Shares of the Mechanical Fruit Company currently trade for $7. Analysts rate the
ID: 2735368 • Letter: S
Question
Shares of the Mechanical Fruit Company currently trade for $7. Analysts rate the company a hold and regard it as fairly valued at its current price. The company has announced that it intends to spend $110.5650 million on an open market repurchase. In their press release management claims that the company's shares are occasionally undervalued and that buying shares at those undervalued prices represents a good investment. Assume that the company is able to repurchase shares at a price of $6.50. There are 150 million shares outstanding prior to the repurchase. Assume that the company is all equity financed.
a. What fraction of shares does the company repurchase?
b. What stock price prevails after the repurchase?
c. What is the aggregate gain in value to all the shareholders who do not sell any shares as a result of the repurchase of undervalued shares? In other words, if you owned all of the shares that were not repurchased, then what is your profit (loss) from before the repurchase to afterwards?
Explanation / Answer
Number of share outstanding before repurchase = 150 million
Market value of Stock = $7
Market capitalization = $7 × 150 million
= $1,050 million
Market Value of stock before repurchase $1,050 million.
a.
Amount spend on repurchase = $110.5650 million
Price at which stock repurchase = $6.50
Number of share repurchase = $110,565,000 / $6.5
= 17,010,000
Number of share repurchase is 17,010,000.
Fraction of share repurchase = 17,010,000 / 150,000,000
= 11.34%
Fraction of share repurchase is 11.34%.
b.
After repurchase number of share outstanding = 150,000,000 – 17,010,000
= 132,990,000
After repurchase number of share outstanding is 132,990,000.
After repurchase value of market capitalization = $1,050 million – 110.5650 million
= $939.435 million
After repurchase value of market capitalization is $939.435 million
Stock price after repurchase = $939,435,000 / 132,990,000
= $7.064
Stock Price after repurchase is $7.064.
c.
Aggregate gain in value to all the shareholders who do not sell any shares as a result of the repurchase is calculated below:
Aggregate gain in value = $7.064 - $7
= $0.064 per share.
Hence, Aggregate gain in value to all the shareholders who do not sell any shares as a result of the repurchase is $0.064 per share.
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