Managing Strategic Investment in an Uncertain World:

A Real Options Approach

Roger A. Morin, PhDGeorgia State University

FI 8360 January 2003

3 Valuation Frameworks

Discounted Cash Flow (DCF)

Comparables

Option Value

Agenda

The value of flexibility Real options as a way to capture flexibility Real options and financial options So what? The importance of real options Implementing real option valuation Next steps

Capital Investments as Options

All kinds of business decisions are options!

Virtually every corporate finance decision

involving the issuance of securities or the

commitment of capital to a project involves

options in one way or another.

Real Options Defined

Nobel Prize-winning work of Black-Merton-Scholes

Applications for real (nonfinancial) assets

Extensions for how real assets are managed

What is the value of a contract that gives you the right, but not the obligation to purchase a share of IBM at $100 six months from now?

What is the value of starting a project that gives you the right, but not the obligation, to launch a sales program at a cost of $7M six months from now?

We operate in a fast changing and uncertain market. How can we better make strategic decisions, manage our investments, and communicate our strategy to Wall St?

Why An Options Perspective?

Some shortcomings in the use of ordinary NPV analysis can be overcome

Common ground for uniting capital budgeting and strategic planning can be established

Risk-adjusted discounted rates problem

Investment Decisions

1. Irreversibility

2. Uncertainty

3. Flexibility– Timing

– Scale

– Operations

Investment Decisions

1 & 2 3 is valuable

1 & 2 & 3 Option (flexibility)

valuation

Option Value (a.k.a. flexibility)

Can be largeSensitive to uncertaintyExplains why firms appear to

underinvest

Flexibility: Investments have uncertainty and decision-points

Fund First Develop Test Product Sales Brand Retire

Research Results More Market Launch Extension Product

Your decision New Information

What types of investments does this describe?

R&D related businesses - biotech, pharmaceuticals, entertainment.

Natural resource businesses - extractive industries.

Consumer product companies High-tech companies

Invest/Grow

Scope Up

Switch Up

Scale Up

Defer/Learn

Study/Start

Disinvest/Shrink

Scope Down

Switch Down

Scale Down

Real Option Category

Real Option Type

Current Applications:Some Frequently Encountered Real Options

Timing -- now or later

Exit -- limiting possible future losses by exiting now

Flexibility -- today’s value of the future opportunity to switch

Operating -- the value of temporary shutdown Learning -- value of reducing uncertainty to make better decision

Growth -- today’s value of possible future payoffs

Future Growth Options

Valuable new investment opportunities (“follow-on projects”) can be viewed as call options on assets

Examples:– Exploration

– Capacity expansion projects

– New product introductions

– Acquisitions

– Advertising outlays

– R&D outlays

– Commercial development

Investment Project Options: Examples

Growth Option (“Follow-On Projects”)– Nortel commits to production of digital switching equipment specially

designed for the European market. The project has a negative NPV, but is justified by the need for a strong market position in this rapidly growing, and potentially very profitable, market.

Switching Option– Atlanta Airways buys a jumbo jet with special equipment that allows the

plane to be switched quickly from freight to passenger use or vice versa.

Investment Project Options: Examples

Timing Option– Dow Chemical postpones a major plant expansion. The expansion has

positive NPV, but top management wants to get a better fix on product demand before proceeding.

Flexible Production Facilities– Lucent Technologies vetoes a fully-integrated, automated production line

for the new digital switches. It relies on standard, less-expensive equipment. The automated production line is more efficient overall, according to a NPV calculation.

Investment Project Options: Examples

Fuel Switching– A power plant has the capacity of burning oil or gas. Mgrs can decide

which fuel to burn in light of fuel prices prevailing in the future

Shut-Down Option– A power plant can be shut down temporarily. Mgt. can decide whether or

not to operate the plant in light of the avoided cost of power prevailing in the future

Investment Timing– Mgt. can invest in new capacity now or defer when more information on

demand growth and fuel prices is available

Which is a closer analogy to these types of projects?

