Question

Problem 10-08

A stock is currently trading for $30. The company has a price–earnings multiple of 10. There are 100 million shares outstanding. Your model indicates that the stock is actually worth $25. The company announces that it will use $310 million to repurchase shares.

1. After the repurchase, what is the value of the stock, according to your model? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. After the repurchase, what is the actual price–earnings multiple of the stock? Do not round intermediate calculations. Round your answer to two decimal places.

3. If the company had used the $310 million to pay a cash dividend instead of doing a repurchase, how would the value of the stock have changed, according to your model? Do not round intermediate calculations. Round your answer to the nearest cent.

   The market value of the stock is now $   .

4. If the company had used the $310 million to pay a cash dividend instead of doing a repurchase, what would be the actual price–earnings multiple after the dividend? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Current traded price of the stock = $30

Price-earning multiple = 10

Shares outstanding = 100,000,000

Price of the stock valued under our model = $25

Repurchase value announced = $310,000,000

Solution to Part a:

Total value of the stock before the repurchase = valuation per share under our model * number of shares outstanding before repurchase

= $25 * 100 million

= $2500 million

Total value of the stock after the repurchase = Value before repurchase - Value of repurchase

= $2500 million - $310 million

= $2190 million

The number of shares to be repurchased at the current traded price = Repurchase value / Current traded price

= $310,000,000 / $30   

= 10,333,333 shares

Number of shares outstanding after the repurchase = 100,000,000 - 10,333,333 = 89,666,667 shares ... ...(= total shares - shares repurchased)

Value of stock per share after repurchase = Total value of the stock after repurchase / Number of shares outstanding after repurchase

= $2,190,000,000 / 89,666,667

= $24.42 per share

After the repurchase, value of the stock, according to our model = $2,190 million or $24.42 per share

Solution to Part b:

Price-earnings multiple = Stock price per share / Earning per share

We have the price-earnings multiple = 10 and the value of stock per share = $25

10 = $25 / Earnings per share before repurchase

10 * Earnings per share = $25

Earnings per share = $25 / 10

Earnings per share before repurchase = $2.50 .......(i)

Total earnings before repurchase = Earnings per share before repurchase * Number of shares outstanding before repurchase = $2.50 * 100 million = $250 million

Assuming that the company uses idle cash to finance the repurchase, there would be no change to earnings after the repurchase. So the earning before or after repurchase would be $250 million.

Earning per share after repurchase = Total earnings / Number of shares outstanding after repurchase

= $250,000,000 / 89,666,667

= $2.79 per share

New price-earning multiple after the repurchase = New price per share after repurchase / New earnings per share after repurchase

= $24.42 / $2.79

= 8.75

After the repurchase, the actual price–earnings multiple of the stock = 8.75

Solution to Part c:

If the company had used the $310 million to pay a cash dividend instead of doing a repurchase, while the total value of the stock would reduce to $2190 as explained below (due to utilization of retained earnings for the payout of cash dividend), however, the number of shares outstanding would remain the same i.e. 100 million shares

Total value of the stock after the cash dividend payout = Value before cash dividend payout - Value of cash dividend payout

= $2500 million - $310 million

= $2190 million

So the value of the stock per share after cash dividend = Value of the stock after cash payout / Number of shares outstanding

= $2,190 million / 100 million

=$21.90 per share

If the company had used the $310 million to pay a cash dividend instead of doing a repurchase, the value of the stock would have changed to $2190 million or $21.90 per share

Solution to Part d:

Assuming that the company uses idle cash to pay the dividend, there would be no change to earnings after the dividend payout. So the earning before or after dividend payout would be $250 million and since the number of shares after dividend payout would be the same (100 million). the earnings per share would be the same too as calculated in part b [line marked (i) above] of the solution above i.e. $2.50

The new price-earnings multiple = Price of the stock per share after dividend payout / Earnings per share after payout

= $21.90 / $2.50

= 8.76

If the company had used the $310 million to pay a cash dividend instead of doing a repurchase, the actual price–earnings multiple after the dividend = 8.76