Let's go step-by-step through this problem.

Part (a): Ex-Dividend Price

When the firm pays out the excess cash as a one-time dividend, in a perfect capital market, the ex-dividend price of the stock will drop by the amount of the dividend per share. The reason is that the value of the firm decreases by the amount of the dividend, and the stock price reflects this change.

Formula for Ex-Dividend Price:

$\text{Ex-dividend price} = \text{Current price} - \text{Dividend per share}$

1. Current market price = $11.50
2. Excess cash = $253 million
3. Shares outstanding = 535.535 million shares

First, calculate the dividend per share: $\text{Dividend per share} = \frac{\text{Excess cash}}{\text{Shares outstanding}} = \frac{253 \text{ million}}{535.535 \text{ million}} = 0.4725 \text{ (rounded to 4 decimal places)}$

Now, subtract this dividend from the current stock price: $\text{Ex-dividend price} = 11.50 - 0.4725 = 11.0275 \approx 11.03$

Thus, the ex-dividend price per share is $11.03.

Part (b): Share Repurchase Price

When the firm uses the excess cash for a one-time share repurchase, the share price after the repurchase can be calculated by determining the number of shares the firm can repurchase and then finding the new price per share.

1. Excess cash = $253 million
2. Shares outstanding = 535.535 million shares
3. Current market price = $11.50

Number of shares repurchased:

$\text{Shares repurchased} = \frac{\text{Excess cash}}{\text{Current market price}} = \frac{253 \text{ million}}{11.50} = 22 \text{ million shares (rounded to nearest million)}$

Now, after the repurchase, the number of shares outstanding will be: $\text{Remaining shares} = 535.535 \text{ million} - 22 \text{ million} = 513.535 \text{ million shares}$

The total market capitalization (value) of the firm remains the same, minus the cash used for repurchase: $\text{New firm value} = 535.535 \text{ million shares} \times 11.50 - 253 \text{ million} = 6,158.65 \text{ million}$

The new price per share is the total firm value divided by the remaining number of shares: $\text{New price per share} = \frac{6,158.65 \text{ million}}{513.535 \text{ million shares}} = 11.99$

Thus, the price per share after the repurchase is $11.99.

Part (c): Which policy makes investors better off?

In a perfect capital market, investors are indifferent to whether the firm uses the cash for a dividend payout or a share repurchase. This is because the total value they receive is the same in both cases. In a dividend payout, they get cash directly, while in a share repurchase, the value is reflected in the higher share price.

Thus, the best answer is C. Investors are indifferent to either policy.

Summary:

• (a) The ex-dividend price is $11.03.
• (b) The price after the share repurchase is $11.99.
• (c) Investors are indifferent to either policy in a perfect capital market.

Do you have any questions or want further details?

Related Questions:

1. How would taxes affect the choice between dividends and share repurchase?
2. What happens if the firm decides to reinvest the excess cash instead of paying it out?
3. How would the results change if the firm had debt in its capital structure?
4. What are the real-world factors that might make investors prefer dividends over repurchases?
5. How would a stock price react if the market did not expect a dividend or share repurchase?

Tip:

Always consider tax implications and market imperfections when comparing dividend payouts and share repurchases, as these can significantly impact investor preferences in real-world scenarios.