There are no taxes. EBIT is expected to be $2.5 million, but could be as high as $3.5 million if an economic expansion occurs, or as low as $2 million if a recession occurs. All values are market
Values.
How many shares are outstanding under the proposed capital structure?
A) 100,000
B) 200,000
C) 300,000
D) 400,000
E) 500,000

Question

Quizplus · Accepted Answer

To find the number of outstanding shares, we need to use the formula for the market value of equity (MVE): MVE = EBIT / r. We know that MVE = $2 million when there is a recession, MVE = $2.5 million when the expected EBIT occurs, and MVE = $3.5 million during an economic expansion. Assuming a constant cost of equity (r), we can solve for the MVE with any of these values and then solve for the number of outstanding shares using the MVE and the given market value per share (MVPS) of $20: 
- MVE = $2 million: MVE = MVPS * number of shares -> 2,000,000 = 20 * number of shares -> number of shares = 100,000
- MVE = $2.5 million: 2,500,000 = 20 * number of shares -> number of shares = 125,000
- MVE = $3.5 million: 3,500,000 = 20 * number of shares -> number of shares = 175,000
Since the number of outstanding shares must be the same under all three scenarios, we can determine that the correct answer is D) 400,000, which is 2 * 200,000 (the number of shares in the proposed financing mix).

There Are No Taxes