Question

A stock is currently trading for $38. The company has a price–earnings multiple of 10. There are 100 million shares outstanding. Your model indicates that the stock is actually worth $28. The company announces that it will use $350 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 $350 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 $350 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

Share price = $38

P/E multiple =10

P/E = price / EPS

EPS = 38/10 = 3.8

A)

Shares before Repurchase = 100M

Shares Repurchased = Amt used for Repurchase / Current price of shares

= 350M / 38 = 9210526

Shares outstanding after repurchase =  Shares before Repurchase - Shares Repurchased

= 100000000 - 9210526

= 90789474

New EPS = Current EPS * Shares before Repurchase / Shares outstanding after repurchase

= 3.8 * 100000000 / 90789474

= 4.185

Price as per Model $28

P/E multiple as per our model = 28/3.8 = 7.37

Now,

EPS increases after Repurchase of stock = 4.185

so Value of the stock as per our Model = P/E * EPS

= 7.37 * 4.18

= 30.84

B)

The P/E multiple decreases after share repurchase as repurchase decreases the number of shares which increases EPS thereby leading to decrease in P/E multiple

Actual P/E multiple of the stock after repurchase = Price / New EPS

New EPS = 4.185 (as calculated in a)

= 38 / 4.185

= 9.08

C)

Dividend = $ 350 M

DPS = Dividend / Shares Outstanding

= 350 M / 100 M

= 3.5

Price as per our model before dividend = $ 28

Theoretically the share price increases by the same amount of Dividend per share (DPS) given

Therefore new Price as per our model = 28 + 3.5

= $ 31.5

D)

New P/E = New Price / New EPS

Theoretically the share price increases by the same amount of Dividend per share (DPS) given

DPS = $ 350M / 100M

= 3.5

New Price = 38 + 3.5

= $ 41.5

Current EPS = Stock price / P/E Multiple

= 38 / 10 = 3.8

New EPS = EPS - DPS

= 3.8 - 3.5 (as dividend is paid out of earnings)

= 0.3

=41.5 / 0.3 (as calculated in C above)

New P/E = 138.33