CHAPTER. 24. Warrants and Convertibles. Executive Summary. This chapter describes the basic features of warrants and convertibles. The important questions are: How can warrants and convertibles be valued? What impact do warrants and convertibles have on firm value?
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24.1 Warrants
24.2 The Difference between Warrants and Call Options
24.3 Warrant Pricing and the BlackScholes Model (Advanced)
24.4 Convertible Bonds
24.5 The Value of Convertible Bonds
24.6 Reasons for Issuing Warrants and Convertibles
24.7 Why are Warrants and Convertibles Issued?
24.8 Conversion Policy
24.9 Summary and Conclusions
(Book Value)
Assets
Liabilities and
Equity
Gold:
$3,000
Debt Equity
(2 shares)
0
$3,000
Total Assets $3,000
Total $3,000
Dilution Example(Market Value)
Assets
Liabilities and
Equity
Gold:
$3,500
Debt Equity
(2 shares)
0
$3,500
Total Assets $3,500
Total $3,500
Dilution(Market Value)
Assets
Liabilities and
Equity
Gold:
Cash:
$3,500
$1,500
Debt Equity
(3 shares)
0
$5,000
Total Assets $5,000
Total $5,000
DilutionNote that Mr. Armstrong’s claim falls in value from $1,750 = $3,500 ÷ 2 to $1,666.67 = $5,000 ÷ 3
+
n
n
w
Warrant Pricing and the BlackScholes Model (Advanced)Where
n = the original number of shares
nw = the number of warrants
share
price
exercise
price
Firm'
s
value
net
of
debt
n
Firm'
s
value
net
of
debt

exercise
price
n
Warrant Pricing and the BlackScholes Model (Advanced)To see why, compare the gains from exercising a call with the gains from exercising a warrant.
The gain from exercising a call can be written as:
Note that when n = the number of shares, share price is:
Thus, the gain from exercising a call can be written as:
share
price
after warr
ant
exercise
exercise
price
é
ù
share
price
+
´
Firm'
s
value
net
of
debt
exercise
price
n
ê
ú
=
w
after
ê
ú
+
n
n
ê
ú
w
warrant
exercise
ë
û
+
´
Firm'
s
value
net
of
debt
exercise
price
n

w
exercise
price
+
n
n
w
Warrant Pricing and the BlackScholes Model (Advanced)The gain from exercising a warrant can be written as:
Note that when n = the original number of shares and nw = the number of warrants,
Thus, the gain from exercising a warrant can be written as:
s
value
net
of
debt

exercise
price
n
+
´
Firm'
s
value
net
of
debt
exercise
price
n

w
exercise
price
+
n
n
w
n
+
n
n
w
n
+
n
n
w
Warrant Pricing and the BlackScholes Model (Advanced)The gain from exercising a warrant can be written as:
A bit of algebra shows that these equations differ by a factor of
So to value a warrant, multiply the value of an otherwiseidentical call by
The value of a convertible bond has three components:
1
,
000
=
=
SBV
$
385
.
54
10
(
1
.
10
)
Convertible Bond Problem (continued)floor value
Straight bond value
floor value
Option value
= conversion ratio
24.5 The Value of Convertible BondsConvertible Bond Value
Conversion Value
Stock Price