Week 5 Slides

J. K. Dietrich - FBE 532 – Spring, 2006

Module II: Private EquityFinancing, 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

0Strike Price (X)

Profit

Asset Value (S)

Payoffto Buyer


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”


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)


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


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.


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:

St $62.56

X $60.00 T-t 72 days Rf 5.09%

45%


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


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:

P C S Xet t t

R T tf


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:

WN

N MC


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)

Economy & Finance

Week 5 Slides