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.