A firm has 60 million shares outstanding, each trading at $80. A hostile bidder acquires 15% of the firm’s shares in the open market, triggering a poison pill. According to the pill, all non-bidder shareholders are allowed to buy 1 new share for each share they own at a 50% discount to the current market price. What is the value lost by the hostile bidder due to the share dilution (millions)?

Question

BlackTom AI · Accepted Answer

Question restatement: A firm has 60 million shares outstanding, each trading at $80. A hostile bidder acquires 15% of the firm’s shares in the open market, triggering a poison pill. Under the pill, all non-bidder shareholders may buy 1 new share for each share they own at a 50% discount to the current market price. What is the value lost by the hostile bidder due to the share dilution (millions)?

Option-by-option analysis:
Option A: 165.4
- To evaluate dilution, first note the pre-pill market value of the firm’s equity: 60 million shares × $80 = $4,800 million.
- The bidder already owns 15% of the firm, i.e., 9 million shares (0.15 × 60m).
- After the pill, non-bidder shareholders (the remaining 51 million shares) can purchase 51 million new shares at 50% off the current price, i.e., at $40 per new share. This creates 51 million new shares.
- The post-pill total number of shares becomes 60m + 51m = 111m.
- The new cash raised by the company from the discounted issue is 51m × $40 = $2,040 million. This cash effectively increases the firm’s equity value by $2,040 million, assuming the market values the cash infusion positively.
- A reasonable way to estimate the post-dilution equity value is to take the original market value and add the new cash: $4,800m + $2,040m = $6,840m.
- If the price then normalizes to this new implied value spread across 111m shares, the new price per share is $6,840m / 111m ≈ $61.62.
- The bidder still owns 9 million shares, so the post-dilution value of the bidder’s stake is 9m × $61.62 ≈ $554.6 million.
- The value lost by the bidder due to dilution is the initial value of the bidder’s stake minus its post-dilution value: (9m × $80) − $554.6m = $720m − $554.6m ≈ $165.4 million.

Option B: 155.4
- If one assumed a different post-dilution price (e.g., using a different method to incorporate the new cash or adjusting for other market dynamics), you might arrive at a smaller loss. For instance, if you instead used a higher post-dilution price estimate, the bidder’s post-dilution stake would be valued higher, reducing the loss. However, to reach 155.4, the implied post-dilution price would have to be around ($720m − $155.4m) / 9m ≈ $63.27 per share, which would require a different accounting of the new cash impact or other adjustments not specified in the problem.

Option C: 135.4
- A loss of 135.4 million would imply an even higher post-dilution stake value (approximately $584.6m), which would require a post-dilution price around $64.95 per share. That would correspond to a larger per-share value than what the straightforward addition of $2,040m in new cash suggests, unless other factors push the price up.

Option D: 175.4
- A loss of 175.4 million suggests a post-dilution stake value of about $544.6m, meaning a post-dilution price of roughly $60.51 per share. That would indicate a weaker post-dilution price than the $61.62 derived from the simple sum-of-values approach, which seems inconsistent with the basic cash infusion effect described in the pill.

Additional notes:
- The key mechanism is that the pill increases the total number of shares from 60m to 111m, while the total equity value increases by the amount of cash raised from the discounted share issuance (51m new shares at $40 each equals $2,040m).
- The simplest and commonly accepted approach to approximate the post-dilution share price in this setup is to add the cash proceeds to the pre-dilution market value and divide by the new total shares, yielding around $61.62 per share and a bidder loss near $165.4m.
- If any step of these assumptions is altered (e.g., different interpretation of how price adjusts or whether the cash infusion fully translates to market value immediately), the resulting loss figure could differ, potentially aligning with other options.

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