Sol Company has announced plans to acquire Luna Corporation at a premium of 30% over the pre-announcement share price.Sol is trading for $19 per share,and has a premerger value of $37 billion.Prior to the announcement,Luna was trading for $12 per share,and currently has 192 million shares outstanding.The projected synergies from the merger are $2 billion.What is the maximum exchange ratio that Sol could offer in a stock swap transaction and still generate a positive NPV?

Question

Quizplus · Accepted Answer

To find the maximum exchange ratio that Sol could offer in a stock swap transaction and still generate a positive NPV, we first calculate the value of Luna with the premium: $12 * 1.30 = $15.6 per share. The total value of Luna with the premium is $15.6 * 192 million = $2,995.2 million. The combined value of Sol and Luna with synergies is $37 billion + $2,995.2 million + $2 billion = $41,995.2 million. The number of Sol shares pre-merger is $37 billion / $19 = 1,947.37 million shares. To ensure a positive NPV, the value per share post-merger must be greater than $19. The maximum number of shares Sol can issue is when the post-merger value per share equals the pre-merger price: $41,995.2 million / (1,947.37 million shares + X) = $19, where X is the number of new shares issued. Solving for X gives the maximum number of shares Sol can issue without diluting the value below $19 per share. The exchange ratio is the number of new shares issued (X) divided by the number of Luna shares: X / 192 million. Given the calculations and choices, the correct answer involves calculating the specific exchange ratio that meets these conditions, which is 1.37. This implies that for each Luna share, Sol could offer up to 1.37 of its shares and still maintain a positive NPV from the merger, taking into account the premium paid for Luna, the pre-merger values of both companies, and the projected synergies.

Sol Company Has Announced Plans to Acquire Luna Corporation at a Premium