Let's break down the problem step by step: ### The Problem - Firm A (value = $50 million) is considering acquiring Firm B (value = $11 million). - The combined firm will have a merger gain (synergy) of $9 million. - A will pay $15 million cash Firm B. - **Question:** What is the NPV (Net Present Value) of the acquisition? --- ## Step 1: Calculate the Combined Value After Merger The combined value = Value of A + Value of B + Merger Gain \[ \text{Combined Value} = \$50\text{ million} + \$11\text{ million} + \$9\text{ million} = \$70\text{ million} \] --- ## Step 2: Calculate the Cost of Acquisition Firm A pays $15 million to acquire Firm B. --- ## Step 3: NPV of Acquisition Formula \[ \text{NPV of Acquisition} = \text{Combined Value} - (\text{Value of A} + \text{Cash Paid}) \] - Combined Value = $70 million - Value of A (before acquisition) = $50 million - Cash Paid = $15 million So, \[ \text{NPV} = \$70\text{ million} - (\$50\text{ million} + \$15\text{ million}) = \$70\text{ million} - \$65\text{ million} = \$5\text{ million} \] --- ## Step 4: Answer The correct answer is: - **$5 million** --- ### Why? The NPV tells us how much value Firm A gains from this acquisition **after accounting for the price paid**. Here, the value created by the merger (including synergy) is $5 million more than what Firm A had before, after paying for Firm B. --- **Let me know if you want to see this using another approach or have more questions about mergers!**

# Detailed Solution to Acquisition NPV Calculation ## Problem Overview - **Firm A's Value:** $50 million - **Firm B's Value:** $11 million - **Merger Gain (Synergy):** $9 million - **Cash Paid to Acquire Firm B:** $15 million **Goal:** Calculate the Net Present Value (NPV) of the acquisition. --- ## Step 1: Calculate the Combined Value After Merger To find the total value of the combined firms post-merger, we use the formula: \[ \text{Combined Value} = \text{Value of Firm A} + \text{Value of Firm B} + \text{Merger Gain} \] ### Calculation: \[ \text{Combined Value} = 50\text{ million} + 11\text{ million} + 9\text{ million} \] \[ \text{Combined Value} = 70\text{ million} \] --- ## Step 2: Calculate the Total Cost of Acquisition The total cost for Firm A to acquire Firm B is the cash paid: \[ \text{Cost of Acquisition} = \text{Cash Paid} = 15\text{ million} \] --- ## Step 3: NPV of Acquisition Formula The NPV of the acquisition can be calculated using the following formula: \[ \text{NPV} = \text{Combined Value} - (\text{Value of Firm A} + \text{Cash Paid}) \] ### Inputs: - **Combined Value:** $70 million - **Value of Firm A Before Acquisition:** $50 million - **Cash Paid:** $15 million ### Calculation: \[ \text{NPV} = 70\text{ million} - (50\text{ million} + 15\text{ million}) \] \[ \text{NPV} = 70\text{ million} - 65\text{ million} \] \[ \text{NPV} = 5\text{ million} \] --- ## Step 4: Conclusion The Net Present Value (NPV) of the acquisition is: - **NPV = $5 million** ### Interpretation A positive NPV indicates that Firm A will gain an additional value of $5 million from acquiring Firm B, after accounting for the cash paid in the acquisition. --- ## Summary of Key Points - **Combined Value:** $70 million - **Total Cost of Acquisition:** $15 million - **NPV of Acquisition:** $5 million If you have any more questions or need further clarification, feel free to ask!