Real Options&

Business Decision Making

Real Options&

Business Decision Making

John CurtisJohn Curtis

IntroductionIntroduction

NPV is dominant tool for evaluating projects and strategies today

Major flaw - cannot measure value of flexibility hence systematically undervalues project

Typically future configurations of project separately evaluated and one with highest positive NPV chosen

NPV is dominant tool for evaluating projects and strategies today

Major flaw - cannot measure value of flexibility hence systematically undervalues project

Typically future configurations of project separately evaluated and one with highest positive NPV chosen

Examples of Flexibility?Examples of Flexibility?

DeferringContractingExpandingAbandoningStaging

Switching

DeferringContractingExpandingAbandoningStaging

Switching

Why is Flexibility Valuable?Why is Flexibility Valuable?

It allows one to do something or not do something

when such an action adds value or avoids loss of value

It allows one to do something or not do something

when such an action adds value or avoids loss of value

Flexibility ExampleFlexibility Example

Consider a situation where you have two alternatives:

1. Commit right now to a project that will cost $115m in 1 year with certainty but which will produce an uncertain value – a 50-50 probability of either $170m (expected) or $65m (expected)

2. Wait the year before deciding to invest

Consider a situation where you have two alternatives:

1. Commit right now to a project that will cost $115m in 1 year with certainty but which will produce an uncertain value – a 50-50 probability of either $170m (expected) or $65m (expected)

2. Wait the year before deciding to invest

NPV of Alternative 1NPV of Alternative 1

NPV of project based on committing now

= 0.5 x $170m + 0.5 x $65m - $115m _____________________ _____ 1.175 1.08= $100m - $106.5m= -$6.5m

where project cost of capital is 17.5% and risk free rate is 8%.

Therefore reject project. BUT flexibility of delaying decision not valued here so rejection may be wrong decision.

NPV of project based on committing now

= 0.5 x $170m + 0.5 x $65m - $115m _____________________ _____ 1.175 1.08= $100m - $106.5m= -$6.5m

where project cost of capital is 17.5% and risk free rate is 8%.

Therefore reject project. BUT flexibility of delaying decision not valued here so rejection may be wrong decision.

Decision Tree Approach - Alternative 2Decision Tree Approach - Alternative 2t=0t=0

Max[$170m-$115m,$0m] = $55m

Max[$65m-$115m,$0m] = $0m

q = 0.5

1-q = 0.5

t=1

Temptation: Value = (0.5 x $55m + 0.5 x $0m) / 1.175 = $23.4m (Compare with -$6.5m for Alternative 1)

Problem: What is the correct discount rate?

What is Solution?What is Solution?

Use option valuation methodology

Call option : right but not obligation to acquire something by paying predetermined price (exercise price) by or within predetermined time

Put option : right but not obligation to dispose of something for a predetermined price (exercise price) by or within predetermined time

Use option valuation methodology

Call option : right but not obligation to acquire something by paying predetermined price (exercise price) by or within predetermined time

Put option : right but not obligation to dispose of something for a predetermined price (exercise price) by or within predetermined time

OptionsOptions

Pay-off diagrams : an option is exercised only if the option holder benefitsPay-off diagrams : an option is exercised only if the option holder benefits

Call Option Value

Value of Underlying Asset

Exercise Price

Put Option Value

Value of Underlying Asset

Exercise Price

Call Option in Decision TreeCall Option in Decision Tree

t=0

Max[$170m-$115m,$0m] = $55m

Max[$65m-$115m,$0m] = $0m

q = 0.5

1-q = 0.5

t=1

$115m $170m

$55m

Payoffs and Flexibility BenefitPayoffs and Flexibility Benefit

State of nature

Payoffs without flexibility (decision made at t=0 to spend $115m at t=1)

Payoffs with flexibility (no decision made until t=1 whether to spend $115m) THESE ARE CALL OPTION PAYOFFS

Flexibility benefit

Up $170m-$115m = $55m Max[$170m-$115m,0] = $55m $0m

Down $65m-$115m = -$50m Max[$65m-$115m,0] = $0m $50m

Real OptionsReal Options Option to defer commitment to project with defined start-up date until

the last possible moment - deferral option based on European call option.

Option to start project within specified period by incurring cost of start-up - American call option.

Option to abandon project for a fixed price - American put. Option to expand project by paying defined amount to scale up

operations - American call. Option to contract (scale back) involvement in project by selling portion

of it at set price - American put. Option to extend life of project by expending specified amount -

European call option. Option to switch between two modes of operation (for example, on and

off) by paying fixed associated costs of so doing - portfolio of put and call options.

