Foster​ Enterprises' stock is trading for 

​$47.7047.70 

per share and there are currently 

55 

million shares outstanding. It would like to raise 

​$105105 

million. If its underwriter charges 

7 %7% 

of gross​ proceeds,

**a.** How many shares must it​ sell?

**b.** If it expects the stock price to drop by 

1 %1% 

upon announcement of the​ SEO, how many shares should it plan to​ sell?

**c.** If all of the shares are primary shares and are sold to new​ investors, what percentage reduction in ownership will all of the existing shareholders​ experience?

Question content area bottom

Part 1

**a.** How many shares must it​ sell?

The total number of shares it must sell will be 

enter your response here 

shares. ​ (Round to the nearest​ integer.)

Part 2

**b.** If it expects the stock price to drop by 

1 %1% 

upon announcement of the​ SEO, how many shares should it plan to​ sell?

If the stock price drops by 

1 %1%​, 

the total number of shares it must sell will be 

enter your response here 

shares. ​ (Round to the nearest​ integer.)

Part 3

**c.** If all of the shares are primary shares and are sold to new​ investors, what percentage reduction in ownership will all of the existing shareholders​ experience?

If all of the shares are primary shares and are sold to new​ investors, the existing ownership will drop by 

enter your response here​%. 

** ​(Round to two decimal​ places.)

Let's break down the problem step-by-step.

### Part 1: How many shares must it sell?

To calculate the number of shares Foster Enterprises needs to sell, we need to account for the underwriter's fee. The formula to find the required number of shares is:

\[
\text{Number of Shares} = \frac{\text{Amount to be Raised}}{\text{Stock Price} \times (1 - \text{Underwriter Fee})}
\]

Given:
- Amount to be raised = $105,000,000
- Stock price per share = $47.70
- Underwriter fee = 7% (or 0.07)

\[
\text{Number of Shares} = \frac{105,000,000}{47.70 \times (1 - 0.07)}
\]

Let's calculate it:

\[
\text{Number of Shares} = \frac{105,000,000}{47.70 \times 0.93}
\]

\[
\text{Number of Shares} \approx \frac{105,000,000}{44.36} \approx 2367286
\]

Rounding to the nearest integer, the number of shares is 2,367,286.

### Part 2: How many shares should it plan to sell if the stock price drops by 1%?

If the stock price drops by 1%, the new stock price will be:

\[
\text{New Stock Price} = \text{Original Stock Price} \times (1 - 0.01)
\]

\[
\text{New Stock Price} = 47.70 \times 0.99 = 47.223
\]

Using the same formula as in Part 1, but with the new stock price:

\[
\text{Number of Shares} = \frac{105,000,000}{47.223 \times 0.93}
\]

\[
\text{Number of Shares} \approx \frac{105,000,000}{43.918} \approx 2390522
\]

Rounding to the nearest integer, the number of shares is 2,390,522.

### Part 3: Percentage reduction in ownership

If all the shares are sold as primary shares to new investors, the reduction in ownership for existing shareholders can be calculated using the formula:

\[
\text{Ownership Reduction} = \frac{\text{New Shares}}{\text{Current Shares} + \text{New Shares}} \times 100
\]

- Current shares = 55,000,000

Using the shares calculated in Part 1:

\[
\text{Ownership Reduction} = \frac{2,367,286}{55,000,000 + 2,367,286} \times 100
\]

\[
\text{Ownership Reduction} \approx \frac{2,367,286}{57,367,286} \times 100 \approx 4.13\%
\]

### Summary

1. **Number of Shares to Sell:** 2,367,286 shares
2. **Number of Shares to Sell (with 1% price drop):** 2,390,522 shares
3. **Ownership Reduction:** 4.13%

Do you want more details or have any questions?

---

**Further Questions:**
1. What is the formula for calculating the proceeds after accounting for underwriter fees?
2. How does a change in stock price affect the number of shares needed to be sold?
3. What impact does a higher underwriter fee have on the number of shares required to be sold?
4. What would be the ownership reduction if only half of the shares are sold as primary shares?
5. How would the required number of shares change if the company wants to raise more capital?

**Tip:** Always account for underwriter fees and expected stock price drops when calculating the number of shares to be sold to avoid underestimating the dilution effect.

Foster Enterprises' stock is trading for $47.70 per share and there are currently 55 million shares outstanding. It would like to raise $105 million. If its underwriter charges 7% of gross proceeds: a. How many shares must it sell? b. If it expects the stock price to drop by 1% upon announcement of the SEO, how many shares should it plan to sell? c. If all of the shares are primary shares and are sold to new investors, what percentage reduction in ownership will all of the existing shareholders experience?

Learn how to calculate the number of shares Foster Enterprises must sell to raise $105 million, factoring in underwriter fees and stock price changes. Discover the ownership reduction experienced by existing shareholders. Suitable for finance students and professionals.

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