Part 1: Maximum number of secondary shares you can sell while retaining more than 50% ownership

1. Total shares before the IPO: 1,111 million shares
2. Your current ownership: 88 million shares

You want to retain more than 50% of the company after selling shares in the IPO. To do that, the number of shares you own must remain greater than 50% of the new total shares (after the IPO).

Let’s define:

• $x$ = the number of shares you sell.

After selling $x$ shares, your new ownership will be $88 - x$ shares, and the total shares will increase to $1,111 + x$.

To retain more than 50% ownership, the following inequality must hold:

$88 - x > 0.5 \times (1,111 + x)$

Now, solve this inequality:

$88 - x > 0.5 \times (1,111 + x)$ $88 - x > 555.5 + 0.5x$ $88 - 555.5 > 0.5x + x$ $-467.5 > 1.5x$ $x < \frac{467.5}{1.5}$ $x < 311.67$

Since the number of shares must be a whole number, the maximum number of shares you can sell is 311 million.

Part 2: How much would the firm raise?

You are selling $11$ million shares for $21.60 each.

The total amount the firm would raise is:

$\text{Amount raised} = 11 \times 21.60 = 237.6 \text{ million dollars}$

Rounding to the nearest dollar:

$\text{Amount raised} = \$237,600,000$

Summary:

1. The maximum number of secondary shares you could sell is 311 million.
2. The firm would raise $237,600,000.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:

1. How does selling shares affect the overall value of the company?
2. What factors influence the decision to go public in an IPO?
3. How does dilution affect existing shareholders after an IPO?
4. What are primary and secondary shares in the context of an IPO?
5. How do companies determine the price per share in an IPO?

Tip: It's important to assess market conditions and investor demand when setting the IPO price to ensure a successful public offering.