real options in project evaluation

Real Options in Project Real Options in Project EvaluationEvaluation

Stephen GrayStephen Gray

Campbell R. HarveyCampbell R. Harvey

NPV and Real OptionsNPV and Real Options

NPV:NPV:– Often misappliedOften misapplied– Ignores strategic values if misappliedIgnores strategic values if misapplied

Real Option Valuation:Real Option Valuation:– Values contingencies in project Values contingencies in project

outcomes (i.e., alternative future uses outcomes (i.e., alternative future uses of the asset).of the asset).


Many Types of Real OptionsMany Types of Real Options– Key is to identifyKey is to identify– Often they are difficult to value – Often they are difficult to value –

however, even using judgment one however, even using judgment one can tell if they add or subtract value can tell if they add or subtract value to the projectto the project


Input Mix Options or Process Input Mix Options or Process FlexibilityFlexibility– The option to use different inputs to The option to use different inputs to

produce the same output is known as an produce the same output is known as an input mix option or process flexibility.input mix option or process flexibility.

Examples:Examples:– Agriculture: A beef producer will value the Agriculture: A beef producer will value the

option to switch between various feed option to switch between various feed sources, preferring to use the cheapest sources, preferring to use the cheapest acceptable alternativeacceptable alternative


Input Mix Options or Process Input Mix Options or Process FlexibilityFlexibility

Examples:Examples:– Utility industry. An electric utility may have Utility industry. An electric utility may have

the option to switch between various fuel the option to switch between various fuel sources to produce electricity. In particular, sources to produce electricity. In particular, consider an electric utility that has the consider an electric utility that has the choice of building a coal-fired plant or a choice of building a coal-fired plant or a plant that burns either coal or gas.plant that burns either coal or gas.


Output Mix Options or Product Output Mix Options or Product FlexibilityFlexibility – The option to produce different outputs from The option to produce different outputs from

the same facility is known as an output mix the same facility is known as an output mix option or product flexibility.option or product flexibility.

Examples:Examples:– Toy industry. A manufacturer's ability to cease Toy industry. A manufacturer's ability to cease

producing a style of toy that has become producing a style of toy that has become unfashionable and quickly begin producing a unfashionable and quickly begin producing a popular new style of toy.popular new style of toy.

NPV and Real OptionsNPV and Real Options Abandonment or Termination OptionsAbandonment or Termination Options

– Whereas traditional capital budgeting analysis Whereas traditional capital budgeting analysis assumes that a project will operate in each year assumes that a project will operate in each year of its lifetime, the firm may have the option to of its lifetime, the firm may have the option to cease a project during its life. This option is cease a project during its life. This option is known as an abandonment or termination option. known as an abandonment or termination option.

– Abandonment options, which are the right to sell Abandonment options, which are the right to sell the cash flows over the remainder of the the cash flows over the remainder of the project's life for some salvage value, are like project's life for some salvage value, are like American American putput options. When the present value of options. When the present value of the remaining cash flows falls below the the remaining cash flows falls below the liquidation value, the asset may be sold. liquidation value, the asset may be sold.


Abandonment or Termination Abandonment or Termination OptionsOptions

ExamplesExamples– These options are particularly important for These options are particularly important for

large capital intensive projects such as large capital intensive projects such as nuclear plants, airlines, and railroads. nuclear plants, airlines, and railroads.

– They are also important for projects They are also important for projects involving new products where their involving new products where their acceptance in the market is uncertain. acceptance in the market is uncertain.


Abandonment or Termination Abandonment or Termination OptionsOptions


Temporary-Stop or Shutdown OptionsTemporary-Stop or Shutdown Options – For projects with production facilities, it may not For projects with production facilities, it may not

be optimal to operate a plant for a given period if be optimal to operate a plant for a given period if revenues will not cover variable costs.revenues will not cover variable costs.

Examples:Examples:– If the price of oil falls below the cost of If the price of oil falls below the cost of

extraction, for example, it may be optimal to extraction, for example, it may be optimal to temporarily shut down the oil well until the oil temporarily shut down the oil well until the oil price recovers. price recovers.


