22-1
Chapter 22
Convertibles,
Exchangeables,
and Warrants
22-2
Convertibles,Exchangables,
and Warrants
?Convertible Security Features
?Use of Convertibles
?Value of Convertible
Securities
?Exchangeable Bonds
?Warrants
22-3
Derivative Security -- A financial contract
whose value derives in part from the value and
characteristics of one or more underlying
assets (e.g.,securities,commodities),interest
rates,exchange rates,or indices.
Derivative Security
?Straight debt or equity cannot be exchanged for
another asset,but options are exchangeable.
?An option is part of the broader category of
derivative securities.
?We examine the convertible security,exchangeable
bond,and warrant in this chapter.
22-4
Convertible Security -- A bond or a
preferred stock that is convertible into a
specified number of shares of common
stock at the option of the holder.
Convertible Security
?This provides the convertible holder a fixed return
(interest or dividend) and the option to exchange a
bond or preferred stock for common stock.
?The option allows the company to sell convertible
securities at a lower yield than it would have to pay
on a straight bond or preferred stock issue.
22-5
Conversion Price -- The price per share at
which common stock will be exchanged for a
convertible security,It is equal to the face
value of the convertible security divided by
the conversion ratio.
Convertible Security
Conversion Ratio -- The number of shares of
common stock into which a convertible
security can be converted,It is equal to the
face value of the convertible security
divided by the conversion price.
22-6
FunFinMan,Inc.,has an issue of 8%,
$100 par value preferred stock
outstanding,The security has a
conversion price of $30 per share,
What is the conversion ratio?
Conversion Example
Conversion Ratio
= $100 par value / $30 conversion price
= 3.33 shares
22-7
Antidilution and the
Convertible Security
?Conversion terms are not necessarily constant
over time.
?Example,The conversion price on 20-year
convertible-debt might step-up?over time from $30
during the first 5 years,$35 the next 5 years,and $40
for the the remaining 10 years until maturity.
?The conversion price is usually adjusted for
any stock splits or stock dividends to protect
the convertible bondholder from antidilution
(known as the antidilution clause).
22-8
Conversion Value -- The value of the
convertible security in terms of the common
stock into which the security can be
converted,It is equal to the conversion ratio
times the current market price per share of the
common stock.
Conversion Value
For example,if the market value per share of common
stock in FunFinMan,Inc.,were trading at $42 per
share,then the conversion value is:
3.33 shares x $42 = $140 per share of preferred stock
22-9
Premium Over Conversion Value -- The
market price of a convertible security
minus it conversion value; also called
conversion premium.
Premium Over
Conversion Value
For example,if the market value per share of
preferred stock in FunFinMan,Inc.,were
trading at $154 per share,then the conversion
premium is:
$154 - $140 = $14 premium per share of
preferred stock (or a 10% premium).
22-10
Other Issues with
Convertible Securities
?Virtually all convertible securities provide for a call
price,which allows the company to force
conversion when the security market value is
significantly above the call price.
?Almost all convertible bond issues are subordinated
to other creditors,which allows a lender to treat
convertibles as a part of the equity base when
evaluating the financial condition of the issuer.
?The potential dilution effect is recognized by
investors who evaluate earnings based on a diluted
earnings per share.
22-11
Use of
Convertible Securities
?In many cases,convertible securities are employed
as referred?common stock financing.
? Does not immediately dilute earnings.
? Securities are converted at a higher price than if they
would have been directly issued,This has the
impact of reducing the dilution effect.
?The interest or dividend rate is likely to be less than
that of straight debt or preferred stock,The greater
the growth prospects of the firm’s common stock,
the lower the stated rate the firm will need to pay.
22-12
Forcing or
Stimulating
Conversion
? Investors can exercise their option to convert to
common stock at any time.
? Companies can force conversion by calling the
issue,
? The company has an incentive to call only when the
conversion price exceeds the call price by around
15% and when the common dividend rate is less than
the interest or pfd,dividend rate investors are
earning.
