Module II: Private Equity Financing, Options and Warrants Week 5 – February 9, 2006
Lecture Topics <ul><li>Venture capital financing terms </li></ul><ul><ul><li>Different types of venture capital financing ...
Venture Capital Terms <ul><li>Term sheets  are standard means of communicating all aspects of a deal (not just venture cap...
Venture Capital Terms <ul><li>Venture capitalists </li></ul><ul><ul><li>Have high risk-adjusted expected returns </li></ul...
Negotiations: Valuation <ul><li>Pre-money valuation  = value placed on business by venture capital firm </li></ul><ul><li>...
Negotiations: Share Allocation <ul><li>Share allocation affects distribution of control and future wealth gains from the f...
Vesting Alternatives <ul><li>Immediate vesting means taking ownership of some or all shares at once </li></ul><ul><li>Patt...
Control Issues <ul><li>Voting rights of shares </li></ul><ul><li>Board membership </li></ul><ul><li>Share ownership upon m...
Exit Alternatives for VC <ul><li>Liquidation alternatives </li></ul><ul><ul><li>Assumes cash purchase or merger </li></ul>...
Options and Warrants <ul><li>A call option or warrant is the right to buy an asset at a given price before a given date </...
Option Pricing  <ul><li>Major theoretical breakthrough in finance in 1973 by Fisher Black and Myron Scholes </li></ul><ul>...
Major Assumptions <ul><li>European call option </li></ul><ul><ul><li>Can be relaxed easily in some cases </li></ul></ul><u...
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 ...
Inputs <ul><li>S t   Stock Price at time  t </li></ul><ul><li>X   Exercise Price </li></ul><ul><li>T-t   Time remaining to...
The Black-Scholes formula <ul><li>European Call: </li></ul><ul><li>where </li></ul><ul><li>and </li></ul>
Option prices in the  WSJ
Estimating    <ul><li>Use historical returns on the stock </li></ul><ul><ul><li>Remember to adjust for the time interval...
Inputs for this Example: <ul><li>S t   $62.56 </li></ul><ul><li>X   $60.00 </li></ul><ul><li>T-t   72 days </li></ul><ul><...
Option.xls (from Prof. Madhavan)
Some Fine Points <ul><li>Notice that the Black-Scholes formula does not depend on the following “intuitive” inputs: </li><...
Extensions:  Dividends <ul><li>Pricing calls with known dividends is straightforward.  The intuition is as follows: </li><...
Extensions: Pricing Puts  <ul><li>The put-call parity theorem relates the price of a put to the price of a call </li></ul>...
Pricing Warrants  <ul><li>Since warrants are issued by the firm, there is an immediate dilution effect upon the exercise o...
Black-Scholes for Warrants <ul><li>In venture capital situations, warrant exercise may result in substantial dilution and ...
The General Formula <ul><li>Denote by  C  the Black-Scholes call price,  W  the warrant price,  N  the number of shares ou...
Next Week – February 16 <ul><li>Next week we will discuss derivatives securities (options, futures, and swaps) and how the...
Upcoming SlideShare
Loading in …5
×

Week 5 Slides

489 views

Published on

Published in: Economy & Finance, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
489
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • 1
  • Week 5 Slides

