Chartered Financial Analyst Level 2
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18 An analyst gathers the following information about the common stock of a company that is planning to buy back shares:
- Book value per share: $20
- Market price per share: $25
- Number of shares outstanding before repurchase: 9 million
After the repurchase of 400 thousand shares at the market price, the company's book value per share will be closest to:
A. 19.77.
C. $20.93.
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A
$18.89.
B
$19.77.
C
$20.93.
Explanation:
Calculation Process
Step 1: Calculate initial total book value
- Book value per share = $20
- Shares outstanding = 9,000,000
- Total book value = 180,000,000
Step 2: Calculate cash used for repurchase
- Shares repurchased = 400,000
- Market price = $25
- Cash used = 400,000 × 10,000,000
Step 3: Calculate new total book value after repurchase
- New total book value = Initial total book value - Cash used
- New total book value = 10,000,000 = $170,000,000
Step 4: Calculate new shares outstanding
- New shares outstanding = 9,000,000 - 400,000 = 8,600,000
Step 5: Calculate new book value per share
- New book value per share = 19.767 ≈ $19.77
Explanation
When a company repurchases shares at a price higher than the current book value per share (20), the book value per share decreases. This occurs because the company is paying more than the accounting value of the shares, effectively reducing the overall equity per remaining share. The calculation shows the new book value per share is $19.77, which matches option B.
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