? Firms attempt to stimulate conversion by
including the Step-up?feature to the conversion
price or increasing the common dividend,
22-13
Straight Bond Value
The value of a nonconvertible bond with
the same coupon rate,maturity,and
default risk as the convertible bond.
(1 + i/2)1 (1 + i/2)2 (1 + i/2) 2*nVSB = + +,.,+
I / 2 I / 2 + F
= ?2*n
t=1 (1 + i/2)
t
= (I / 2)(PVIFA i/2,n) + F (PVIF i/2,n)
(1 + i/2)2*n+
F
I / 2
I / 2
22-14
Straight Bond Value
of the Convertible
Company C has a convertible debenture outstanding
that provides an 8% coupon (interest is paid
semiannually) and exactly 20 years until final maturity,
A similar nonconvertible bond will currently provide a
5% semiannual yield to maturity,What is the straight
bond value of Company C’s convertible bond?
V = $40 (PVIFA5%,20x2) + $1,000 (PVIF5%,20x2)
= $40 (17.159) + $1,000 (.142)
= $686.36 + $142
= $828.36
22-15
Why Care About Straight
Bond Value?
? The convertible bond value equals straight
bond value plus conversion option value.
? The $828.36 represents a floor (minimum)
below which the convertible value will not
fall,This occurs when the conversion option
value is essentially worthless.
? The straight bond value is subject to change
as interest rates,firm risk,and time change,
This,in turn,is likely to impact the
convertible bond value.
22-16
Relationships
Among Premiums
?The leftmost portion
of the graph
represents a firm
that is in financial
distress.
?The stronger the
financial health of
the firm the greater
the straight bond
value until it reaches
a ceiling level.
Va
lu
e o
f C
on
ve
rti
bl
e Se
cu
rity
Market Value of Common Stock
Market
value line
Premium
Straight
bond value
Convertible
security
value
22-17
Relationships Among
Premiums -- Summary
? A convertible security offers holders partial
protection on the downside (similar to the
straight bond) based on the going-concern
and liquidation values of the firm.
? A convertible security also provides
holders with the ability to participate in the
upward movement in common stock prices.
? The greater the volatility of common stock
price,the greater the potential gain and the
more valuable the option.
22-18
Exchangeable Bond -- A bond that allows the
holder to exchange the security for common
stock of another company -- generally,one in
which the bond issuer has an ownership
interest.
Exchangeable Bond
?These issues usually occur when the issuer owns
common stock in the company in which the bonds
can be exchanged.
?Exchange requests are satisfied either by open
market purchases or directly using the firm抯
investment holdings of the other company抯 stock.
22-19
Valuation of
an
Exchangeable
? Investors may realize diversification benefits since
the bond and the common stock are from different
companies.
? Potentially,diversification leads to a higher
valuation for the exchangeable versus the
convertible.
? A major disadvantage is that the difference between
the cost of the bond and the market value of the
exchanged common stock,at the time of exchange,
is treated as a capital gain,A convertible gain is not
recognized until the common stock is sold.
22-20
Warrant -- A relatively long-term option to
purchase common stock at a specified
exercise price over a specified period of time.
Warrants
? To obtain a lower interest rate.
? To raise funds when the firm is
considered a marginal credit risk.
? To compensate underwriters and venture
capitalists when founding a company.
Warrants are employed as Sweeteners?
22-21
Warrant Features
? The warrant contains provisions for:
?the number of shares that can be purchased per
warrant.
?the price at which the warrant can be exercised.
?the warrant expiration date.
? Warrant holders are not entitled to any
dividends nor do they have any voting power.
? The exercise price is generally adjusted for
any common stock dividends and splits.
22-22
Example of
Exercise of
Warrants
FunFinMan,Inc.,is currently financed entirely
with common stock,The firm is composed
of $10 million in common stock ($5 par
value) and $20 million in retained earnings,
The company is considering issuing $20
million of 8%,20-year debentures including 1
warrant per bond that can be converted into
5 shares of common stock at an exercise
price of $40 per share,How will this impact
the capitalization of the firm?