    1. 1. Module II: Private Equity Financing, Options and Warrants Week 5 – February 9, 2006
    2. 2. Lecture Topics <ul><li>Venture capital financing terms </li></ul><ul><ul><li>Different types of venture capital financing </li></ul></ul><ul><li>Options and warrants in convertible securities </li></ul><ul><li>Pricing options and warrants </li></ul><ul><ul><li>Black-Scholes option pricing </li></ul></ul><ul><ul><li>Adjusting option prices for warrant pricing </li></ul></ul>
    3. 3. Venture Capital Terms <ul><li>Term sheets are standard means of communicating all aspects of a deal (not just venture capital) </li></ul><ul><li>Terms on any deal contain a number of aspects and conditions (e.g. maturity, repayment, etc.) </li></ul><ul><li>Venture capital terms tend to focus on key issues important to venture capitalists </li></ul>
    4. 4. Venture Capital Terms <ul><li>Venture capitalists </li></ul><ul><ul><li>Have high risk-adjusted expected returns </li></ul></ul><ul><ul><li>Short investment horizons (e.g. 5 years) </li></ul></ul><ul><ul><li>Option to influence or exercise control </li></ul></ul><ul><ul><li>Exit strategies </li></ul></ul><ul><li>Basic terms are amounts invested, the extent of control, factors determining returns under various outcomes, exit alternatives </li></ul>
    5. 5. Negotiations: Valuation <ul><li>Pre-money valuation = value placed on business by venture capital firm </li></ul><ul><li>Post-money valuation = value of firm after venture capital financing </li></ul><ul><li>Valuation can have range under different circumstances, e.g. benchmark performance or milestones and effects entrepreneur’s claim on future firm value </li></ul>
    6. 6. Negotiations: Share Allocation <ul><li>Share allocation affects distribution of control and future wealth gains from the firm </li></ul><ul><ul><li>Founders’ pool is equity before financing </li></ul></ul><ul><ul><li>Employee option pool may be part of founders’ pool or out of capital raised </li></ul></ul><ul><li>Allocation of shares to founders and employees is vesting </li></ul>
    7. 7. Vesting Alternatives <ul><li>Immediate vesting means taking ownership of some or all shares at once </li></ul><ul><li>Pattern of gradual investing can be different: </li></ul><ul><ul><li>Cliff meaning large amount at one time </li></ul></ul><ul><ul><li>Linear investing means gradual allocation of shares </li></ul></ul><ul><li>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 </li></ul>
    8. 8. Control Issues <ul><li>Voting rights of shares </li></ul><ul><li>Board membership </li></ul><ul><li>Share ownership upon management or employee dismissal or quitting </li></ul><ul><li>Reporting and information rights </li></ul><ul><li>Antidilution protection </li></ul><ul><li>Purchase rights in case of changes </li></ul><ul><li>Conversion privileges </li></ul>
    9. 9. Exit Alternatives for VC <ul><li>Liquidation alternatives </li></ul><ul><ul><li>Assumes cash purchase or merger </li></ul></ul><ul><ul><li>Liquidation preference of securities </li></ul></ul><ul><ul><li>Optional conversion of securities to common shares </li></ul></ul><ul><li>Initial public offering (IPO) </li></ul><ul><ul><li>Piggyback registration </li></ul></ul><ul><ul><li>S-3 registration </li></ul></ul>
    10. 10. Options and Warrants <ul><li>A call option or warrant is the right to buy an asset at a given price before a given date </li></ul><ul><li>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) </li></ul><ul><li>Conversion feature is similar to call option or warrant </li></ul>
    11. 11. Option Pricing <ul><li>Major theoretical breakthrough in finance in 1973 by Fisher Black and Myron Scholes </li></ul><ul><ul><li>Scholes and Robert Merton received a Nobel Prize in economics for their work in option pricing, Black died relatively young </li></ul></ul><ul><li>Basic argument is that you should not be able to make money with no investment and no risk </li></ul><ul><li>Logic is called arbitrage pricing theory (APT) </li></ul>
    12. 12. Major Assumptions <ul><li>European call option </li></ul><ul><ul><li>Can be relaxed easily in some cases </li></ul></ul><ul><li>No dividends </li></ul><ul><ul><li>Easy to adjust for dividends </li></ul></ul><ul><li>Returns are normally distributed </li></ul><ul><ul><li>Can be extended for jump discontinuities </li></ul></ul><ul><li>Constant volatility of returns </li></ul><ul><ul><li>Stochastic volatility can be incorporated </li></ul></ul>
    13. 13. Call Options Profits at Maturity 0 Strike Price (X) Profit Asset Value (S) Payoff to Buyer
    14. 14. Value of Call Options 0 Call Price (C) Asset Value Option Premium Strike Price “Out of the Money” “At the Money” “In the Money”
    15. 15. Inputs <ul><li>S t Stock Price at time t </li></ul><ul><li>X Exercise Price </li></ul><ul><li>T-t Time remaining to maturity </li></ul><ul><li>R f Risk-free Rate </li></ul><ul><li> Volatility ( standard deviation of stock returns, annualized ) </li></ul>
    16. 16. The Black-Scholes formula <ul><li>European Call: </li></ul><ul><li>where </li></ul><ul><li>and </li></ul>
    17. 17. Option prices in the WSJ
    18. 18. Estimating   <ul><li>Use historical returns on the stock </li></ul><ul><ul><li>Remember to adjust for the time interval to get the annualized return! </li></ul></ul><ul><li>Use implied volatility from previous trading prices of the option </li></ul>
    19. 19. Inputs for this Example: <ul><li>S t $62.56 </li></ul><ul><li>X $60.00 </li></ul><ul><li>T-t 72 days </li></ul><ul><li>R f 5.09% </li></ul><ul><li> 45% </li></ul>
    20. 20. Option.xls (from Prof. Madhavan)
    21. 21. Some Fine Points <ul><li>Notice that the Black-Scholes formula does not depend on the following “intuitive” inputs: </li></ul><ul><ul><li>The expected rate of growth of the stock price </li></ul></ul><ul><ul><li>Beta </li></ul></ul><ul><ul><li>Investors concerns about risk </li></ul></ul><ul><ul><li>This is because the option is a combination of a bond and a stock, both of which are currently priced </li></ul></ul>
    22. 22. Extensions: Dividends <ul><li>Pricing calls with known dividends is straightforward. The intuition is as follows: </li></ul><ul><ul><li>When a stock pays a dividend, the price falls (in theory) by the amount of the dividend. </li></ul></ul><ul><ul><li>We need to adjust the stock price for the dividend. Formally, we subtract the present value of the known dividend from the stock price </li></ul></ul>
    23. 23. Extensions: Pricing Puts <ul><li>The put-call parity theorem relates the price of a put to the price of a call </li></ul><ul><li>The basic formula is: </li></ul>
    24. 24. Pricing Warrants <ul><li>Since warrants are issued by the firm, there is an immediate dilution effect upon the exercise of warrants </li></ul><ul><li>This means that the warrant is worth less than a comparable call </li></ul><ul><li>For most firms, the dilution effect is so small that the call value is a good approximation to true value </li></ul>
    25. 25. Black-Scholes for Warrants <ul><li>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 </li></ul><ul><li>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? </li></ul>
    26. 26. The General Formula <ul><li>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: </li></ul>
    27. 27. Next Week – February 16 <ul><li>Next week we will discuss derivatives securities (options, futures, and swaps) and how they are used to hedge risk </li></ul><ul><li>These topics are crucial to the Union Carbide Corporation Interest Rate Risk Management case so you should read the case and review recommended chapters </li></ul><ul><li>Continue to review your comprehension of topics covered to date (midterm March 9) </li></ul>

    ×