Lecture 5: Warrants & Convertible bonds

What are convertible bonds?

1. Convertible bonds are fixed interest debt securities. 2. They can be converted into another security, typically ordinary shares at a specified price for a specified period of time. 3. Thus, unlike a common bond, a convertible security started its life as a bond, but subsequently may turn into common stock. 4. CBs can be thought of as equivalent to a straight bond and an option to acquire common stock. 5. When convertible bond holders exercise this option, they don't pay cash but give up their bonds in exchange for shares. 6. If bondholders don't decide to exercise this option, the CB are redeemed at a date usually some time after the conversion date. 7. Interest with bonds are risk free (for the investors) 8. CBs used to raise finance, they are different to normal bonds as you have an option to convert bonds to shares before point bond is paid back. Therefore they are worth more than additional bonds. 9. Swap bonds for shares. If the value of shares, is more than the bond value than it may be beneficially to swap bonds for shares and make a gain (e.g with the call options, if the share price is less than the exercise price we shouldn't exercise it) 10. Cos receive a higher interest. 11. Investor exercises right to convert money to shares. Its not the other way round.

What formulas / calculations information do we need to price warrants?

1. If the holder exercises the warrant the company receives MX (Number of warrants time exercise price) 2. ( N/N+M) max (Et/N-X,0)- See formula sheet. 3. (N/N+M)- The dilution factor, the one factor that differentiates warrants from convertible bonds. 4. W0= (N/M+N)C0, C0- Call option.

Explain how the dilution factor?

1. Once the warrants are exercised, the number of shares outstanding increases, and the stock price decreases. 2. e.g, if a person takes out a warrant with a firm. Imagine the firm has 5 shares at £10, therefore £2 per share. 3. If the person wants to exercise the shares as part of warrant with the firm, then the firm will need to get 5 more shares to give to the person. 4. This means they now have 10 shares and the share price reduces/dilutes to £1 per share. 5. Since the stock price decreases, the value of the warrant must be lower than that of a call option with similar features ( Note: N<1). 6. In other words, with this dilution you must still have a higher stock price than exercise price if you wish you exercise option.

How do we price warrants?

1. The black-scholes formula can be employed to value option packages on warrants. 2. The choice of whether to exercise a warrant depends on what the stock price would be with the new shares.

Why are warrants used?

1. The main differences between call option & warrant is that the former is issued by individuals and the latter by firms. 2. When the holder wants to exercise a warrant, she has to pay the necessary amount of money needed to cover the exercise price. 3. In many cases, warrants are issued to investment bankers as part of their compensation for underwriting services-long term executive stock options can also be considered warrants. 4. Companies rarely sell warrants directly to their investors.

What are the basics of warrants?

1. Warrants are long term call options (some of them are perpetual) that give the investor the right to buy the firms common stock. 2. The firm is the writer of the warrant and issues new shares if the warrant is exercised by the holder. 3. A warrant gives the owner the right to buy shares in the issuing company for a fixed price, on or before the specified date,usually years away. 4. e.g- Each warrant may allow the holder to buy a share of stock for $50 at any time during the next 5 years. 5. The warrant is normally protected against stock splits but not dividends.

What do the following notions stand for? Et? St? N? Wt? M? X? T?

Et: Is the value of the firm's equity at time t. St: Is the common share price of the outstanding shares at time t. N: Is the number of old common shares outstanding prior to any exercise of the warrants. Wt: Is the value of the warrants at time t. M: Is the number of warrants. X: Is the exercise price of the warrants. T: European option.

What type of debt are CBs?

Fixed interest debt securities.