Warrants and Convertibles

Principles of Corporate Finance

Seventh Edition

Richard A. Brealey

Stewart C. Myers

Slides by

Matthew Will

Chapter 23

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23- 2

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Topics Covered

What is a Warrant? What is a Convertible Bond? The Difference Between Warrants and

Convertibles Why do Companies Issue Warrants and

Convertibles?

23- 3

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Warrant Value

Example: BJ Services warrants, April 2000

Exercise price $ 15 Warrant Value $110 Share price $ 70

BJ Services share price

15

Warrant price at maturity

23- 4

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Warrant Value vs. Stock Price

Value of warrant

Exercise price = $15

Actual warrant value prior to expiration

Theoretical value (warrant lower limit)

Stock price

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United Glue Warrants

# shares outstanding = 1 mil Current stock price = $12 Number of shares issued per share outstanding = .10 Total number of warrants issued = 100,000 Exercise price of warrants = $10 Time to expiration of warrants = 4 years Annualized standard deviation of stock daily returns = .40 Rate of return = 10 percent

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

23- 6

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United Glue Warrants

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

warranteach ofCost 100,000

500,000$5

1,500,000-2,000,000500,000

warrants w/oloans of value- financing total warrantsofCost

23- 7

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United Glue Warrants

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

(d1) = 1.104

N(d1) = .865

(d2) = .304

N(d2) = .620

23- 8

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United Glue Warrants

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

Warrant = 12[.865] - [.620]{10/1.14]

= $6.15

23- 9

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United Glue Warrants

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

Value of warrant with dilution

loans of value-assets total

s United'of Value

firm ealternativ

of ueequity valCurrent V

millionV 5.12$5.518

23- 10

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United Glue Warrants

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

Value of warrant with dilution

$12.50 1

million 12.5

firm ealternativ

of price shareCurrent

millionN

V

64.6$ valuegivesformula ScholesBlack

23- 11

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United Glue Warrants

United glue has just issued $2 million package of debt and warrants. Using the following data, calculate the warrant value.

Value of warrant with dilution

03.6$64.610.1

1

firm ealternativ on call of value1

1

q

23- 12

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What is a Convertible Bond?

Amazon 4.75% Convertible 2009 Convertible into 6.41 shares Conversion ratio 6.41 Conversion price = 1000/6.41 = $156.05 Market price of shares = $120

Lower bound of value Bond value Conversion value = 6.41 x 120 = $768.00

23- 13

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What is a Convertible Bond?

How bond value varies with firm value at maturity

0

1

2

3

0 1 2 3 4 5

Value of firm ($ million)

default

bond repaid in full

Bond value ($ thousands)

23- 14

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What is a Convertible Bond?

How conversion value at maturity varies with firm value

0

1

2

3

0 0.5 1 1.5 2 2.5 3 3.5 4

Value of firm ($ million)

Conversion value ($ thousands)

23- 15

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What is a Convertible Bond? How value of convertible at maturity varies with firm value

0

1

2

3

0 1 2 3 4

Value of firm ($ million)

default

bond repaid in full

convert

Value of convertible ($ thousands)