The firm you founded currently has 

1111 

million​ shares, of which you own 

88 

million. You are considering an IPO where you would sell 

11 

million shares for 

​$21.6021.60. 

What is the maximum number of secondary shares you could sell and still retain more than 

5050​% 

ownership of the​ firm? How much would the firm raise in that​ case?

Question content area bottom

Part 1

The maximum number of secondary shares you could sell is 

enter your response here 

shares.  ​(Round to the nearest whole​ number.)

Part 2

The amount that the firm would raise is 

​$enter your response here. 

 ​(Round to the nearest​ dollar.)

### 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.

The firm you founded currently has 1,111 million shares, of which you own 88 million. You are considering an IPO where you would sell 11 million shares for $21.60. What is the maximum number of secondary shares you could sell and still retain more than 50% ownership of the firm? How much would the firm raise in that case?

Part 1: The maximum number of secondary shares you could sell is _______ shares. (Round to the nearest whole number.)

Part 2: The amount that the firm would raise is _______ (Round to the nearest dollar).

Learn how to calculate the maximum number of secondary shares you can sell while retaining more than 50% ownership in an IPO. This problem also includes how to compute the total amount raised based on the share price and the number of shares sold. Suitable for high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation