1

CHAPTER 25: WARRANTS AND CONVERTIBLES

Topics

• 25.1-25.3 Warrants

• 25.4-25.5 Convertibles

• 25.6-25.7 Why Issue Convertibles and Warrants?

• 25.8 Conversion policy

2

Warrants

• A warrant gives its owner the right to buy other securities issued by the firm (usually stock)

• Quite a bit like call options, except new shares are created when the warrant is exercised.– Typically has a longer maturity

– Possibly has a time-varying strike price

– Issued by the firm, not by another investor (unlike option)

– When exercised, results in increase in the # of shares

3

An example

• Ceres Global Ag Corp. news release, Dec. 19, 2007:

An application has been granted for the original listing in the Industrial category of up to 28,750,000 units (the “Units”) of Ceres Global Ag Corp. (the “Company”)…The Units will be posted for trading at the opening on Friday, December 21, 2007. Each Unit consists of one common share of the Company (the “Common Share”) and one full Common Share purchase warrant (the “Warrant”). The Units will separate into Common Shares and Warrants on March 1, 2008. Upon such separation, each Warrant entitles the holder thereof to purchase one Common Share at a price of $13.50 at any time on or prior to the close of business on the date that is 36 months from the closing of the Offering. Upon separation of the Units, the Common Shares and the Warrants will be listed on Toronto Stock Exchange.

• If all the warrants are exercised, they will increase shares outstanding

4

Dilution Effect of Warrant

• Call options can be valued w/o considering dilution factor, warrants cannot.

• Black-Scholes price for warrant will be too high– B/c exercise of warrants increases the # of shares

outstanding…

• B/c of the dilution effect, a lot of warrants are exercised when stock price is (significantly) above the exercise price.

5

Dilution effect Example

• ABC Inc. has 10 million common shares outstanding and 200,000 warrants. Each warrant can purchase five shares of common stock at $30 per share. Warrant holders exercised all their warrants today. ABC’s stock price before the exercise was $33. What should the new stock price be after the exercise?

6

Valuation of warrants

XN

debtofnetvaluefirm

XNN

NXdebtofnetvaluefirm

W

W

callgexercifromPayoffNN

NX

N

debtofnetvaluefirm

NN

N

WW

sin*

WNN

N

We can get an approximate estimate for the value of a warrant using a modified version of Black-Scholes:

1. For a standard call:Payoff from exercising call = ST – X =

where N is the number of shares outstanding

2. For a warrant:Payoff from exercising warrant =

=

where NW is the number of shares from exercising the warrants

So to value a warrant, multiply the value of an otherwise-identical call by a factor of

7

Example• A stock is currently selling for $30 per share. The stock does not pay

any dividends. A European put option on this stock with an exercise price of $45 and five years until expiration is currently selling for $5. The continuously compounded annual risk free interest rate is 10%. Suppose that the firm has 1,000,000 shares outstanding currently. There are also 100,000 warrants outstanding. Each warrant entitles its holder to purchase one additional share. The warrants have an exercise price of $45 and expire 5 years from now. What is the value of each warrant? (Assume that the warrants cannot be exercised early)

8

Problems with valuing warrants

• Why is this an approximate value? – effectively assumes the firm does nothing with the proceeds

from selling the warrant (i.e. pays it out right away to existing shareholders as a dividend)

– ignores dividends during the life of the warrant and early exercise

– ignores changing strike price over time

• In practice, it is relatively difficult to accurately determine the value of a warrant

• However, just as in a standard IPO, it is an important calculation since overpricing a warrant runs the risk that the issue may not sell and underpricing it means that the firm is selling part of itself for less than it is really worth

9

25.4 Convertibles

• A convertible bond gives its owner the right to exchange bond for stocks issued by the firm

• Terminology– Conversion ratio: the number of shares which the bond can be

converted into

– Conversion price: The face value of debt surrendered for each common share received onconversion (par value /number of shares received)

– Conversion premium: conversion price – stock price

• Conversion price is usually 10-30% above the current stock price when issued

10

Convertible Basics

• A convertible bond gives its owner the right to exchange bond for stocks issued by the firm

• Terminology– Conversion ratio: the number of shares which the bond can be

converted into

– Conversion price: The face value of debt surrendered for each common share received onconversion (par value /number of shares received)

– Conversion premium: conversion price – stock price

• Conversion price is usually 10-30% above the current stock price when issued

11

An Example

In 1999, Amazon raised 1.25 billion by selling convertible bonds with the following features:– Coupon rate = 4.75%

– $1000 face value in debt converts at any time to 6.41 shares

– Stock price at the time was around $120

Conversion ratio:

Conversion price:

Conversion premium:

12

Convertibles & Options

• Convertibles are a lot like “bond + call option”– Except, again, new shares are created

– Bond is forfeited when conversion occurs

• Convertibles are a lot like “bond + warrants”– Except they are indivisible and cannot trade (or be issued)

separately

– Bond is forfeited when conversion occurs• the strike price is really the value of the bond, which will be

changing over time

13

Value components of a Convertible Bond

• The value depends on – its straight bond value – what the convertible bond would sell

for if it could not be converted into common stock

– its conversion value – what the bond would be worth if it were immediately converted into common stock at current prices

