Sol Company has announced plans to acquire Luna Corporation.Sol is trading for $23 per share,and has a premerger value of $7 billion,while Luna is trading for $56 per share and has a premerger value of $5 billion.The projected synergies from the merger are $500 million.If the offer is for $2 billion in cash and the remainder in stock,what is the maximum exchange ratio that Sol could offer in the stock swap portion and still generate a positive NPV?

Question

Quizplus · Accepted Answer

To calculate the maximum exchange ratio that Sol could offer in the stock swap portion, we need to find the total value of the offer. The offer is $2 billion in cash and the remainder in stock. Let's assume the exchange ratio is x. Then, the total value of the offer can be written as:
Total Value = $2 billion + (x * $23 * Number of Sol shares)

We need to find the value of x such that the Total Value is equal to the combined premerger value of Sol and Luna plus the synergies. That is:
Total Value = $7 billion + $5 billion + $500 million
Total Value = $12.5 billion

Substituting the values, we get:
$2 billion + (x * $23 * Number of Sol shares) = $12.5 billion
x * $23 * Number of Sol shares = $10.5 billion
x = $10.5 billion / ($23 * Number of Sol shares)

We don't know the exact number of Sol shares outstanding, but we can assume it to be some value y. Then, we can simplify the equation as:
x = $10.5 billion / ($23 * y)

Now, we need to find the value of y that makes the NPV positive. The NPV can be calculated as follows:
NPV = Total Value - Cost of Acquisition
NPV = ($12.5 billion) - ($2 billion in cash + x * $23 * y in stock)
NPV = $10.5 billion - $2 billion - ($23 / $56 * x * $56 * y)
NPV = $8.5 billion - $23/56 * x * $56 * y

We know that the synergies are $500 million, which means the Cost of Acquisition is $12 billion. Substituting this in the equation, we get:
$8.5 billion - $23/56 * x * $56 * y = -$500 million
$8.5 billion = $23/56 * x * $56 * y - $500 million
$9 billion = $23/56 * x * $56 * y
$9 billion = $23 * x * y
x * y = $391.3 million

We want the NPV to be positive, which means the Total Value should be greater than the Cost of Acquisition ($12 billion). Substituting the value of x from earlier, we get:
$2 billion + ($10.5 billion / ($23 * y)) * $23 * y > $12 billion
$2 billion + $10.5 billion > $12 billion
$12.5 billion > $12 billion

This is true for any value of y, which means we can choose any value of y that makes x * y = $391.3 million. The maximum value of x can be calculated as:
x = ($10.5 billion / ($23 * y))
x * y = $391.3 million
($10.5 billion / ($23 * y)) * y = $391.3 million
y = $391.3 million / ($10.5 billion / $23)
y = 0.845 billion

Substituting this value of y, we get:
x = ($10.5 billion / ($23 * 0.845 billion))
x = 2.844

Rounding off to 2 decimal places, the maximum exchange ratio Sol can offer is 2.84. Therefore, the correct answer is C) 2.84.

Sol Company Has Announced Plans to Acquire Luna Corporation