Post on 20-Jun-2015
J. K. Dietrich - FBE 532 – Spring, 2006
Module II: Private EquityFinancing, Options and Warrants
Week 5 – February 9, 2006
J. K. Dietrich - FBE 532 – Spring, 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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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)
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
Call Options Profits at Maturity
0Strike Price (X)
Profit
Asset Value (S)
Payoffto Buyer
J. K. Dietrich - FBE 532 – Spring, 2006
Value of Call Options
0
Cal
l Pri
ce (
C)
Asset Value
OptionPremium
Strike Price
“Out of the Money”“At the Money”
“In the Money”
J. K. Dietrich - FBE 532 – Spring, 2006
Inputs
St Stock Price at time t
X Exercise Price T-t Time remaining to maturity Rf Risk-free Rate
Volatility (standard deviation of stock returns, annualized)
J. K. Dietrich - FBE 532 – Spring, 2006
The Black-Scholes formula
European Call:
where
and
C S N d Xe N dt tR T tf
1 2
d
S X R T t
T t
t f
1
2
2
ln /
d d T t2 1
J. K. Dietrich - FBE 532 – Spring, 2006
Option prices in the WSJ -Call- -Put-
Option/Strike Exp. Vol. Last Vol. Last
Micsft 55 Feb 482 825 507 025 6256 60 Feb 14073 350
2283 094
6256 60 Mar 63 538 3432 213
6256 60 Apr 134 650
947 325
6256 65 Feb 4786 094
510 325
6256 65 Mar 2166 244
50 438
6256 70 Feb 2301 019
74 725
6256 70 Mar 2098 088
112 775
6256 70 Apr 1112 194
26 863
Source: Listed Options Quotations. WSJ February 7, 2001, p. C16.
Note: April expiration is April 20.
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
Inputs for this Example:
St $62.56
X $60.00 T-t 72 days Rf 5.09%
45%
J. K. Dietrich - FBE 532 – Spring, 2006
Option.xls (from Prof. Madhavan)THE BLACK-SCHOLES OPTION PRICING FORMULA
INPUT PANEL: ENTER OPTION DATA
T 72 Time to Maturity (days)Sigma 45.00% Stock Price Volatility (enter in percentage form)
X 60.00 Exercise Pricer 5.09% Interest Rate (enter in percentage form)S 62.56 Stock Price
OUTPUT PANEL:
C 6.60 Black-Scholes Call PriceDelta 0.64 Delta (Hedge Ratio)
E 6.07 Elasticity* P 3.44 Black-Scholes Put Price
---------------------------------------------------------------------*Percent change in call from a one percent change in the stock price
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
Extensions: Pricing Puts
The put-call parity theorem relates the price of a put to the price of a call
The basic formula is:
P C S Xet t t
R T tf
J. K. Dietrich - FBE 532 – Spring, 2006
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
J. K. Dietrich - FBE 532 – Spring, 2006
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?
J. K. Dietrich - FBE 532 – Spring, 2006
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:
WN
N MC
J. K. Dietrich - FBE 532 – Spring, 2006
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)