Bond Option

Standard NPV analysis treats projects like bonds

Average promised cash flow

up-front investment

Learn

DecideDo not invest

Invest

NPV ignores valuable flexibility

Shortcomings of NPV Analysis

– Passive, assumes business as usual with no management intervention

– Strategic factors ignored– NPV understates value

Operating flexibility ignored Valuable follow-on investment projects ignored

– Many investments have uncertain payoffs that are best valued with an Options approach

– Risk-adjusted discounted rates problem

NPV ROV

Certainty is a narrow path!

Flexibility Active Management

NPV’ = NPVpassive + Option Value

Financial Options A Brief Review

What is an option?

An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (exercise price) at or before the expiration date of the option.

Since it is a right and not an obligation, the holder can choose not to exercise the right and allow the option to expire.

Two types – call options (right to buy) and put options (right to sell).

Call Options

A call option gives the buyer of the option the right to buy the underlying asset at a fixed price (E) at any time prior to the expiration date. The buyer pays a price for this right (premium)

At expiration,– If the value of the underlying asset S > E

Buyer makes the difference: S – E

– If the value of the underlying asset S < E Buyer does not exercise

More generally,– Value of a call increases as the value of the underlying asset increases– Value of a call decreases as the value of the underlying asset decreases

Payoff on Call Option

Price of underlying asset

Net payoff on

call option

Exercise price

If asset value < exercise price, you lose what you paid for call

Payoff on IBM Call Option

IBM Stock price

Net payoff

E = $100

Maximum loss = $5Breakeven = $105

Put Options

A put option gives the buyer of the option the right to sell the underlying asset at a fixed price (E) at any time prior to the expiration date. The buyer pays a price for this right (premium)

At expiration,– If the value of the underlying asset S < E

Buyer makes the difference: E – S

– If the value of the underlying asset S > E Buyer does not exercise

More generally,– Value of a put decreases as the value of the underlying asset increases– Value of a put increases as the value of the underlying asset decreases

Payoff on Put Option

Price of underlying asset

Net payoff on put

Exercise price

If asset value > exercise price, you lose what you paid for put

Determinants of Call Option Value

Stock Price - the higher the price of the underlying stock, the greater the option’s intrinsic value

Exercise Price - the higher the exercise price, the lower the intrinsic value

Interest Rates - the higher interest rates, the more valuable the call option

Volatility of the Stock Price - the more volatile the stock price, the more valuable the option

Time to Maturity - call options increase in value the more time there is remaining to maturity

Effect of Volatility on Option Values

Asset Price

Pro

babi

lity

Time to expiration is one year.

30% Volatility

10% Volatility

Call Option Payoff

Effect of Maturity on Option Value

Asset Price

Pro

babi

lity

Volatility is 20%.

1 Yr Expiration

Call Option Payoff5 Yrs Expiration

Option Premium vs Intrinsic Value

0X

Cal

l opt

ion

pric

e

C

C

Stock Price

X = Exercise PriceCC = Call option premium as function of stock price

Intrinsic value

Time value

Determinants of option value

Variables Relating to Underlying Asset Value of Underlying Asset Variance in that value Expected dividends on the asset

Variables Relating to Option Exercise Price Life of the Option

Level of Interest Rates

Summary of Determinants of Option Value

Factor Call Put

Increase in Stock Price

Increase in Exercise Price

Increase in risk

Increase in maturity

Increase in interest rates

Increase in dividends paid

American vs European Options

American: exercise at any time European: exercise at maturity American options more valuable

Time premium makes early exercise sub-optimal

Exception: Asset pays large dividends

Option Valuation

Binomial Option Pricing Model– Portfolio Replication Method– Risk Neutral Method

Black-Scholes Model– Dividend adjustment– Diffusion vs Jump process

Binomial Option Pricing Model

The Binomial Option Pricing Model assumes that there are two possible outcomes for the price of the underlying asset in each period.

