Chapter 24
Warrants and Convertibles
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24.4 Convertible Bonds
• A convertible bond is like a bond with warrants.
• Convertible bond is ONE security.
• A convertible bond…
– Earns interest…like a straight bond
– Can be converted to equity…like a warrant
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24.5 The Value of Convertible Bonds
The value of a convertible bond has three
components:
1. straight bond value
2. conversion value
3. option value
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The Value of Convertible Bonds
Convertible
Bond Value
Convertible bond
values
Conversion
Value
floor value
floor
value
= conversion ratio
Straight bond
value
Option
value
Stock
Price
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Litespeed Inc. just issued a 10-year, 8% annual coupon convertible bond. The YTM
on regular coupon bonds for companies with the same credit rating as Litespeed is
10%. The bond was just sold yesterday at par of $1,000. The bond is convertible
into 25 shares of Litespeed stock with is currently priced at $12.
1.) What is the straight bond value?
straight bond value = PV of coupons and face
2.) What is the conversion value?
conversion value = current share price x shares
3.) What is the option value of the bond?
option value = convertible bond value – MAX[straight bond value,
conversion value]
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Litespeed Inc. just issued a 10-year, 8% annual coupon convertible bond. The
YTM on regular coupon bonds for companies with the same credit rating as
Litespeed is 10%. The bond was just sold yesterday at par of $1,000. The
bond is convertible into 25 shares of Litespeed stock with is currently priced at
$12.
4.) What is the conversion price of the bond?
conversion price = face value/conversion ratio
5.) What is the conversion premium?
conversion premium = conversion price / stock price at issue - 1
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24.6 Reasons for Issuing Warrants and
Convertibles
• A reasonable place to start is to compare convertible
debt to both straight debt and straight equity.
– Convertible vs. Straight debt
– Convertible vs. Straight equity
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Convertible Debt vs. Straight Debt
• Convertible debt carries a lower coupon rate than
does otherwise-identical straight debt. (if high RB
these are attractive)
• If the company subsequently does poorly, it will turn
out that the conversion option finishes out-of-themoney. (just debt, owe coupons & face, S down)
• But if the stock price does well, the firm would have
been better off issuing straight debt. (oh well)
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Convertible Debt vs. Straight Equity
• If the company subsequently does poorly, it will turn
out that the conversion option finishes out-of-themoney, but the firm would have been even better off
selling equity when the price was high. (oh well)
• But if the stock price does well, the firm is better off
issuing convertible debt rather than equity. (equity
sales takes place at higher price per share)
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24.7 Why Are Warrants and Convertibles Issued?
• Research shows…for convertibles…
– bond ratings of firms using convertibles are lower
– convertibles tend to be used by smaller firms with high
growth rates and more financial leverage
– convertibles are usually subordinated and unsecured.
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24.7 Why Are Warrants and Convertibles Issued?
• Matching Cash Flows
– If financing is costly, it makes sense to issue securities
whose cash flows match those of the firm’s needs.
– Convertible bonds also allow young firms to delay
expensive interest costs until they can afford them.
– When firm is successful, conversion occurs, expensive
dilution occurs, but this is when the firm can most afford it.
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24.7 Why Are Warrants and Convertibles Issued?
• Risk Synergy
– Suppose the market does not know if the firm is a high risk
or low risk firm. If a firm issues a convertible bond, then:
• If high risk company
–
–
Straight bond value is relatively low
Option value is relatively high
• If low risk company
–
–
Straight bond value is relatively high
Option value is relatively low
– Conclusion: The market will pay a fair value even if it does
not know what kind of firm it is.
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24.7 Why Are Warrants and Convertibles Issued?
• Backdoor Equity
– Young, small, high growth firms cannot issue debt on
reasonable terms due to high financial distress costs
– However, owners may be unwilling to issue equity if
current stock price is too low
– So, they look to warrants/convertibles
• Agency Costs
– Convertible bonds reduce agency costs by aligning the
incentives of stockholders and bondholders.
– The incentive to take on excessive risk (with straight
debt)…let’s do an example…
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Convertible Bond Problem
Ms. North is proposing to form a new start-up firm. She can
invest in one of two projects.
• The relatively safe project offers a 40 percent chance of a
$9 million payoff and a 60 percent chance of an $8 million
payoff.
• The risky project offers a 20 percent chance of a $20
million payoff and an 80 percent chance of a $5 million
payoff.
• Ms. North initially proposes to finance the firm by an issue
of straight bonds with a promised payoff of $7 million.
Which project will she choose if she issues straight bonds?
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Safe Project
Safe project payoff
Payoff to lender
Payoff to Ms. North
60% 40% Expected
$8.0 $9.0
$8.4
$7.0 $7.0
Risky Project
Risky project payoff
Payoff to lender
Payoff to Ms. North
80% 20% Expected
$5.0 $20.0
$8.0
$5.0 $7.0
• Ms. North will choose the risky project because her expected
payoff is higher
• The lender would want Ms. North to choose the safe project
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• Suppose now that Ms. North offers to make the
debt convertible into ¾ of the firm’s equity.
• So lender has choice:
$7 million debt payment
or
(3/4) ownership of equity
• Which project does Ms. North choose if she
finances the firm with convertible debt?
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Safe Project
Safe project payoff
Payoff to lender
- debt value
- conversion value
- lender chooses
Payoff to Ms. North
60%
$8.0
40%
$9.0
$7.0
$7.0
Risky Project
Risky project payoff
Payoff to lender
- debt value
- conversion value
- lender chooses
Payoff to Ms. North
80%
$5.0
20%
$20.0
$5.0
$7.0
Expected
$8.4
Expected
$8.0
• Lender: Expected payoff is the same no matter which project chosen
• Ms. North’s expected payoff is higher for safe project, she would choose
safe project
• Safe project has higher total expected payoff $8.4 vs. $8.0
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