Compound options which permit flexibility in sequential developments. Rainbow options which permit multiple types of uncertainty.

Option to defer commitment to project with defined start-up date until the last possible moment - deferral option based on European call option.

Option to start project within specified period by incurring cost of start-up - American call option.

Option to abandon project for a fixed price - American put. Option to expand project by paying defined amount to scale up

operations - American call. Option to contract (scale back) involvement in project by selling portion

of it at set price - American put. Option to extend life of project by expending specified amount -

European call option. Option to switch between two modes of operation (for example, on and

off) by paying fixed associated costs of so doing - portfolio of put and call options.

Compound options which permit flexibility in sequential developments. Rainbow options which permit multiple types of uncertainty.

Option Value DeterminantsOption Value Determinants

Variable Impact of Increase on Value of Call Option

Impact of Increase on Value of Put Option

Value of underlying asset

Positive Negative

Exercise price Negative Positive

Time to expiration Positive Positive

Volatility of asset value Positive Positive

Interest rate Positive Negative

Real Option ValuationReal Option Valuation

USING RISK NEUTRAL PROBABILITY APPROACH

This technique converts option payoffs into certainty equivalents such that they may be discounted at the risk free rate to calculate the net present value of a project which has embedded flexibility.

USING RISK NEUTRAL PROBABILITY APPROACH

This technique converts option payoffs into certainty equivalents such that they may be discounted at the risk free rate to calculate the net present value of a project which has embedded flexibility.

Real Option ValuationReal Option Valuation

C0 = [p.Cu + (1-p).Cd] / (1+rf)where Cu is up-state payoff=$55m Cd is down-state payoff=$0m p=((1+rf)-d)/(u-d) u=Vu/V0 , d=Vd/V0

V0=value of underlying asset at t=0 (no flex)=$100m Vu=Up-state underlying asset value at t=1,=$170m Vd=Down-state equivalent=$65m

C0 = [p.Cu + (1-p).Cd] / (1+rf)where Cu is up-state payoff=$55m Cd is down-state payoff=$0m p=((1+rf)-d)/(u-d) u=Vu/V0 , d=Vd/V0

V0=value of underlying asset at t=0 (no flex)=$100m Vu=Up-state underlying asset value at t=1,=$170m Vd=Down-state equivalent=$65m

Real Option ValuationReal Option Valuation

u=Vu/V0=$170m/$100m=1.7

d=Vd/V0=$65m/$100m=0.65

rf=8%

p=((1+0.08)-0.65)/(1.7-0.65)=0.4095Cu=$55m

Cd=$0m

C0 = [p.Cu + (1-p).Cd] / (1+rf)

= [0.4095 x $55m + (1-0.4095) x $0m] / (1+0.08) = $20.9mThis is value of project with flexibilityThus project is not rejected at t=0.Difference C0-NPV=$20.9m - (-$6.5m)=$27.4m is value of flexibility at t=0

u=Vu/V0=$170m/$100m=1.7

d=Vd/V0=$65m/$100m=0.65

rf=8%

p=((1+0.08)-0.65)/(1.7-0.65)=0.4095Cu=$55m

Cd=$0m

C0 = [p.Cu + (1-p).Cd] / (1+rf)

= [0.4095 x $55m + (1-0.4095) x $0m] / (1+0.08) = $20.9mThis is value of project with flexibilityThus project is not rejected at t=0.Difference C0-NPV=$20.9m - (-$6.5m)=$27.4m is value of flexibility at t=0

Real LifeReal Life

Even for simple put and call options, a much more expanded lattice of figures than the simple 1 period set in the above example must be calculated

Real life situations may involve quite complex decision trees with multiple options embedded

In some cases there may be multiple independent options in play simultaneously, e.g. simultaneous but independent options to contract or expand an activity

In other cases there may be multiple dependent options each of which comes sequentially into play only if another is exercised, e.g. for staged projects

Even for simple put and call options, a much more expanded lattice of figures than the simple 1 period set in the above example must be calculated

Real life situations may involve quite complex decision trees with multiple options embedded

In some cases there may be multiple independent options in play simultaneously, e.g. simultaneous but independent options to contract or expand an activity

In other cases there may be multiple dependent options each of which comes sequentially into play only if another is exercised, e.g. for staged projects

