LECTURES ON REAL OPTIONS: PART I — BASIC · PDF fileLECTURES ON REAL OPTIONS: PART I — BASIC CONCEPTS Robert S. Pindyck Massachusetts Institute of Technology Cambridge, MA 02142

LECTURES ON REAL OPTIONS:

PART I — BASIC CONCEPTS

Robert S. Pindyck

Massachusetts Institute of TechnologyCambridge, MA 02142

Robert Pindyck (MIT) LECTURES ON REAL OPTIONS — PART I August, 2008 1 / 44

Introduction

Main Idea: Investment decision can be treated as the exercisingof an option.

Firm has option to invest.Need not exercise the option now — can wait for moreinformation.If investment is irreversible (sunk cost), there is an opportunitycost of investing now rather than waiting.Opportunity cost (value of option) can be very large.The greater the uncertainty, the greater the value of the firm’soptions to invest, and the greater the incentive to keep theseoptions open.

Note that value of a firm is value of its capital in place plus thevalue of its growth options.


Introduction


Firm has option to invest.

Need not exercise the option now — can wait for moreinformation.If investment is irreversible (sunk cost), there is an opportunitycost of investing now rather than waiting.Opportunity cost (value of option) can be very large.The greater the uncertainty, the greater the value of the firm’soptions to invest, and the greater the incentive to keep theseoptions open.



Introduction


Firm has option to invest.Need not exercise the option now — can wait for moreinformation.

If investment is irreversible (sunk cost), there is an opportunitycost of investing now rather than waiting.Opportunity cost (value of option) can be very large.The greater the uncertainty, the greater the value of the firm’soptions to invest, and the greater the incentive to keep theseoptions open.



Introduction


Firm has option to invest.Need not exercise the option now — can wait for moreinformation.If investment is irreversible (sunk cost), there is an opportunitycost of investing now rather than waiting.

Opportunity cost (value of option) can be very large.The greater the uncertainty, the greater the value of the firm’soptions to invest, and the greater the incentive to keep theseoptions open.



Introduction


Firm has option to invest.Need not exercise the option now — can wait for moreinformation.If investment is irreversible (sunk cost), there is an opportunitycost of investing now rather than waiting.Opportunity cost (value of option) can be very large.

The greater the uncertainty, the greater the value of the firm’soptions to invest, and the greater the incentive to keep theseoptions open.



Introduction





Introduction





Introduction (Continued)

Any decision involving sunk costs can be viewed this way:

Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.

Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.

Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.

Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.

Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.

Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.

Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.

Signing a long-term fuel contract.Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.

Undertaking an R&D program.




Opening a copper mine.Closing a copper mine.Building an oil tanker.Mothballing an oil tanker.Reactivating a mothballed tanker.Scrapping a tanker.Installing scrubbers on coal-burning power plant.Signing a long-term fuel contract.Undertaking an R&D program.



Why look at investment decisions this way? What’s wrong withthe standard NPV rule?

With uncertainty and irreversibility, NPV rule is often wrong —very wrong. Option theory gives better answers.Can value important “real” options, such as value of land,offshore oil reserves, or patent that provides an option to invest.Can determine value of flexibility. For example:

Flexibility from delaying electric power plant construction.Flexibility from installing small turbine units instead of buildinga large coal-fired plant.Flexibility from buying tradeable emission allowances instead ofinstalling scrubbers.Value of more flexible contract provisions.




With uncertainty and irreversibility, NPV rule is often wrong —very wrong. Option theory gives better answers.

Can value important “real” options, such as value of land,offshore oil reserves, or patent that provides an option to invest.Can determine value of flexibility. For example:





With uncertainty and irreversibility, NPV rule is often wrong —very wrong. Option theory gives better answers.Can value important “real” options, such as value of land,offshore oil reserves, or patent that provides an option to invest.

Can determine value of flexibility. For example:











Flexibility from delaying electric power plant construction.

Flexibility from installing small turbine units instead of buildinga large coal-fired plant.Flexibility from buying tradeable emission allowances instead ofinstalling scrubbers.Value of more flexible contract provisions.





Flexibility from delaying electric power plant construction.Flexibility from installing small turbine units instead of buildinga large coal-fired plant.

Flexibility from buying tradeable emission allowances instead ofinstalling scrubbers.Value of more flexible contract provisions.





Flexibility from delaying electric power plant construction.Flexibility from installing small turbine units instead of buildinga large coal-fired plant.Flexibility from buying tradeable emission allowances instead ofinstalling scrubbers.

Value of more flexible contract provisions.








Option theory emphasizes uncertainty and treats it correctly.(NPV rule often doesn’t.) Helps to focus attention on nature ofuncertainty and its implications.

Managers ask: “What will happen (to oil prices, to electricitydemand, to interest rates,...)?” Usually, this is the wrongquestion. The right question is: “What could happen (to oilprices, to...), and what would it imply?”

Managers often underestimate or ignore the extent ofuncertainty and its implications.

Option theory forces managers to address uncertainty.




















