Chapter 25: Warrants and Convertibles
If the stock price is less than the exercise price of the warrant at expiration, the warrant is
worthless. Prior to expiration, however, the warrant will have value as long as there is
some probability that the stock price will rise above the exercise price in the time
remaining until expiration. Therefore, if the stock price is below the exercise
price of the
warrant, the lower bound on the price of the warrant is zero.
If the stock price is above the exercise price of the warrant, the warrant must be worth at
least the difference between these two prices. If warrants were selling for less than the
difference between the current stock price and the exercise price, an investor
an arbitrage profit (i.e. an immediate cash inflow) by purchasing
them immediately, and selling the stock.
If the warrant is selling for more than the stock, it would be cheaper to purchase the stock
than to purchase the warrant, which gives its owner the right to buy the stock. Therefore,
an upper bound on the price of any warrant is the firm’s current stock price.
When a warrant is issued by the company, and when a warrant is exercised, the number of shares
increases. A call option is a contract between investors and does not affect the number of shares of the
The total exercise price of each warrant is shares each warrant can purchase times the exercise
which in this case will be:
Exercise price = 3($32)
Exercise price = $96
Since the shares of stock are selling at $39, the value of three shares is:
Value of shares = 3($39)
Value of shares = $117
Therefore, the warrant effectively gives its owner the right to buy $117 worth of stock for $96. It
follows that the minimum value of the warrant is the difference between these numbers, or:
Minimum warrant value = $117 – $96
Minimum warrant value = $21
If the warrant were selling for less than $21, an investor could earn an arbitrage profit by purchasing the
warrant, exercising it immediately, and selling the stock. Here, the warrant holder
pays less than
$21 while receiving the $21 difference between the price of three shares and the exercise price.
Since the stock price is currently below the exercise price of the warrant, the lower bound
on the price of the warrant is zero. If there is only a small probability that the firm’s stock
price will rise above the exercise price of the warrant, the warrant has little value. An
upper bound on the price of the warrant is $33, the current price of the common
One would never pay more than $33 to receive the right to purchase a share of
company’s stock if the firm’s stock were only worth $33.
Answers to End–of–Chapter Problems