• Need to consider the dilution factor

– option value = the value of the embedded “warrant”

14

Straight Bond Value

• Consider an issue of zero-coupon debt with a total amount owed of F at maturity T (and suppose the firm has no other debt)

• At T the firm is obligated to pay bondholders F, but if it defaults the bondholders take over the firm and receive VT

15

Conversion Value

• Suppose that there are N existing shares and if all bonds are converted there will be NC new shares

• Firm value V does not change with conversion, but the allocation of ownership does

• After conversion, there are ________ shares, so the convertible owners’ claim is worth __________

16

Convertible Bond Value At Maturity

• Combine the two previous diagrams to obtain the convertible value at maturity:

• There are two lower bounds for the convertible value: (i) the straight bond value (since convertible is this plus a call option); and (ii) the conversion value

17

Value of convertible before maturity

Value of convertible bond = max (straight bond value or conversion value) + warrant value

• The warrant value is the value of the option to delay conversion – The convertible value would be the lower bound if a

conversion decision had to be made immediately

18

Assuming no default probability, the Value of a Convertible Bond is …

Convertible Bond Value

Stock Price

Straight bond value

Conversion Value

floor value

floor value

Convertible bond values

Warrant value

19

Example

Zero-coupon convertible bond. T = 10 years. Face value = $1,000. Conversion ratio = 25. Discount rate for the firm’s straight bond = 10%. Current stock price = $12. Current convertible bond price = $400.

(1) What is the value of the embedded warrant in the convertible?

(2) Suppose the conversion date is 10 years from now and it is the only conversion date. The stock does not pay dividend. The debt has 40 units outstanding, and current number of shares outstanding is 4,000. What would be the value of a corresponding call?

20

Problems With Valuing Convertibles

• The following factors make valuing convertibles difficult:– Dilution (as with warrants)

– Bond value will change randomly over time if interest rates move randomly (this implies that we have a random strike price in addition to a random underlying asset value)

– Callability• The issuing firm usually retains the option to buy back the

convertible bond at a pre-set price (possibly changing over time)

• If a convertible bond is called, the owner of the bond has the choice of either selling it back to the issuer or converting (this is called forced conversion)

• With callability, a convertible bond can be viewed as a straight bond plus a call option (held by the owner on the firm’s equity) minus a call option (held by the issuer on the bond)

21

Why issue convertibles and warrants?• Weak argument: “Cheap” debt or equity

– Not if investors pay a fair price (for the embedded option)

– Suppose a firm issues a convertible and the firm subsequently does poorly, so that holders of the convertible do no convert ) the firm got the benefit of paying a lower coupon rate on debt

– If the firm subsequently does well, then the holders of the convertible will convert, but the conversion price will be higher than when the convertible was originally issued, so the firm is better off in this case too

– The problem with this argument is that a comparison is being made to straight debt if the firm does poorly and to common shares if the firm does well

22

Good reasons for issuing convertibles and warrants

• Matching cash flows– young, risky, growth firms often issue convertibles because

they are cash constrained initially (so they benefit from lower coupon rates) and, if they do well, there will be expensive dilution due to conversion, but the firm is better able to afford it then

• Risk synergy (Risk-shifting)– Useful in cases where it is hard to assess the risk of the issuer

– if the issuer subsequently turns out to be low risk, the straight bond will have high value (but the call option will not have much value)

– If it turns out to be high risk, the call option will be valuable (but the straight bond portion will not be)

23

Good reasons cont’d

• Mitigate agency costs: S/H less prone to take high-risk projects due to the equity component

• Backdoor equity– this is an asymmetric information argument

– the basic idea is that young, small, high growth firms often cannot issue debt without paying high interest due to high risk of financial distress

– if management knows that current shares are undervalued (e.g. due to inside information about future prospects), it may be unwilling to issue equity

– a convertible issue might be a good choice since it reduces interest costs and avoids selling equity at currently depressed prices

24

Review Q1. Suppose that Maple Aircraft has issued a 4% convertible bond due December 2003. The face value of the bond is $1,000. The conversion price is $47.00. The market price of the convertible is 91% of the face value of the bond and the price of the common share is $41.50. Assume the value of the bond in the absence of the conversion feature would be $650. Suppose that Nc is sufficiently small relative to N.

a. What is the conversion ratio of the convertible bond?

b. What is the conversion value?

c. How much is a buyer of the convertible paying for the option to buy one share of the common stock?

25

#25.3 A Warrant gives its owner the right to purchase three shares of common stock at an exercise price of $32 per share. The current market price of Firm Y is $39 per share. What is the minimum value of the warrant?

Can you do better if the following is given: The only exercise date for the warrant is one year from now. The firm pays no dividend. The riskfree rate is 10%. The outstanding # of warrant is 1. The outstanding # of shares is 7.

26

Assigned Problems # 25.2, 3, 4, 6, 8, 9, 11, 13, 14, 19, 20