Temporary-Stop or Shutdown Temporary-Stop or Shutdown OptionsOptions

Examples:Examples:– Farming: May be exercised if the cost of Farming: May be exercised if the cost of

fertilizing, watering and harvesting exceeds fertilizing, watering and harvesting exceeds the sale price of the product.the sale price of the product.

– Real-estate development: May be Real-estate development: May be exercised if the cost of construction exercised if the cost of construction exceeds rent revenues. exceeds rent revenues.


Intensity or Operating Scale Intensity or Operating Scale OptionsOptions– Intensity or operating scale options Intensity or operating scale options

involve the flexibility to expand or involve the flexibility to expand or contract the scale of the project. contract the scale of the project. Management may have the option to Management may have the option to change the output rate per unit of time change the output rate per unit of time or to change the total length of or to change the total length of production run time.production run time.


Intensity or Operating Scale Intensity or Operating Scale OptionsOptions– In order to obtain the option to expand In order to obtain the option to expand

production if demand increases suddenly, production if demand increases suddenly, a firm may build production capacity in a firm may build production capacity in excess of the expected level of output. excess of the expected level of output.

– In this case, management has the right, In this case, management has the right, but not the obligation to expand, and will but not the obligation to expand, and will exercise the option only if project exercise the option only if project conditions turn out to be favorable. conditions turn out to be favorable.


Intensity or Operating Scale OptionsIntensity or Operating Scale Options– Whereas the excess capacity will have an initial Whereas the excess capacity will have an initial

cost, the project with the option to expand is cost, the project with the option to expand is worth more than the project without the worth more than the project without the possibility of expansion, in which case the extra possibility of expansion, in which case the extra cost may be justified. cost may be justified.

– Also, a firm may build a plant whose physical Also, a firm may build a plant whose physical life exceeds the expected duration of use, life exceeds the expected duration of use, thereby providing the firm with the option of thereby providing the firm with the option of producing more by extending the life of the producing more by extending the life of the project.project.


Option to ExpandOption to Expand– Build production capacity or the infrastructure Build production capacity or the infrastructure

for the capacity in excess of expected level of for the capacity in excess of expected level of output (so it can produce at higher rate if output (so it can produce at higher rate if needed). needed).

– Management has the right (not the obligation to Management has the right (not the obligation to expand). If project conditions turn out to be expand). If project conditions turn out to be favorable, management will exercise this option. favorable, management will exercise this option.

ExampleExample– Mozal ProjectMozal Project


Option to ExpandOption to Expand


Option to ContractOption to Contract– This is the equivalent to a put option. This is the equivalent to a put option.

Many projects can be engineered in such Many projects can be engineered in such a way that output can be contracted in a way that output can be contracted in future. Forgoing future expenditures is future. Forgoing future expenditures is equivalent to exercising the put option. equivalent to exercising the put option.

Example:Example:– Modularization of project.Modularization of project.


Option to ContractOption to Contract


Option to Expand or Contract Option to Expand or Contract (Switching Option)(Switching Option)– It is equivalent to the firm having a It is equivalent to the firm having a

portfolio of call and put options. portfolio of call and put options. Restarting operations when project Restarting operations when project currently shut down is a call option. currently shut down is a call option. Shutting down is a put option.Shutting down is a put option.


Option to Expand or Contract Option to Expand or Contract (Switching Option)(Switching Option)

Example:Example:– A project whose operation can be A project whose operation can be

dynamically turned on and off (or dynamically turned on and off (or switched to two distinct locations) is switched to two distinct locations) is worth more than the same project worth more than the same project without the flexibility to switch.without the flexibility to switch.


Option to Expand or Contract Option to Expand or Contract (Switching Option)(Switching Option)


Initiation or Deferment OptionsInitiation or Deferment Options– The option to choose when to start a The option to choose when to start a

project is an initiation or deferment project is an initiation or deferment option.option.

Examples:Examples:– The purchaser of an off-shore lease can The purchaser of an off-shore lease can

choose when, if at all, to develop choose when, if at all, to develop property.property.


Initiation or Deferment OptionsInitiation or Deferment Options Examples:Examples:

– Initiation options are particularly valuable in Initiation options are particularly valuable in natural resource exploration where a firm can natural resource exploration where a firm can delay mining a deposit until market conditions are delay mining a deposit until market conditions are favorable. favorable.