22-23
Example of Exercise
of Warrants (in millions)
Debentures $ 0 $ 10
Common stock ($5 par) 10 10
Additional paid-in-capital 0 0
Retained earnings 20 20
Shareholders?equity $ 30 $ 30
Total Capitalization $ 30 $ 40
Before After*
Financing Financing
22-24
Example of Exercise
of Warrants (in millions)
Debentures $ 0 $ 10
Common stock ($5 par) 10 10.5
Additional paid-in-capital 0 3.5
Retained earnings 20 20
Shareholders?equity $ 30 $ 34
Total Capitalization $ 30 $ 44
Before After*
Financing Exercise
22-25
Valuation of a Warrant
Theoretical value of a
warrant:
max [ (N)(Ps) - E,0]
N = number of shares per
warrant
Ps = market price of one
share of stock
E = exercise price
associated with the
purchase of N shares
W
ar
ra
nt
Va
lu
e
Associated Common Stock Price
Theoretical
value line
45o
Market
value line
Exercise
price
22-26
Example of the
Valuation of a Warrant
Theoretical value of a
warrant:
max [ (N)(Ps) - E,0]
N = 1,Ps = $10,E = $5
max[(1)($10)-$5,0] = $5
N = 1,Ps = $15,E = $5
max[(1)($15)-$5,0] =$10
W
ar
ra
nt
Va
lu
e
Associated Common Stock Price
$5
$10
Stock appreciates 50%
Theoretical warrant
value appreciates 100%
Minimum
value is 0.
22-27
Summary of the Example
of Warrant Valuation
? The market value of a warrant equals or
exceeds the theoretical value of the warrant.
? The greater market value is generated by the
unlimited upside potential of the stock price
combined with the limited downside risk to
the warrant holder (minimum value is 0).
? The greater the time to expiration,the
greater the opportunity of the upside
potential of the stock and the greater the
market value of the warrant.
Chapter 22
Convertibles,
Exchangeables,
and Warrants
22-2
Convertibles,Exchangables,
and Warrants
?Convertible Security Features
?Use of Convertibles
?Value of Convertible
Securities
?Exchangeable Bonds
?Warrants
22-3
Derivative Security -- A financial contract
whose value derives in part from the value and
characteristics of one or more underlying
assets (e.g.,securities,commodities),interest
rates,exchange rates,or indices.
Derivative Security
?Straight debt or equity cannot be exchanged for
another asset,but options are exchangeable.
?An option is part of the broader category of
derivative securities.
?We examine the convertible security,exchangeable
bond,and warrant in this chapter.
22-4
Convertible Security -- A bond or a
preferred stock that is convertible into a
specified number of shares of common
stock at the option of the holder.
Convertible Security
?This provides the convertible holder a fixed return
(interest or dividend) and the option to exchange a
bond or preferred stock for common stock.
?The option allows the company to sell convertible
securities at a lower yield than it would have to pay
on a straight bond or preferred stock issue.
22-5
Conversion Price -- The price per share at
which common stock will be exchanged for a
convertible security,It is equal to the face
value of the convertible security divided by
the conversion ratio.
Convertible Security
Conversion Ratio -- The number of shares of
common stock into which a convertible
security can be converted,It is equal to the
face value of the convertible security
divided by the conversion price.
22-6
FunFinMan,Inc.,has an issue of 8%,
$100 par value preferred stock
outstanding,The security has a
conversion price of $30 per share,
What is the conversion ratio?
Conversion Example
Conversion Ratio
= $100 par value / $30 conversion price
= 3.33 shares
22-7
Antidilution and the
Convertible Security
?Conversion terms are not necessarily constant
over time.
?Example,The conversion price on 20-year
convertible-debt might step-up?over time from $30
during the first 5 years,$35 the next 5 years,and $40
for the the remaining 10 years until maturity.