Simple NPV Criterion for Project Evaluation

Net Present Value (NPV) = Present value of inflows – presentvalue of outflows.

Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:

It is expected investment expenditure in year t.NCFt is expected net cash flow from project in year t.rt is discount rate in year t.

For the time being, we will keep the discount rate constant forsimplicity.




Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:






Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:






Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:

It is expected investment expenditure in year t.

NCFt is expected net cash flow from project in year t.rt is discount rate in year t.





Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:

It is expected investment expenditure in year t.NCFt is expected net cash flow from project in year t.

rt is discount rate in year t.





Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:






Invest if NPV > 0.

For example:

NPV = −I0−I1

1 + r1− I2

(1 + r2)2+

NCF3

(1 + r3)3+ ...+

NCF10

(1 + r10)10

where:




Another Example with Option

Consider building a widget factory that will produce one widgetper year forever. Price of a widget now is $100, but next year itwill go up or down by 50%, and then remain fixed:

t = 0 t = 1 t = 2 · · ·

P1 = $150 → P2 = $150 →12 ↗

P0 = $10012 ↘

P1 = $50 → P2 = $50 →

Cost of factory is $800, and it only takes a week to build. Is thisa good investment? Should we invest now, or wait one year andsee whether the price goes up or down?


Another Example with Option

Consider building a widget factory that will produce one widgetper year forever. Price of a widget now is $100, but next year itwill go up or down by 50%, and then remain fixed:

t = 0 t = 1 t = 2 · · ·

P1 = $150 → P2 = $150 →12 ↗

P0 = $10012 ↘

P1 = $50 → P2 = $50 →

Cost of factory is $800, and it only takes a week to build. Is thisa good investment? Should we invest now, or wait one year andsee whether the price goes up or down?


Another Example with Option (Continued)

Suppose we invest now.

NPV = −800 +∞

∑t=0

100

(1.1)t= −800 + 1, 100 = $300

So NPV rule says we should invest now.

But suppose we wait one year and then invest only if the pricegoes up:

NPV = (.5)

[−800

1.1+

∞

∑t=1

150

(1.1)t

]=

425

1.1= $386

Clearly waiting is better than investing now.

Value of being able to wait is $386− $300 = $86.




NPV = −800 +∞

∑t=0

100

(1.1)t= −800 + 1, 100 = $300



NPV = (.5)

[−800

1.1+

∞

∑t=1

150

(1.1)t

]=

425

1.1= $386






NPV = −800 +∞

∑t=0

100

(1.1)t= −800 + 1, 100 = $300



NPV = (.5)

[−800

1.1+

∞

∑t=1

150

(1.1)t

]=

425

1.1= $386






NPV = −800 +∞

∑t=0

100

(1.1)t= −800 + 1, 100 = $300



NPV = (.5)

[−800

1.1+

∞

∑t=1

150

(1.1)t

]=

425

1.1= $386






NPV = −800 +∞

∑t=0

100

(1.1)t= −800 + 1, 100 = $300



NPV = (.5)

[−800

1.1+

∞

∑t=1

150

(1.1)t

]=

425

1.1= $386




Another Example (Continued)

Another way to value flexibility: How high an investment cost Iwould we accept to have a flexible investment opportunity ratherthan a “now or never” one?

Answer: Find I that makes the NPV of the project when we waitequal to the NPV when I = $800 and we invest now, i.e., equalto $300. Substituting I for the 800 and $300 for the $386 inequation for NPV above:

NPV = (.5)

[−I

1.1+

∞

∑t=1

150

(1.1)t

]= $300

Solving for I yields I = $990.

So opportunity to build factory now and only now at cost of$800 has same value as opportunity to build the factory now ornext year at cost of $990.





NPV = (.5)

[−I

1.1+

∞

∑t=1

150

(1.1)t

]= $300







NPV = (.5)

[−I

1.1+

∞

∑t=1

150

(1.1)t

]= $300




Introduction

So far, we have examined investment decisions for which allinformation comes from ”nature”:

Oil reserve: price of oil is determined in world market, and wesimply observe it from day to day.Price of widgets: goes up or down independently of what we do.

Now we turn to investment decisions for which informationcomes from different sources:

Learning from our own actions. R&D, for example, yieldsinformation about the feasibility or cost of developing a newproduct.Learning from others. A drug company might learn about themarket potential for a new type of drug from the experience ofits competitors.

Robert Pindyck (MIT) LECTURES ON REAL OPTIONS—PART IV August, 2008 2 / 32

Introduction


Oil reserve: price of oil is determined in world market, and wesimply observe it from day to day.

Price of widgets: goes up or down independently of what we do.




Introduction






Introduction






Introduction




Learning from our own actions. R&D, for example, yieldsinformation about the feasibility or cost of developing a newproduct.

Learning from others. A drug company might learn about themarket potential for a new type of drug from the experience ofits competitors.


