To solve this problem, let’s go step-by-step through each question.

Step 1: Expected Market Price of the Common Stock After the Announcement

Since there are no taxes, the firm's value remains the same before and after the debt issuance due to the Modigliani-Miller theorem. This means that the price per share should remain the same after the announcement. Thus, the expected market price of the common stock after the announcement will still be $15 per share.

Step 2: Number of Shares the Company Can Buy Back

The company plans to issue $330 million in debt and use it to buy back shares. Since each share is priced at $15:

$\text{Number of shares to buy back} = \frac{\text{Total debt issued}}{\text{Price per share}} = \frac{330}{15} = 22 \text{ million shares}$

So, the company can buy back 22 million shares.

Step 3: Market Value of the Firm After the Change in Capital Structure

The market value of the firm is the sum of equity and debt. Initially, the firm has 42 million shares valued at $15 each, so the initial market value of equity is:

$\text{Initial market value of equity} = 42 \times 15 = 630 \text{ million}$

After issuing $330 million in debt and buying back $330 million in shares, the total market value of the firm becomes:

$\text{Market value of the firm after the change} = \text{Equity} + \text{Debt} = 630 = 630 \text{ million}$

Thus, the market value of the firm after the change is 960 million.

Step 4: Debt Ratio After the Change in Capital Structure

The debt ratio is calculated as:

[ \text{Debt Ratio} = \frac{\text{Debt}}{\text{Total Value of the Firm}} \times 100 = \frac{330}{960}