Real LifeReal Life

Some situations may involve dependent options in a switching arrangement

Still other situations may involve options that are driven by more than one source of uncertainty, e.g. price, volume, interest rates

Some of the parameters used may need to be estimated using other complex techniques such as Monte Carlo simulation

Specialist analytical staff or access to outside expertise will be required

As for all matters involving some complexity, the methodology is unlikely to gain ready acceptability without the understanding and imprimatur of top management

Some situations may involve dependent options in a switching arrangement

Still other situations may involve options that are driven by more than one source of uncertainty, e.g. price, volume, interest rates

Some of the parameters used may need to be estimated using other complex techniques such as Monte Carlo simulation

Specialist analytical staff or access to outside expertise will be required

As for all matters involving some complexity, the methodology is unlikely to gain ready acceptability without the understanding and imprimatur of top management

Deferral OptionDeferral Option

DEVELOPMENT COST $m 700$ esc each yearPRESENT VALUE $m 635$ NPV $m (65)$

Risk free rate 5%Capital cost esc 3%Variance of returns 30%Up factor 1.3498588Down factor 0.7408182RA Prob Up p 0.5076538RA Prob Down 1-p 0.4923462

Time (end year) 0 1 2 3 4 5

VALUE UNCERTAINTY LATTICE2,846$

2,108$ 1,562$ 1,562$

1,157$ 1,157$ 857$ 857$ 857$

PV 635$ 635$ 635$ NPV (65)$ 470$ 470$ 470$

348$ 348$ 258$ 258$

191$ 142$

NPV+DEFERRAL OPTION CALC2,034$

1,335$ 819$ 750$

480$ 369$ 274$ 180$ 8$

NPV+OPTION 152$ 88$ 4$ 43$ 2$ -$

1$ -$ -$ -$

-$ VALUE OF FLEXIBILITY 217$ -$

Compound Rainbow (a)

Compound Rainbow (a)

Research cost 20.00$ Development cost 90.00$ Exploitation cost 150.00$ Probability of research success 0.20Probability research failure 0.80Probability of great product 0.20Probability of mediocre product 0.25Probability of poor product 0.55Value at t=2 if good product 800.00$ Value at t=2 if mediocre product 400.00$ Value at t=2 if poor product 25.00$ Risk free rate 5.00%

Technological uncertainty End period 0 End period 1 End period 2 Research Prob Development Prob Exploit

Capex 20.00$ success 90.00$ great product 150.00$ Invest $Xm? 0.20 Invest $Ym? 0.20 Invest $Zm?

0.25 Invest $Zm?

poor product0.55 Invest $Zm?

failure0.80 Invest $Ym?

Market certainty Prob Value at t=2great product

0.20 800.00$

0.25 400.00$

poor product0.55 25.00$

mediocre product

mediocre product

Compound Rainbow (b)Compound Rainbow (b)

Conventional NPV - No Flexibility NPV Prob NPV component Prob NPV componentTechnological uncertainty success great productMarket certainty (83.27)$ 0.20 27.86$ 0.20 650.00$

mediocre product0.25 250.00$

poor product0.55 (125.00)$

failure0.80 (90.00)$

Decision Tree NPV - Flexibility NPV Prob NPV component Prob NPV componentTechnological uncertainty success great productMarket certainty -$ 0.20 93.33$ 0.20 650.00$

Value of flexibility 83.27$ mediocre product0.25 250.00$

poor product0.55 -$

failure0.80 -$

End period 0 End period 1 End period 2

Compound Rainbow (c)Compound Rainbow (c)

End period 0 End period 1 End period 2

Market uncertaintyUp 1.2000 1,152.00$ greatDown 0.8333 576.00$ mediocrep 0.5909 36.00$ poor1-p 0.4091 960.00$ great

480.00$ mediocre30.00$ poor

800.00$ great 800.00$ great400.00$ mediocre 400.00$ mediocre

25.00$ poor 25.00$ poor666.67$ great333.33$ mediocre

20.83$ poor555.56$ great277.78$ mediocre

17.36$ poor

Decision Tree NPV - Flexibility NPV Prob NPV component Prob NPV componentTechnological uncertainty success great productMarket uncertainty 2.61$ 0.20 157.71$ 0.20 1,002.00$

62.38$ 650.00$ Value of flexibility 85.88$ 405.56$

mediocre product0.25 426.00$

250.00$ 127.78$

poor product0.55 -$

-$ -$

failure0.80 -$

-$