?The conversion price is usually adjusted for
any stock splits or stock dividends to protect
the convertible bondholder from antidilution
(known as the antidilution clause).
22-8
Conversion Value -- The value of the
convertible security in terms of the common
stock into which the security can be
converted,It is equal to the conversion ratio
times the current market price per share of the
common stock.
Conversion Value
For example,if the market value per share of common
stock in FunFinMan,Inc.,were trading at $42 per
share,then the conversion value is:
3.33 shares x $42 = $140 per share of preferred stock
22-9
Premium Over Conversion Value -- The
market price of a convertible security
minus it conversion value; also called
conversion premium.
Premium Over
Conversion Value
For example,if the market value per share of
preferred stock in FunFinMan,Inc.,were
trading at $154 per share,then the conversion
premium is:
$154 - $140 = $14 premium per share of
preferred stock (or a 10% premium).
22-10
Other Issues with
Convertible Securities
?Virtually all convertible securities provide for a call
price,which allows the company to force
conversion when the security market value is
significantly above the call price.
?Almost all convertible bond issues are subordinated
to other creditors,which allows a lender to treat
convertibles as a part of the equity base when
evaluating the financial condition of the issuer.
?The potential dilution effect is recognized by
investors who evaluate earnings based on a diluted
earnings per share.
22-11
Use of
Convertible Securities
?In many cases,convertible securities are employed
as referred?common stock financing.
? Does not immediately dilute earnings.
? Securities are converted at a higher price than if they
would have been directly issued,This has the
impact of reducing the dilution effect.
?The interest or dividend rate is likely to be less than
that of straight debt or preferred stock,The greater
the growth prospects of the firm’s common stock,
the lower the stated rate the firm will need to pay.
22-12
Forcing or
Stimulating
Conversion
? Investors can exercise their option to convert to
common stock at any time.
? Companies can force conversion by calling the
issue,
? The company has an incentive to call only when the
conversion price exceeds the call price by around
15% and when the common dividend rate is less than
the interest or pfd,dividend rate investors are
earning.
? Firms attempt to stimulate conversion by
including the Step-up?feature to the conversion
price or increasing the common dividend,
22-13
Straight Bond Value
The value of a nonconvertible bond with
the same coupon rate,maturity,and
default risk as the convertible bond.
(1 + i/2)1 (1 + i/2)2 (1 + i/2) 2*nVSB = + +,.,+
I / 2 I / 2 + F
= ?2*n
t=1 (1 + i/2)
t
= (I / 2)(PVIFA i/2,n) + F (PVIF i/2,n)
(1 + i/2)2*n+
F
I / 2
I / 2
22-14
Straight Bond Value
of the Convertible
Company C has a convertible debenture outstanding
that provides an 8% coupon (interest is paid
semiannually) and exactly 20 years until final maturity,
A similar nonconvertible bond will currently provide a
5% semiannual yield to maturity,What is the straight
bond value of Company C’s convertible bond?
V = $40 (PVIFA5%,20x2) + $1,000 (PVIF5%,20x2)
= $40 (17.159) + $1,000 (.142)
= $686.36 + $142
= $828.36
22-15
Why Care About Straight
Bond Value?
? The convertible bond value equals straight
bond value plus conversion option value.
? The $828.36 represents a floor (minimum)
below which the convertible value will not
fall,This occurs when the conversion option
value is essentially worthless.
? The straight bond value is subject to change
as interest rates,firm risk,and time change,
This,in turn,is likely to impact the
convertible bond value.
22-16
Relationships
Among Premiums
?The leftmost portion
of the graph
represents a firm
that is in financial
distress.
?The stronger the
financial health of
the firm the greater
the straight bond
value until it reaches
a ceiling level.
Va
lu
e o
f C
on
ve
rti
bl
e Se
cu
rity
Market Value of Common Stock
Market
value line
Premium
Straight
bond value
Convertible
security
value
22-17
Relationships Among
Premiums -- Summary
? A convertible security offers holders partial
protection on the downside (similar to the
straight bond) based on the going-concern
and liquidation values of the firm.
