Grullon Co.is considering a 7-for-3 stock split.The current stock price is $75.00 per share,and the firm believes that its total market value would increase by 5% as a result of the improved liquidity that should follow the split.What is the stock's expected price following the split?
A)$32.06
B)$33.75
C)$35.44
D)$37.21
E)$39.07

Question

Quizplus · Accepted Answer

After the split, the total number of shares would be (7/3) times the current number of shares. So, the new price per share would be:

New Price = Current Price / (7/3)
New Price = $75.00 / (7/3)
New Price = $32.14

However, the firm expects that its total market value would increase by 5% as a result of the split. So, the new market value would be:

New Market Value = Current Market Value x 1.05
New Market Value = Current Price x Current Number of Shares x 1.05
New Market Value = $75.00 x N x 1.05

To keep the new market value the same as the current market value, we can solve for the new number of shares:

New Number of Shares = Current Number of Shares x (New Price / Current Price)
New Number of Shares = N x ($32.14 / $75.00)
New Number of Shares = N x 0.42853

So, the new price per share that would result in a 5% increase in market value is:

$75.00 x 1.05 / (N x 0.42853) = $33.75

Therefore, the expected price following the split is $33.75 per share, which corresponds to choice B.