Module II: Private Equity Financing, Options and Warrants

1. Module II: Private EquityFinancing, Options and Warrants Week 5 – February 9, 2006

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Exit Alternatives for VC • Liquidation alternatives • Assumes cash purchase or merger • Liquidation preferenceof securities • Optional conversion of securities to common shares • Initial public offering (IPO) • Piggyback registration • S-3 registration

10. 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

11. 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)

12. 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

13. Call Options Profits at Maturity Profit Payoff to Buyer 0 Strike Price (X) Asset Value (S)

14. Value of Call Options Option Premium Call Price (C) 0 Asset Value Strike Price “In the Money” “Out of the Money” “At the Money”

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

16. The Black-Scholes formula European Call: where and

17. Option prices in the WSJ

18. 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

19. Inputs for this Example: • St $62.56 • X $60.00 • T-t 72 days • Rf5.09% • s 45%

20. Option.xls (from Prof. Madhavan)

21. 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

22. 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

23. Extensions: Pricing Puts • The put-call parity theorem relates the price of a put to the price of a call • The basic formula is:

24. 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

25. 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?

26. 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:

27. 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 Managementcase so you should read the case and review recommended chapters • Continue to review your comprehension of topics covered to date (midterm March 9)