LOS d: Calculate the book value effect of a share repurchase when the market value of a share is greater (less) than book value per share.

Q1. The share price of Solar Automotive Industries is $50 per share. It has a book value of $500 million and 50 million shares outstanding. What is the book value per share (BVPS) after a share repurchase of $10 million?

A)   $10.12

B)   $10.00.

C)   $9.84.

Q2. The share prices of Solar Automotive Industries and Winnipeg Auto Unlimited are both $50 per share, and each company has 50 million shares outstanding. On September 30, both companies announced a $10 million stock buyback. Solar has a book value of $500 million, while Winnipeg has a book value of $900 million. How much did the book value per share (BVPS) of each company increase or decrease after the share repurchase?

          Solar Automotive Industries       Winnipeg Auto Unlimited

A) Decrease by $0.13                            Decrease by $0.13

B) Decrease by $0.16                            Decrease by $0.13

C) Increase by $0.13                              Increase by $0.16

Q3. The share price of Winnipeg Auto Unlimited is $5 per share. There are 50 million shares outstanding, and Winnipeg has a book value of $900 million. What is the book value per share (BVPS) after the share repurchase of $10 million?

A)   $18.54.

B)   $21.24.

C)   $14.76.

LOS d: Calculate the book value effect of a share repurchase when the market value of a share is greater (less) than book value per share. fficeffice" />

Q1. The share price of Solar Automotive Industries is $50 per share. It has a book value of $500 million and 50 million shares outstanding. What is the book value per share (BVPS) after a share repurchase of $10 million?

A)   $10.12

B)   $10.00.

C)   $9.84.

Correct answer is C)       

The share buyback is $10 million / $50 per share = 200,000 shares.
Remaining shares: 50 million ? 200,000 = 49.8 million shares.

Solar Automotive Industries’ current BVPS = $500 million / 50 million = $10.
Book value after repurchase: $500 million ? $10 million = $490 million.
BVPS = $490 million / 49.8 million = $9.84.
BVPS decreased by $0.16.

Book value per share (BVPS) decreased because the share price is greater than the original BVPS. If the share prices were less than the original BVPS, then the BVPS after the repurchase would have increased.

Q2. The share prices of Solar Automotive Industries and Winnipeg Auto Unlimited are both $50 per share, and each company has 50 million shares outstanding. On September 30, both companies announced a $10 million stock buyback. Solar has a book value of $500 million, while ffice:smarttags" />Winnipeg has a book value of $900 million. How much did the book value per share (BVPS) of each company increase or decrease after the share repurchase?

          Solar Automotive Industries       Winnipeg Auto Unlimited

A) Decrease by $0.13                            Decrease by $0.13

B) Decrease by $0.16                            Decrease by $0.13

C) Increase by $0.13                              Increase by $0.16

Correct answer is B)

The share buyback for each company is $10 million / $50 per share = 200,000 shares.
Remaining shares for each company = 50 million ? 200,000 = 49.8 million shares.

For Solar Automotive Industries:
Solar Automotive Industries’ current BVPS = $500 million / 50 million = $10.
The market price per share of $50 is greater than the BVPS of $10.
Book value after repurchase = $500 million – $10 million = $490 million
BVPS = $490 million / 49.8 million = $9.84
BVPS decreased by $0.16

For Winnipeg Auto Unlimited:
Winnipeg Auto Unlimited’s current BVPS = $900 million / 50 million = $18.
The market price per share of $50 is greater than the BVPS of $18.
Book value after repurchase = $900 million – $10 million = $890 million
BVPS = $890 million / 49.8 million = $17.87
BVPS decreased by $0.13.

In the case of both Solar Automotive Industries and Winnipeg Auto Unlimited, book value per share (BVPS) decreased because the share price is greater than the original BVPS. If the share prices were less than the original BVPS, then the BVPS after the repurchase for each firm would have increased.

Q3. The share price of Winnipeg Auto Unlimited is $5 per share. There are 50 million shares outstanding, and Winnipeg has a book value of $900 million. What is the book value per share (BVPS) after the share repurchase of $10 million?

A)   $18.54.

B)   $21.24.

C)   $14.76.

Correct answer is A)

The share buyback is $10 million / $5 per share = 2,000,000 shares.
Remaining shares: 50 million ? 2 million = 48 million shares.

Winnipeg Auto Unlimited’s current BVPS = $900 million / 50 million = $18.
Book value after repurchase: $900 million ? $10 million = $890 million.
BVPS = $890 million / 48.0 million = $18.54.
BVPS increased by $0.54.

Book value per share (BVPS) increased because the share price is less than the original BVPS. If the share prices were more than the original BVPS, then the BVPS after the repurchase would have decreased.

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