A firm that is worth $800 million initiates a rights offering that will allow each of its 100 million shareholders to buy one additional share at a discount of 15%. If only 25% of the existing
Shareholders participate in the rights offering and the others simply let their rights expire,
What is the percentage gain to the participating shareholders? Assume the firm is all-equity
Financed, and round your answer to the nearest tenth of a percent.

Question

Quizplus · Accepted Answer

The number of shares outstanding will increase from 100 million to 125 million (25% participation*100 million shares). Each shareholder who participates will be able to buy one additional share for every four shares they currently own. Therefore, the total number of shares that will be issued through the rights offering is 100 million/4 = 25 million new shares.

The price at which the new shares will be issued is discounted by 15%, so the price per share will be 100% - 15% = 85% of the current share price. Thus, the per-share price is $800 million/100 million shares = $8 per share, and the price at which the new shares will be issued is 85%*$8 = $6.80 per share.

The total amount of money raised through the rights offering is equal to the number of new shares issued (25 million) multiplied by the price per share ($6.80), which equals $170 million.

The value of the firm prior to the rights offering is $800 million, and after the rights offering, the firm will have raised an additional $170 million in capital, so the firm will be worth a total of $970 million.

The percentage gain to the participating shareholders can be calculated as follows:

- A shareholder who holds 100 shares prior to the rights offering will be able to purchase 25 new shares at a price of $6.80, for a total cost of 25*$6.80 = $170. 
- The shareholder's total investment in the firm will then be 125 shares*$8 per share = $1,000 prior to the rights offering, plus the $170 spent on the new shares, for a total investment of $1,170. 
- After the rights offering, the shareholder will own 150 shares (125 original shares plus 25 new shares), which based on the new total value of the firm of $970 million, are worth $6.47 per share ($970 million/150 million shares). 
- The shareholder's total investment, including the cost of the new shares, is now worth $970 million/150 million shares*$150 shares + $170 = $1,037.33.

The percentage gain to the participating shareholders is therefore ($1,037.33 - $1,000)/$1,000 = 3.733%, rounded to the nearest tenth of a percent. The correct answer is D.

A Firm That Is Worth $800 Million Initiates a Rights