lecture5-warrants - Warrants, Convertibles and other...

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Warrants, Convertibles and other instruments 3 October 2005
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Corporate Finance 2 Definitions Warrants are call options issued by the firm They are equal to call options in all respects but: » They increase the number of existing shares » Hence dilute the existing equity To value them usual option pricing
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Corporate Finance 3 Notation W t = value of 1 warrant X = exercise price n = No. shares before warrant exercise NW = No. warrants = q n q = NW / n = Dilution factor S t , σ t = share price, volatility with warrants P t , σ t = same, without warrants Total value is V t = n x S t + NW x W t = n x P t
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Corporate Finance 4 Pricing a warrant If the warrant is exercised, the stock price is: The value of the warrant at maturity, if exercised, is: q qX P n NW X NW V S t t t + + = + × + = 1 q X P X q qX P X S t t t + - = - + + = - 1 1
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Corporate Finance 5 Warrants and Calls Thus, the value at maturity is: Therefore, a warrant can be priced as a call option multiplied by a constant: The call option is on a firm without the warrants! ) , 0 ( 1 1 ) 1 , 0 ( ) 0 , ( X P Max q q X P Max X S Max t t t - + = + - = - ) , , , , ( 1 1 ' 0 0 0 r T X P C q W σ + =
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Corporate Finance 6 Alternative method: example Company issues a € 2m package of debt and warrants The debt part is worth € 1.5m No. shares outstanding, n 1 m Current stock price, P 0 € 12 Warrants issued per share, q 0.10 Total warrants, NW 100,000 Exercise price, X € 10 Maturity 4 years Volatility, σ t ’ (before the issue) 0.38 Interest rate, r 10%
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Corporate Finance 7 Example, cont The warrants are thus worth € 2m - € 1.5 = € 0.5 m Per warrant, 0.5 m / 100,000 = € 5 Q: is this a fair price?
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Corporate Finance 8 Example, cont Balance sheet before and after the issue: Assets 16 Total 16 Loans 4 Equity 12 Total 16 1 m shares x 12 per share Before
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Corporate Finance 9 Example, cont Balance sheet after the issue: Assets 16 New assets 2 Total 18 Loans 4 New loan 1.5 Total debt 5.5 Warrants 0.5 Common Equity 12 Total equity 12.5 Total 18
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Corporate Finance 10 Example, cont Equity value without the warrants is: Total assets – debt = 18 – 5.5 = € 12.5m?
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lecture5-warrants - Warrants, Convertibles and other...

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