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Week 5 Slides Week 5 Slides Presentation Transcript

  • Module II: Private Equity Financing, Options and Warrants Week 5 – February 9, 2006
  • 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
  • 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
  • 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
  • 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 entrepreneur’s claim on future firm value
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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)
  • 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
  • Call Options Profits at Maturity 0 Strike Price (X) Profit Asset Value (S) Payoff to Buyer
  • Value of Call Options 0 Call Price (C) Asset Value Option Premium Strike Price “Out of the Money” “At the Money” “In the Money”
  • Inputs
    • S t Stock Price at time t
    • X Exercise Price
    • T-t Time remaining to maturity
    • R f Risk-free Rate
    •  Volatility ( standard deviation of stock returns, annualized )
  • The Black-Scholes formula
    • European Call:
    • where
    • and
  • Option prices in the WSJ
  • Estimating  
    • 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
  • Inputs for this Example:
    • S t $62.56
    • X $60.00
    • T-t 72 days
    • R f 5.09%
    •  45%
  • Option.xls (from Prof. Madhavan)
  • 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
  • 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
  • Extensions: Pricing Puts
    • The put-call parity theorem relates the price of a put to the price of a call
    • The basic formula is:
  • 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
  • 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?
  • 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:
  • Next Week – February 16
    • 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 March 9)