1. Warrants and Convertibles
Francesca Cornelli
Fall 1999

2. OUTLINE Warrants: Convertible Bonds: how to value a warrant
Main features
How to value a convertible bond
Why issue convertible bonds?

3. WARRANTS
Warrants are similar to standard traded call options. The holder has the right to buy stock at the exercise price on or before the maturity date. There are, however, important differences.
When a warrant is issued, the purchase price is received by the company
When a warrant is exercised, the exercise price is received by the company
When a warrant is exercised, new shares are issued by the company.

4. VALUING WARRANTS
Since exercising warrants increases the number of shares, exercise means that the firm’s assets and profits are spread over a larger number of shares.
Consider a firm with shares and warrants, each convertible into 1 share at an exercise price of K
Let be the value of the firm at maturity if warrants are not exercised
Payoff to warrants if exercised:
The dilution factor of the warrants is

5. Value of warrants at maturity

6. Payoff to all warrants if exercised:
Consider a firm with n shares and m warrants, each convertible into r shares at an exercise price of K
Let V be the value of the firm at maturity if warrants are not exercised
Payoff to all warrants if exercised:
The dilution factor of the warrants is:
In the good state the EPS is higher for the leveraged firm. It
is only because of the gearing.
In the good state.
Price-earning ratio decreases, since the stock price
remains the same and expected earning per share
increases.
This is an important observation because people use this
ratio to evaluate stocks.

7. Example of warrant pricing
All equity firm:
Shares (n) = 1 million
Number of warrants (m) with r = =100,000
Exercise price (K) =10
Time to maturity (t ) = 4 years
Value of assets = 12 million
Volatility ( ) = 40%
Risk-free rate ( ) = 10% per year
Value of warrants =
= .909 X 6.152mil =

8. Alternatively, the warrant can be viewed as a call on the equity on a per share basis.
Each warrant has a value at maturity:
Warrant value = where S is the “pseudo-share price”
In the previous example, the value of each warrant is:
= .909 X =

9. CONVERTIBLE BONDS
Convertible bonds are bonds that can be converted into a specified number of shares at the bondholder discretion
A convertible bond is a package of an ordinary bond and a warrant

10. EXAMPLE
A $1000 bond pays a coupon of $100 per year (10%) and can be converted at the option of the holder into 50 shares
CONVERSION RATIO : the number of shares received for each bond (50)
The conversion option may also be expressed in terms of the
CONVERSION PRICE =
The previous bond is said to be convertible into common shares at a conversion price of 1000/50 = 20

11. It is customary to distinguish between the straight debt value and the conversion value.
STRAIGHT DEBT VALUE = Value as a corporate bond without the conversion option. That is, based on the convertible bond’s cash flows if not converted
CONVERSION VALUE = Value of the bond if it is converted immediately. It is given by: share price X conversion ratio
Since the bond is convertible at the option of the holder, its value can never fall below the greater of the straight debt and the conversion value.

12. EXAMPLE XYZ Convertible Bond
Maturity = 10 years
Coupon rate = 10%
Conversion ratio = 50
Face value = 1000
Current market price of XYZ convertible bond = $950
Current market price of XYZ stock = $17
Conversion price =
Conversion value =

13. Coupon on similar straight bond: 14%
Straight value =
Minimum price of convertible bonds =

17. CONVERTIBLE BOND VALUATION
Existing shares = 45.2 mil.
Current share price = 31
Convertible bonds = 130,500
Face value = 1000 per bond
Conversion price = (per new share)
Conversion ratio = (shares per conv. bond)
The fraction of equity convertible bondholders possess if they convert is:

18. VALUE COMPONENTS SEPARATELY
To value the convertible bond, value the straight bond component and the warrant component separately
Straight bond component:
Face value = 130,500
Coupon = 4.5%
Time to maturity = 5 years
Coupon on similar straight bond = 7%
Value straight bond component:

19. WARRANT COMPONENT
The value of the warrant component (of the entire issue of convertible bonds) is:
7.038% X 45.2mil X Call (S, t,K)
where t = , K=
S = pseudo-share price. That is:
Assuming = 20% and = 6.5%, the value of the warrant component is:

20. Valuing a convertible
The total value of the convertible bonds would be:
Straight debt component + warrant component
But the bonds were sold for 130.5mil

21. Major Determinants of a Convertible Value
Coupon rate
Current level of interest rates
Conversion price
Level and volatility of the company’s stock price
Dividend yield on the stock
Maturity
Call provisions

22. CALL PROVISION
A bondholder will not convert his bond as long as the coupon on the bond exceeds the dividend on the shares into which the bond is convertible.
In order to force conversion, the issuing corporation typically has the right to call the bond for redemption at a predetermined series of call prices.
When should a company call its convertibles?
The call policy should maximize the existing shareholders wealth. This implies minimizing the convertibles value

23. CALL POLICY
The optimal rule is to call the bond as soon as the value of the convertible reaches the call price.
In practice, however, firms do not call according to this principle.
Ingersoll found that on average they wait until the convertible bond is 44% over the call price.

24. Why issue convertible bonds?
Common misconception:
Convertible debt is a cheap source of finance:
If company does poorly no conversion
cheap debt
If company prospers conversion
sell shares at a high price

25. A technical point about convertibles
Suppose a firm’s assets become more volatile. How does that affect the value of a convertible?
Two effects:
Bond value declines
Value of conversion option increases
You can design a convertible so that these two effects cancel out.

26. Possible rationales for the use of convertible debt
MORAL HAZARD (Green, 1984): the value of straight debt may be reduced if the firm increases the risk of the assets. The conversion feature protects the convertible bonds.
ADVERSE SELECTION (Brennan & Schwartz, 1982): for a given coupon rate, a straight bond is more attractive to an issuer the higher the issuer’s risk. But the warrant element goes in the opposite direction. Different terms for different risks.
DELAYED EQUITY FINANCING (Stein, 1992): firms issue convertibles in the expectation that they will be able to force conversion when good news about their future prospects is revealed.

27. Convertible Debt as Delayed Equity
Firm issues convertibles and later forces conversion when conversion value > call price
Is it advantageous to issue equity in this delayed manner since an issue of convertibles entails less of a negative price reaction than issuing equity outright?
Issue Abnormal Return
Straight debt
Convertible debt
Equity
Why don’t all firms that wish to issue equity first issue convertibles and later force conversion?

28. Forcing conversion also entails a negative stock price reaction
Issue of convertibles Forcing conversion Total
Advantage to convertibles as delayed equity only preserved if voluntary conversion is achieved or conversion in better circumstances (so that there is no negative reaction).