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 -$
-$