11-10. A U.S. firm wants to raise $15 million by selling 1 million shares

at a net price of $15. We know that some say that firms “leave
money on the table” because of the phenomenon of underpricing.
a. Using the average amount of underpricing in U.S. IPOs, how
many fewer shares could it sell to raise these funds if the firm
received a net price per share equal to the value of the shares
at the end of the first day’s trading?

b. How many less shares could it sell if the IPO was occurring in
Germany?

c. How many less shares could it sell if the IPO was occurring in
Korea?

d. How many less shares could it sell if the IPO was occurring in
Canada?

To answer these questions, we need to determine the average underpricing in U.S. IPOs and understand how it affects the number of shares that need to be sold to raise the desired funds. Then, we can apply this understanding to analyze the IPO scenarios in Germany, Korea, and Canada.

a. To find the average underpricing in U.S. IPOs, we need specific data. We can refer to IPO databases or financial research reports to get these figures. Once we have the average underpricing percentage, we can calculate the net price per share, which would be the value of the shares at the end of the first day's trading. Let's assume the average underpricing is 15% in U.S. IPOs, and the net price per share would be $15 * (1 + 15%) = $17.25.

To find the number of fewer shares needed to raise $15 million at the net price per share of $17.25, we divide the desired funds by the net price per share: $15 million / $17.25 = 869,565.22 shares. Rounding down to the nearest whole number, the firm would need to sell 869,565 shares, which is approximately 130,435 fewer shares compared to selling 1 million shares at a net price of $15.

b. To determine the impact of underpricing in Germany, we would need to know the average underpricing percentage in German IPOs. Let's assume it is 10%. Applying the same formula as before, the net price per share would be $15 * (1 + 10%) = $16.50.

So, to raise $15 million at the net price per share of $16.50, the firm would need to sell $15 million / $16.50 = 909,090.91 shares. Rounded down to the nearest whole number, the firm would need to sell 909,090 shares, which is approximately 90,910 fewer shares compared to a U.S. IPO scenario.

c. Similarly, to analyze the impact in Korea, we need to know the average underpricing percentage in Korean IPOs. Let's assume it is 5%. Applying the formula, the net price per share would be $15 * (1 + 5%) = $15.75.

To raise $15 million at the net price per share of $15.75, the firm would need to sell $15 million / $15.75 = 952,380.95 shares. Rounded down to the nearest whole number, the firm would need to sell 952,380 shares, which is approximately 47,620 fewer shares compared to a U.S. IPO scenario.

d. Finally, to analyze the impact in Canada, we need to know the average underpricing percentage in Canadian IPOs. Let's assume it is 20%. Applying the formula, the net price per share would be $15 * (1 + 20%) = $18.

To raise $15 million at the net price per share of $18, the firm would need to sell $15 million / $18 = 833,333.33 shares. Rounded down to the nearest whole number, the firm would need to sell 833,333 shares, which is approximately 166,667 fewer shares compared to a U.S. IPO scenario.

Please note that the assumed underpricing percentages and the resulting calculations are for illustrative purposes only. Actual underpricing percentages vary, so it is essential to use accurate and up-to-date data when performing real-world analysis.