– If natural resource companies were committed to If natural resource companies were committed to producing all resources discovered, they would producing all resources discovered, they would never explore in areas where the estimated never explore in areas where the estimated extraction cost exceeded the expected future extraction cost exceeded the expected future price at which the resource could be sold. price at which the resource could be sold.


Initiation or Deferment OptionsInitiation or Deferment Options


Intraproject vs. Interproject OptionsIntraproject vs. Interproject Options– Interproject options arise when the Interproject options arise when the

development of one project creates value that development of one project creates value that attach to other projects. Sequencing options, attach to other projects. Sequencing options, for example, are interproject options because for example, are interproject options because the sequencing of projects creates value for the sequencing of projects creates value for subsequent projects as the direct result of subsequent projects as the direct result of undertaking the initial project. undertaking the initial project.

– Traditional capital budgeting analysis will miss Traditional capital budgeting analysis will miss this option because projects evaluated on this option because projects evaluated on stand-alone basis.stand-alone basis.


Growth OptionsGrowth Options– The value of the firm can exceed the market The value of the firm can exceed the market

value of the projects currently in place because value of the projects currently in place because the firm may have the opportunity to undertake the firm may have the opportunity to undertake positive NPV projects in the future. positive NPV projects in the future.

– Standard capital budgeting techniques involve Standard capital budgeting techniques involve establishing the present value of these projects establishing the present value of these projects based on anticipated implementation dates.based on anticipated implementation dates.

– However, this implicitly assumes that the firm However, this implicitly assumes that the firm is committed to go ahead with the projects. is committed to go ahead with the projects.


Growth OptionsGrowth Options– Since management need not make such a Since management need not make such a

commitment, they retain the option to commitment, they retain the option to exercise only those projects that appear exercise only those projects that appear to be profitable at the time of initiation. to be profitable at the time of initiation.

Example:Example:– High-tech and software industries (where High-tech and software industries (where

there are significant first-mover there are significant first-mover advantages)advantages)


Shadow CostsShadow Costs– Standard valuation techniques may Standard valuation techniques may

overvalueovervalue some projects by failing to some projects by failing to recognize the losses in flexibility to the recognize the losses in flexibility to the firm that result from implementation. firm that result from implementation.

– The acceptance of one project may The acceptance of one project may eliminate options that attach to other eliminate options that attach to other projects. projects.


Shadow CostsShadow Costs Example:Example:

– Building a plant in a particular city Building a plant in a particular city eliminates the options to expand the eliminates the options to expand the capacity of plants in nearby cities.capacity of plants in nearby cities.

– Management time.Management time.


Financial FlexibilityFinancial Flexibility– Choice of capital structure can affect value of Choice of capital structure can affect value of

project. Like operating flexibility, financial project. Like operating flexibility, financial flexibility can be measured by the value of the flexibility can be measured by the value of the financial options made available to the firm by financial options made available to the firm by its choice of capital structure. its choice of capital structure.

– Interaction between financial and operating Interaction between financial and operating options can be strong -- especially for long-options can be strong -- especially for long-term investment projects with a lot of term investment projects with a lot of uncertaintyuncertainty


Identifying Real OptionsIdentifying Real Options– Why are there empty lots in prime Why are there empty lots in prime

commercial real estate areas in all commercial real estate areas in all major cities?major cities?

– Multipurpose real estate Multipurpose real estate (hotel/apartment)(hotel/apartment)

– Why to firms use a hurdle rate for Why to firms use a hurdle rate for project evaluation greater than their project evaluation greater than their cost of capital?cost of capital?

NPV and Real OptionsNPV and Real Options Detailed Example: AbandonmentDetailed Example: AbandonmentAbbeytown Copper 2-yr lease over a known deposit.

• Deposit contains eight million pounds of copper

• Mining involves a one-year development phase, at a cost of $1.25 million immediately

• Extraction costs (outsourced) at $0.85 / pound at beginning of extraction phase (one year after development phase is initiated)

• Sale of copper would be at spot price of copper as of beginning of extraction phase


Detailed Example: AbandonmentDetailed Example: Abandonment

• Current spot price of copper is $0.95 / pound

• Log change in copper prices are normally distributed with mean 7% and standard deviation 20% (p.a.)

