total number of outstanding shares (which includes newly issued shares) by the secondary market price.

$\text{Market Capitalization} = \text{Outstanding Shares} \times \text{Secondary Market Price}$

• Outstanding Shares = 19,189,391
• Secondary Market Price = $21.68

$\text{Market Capitalization} = 19,189,391 \times 21.68 = 415,828,477.68$

Market Capitalization = $415,828,478

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Part 5: IPO Underpricing

IPO underpricing is calculated as the percentage difference between the secondary market price and the IPO offer price, relative to the IPO offer price.

$\text{IPO Underpricing} = \frac{\text{Secondary Market Price} - \text{IPO Offer Price}}{\text{IPO Offer Price}} \times 100$

• Secondary Market Price = $21.68
• IPO Offer Price = $15.79

$\text{IPO Underpricing} = \frac{21.68 - 15.79}{15.79} \times 100 = \frac{5.89}{15.79} \times 100 = 37.3\%$

IPO Underpricing = 37.30%

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Part 6: Explanation of IPO Underpricing

The statement provided is True. IPO underpricing occurs when secondary market investors are willing to pay a higher price for shares than what primary market investors paid during the IPO. This is often seen as a sign of high demand and can result in a "pop" in the stock price on the first day of trading.

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Summary of Results:

1. Total Proceeds = $94,740,000
2. Underwriting Fee = $5,783,140
3. Net Proceeds = $88,956,860
4. Market Capitalization = $415,828,478
5. IPO Underpricing = 37.30%
6. Explanation of IPO Underpricing: The statement is True.

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Do you want more details on any part or have further questions?

Here are some related questions to deepen understanding:

1. How do fluctuations in the secondary market price affect market capitalization?
2. What other factors influence IPO underpricing?
3. How does the underwriting discount typically impact the company's fundraising?
4. How are market capitalization and net proceeds related, if at all?
5. What are the long-term effects of IPO underpricing on a company's stock?

Tip: IPO underpricing can help generate buzz for the stock, but it also means the company may have raised less money than it could have at market value.