# Real Options & Business Decision Making John Curtis.

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Real Options & Business Decision Making John Curtis

Introduction  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? Deferring Contracting Expanding Abandoning Staging Switching Deferring Contracting Expanding Abandoning Staging Switching

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

Flexibility 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 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 2 t=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? 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

Options Pay-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 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 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 = \$55mMax[\$170m-\$115m,0] = \$55m\$0m Down\$65m-\$115m = -\$50mMax[\$65m-\$115m,0] = \$0m\$50m

Real 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 Determinants VariableImpact of Increase on Value of Call Option Impact of Increase on Value of Put Option Value of underlying asset PositiveNegative Exercise priceNegativePositive Time to expirationPositive Volatility of asset valuePositive Interest ratePositiveNegative

Real 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 Valuation C 0 = [p.C u + (1-p).C d ] / (1+r f ) where  C u is up-state payoff=\$55m  C d is down-state payoff=\$0m  p=((1+r f )-d)/(u-d)  u=V u /V 0, d=V d /V 0  V 0 =value of underlying asset at t=0 (no flex)=\$100m  V u =Up-state underlying asset value at t=1,=\$170m  V d =Down-state equivalent=\$65m C 0 = [p.C u + (1-p).C d ] / (1+r f ) where  C u is up-state payoff=\$55m  C d is down-state payoff=\$0m  p=((1+r f )-d)/(u-d)  u=V u /V 0, d=V d /V 0  V 0 =value of underlying asset at t=0 (no flex)=\$100m  V u =Up-state underlying asset value at t=1,=\$170m  V d =Down-state equivalent=\$65m

Real Option Valuation u=V u /V 0 =\$170m/\$100m=1.7 d=V d /V 0 =\$65m/\$100m=0.65 r f =8% p=((1+0.08)-0.65)/(1.7-0.65)=0.4095 C u =\$55m C d =\$0m C 0 = [p.C u + (1-p).C d ] / (1+r f ) = [0.4095 x \$55m + (1-0.4095) x \$0m] / (1+0.08) = \$20.9m This is value of project with flexibility Thus project is not rejected at t=0. Difference C 0 -NPV=\$20.9m - (-\$6.5m)=\$27.4m is value of flexibility at t=0 u=V u /V 0 =\$170m/\$100m=1.7 d=V d /V 0 =\$65m/\$100m=0.65 r f =8% p=((1+0.08)-0.65)/(1.7-0.65)=0.4095 C u =\$55m C d =\$0m C 0 = [p.C u + (1-p).C d ] / (1+r f ) = [0.4095 x \$55m + (1-0.4095) x \$0m] / (1+0.08) = \$20.9m This is value of project with flexibility Thus project is not rejected at t=0. Difference C 0 -NPV=\$20.9m - (-\$6.5m)=\$27.4m is value of flexibility at t=0

Real 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 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 Option

Compound Rainbow (a)

Compound Rainbow (b)

Compound Rainbow (c)