Although this assumption is artificial, realism can be achieved by partitioning the time horizon into many short time intervals, so the number of possible outcomes is large

Useful first approximation

Binomial Price Path

S

Su

Su2

Sud

Sd2

Sd

Binomial Price Path

$100

$110

$90

$120

$100

$80

t = 0 t = 1 t = 2

Creating a replicating portfolio

Objective: use a combination of risk-free borrowing-lending and the underlying asset to create the same cash flows as the option being valued

Call = Borrowing + Buying Δ of Underlying Stock Put = Selling short Δ on Underlying Asset + Lending The number of shares bought or sold is called the option delta

The principles of arbitrage then apply, and the value of the option has to be equal to the value of the replicating portfolio

Creating a Replicating Portfolio

Value of Position Value of Call

If S goes up to Su ΔSu - $B (1 + r) Cu

If S goes down to Sd ΔSd - $B (1 + r) Cd

Replicating Portfolio

Δ Su - $B (1 + r) = Cu

Δ Sd - $B (1 + r) = Cd

Δ = No. of units of underlying asset bought

Cu - Cd

Δ =

Su - Sd

Replicating Portfolio: Example 1

$55

Stock: $50

$45

1-yr Call, E = $50 Rf = 5%

C = $3.57 all investors agree!

Replicating Portfolio: Example 1

Call - Stock Payoffs: (55, 5)

(50, ?) (45, 0)

We can duplicate the above payoffs with a position in common stock and borrowing, that is, by “portfolio replication”.

Replicating Portfolio

Δ Su - $B (1 + r) = Cu

Δ Sd - $B (1 + r) = Cd

Cu - Cd $5 - $0

Δ = = = 0.50

Su - Sd $55 - $45

Δ = 50 shares ! B = $2,142 !

50 shares of stock + 1-year loan of $2,142.86

Portfolio is now worth: 50 x $50 - $2,142.86 = $357.14

Portfolio payoffs: 50 x $55 - 2,250 = 500 (50, ?) 50 x $45 - 2,250 = 0

SAME AS CALL OPTION PAYOFFS! FAIR VALUE OF 100 CALLS = $357.14

No Free Lunch!

Absence of Riskless Arbitrage Profits

If C > $357.14, sell overpriced call

buy duplicating portfolio

KEY: can construct a levered position in underlying stock that gives the same payoffs as the call option.

Binomial Valuation: Example 2

$50

$70

$35

$100

$50

$25

t = 0 t = 1 t = 2

E = $50

Rf = 11%

$50

$0

$0

Call

Binomial Valuation: Example 2

$50

$70

$35

$100

$50

$25

t = 0 t = 1 t = 2

E = $50

Rf = 11%

$50

$0

$0

Call

Replicating Portfolio When S = $70

$70

$100

$50

t = 1 t = 2

E = $50

Rf = 11%

$50

$0

Call Replicating Portfolio

100 Δ - 1.11B = 50

50 Δ - 1.11B = 0

Solving: Δ = 1 B = 45Buy 1 share, borrow $45

Value of Call at t = 1

70 Δ - B = 70 - 45 = $25

Binomial Valuation: Example 2

$50

$70

$35

$100

$50

$25

t = 0 t = 1 t = 2

E = $50

Rf = 11%

$50

$0

$0

Call

Replicating Portfolio When S = $35

$35

$50

$25

t = 1 t = 2

E = $50

Rf = 11%

$0

$0

Call Replicating Portfolio

50 Δ - 1.11B = 0

25 Δ - 1.11B = 0

Solving: Δ = 0 B = 0

Binomial Valuation: Example 2

$50

$70

$35

$100

$50

$25

t = 0 t = 1 t = 2

E = $50

Rf = 11%

$50

$0

$0

Call

Replicating Portfolios for Call Value

$50

$70

$35

t = 0 t = 1

E = $50

Rf = 11%

$25 from Step 1

$0 from Step 1

Call Replicating Portfolio

70 Δ - 1.11B = 25

35 Δ - 1.11B = 0

Solving: Δ = 5/7 B = 22.5Buy 5/7 share, borrow $22.5

Value of Call at t = 0

Cost of replicating portfolio = value of call

50 Δ - B = 50 x 5/7 - 22.5 = $13.20

Binomial PricingRisk-Neutral Method

$55

Stock: $50 $45

1-year Call, E = $50, Rf = 5%

Binomial Pricing: Risk-Neutral Method

Step 1 Solve for probability of rise 0.05 = 0.10 p + (-0.10) (1 - p) p = 0.75Step 2 Solve for expected future value of option

C1 = 0.75 x $5 + 0.25 x $0 = $3.75Step 3 Solve for current value of option

C0 = $3.75/1.05 = $3.57

Note: This is an extremely powerful and useful result from the perspective of devising numerical procedures for computing option values.

