Suppose an all-equity ﬁrm has a value of $10,000 and 100 shares outstanding. The ﬁrm has issued 25 warrants, each of which may be exchanged for one share. The warrants have an exercise price
Of $75. If the ﬁrm will be worth $9,800 in one period (before exercise), what will the price of the
Shares be assuming the warrants are exercised?
A) $88.20
B) $91.60
C) $93.40
D) $96.00
E) $98.40

Question

Quizplus · Accepted Answer

First, we need to calculate the number of shares outstanding after the warrants are exercised. Since there are 25 warrants and each gives the right to one share, there will be 100 + 25 = 125 shares outstanding after the warrants are exercised.

Next, we need to calculate the value of the equity if all of the warrants are exercised. The value of the equity will be (125 shares x current share price) + (25 warrants x (current share price - exercise price)) = (125 x S) + (25 x (S - 75)) = 10,000, where S is the current share price.

Expanding this equation, we get: 
125S + 25S - 1,875 = 10,000 
150S = 11,875 
S = $79.17

Therefore, if all of the warrants are exercised, the share price will be $79.17.

However, we are asked to find the share price assuming the warrants are exercised, which means that the share price will be lower than $79.17 because there will be more shares outstanding.

To calculate the share price assuming the warrants are exercised, we need to use the same formula but with 125 shares already outstanding: 
(125 x S) + (25 x (S - 75)) = 9,800 
150S = 12,575 
S = $83.83

Therefore, the share price assuming the warrants are exercised is $83.83.

However, we need to adjust for the fact that there were only 100 shares outstanding before the warrants were exercised. To do this, we need to calculate the value of the equity based on the original number of outstanding shares (100) and adjust for the value of the warrants: 
(100 x S) + (25 x (S - 75)) = 9,800 
125S = 11,675 
S = $93.40

Therefore, the price of the shares assuming the warrants are exercised is $93.40.

The correct answer is C.

Suppose an All-Equity ﬁRm Has a Value of $10,000 and 100