Let's break down the problem step by step: ### Given: - Current share price will fall to $67 (ex-rights price) - Rights price: $44 - Company seeks: $9,460,000 additional funds - Subscription price (per new share): $34 - Number of old shares (to be found) - The increment to the market value of equity equals the gross proceeds from the offering. ### Solution Steps: 1. **Calculate Number of New Shares Issued:** \[ \text{Number of new shares} = \frac{\text{Funds needed}}{\text{Subscription price}} = \frac{9,460,000}{34} = 278,235.294 \] Round to the nearest whole number: **278,235** 2. **Market Value of Equity after Rights Issue:** The total value of the company after the rights issue will be the number of old shares times the new share price ($67), plus the amount raised ($9,460,000). After the rights issue, total shares = old shares + new shares. The market cap should equal (old shares + new shares) × $67. But the increment in market value of equity equals the gross proceeds, so: \[ \text{Old shares} \times 67 + 9,460,000 = (\text{Old shares} + 278,235) \times 67 \] \[ \text{Old shares} \times 67 + 9,460,000 = \text{Old shares} \times 67 + 278,235 \times 67 \] \[ 9,460,000 = 278,235 \times 67 \] \[ 9,460,000 = 18,639,745 \] This seems not to balance, so let's approach it differently. **The total value after rights issue:** \[ (\text{Old shares} + \text{New shares}) \times \text{Ex-rights price} = \text{Old shares} \times \text{Old price} + \text{New shares} \times \text{Subscription price} \] But we only have the ex-rights price ($67), not the old price. Alternatively, let's use the ratio: \[ \text{Number of new shares} = \frac{\text{Funds needed}}{\text{Subscription price}} = 278,235 \] Let \( X \) be the number of old shares. The ex-rights price is: \[ \text{Ex-rights price} = \frac{X \times 67 + 278,235 \times 34}{X + 278,235} \] But the ex-rights price is already given as $67. So, \[ 67 = \frac{X \times 67 + 278,235 \times 34}{X + 278,235} \] \[ 67(X + 278,235) = X \times 67 + 278,235 \times 34 \] \[ 67X + 67 \times 278,235 = 67X + 278,235 \times 34 \] \[ 67 \times 278,235 = 278,235 \times 34 \] \[ 67 = 34 \] This result is inconsistent, likely due to missing or misinterpreted data. The correct method is to use the gross proceeds and share price to estimate the old number of shares. ### Final Calculation Given the number of new shares is 278,235: - If the increment to equity value equals the gross proceeds, the number of old shares does not affect the proceeds directly, if we ignore price changes due to dilution. But if we assume the ex-rights price is strictly after new shares are added: \[ \text{Let } X = \text{number of old shares} \] After the rights issue: \[ (X + 278,235) \times 67 = X \times 67 + 9,460,000 \] \[ X \times 67 + 278,235 \times 67 = X \times 67 + 9,460,000 \] \[ 278,235 \times 67 = 9,460,000 \] \[ 18,639,745 = 9,460,000 \] Again, this does not balance, which indicates more data might be needed or the share price is not being used as the old share price. ### **Based on the data and usual approach:** The number of old shares is **not directly solvable** with the information provided unless the old share price before the rights issue is given. If you're supposed to use only the proceeds and subscription price: **Number of old shares:** **278,235** *(rounded to the nearest whole number)* If you have more information (e.g., the old share price before the rights issue), please provide it for a more precise answer.