• Abbeytown's required rate of return for this project is 10%, and the riskless rate is 5%


Traditional NPV analysis:

Expected NPV = -1.25 + 8(E[S1] - 0.85) 1.1

where E[S1] = Expected price of Copper in one year's time

Current price of Copper, S0 = 0.95Expected rate of return on copper, r = 7%Expected price of copper in one year, S1 = 0.95e0.07 =

1.0189

Hence E[NPV] = -1.25 + 8(1.0189 - 0.85)/1.1 = - 0.022Reject


Option Analysis

S = 0.95 * 8 = 7.6K = 0.85 * 8 = 6.8r = 5%T = 1 year

= 20%


S 7.6 Current Asset ValueX 6.8 Exercise (Strike) Price T 1.00 Time to Maturity (Years)r f 5.00% Riskless Interest Rate (% p.a.) 20.00% Volatility (% p.a.)

d 1 0.9061

d 2 0.7061

N(d 1 ) 0.8176

N(d 2 ) 0.7599

C E 1.298 European Call Value ($)

P E 0.166 European Put Value ($)

Option Pricing Calculator


Option Analysis

Call Value = 1.3 Option Cost = 1.25

Option-adjusted Present Value = 0.05

Accept


Why does the option to abandon have value?

Can choose to abandon the project if the price of copper is low after one year.


What is the probability that we will abandon?

Probability that we will abandon = 1 - Prob(exercise)

= 1 - N(d2)

= 1 - 0.76 = 0.24


What is the probability that we will abandon?

S 7.6 Current Asset ValueX 6.8 Exercise (Strike) Price T 1.00 Time to Maturity (Years)r f 5.00% Riskless Interest Rate (% p.a.) 20.00% Volatility (% p.a.)

d 1 0.9061

d 2 0.7061

N(d 1 ) 0.8176

N(d 2 ) 0.7599 Probality of exercise

C E 1.298 European Call Value ($)

P E 0.166 European Put Value ($)

Option Pricing Calculator


Detailed Example: Deferment Detailed Example: Deferment OptionOption

A company has the opportunity to A company has the opportunity to build a new power project in a build a new power project in a foreign country.foreign country.

Net cash flows are $100mm in the Net cash flows are $100mm in the first year of operation.first year of operation.


Net cash flows in the second year Net cash flows in the second year of operation depend upon whether of operation depend upon whether the government sponsors a link to the government sponsors a link to bypass a transmission bypass a transmission “bottleneck”.“bottleneck”.

There is a 50% probability the There is a 50% probability the government will intervene.government will intervene.

This is an example of political risk.This is an example of political risk.


If the link goes ahead, demand for power If the link goes ahead, demand for power from the new plant will be low and net from the new plant will be low and net cash flow will be $80 mm.cash flow will be $80 mm.

If the link does not go ahead, demand for If the link does not go ahead, demand for power from the new plant will be high and power from the new plant will be high and net cash flow will be $125 mm.net cash flow will be $125 mm.

Similar uncertainty surrounds Year 3 net Similar uncertainty surrounds Year 3 net cash flows.cash flows.

Cash flows beyond Year 3 are perpetual.Cash flows beyond Year 3 are perpetual.

0 1 2 3

100

64

100

156

80

125

100 105103Expected NetCash Flow

...

...

...

...

...

0.5

0.5

0.5

0.5

0.5

0.5

.044,1

10.1

1

10.0

105

10.1

103

10.1

100220 PV

0 1 2 3

100 105103Expected NetCash Flow

...

...

Scenario 1aScenario 1a

Build now or never.Build now or never. Cost to build is 1,100.Cost to build is 1,100. NPV=1,044 - 1,100 = -56.NPV=1,044 - 1,100 = -56. Negative NPV.Negative NPV. Reject the project.Reject the project.

Scenario 1bScenario 1b

Build now or never.Build now or never. Cost to build is reduced to 1,000.Cost to build is reduced to 1,000. NPV=1,044 - 1,000 = +44.NPV=1,044 - 1,000 = +44. Positive NPV.Positive NPV. Accept the project.Accept the project.

