Let's break down the problem and solve it step by step. --- ### **Given:** - **Cogrelli Cogs (Target Company):** - Shares outstanding: **165,000** - Share price: **$43.85** - Total value: \( 165,000 \times \$43.85 = \$7,235,250 \) - **Spacely Sprockets (Acquiring Company):** - Shares outstanding: **475,500** - Share price: **$32.50** - Total value: \( 475,500 \times \$32.50 = \$15,453,750 \) - **Acquisition Offer:** - Spacely Sprockets is acquiring Cogrelli Cogs for **$7,235,250** by issuing new shares (Stock-for-stock deal). --- ## **(a) How many new shares of the acquirer's stock will be issued to pay for the merger?** The total value to be paid = **$7,235,250** (value of Cogrelli Cogs). - **Spacely Sprockets' share price:** **$32.50** **Number of new shares issued:** \[ \text{Number of new shares} = \frac{\text{Total purchase value}}{\text{Spacely share price}} = \frac{7,235,250}{32.50} = 222,624. (rounded to the nearest whole share) \] **Answer:** \[ \boxed{222,624} \] --- ## **(b) How many shares will the acquirer have after the merger?** - Existing Spacely shares: **475,500** - New shares issued: **222,624** \[ \text{Total shares after merger} = 475,500 + 222,624 = 698,124 \] **Answer:** \[ \boxed{698,124} \] --- ### **Summary Table** | Question | Calculation | Answer | |----------|-------------|--------------| | (a) | \( 7,235,250 / 32.50 \) | 222,624 shares | | (b) | \( 475,500 + 222,624 \) | 698,124 shares | Let me know if you need further explanation!

Introduction: In corporate finance, mergers and acquisitions (M&A) involve the transfer of ownership interests, often through the issuance of new shares by the acquiring company to pay for the target firm. Understanding how to determine the number of new shares to issue and the resulting total outstanding shares post-merger requires familiarity with valuation, share price, and the concept of stock-for-stock deals. The key components include calculating the total value of the target company, translating this value into a number of acquirer's shares based on its stock price, and then summing existing and newly issued shares to find the post-merger equity structure. Explanation: This introduction establishes the fundamental principles involved in stock-based acquisitions, emphasizing the importance of valuation and share pricing. It provides the necessary foundation for understanding how the value of the target company translates into new shares issued by the acquirer, which is crucial for solving the problem accurately. Recognizing that the merger involves exchanging a monetary value for equity shares helps clarify the subsequent calculation process. --- ### Relevant Formulas Required To Solve The Question: 1. **Total Value of the Target Company:** \[ \text{Target's Total Value} = \text{Number of Shares Outstanding} \times \text{Share Price} \] *Rationale:* This formula calculates the total market value of the target firm based on its shares outstanding and share price, essential for determining how much the acquirer needs to pay. 2. **Number of New Shares Issued:** \[ \text{New Shares Issued} = \frac{\text{Total Value to be Paid}}{\text{Acquirer's Share Price}} \] *Rationale:* Converts the monetary value paid for the target into an equivalent number of shares issued by the acquirer, based on its current stock price. 3. **Total Shares Outstanding After Merger:** \[ \text{Total Shares After Merger} = \text{Existing Shares of Acquirer} + \text{New Shares Issued} \] *Rationale:* Summing existing and newly issued shares yields the total number of shares outstanding post-merger, reflecting the combined company's equity structure. --- ### Step-by-Step Solution: **Step 1: Calculate the total value of the target company (Cogrelli Cogs).** - Shares outstanding = 165,000 - Share price = $43.85 \[ \text{Target's Total Value} = 165,000 \times 43.85 = \$7,235,250 \] **Explanation:** Multiplying the number of shares outstanding by the share price provides the total market valuation of Cogrelli Cogs. This value represents the amount the acquirer is effectively paying, in terms of equity exchange, for the target. --- **Step 2: Determine the number of new shares of Spacely Sprockets to be issued.** - Total value to be paid = $7,235,250 - Spacely Sprockets' share price = $32.50 \[ \text{New Shares Issued} = \frac{7,235,250}{32.50} \approx 222,624 \text{ shares} \] **Explanation:** Dividing the total value of the target company by the acquirer's current share price converts the merger consideration into the number of new shares that must be issued to shareholders of Cogrelli Cogs. The rounding to the nearest whole share aligns with standard practice. --- **Step 3: Calculate the total shares outstanding after the merger.** - Existing shares of Spacely Sprockets = 475,500 - Newly issued shares = 222,624 \[ \text{Total Shares After Merger} = 475,500 + 222,624 = 698,124 \] **Explanation:** Adding the newly issued shares to the existing shares of the acquirer yields the total number of shares outstanding after the merger, representing the combined company's equity. --- ### **Conclusion:** The number of new shares of Spacely Sprockets issued to pay for Cogrelli Cogs is approximately **222,624** shares. After the merger, the total shares outstanding for Spacely Sprockets will be approximately **698,124** shares. These calculations demonstrate the process of translating valuation and share price into share issuance and equity structure adjustments in a merger scenario.