The Limiting Distributions……..

As the time interval is shortened, the limiting distribution, as t 0, can take one of two forms:– as t 0, price changes become smaller, the limiting

distribution is the normal distribution and the price process is a continuous one.

– as t 0, price changes remain large, the limiting distribution is the Poisson distribution, i.e. a distribution that allows for price jumps

The Black-Scholes model applies when the limiting distribution is the normal distribution, and assumes that the price process is continuous and that there are no jumps in asset prices

Black-Scholes Model

C = S N(d1) - K e-iT N(d2)

Where:– C = value of the call option

– S = current stock price

– N(d1) = cumulative normal density function of d1

– K = the exercise price of the option

– i = the risk-free rate of interest

– T = expiration date of the option (fraction of a year)

– N(d2) = cumulative density function of d2

– s = standard deviation of the annual rate of return

C = S N(d1) - K e-iT N(d2)Where: d1 = [ln(S/K) + (i + 0.5s2)T] / sT1/2

d2 = d1 - sT1/2

The replicating portfolio is embedded in the Black-Scholes model. To replicate this call, you need to:

– Buy N(d1) shares of stock; N(d1) is the option delta– Borrow K e-iT N(d2)

Black-Scholes Model

Adjusting for Dividends

If the dividend yield (y) of the underlying asset is expected to remain unchanged during the life of the option, the Black-Scholes can be modified:

C = S e-yT N(d1) - K e-iT N(d2)

Where: d1 = [ln(S/K) + (i – y + 0.5s2)T] / sT1/2

d2 = d1 - sT1/2

Application Problems

1. Underlying asset may not be traded; difficult to estimate value and variance of underlying asset

2. Price of the asset may not follow a continuous process3. Variance may not be known and may change over the

life of the option4. Exercise may not be instantaneous5. Some real options are complex and their exercise

creates other options (compound) or involve learning (learning options)

6. More than one source of variability (rainbow options)

Jumping from financial options to real options

FINANCIAL OPTION REAL OPTION

Underlying asset Stock price Value of developed project

Volatility Volatility of stock price returns

Volatility of project returns

Exercise price Exercise price Value of investment

Time to maturity Contract’s maturity License period or rights period

Ownership rights Dividends paid prior to exercise

Cash flow foregone by waiting

Interest rates Interest rate Interest rate

Contract terms American or European Early exercise permitted?

Real Options: Link betweenInvestments and Black-Scholes Inputs

PV of project Free Cash Flow

Outlay to acquireproject assets

Time the decisioncan be deferredTime value of

money

Risk of project assets

Stock price

Exercise price

Time to expiration

Risk-free rate

Variance of returns

S

X

s2

i

T

NPV

“X”Investment

Savg“S”

Value of Developed

Project

“S - X”Conditional

NPV of projectNPV

NPV

“X”Investment

Savg“S”

Value of Developed

Project

“S - X”Intrinsic Value

of Option

LiveOptionValue

DeadOptionValue

Option Value: dead and live

“S”

“S - X”When options really matter

In the

Money

At the

MoneyOut of the Money

“S”

“S - X”When options really matter

In the

Money

At the

MoneyOut of the Money

Characteristics of Projects Where Optionality is Important

“Long-shot” projects (out of the $) Substantial flexibility ignored in project Examples: Valuing investments in oil fields

– Where you are valuing the rights to an “expensive” field– Where you are valuing the rights to produce in a very cheap

field

“ I’m sold, but what do I do?”

Technique

First step is framing the question Next, there are a variety of techniques

– Force-fit problem into stylized model, like Black-Scholes.

– Create customized model to recognize the complicated set of managerial choices

Finally, you have to work through some important nuances.

Framing the question is critical

Identifying the optionality– What is the flexibility?– Is it like a call? A put? A more complicated

structure? Scope out the importance Is this flexibility that is likely to be important to

you? Is the project “marginal” under NPV, but there is phased investment and learning?