Question

firms a and b, both of which are 100% equity, are going to merge. before the merger, firm a (100 shares outstanding) is worth $15,000. firm b (50 shares outstanding) is worth $10,000. the combined firm is worth $30,000. firm a will pay $11,500 in cash for firm b. what is the npv of the merger to firm a?

Answer 1

The Net Present Value (NPV) of the merger to Firm A is $3,500. It is calculated by subtracting the sum of Firm A's value before the merger and the cash paid to acquire Firm B from the value of the combined firm after the merger.

Step-by-step explanation:

The question asks us to calculate the Net Present Value (NPV) of the merger to Firm A, given that both Firm A and Firm B are merging. Firm A is paying $11,500 in cash for Firm B. To calculate NPV, we need to understand the value Firm A will have after the merger, the amount it is paying to acquire Firm B, and the value of the combined firm post-merger.

Here's the calculation:

• Value of Firm A before the merger: $15,000
• Value of Firm B before the merger: $10,000
• Total value of both companies before merger: $15,000 + $10,000 = $25,000
• Combined firm value after the merger: $30,000
• Amount paid by Firm A for Firm B: $11,500

To find the NPV for Firm A, we subtract the amount paid for Firm B from the combined firm value and then subtract the initial value of Firm A:

NPV = Combined firm value after the merger - (Value of Firm A before the merger + Amount paid for Firm B)

NPV = $30,000 - ($15,000 + $11,500) = $30,000 - $26,500 = $3,500

The NPV of the merger for Firm A is $3,500.