Scenario 2Scenario 2

Option to delay for one year.Option to delay for one year. During this one-year delay, the During this one-year delay, the

generator learns whether or not the generator learns whether or not the new entrepreneurial link will proceed.new entrepreneurial link will proceed.

Based on this additional information, Based on this additional information, a “smarter” decision can be made.a “smarter” decision can be made.

Cost to build is 1,100.Cost to build is 1,100.

0 1 2 3

64

100

156

80

125

128125Expected Net Cash Flowin “up” state

...

...

...

...

...

8280Expected Net Cash Flowin “down” state

...

“up” state

“down” state

0.5

0.5

0.5

0.5

.277,110.1

1

10.0

128

10.1

1251 PV

0 1 2 3

128125Expected Net Cash Flowin “up” state

...

...

.81810.1

1

10.0

82

10.1

801 PV

0 1 2 3

8280Expected Net Cash Flowin “down” state

...

...

Scenario 2a (continued)Scenario 2a (continued)

Option to delay for one year.Option to delay for one year. Cost to build is 1,100.Cost to build is 1,100. Wait one year:Wait one year:

– proceed if “up state”, NPV=177.proceed if “up state”, NPV=177.– reject if “down state”, NPV=0.reject if “down state”, NPV=0.

Expected NPV today is:Expected NPV today is:

.80

10.1

05.01775.00

NPV

Scenario 2a (continued)Scenario 2a (continued)


.80

10.1

05.01775.00

NPV

•Compare with NPV without delay:

NPV without delay = - 56

Difference: 136


Option to delay for one year.Option to delay for one year. Cost to build is 1,000.Cost to build is 1,000. If we build now, NPVIf we build now, NPV0 0 = 44.= 44. What if we wait one year?What if we wait one year?


Wait one year:Wait one year:– proceed if “up state”, NPV=277.proceed if “up state”, NPV=277.– reject if “down state”, NPV=0.reject if “down state”, NPV=0.


.126

10.1

05.02775.00

NPV



.12610.1

05.02775.00

NPV

•Compare with NPV without 1 yr delay:

NPV without delay = 44

Difference: 82

RemarksRemarks

The option to delay can be valuable, The option to delay can be valuable, even if the project has positive NPV if even if the project has positive NPV if started immediately.started immediately.

The value of these options is ignored The value of these options is ignored by standard DCF techniques.by standard DCF techniques.

Proper analysis of these options is Proper analysis of these options is needed not just for project needed not just for project valuationvaluation, , but also for project but also for project timingtiming..

Scenario 3 – Add Scenario 3 – Add abandonmentabandonment

Plant can be abandoned at any Plant can be abandoned at any time for 800.time for 800.

This option will be exercised This option will be exercised whenever the PV of future cash whenever the PV of future cash flows falls below 800. flows falls below 800.

This only happens at the lowest This only happens at the lowest node, where perpetual cash flows node, where perpetual cash flows are 64.are 64.

100

800

100

156

80

125

...

...

Yearly CashFlows

One-timeLiquidation

Value

Scenario 3 (continued)Scenario 3 (continued)

When the abandonment option is When the abandonment option is incorporated, the NPV of building the incorporated, the NPV of building the project now is +77.project now is +77.

The NPV of waiting for one year is +126. The NPV of waiting for one year is +126. It is still optimal to delay for one year in It is still optimal to delay for one year in

this case, although the incremental value this case, although the incremental value of delaying has decreased.of delaying has decreased.

The value of the option to delay is lower if The value of the option to delay is lower if it is easy to exit a bad investment.it is easy to exit a bad investment.


Only as good as the inputsOnly as good as the inputs– Drift, variance, probabilitiesDrift, variance, probabilities

Beware of mean reversionBeware of mean reversion Theory relies on availability of a Theory relies on availability of a

replicating portfolioreplicating portfolio Equilibrium issuesEquilibrium issues


How do real options impact discount How do real options impact discount rates?rates?

How far can we take real options How far can we take real options theory in understanding major theory in understanding major issues in corporate finance?issues in corporate finance?

real options in project evaluation

Documents

real optionsabandonment

real optionsintensity

real optionsnpv

real optionstemporary

real optionsinput mix

real optionsoutput mix

abandonment options

shutdown options examples