? A convertible security also provides
holders with the ability to participate in the
upward movement in common stock prices.
? The greater the volatility of common stock
price,the greater the potential gain and the
more valuable the option.
22-18
Exchangeable Bond -- A bond that allows the
holder to exchange the security for common
stock of another company -- generally,one in
which the bond issuer has an ownership
interest.
Exchangeable Bond
?These issues usually occur when the issuer owns
common stock in the company in which the bonds
can be exchanged.
?Exchange requests are satisfied either by open
market purchases or directly using the firm抯
investment holdings of the other company抯 stock.
22-19
Valuation of
an
Exchangeable
? Investors may realize diversification benefits since
the bond and the common stock are from different
companies.
? Potentially,diversification leads to a higher
valuation for the exchangeable versus the
convertible.
? A major disadvantage is that the difference between
the cost of the bond and the market value of the
exchanged common stock,at the time of exchange,
is treated as a capital gain,A convertible gain is not
recognized until the common stock is sold.
22-20
Warrant -- A relatively long-term option to
purchase common stock at a specified
exercise price over a specified period of time.
Warrants
? To obtain a lower interest rate.
? To raise funds when the firm is
considered a marginal credit risk.
? To compensate underwriters and venture
capitalists when founding a company.
Warrants are employed as Sweeteners?
22-21
Warrant Features
? The warrant contains provisions for:
?the number of shares that can be purchased per
warrant.
?the price at which the warrant can be exercised.
?the warrant expiration date.
? Warrant holders are not entitled to any
dividends nor do they have any voting power.
? The exercise price is generally adjusted for
any common stock dividends and splits.
22-22
Example of
Exercise of
Warrants
FunFinMan,Inc.,is currently financed entirely
with common stock,The firm is composed
of $10 million in common stock ($5 par
value) and $20 million in retained earnings,
The company is considering issuing $20
million of 8%,20-year debentures including 1
warrant per bond that can be converted into
5 shares of common stock at an exercise
price of $40 per share,How will this impact
the capitalization of the firm?
22-23
Example of Exercise
of Warrants (in millions)
Debentures $ 0 $ 10
Common stock ($5 par) 10 10
Additional paid-in-capital 0 0
Retained earnings 20 20
Shareholders?equity $ 30 $ 30
Total Capitalization $ 30 $ 40
Before After*
Financing Financing
22-24
Example of Exercise
of Warrants (in millions)
Debentures $ 0 $ 10
Common stock ($5 par) 10 10.5
Additional paid-in-capital 0 3.5
Retained earnings 20 20
Shareholders?equity $ 30 $ 34
Total Capitalization $ 30 $ 44
Before After*
Financing Exercise
22-25
Valuation of a Warrant
Theoretical value of a
warrant:
max [ (N)(Ps) - E,0]
N = number of shares per
warrant
Ps = market price of one
share of stock
E = exercise price
associated with the
purchase of N shares
W
ar
ra
nt
Va
lu
e
Associated Common Stock Price
Theoretical
value line
45o
Market
value line
Exercise
price
22-26
Example of the
Valuation of a Warrant
Theoretical value of a
warrant:
max [ (N)(Ps) - E,0]
N = 1,Ps = $10,E = $5
max[(1)($10)-$5,0] = $5
N = 1,Ps = $15,E = $5
max[(1)($15)-$5,0] =$10
W
ar
ra
nt
Va
lu
e
Associated Common Stock Price
$5
$10
Stock appreciates 50%
Theoretical warrant
value appreciates 100%
Minimum
value is 0.
22-27
Summary of the Example
of Warrant Valuation
? The market value of a warrant equals or
exceeds the theoretical value of the warrant.
? The greater market value is generated by the
unlimited upside potential of the stock price
combined with the limited downside risk to
the warrant holder (minimum value is 0).
? The greater the time to expiration,the
greater the opportunity of the upside
potential of the stock and the greater the
market value of the warrant.
