Module II: Venture Capital Financing, Options and Warrants

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Module II Venture Capital Financing, Options and
Warrants

• Week 6 September 30 and October 2, 2002

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Lecture Topics

• Venture capital financing terms
• Different types of venture capital financing
• Options and warrants in convertible securities
• Pricing options and warrants
• Black-Scholes option pricing
• Adjusting option prices for warrant pricing

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Venture Capital Terms

• Term sheets are standard means of communicating
  all aspects of a deal (not just venture capital)
• Terms on any deal contain a number of aspects and
  conditions (e.g. maturity, repayment, etc.)
• Venture capital terms tend to focus on key issues
  important to venture capitalists

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Venture Capital Terms

• Venture capitalists
• Have high risk-adjusted expected returns
• Short investment horizons (e.g. 5 years)
• Option to influence or exercise control
• Exit strategies
• Basic terms are amounts invested, the extent of
  control, factors determining returns under
  various outcomes, exit alternatives

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Negotiations Valuation

• Pre-money valuation value placed on business by
  venture capital firm
• Post-money valuation value of firm after
  venture capital financing
• Valuation can have range under different
  circumstances, e.g. benchmark performance or
  milestones and effects entrepreneurs claim on
  future firm value

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Negotiations Share Allocation

• Share allocation affects distribution of control
  and future wealth gains from the firm
• Founders pool is equity before financing
• Employee option pool may be part of founders
  pool or out of capital raised
• Allocation of shares to founders and employees is
  vesting

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Vesting Alternatives

• Immediate vesting means taking ownership of some
  or all shares at once
• Pattern of gradual investing can be different
• Cliff meaning large amount at one time
• Linear investing means gradual allocation of
  shares
• Example 50 immediate vesting, remainder over 24
  months allocates 50 of share immediately, the
  remainder 2.083 per month until 100 of
  commitment is satisfied

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Control Issues

• Voting rights of shares
• Board membership
• Share ownership upon management or employee
  dismissal or quitting
• Reporting and information rights
• Antidilution protection
• Purchase rights in case of changes
• Conversion privileges

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Exit Alternatives for VC

• Liquidation alternatives
• Assumes cash purchase or merger
• Liquidation preference of securities
• Optional conversion of securities to common
  shares
• Initial public offering (IPO)
• Piggyback registration
• S-3 registration

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Options and Warrants

• A call option or warrant is the right to buy an
  asset at a given price before a given date
• Convertible securities can be exchanged for other
  securities (usually common stock) at a given
  ratio of face value (e.g. 50 shares per 1000
  bond) or conversion price (e.g. 20 per share)
• Conversion feature is similar to call option or
  warrant

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Option Pricing

• Major theoretical breakthrough in finance in 1973
  by Fisher Black and Myron Scholes
• Scholes and Robert Merton received a Nobel Prize
  in economics for their work in option pricing,
  Black died relatively young\
• Basic argument is that you should not be able to
  make money with no investment and no risk
• Logic is called arbitrage pricing theory (APT)

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Major Assumptions

• European call option
• Can be relaxed easily in some cases
• No dividends
• Easy to adjust for dividends
• Returns are normally distributed
• Can be extended for jump discontinuities
• Constant volatility of returns
• Stochastic volatility can be incorporated

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Call Options Profits at Maturity
Profit
Payoff to Buyer
0
Strike Price (X)
Asset Value (S)
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Value of Call Options
Option Premium
Call Price (C)
0
Asset Value
Strike Price
In the Money
Out of the Money
At the Money
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Inputs

• St Stock Price at time t
• X Exercise Price
• T-t Time remaining to maturity
• Rf Risk-free Rate
• s Volatility (standard deviation of stock
  returns, annualized)

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The Black-Scholes formula

• European Call
• where
• and

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Option prices in the WSJ
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Estimating s2

• Use historical returns on the stock
• Remember to adjust for the time interval to get
  the annualized return!
• Use implied volatility from previous trading
  prices of the option

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Inputs for this Example

• St 62.56
• X 60.00
• T-t 72 days
• Rf 5.09
• s 45

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Computation

• Using the inputs, you can compute the price of
  the call using the spreadsheet option.xls
• Check the answer

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Some Fine Points

• Notice that the Black-Scholes formula does not
  depend on the following intuitive inputs
• The expected rate of growth of the stock price
• Beta
• Investors concerns about risk
• This is because the option is a combination of a
  bond and a stock, both of which are currently
  priced

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Extensions Dividends

• Pricing calls with known dividends is
  straightforward. The intuition is as follows
• When a stock pays a dividend, the price falls (in
  theory) by the amount of the dividend.
• We need to adjust the stock price for the
  dividend. Formally, we subtract the present
  value of the known dividend from the stock price

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Extensions Pricing Puts

• The put-call parity theorem relates the price of
  a put to the price of a call
• The basic formula is

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Pricing Warrants

• Since warrants are issued by the firm, there is
  an immediate dilution effect upon the exercise of
  warrants
• This means that the warrant is worth less than a
  comparable call
• For most firms, the dilution effect is so small
  that the call value is a good approximation to
  true value

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Black-Scholes for Warrants

• In venture capital situations, warrant exercise
  may result in substantial dilution and hence you
  need to know how to use Black-Scholes in this
  situation
• Suppose that a VC holds warrants for 100,000
  shares and that there are 100,000 shares
  outstanding. If the B-S call value is 3, what is
  the warrant value?

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The General Formula

• Denote by C the Black-Scholes call price, W the
  warrant price, N the number of shares outstanding
  and M the number of warrants (the number of
  shares created when warrants are exercised ).
  Then

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Next Week October 7 and 9

• Next week we will discuss derivatives securities
  (options, futures, and swaps) and how they are
  used to hedge risk
• These topics are crucial to the Union Carbide
  Corporation Interest Rate Risk Management case so
  you should read the case and review recommended
  chapters
• Continue to review your comprehension of topics
  covered to date (midterm October 16)