Introduction






Information and Strategic Options

Learning from others:

Return to simple widget factory example we looked at earlier.But now, 2 firms:

Price = $50 per widget, or $150, with equal probability. Cannotfind out until you—or the other firm— actually invests.

Each firm can invest at cost of $800. Hence, for each firm, NPVof investing now is:

NPVNOWi = −800 +

∞

∑t=0

100/(1 + R)t (10)

R= .10, so NPVNOWi = −800 + 1100 = $300.







NPVNOWi = −800 +

∞

∑t=0

100/(1 + R)t (10)

R= .10, so NPVNOWi = −800 + 1100 = $300.







NPVNOWi = −800 +

∞

∑t=0

100/(1 + R)t (10)

R= .10, so NPVNOWi = −800 + 1100 = $300.


Information and Strategic Options (continued)

Suppose Firm 2 will invest now. Should Firm 1 wait? If it waits,it will only invest if it learns that P = $150. NPV for Firm 1from waiting is then:

NPVWAIT1 = 1

2

[−800

1.1+

∞

∑t=1

150/(1.1)t

]= $386 (11)

Hence, better to wait. But Firm 2 is thinking the same thing.Suppose neither firm invests now. If, at end of year, both firmsinvest (without benefit of knowledge), NPV today will be:

NPVWAITi = 300/1.1 = $273 (12)



Suppose Firm 2 will invest now. Should Firm 1 wait? If it waits,it will only invest if it learns that P = $150. NPV for Firm 1from waiting is then:

NPVWAIT1 = 1

2

[−800

1.1+

∞

∑t=1

150/(1.1)t

]= $386 (11)

Hence, better to wait. But Firm 2 is thinking the same thing.Suppose neither firm invests now. If, at end of year, both firmsinvest (without benefit of knowledge), NPV today will be:

NPVWAITi = 300/1.1 = $273 (12)



We thus have a gaming situation:

Firm 2

Invest Now Wait

Invest Now 300, 300 300, 386

Firm 1Wait 386, 300 273, 273



How would you play this game if you were Firm 1? Might assigna probability p that Firm 2 will invest now. Then,

NPVNOW1 = 300

NPVWAIT1 = (p)(386) + (1− p)(273) = 273 + 113p

Hence it is better to wait if 273 + 113p > 300, or p > .24

Of course there is no reason for this process to stop at the endof one year. In this war of attrition, it is possible for a very longtime to go by with neither firm investing.



How would you play this game if you were Firm 1? Might assigna probability p that Firm 2 will invest now. Then,

NPVNOW1 = 300

NPVWAIT1 = (p)(386) + (1− p)(273) = 273 + 113p

Hence it is better to wait if 273 + 113p > 300, or p > .24

Of course there is no reason for this process to stop at the endof one year. In this war of attrition, it is possible for a very longtime to go by with neither firm investing.


Informational Cascades

People are deciding whether to buy real estate in downtownOskosh.

If a person acts, ultimate payoff will be the fundamental valueV , which is either 1 or −1, intitially with probability 1/2.

Individuals receive signals — either high (H) or low (L).

If V = 1, signal will be H with probability p > 12 and L with

probability (1− p) < 12 .

If V = −1, signal will be H with probability (1− p) and L withprobability p.So, a signal is informative, but does not eliminate alluncertainty.
































If V = −1, signal will be H with probability (1− p) and L withprobability p.

So, a signal is informative, but does not eliminate alluncertainty.










Informational Cascades (continued)

Observable Signals. Suppose new signal comes every week,observed by all potential investors. What will happen?

As number of signals increases, uncertainty over true V isreduced.Eventually all investors settle on correct choice: They invest ifV = 1 and don’t if V = −1.

Observable Actions. Suppose each person receives one signal,and you can only observe the actions of others.

Can lead to informational cascade in which many people investeven though in fact V = −1, or many people don’t invest eventhough V = 1.

Consider sequence of risk-neutral investors, A, B, C, etc. Wantto know what each will do given his own signal, and givenobserved actions of predecessors.




As number of signals increases, uncertainty over true V isreduced.

Eventually all investors settle on correct choice: They invest ifV = 1 and don’t if V = −1.


































A will invest if his signal is H, will not if signal is L. Note allothers can infer A’s signal from his action.

Suppose A invested. What should B do?

Clearly B should invest if her signal is H.If B’s signal is L, her posterior probability that V = 1 is 1

2 , soshe is indifferent.Assume in this case she flips a coin.

C faces three possibilities:

1 A and B both invested. Then C will invest, even if his signal isL. (NPV is positive, no matter what signal C received, and eventhough B may have flipped a coin.)

2 Neither A nor B invested. Then C will not invest, even if hissignal is H.

3 A invested and B did not, or vice versa. Then C will only investif his signal is H.















Clearly B should invest if her signal is H.

If B’s signal is L, her posterior probability that V = 1 is 12 , so

she is indifferent.Assume in this case she flips a coin.










2 , soshe is indifferent.

Assume in this case she flips a coin.































C faces three possibilities:1 A and B both invested. Then C will invest, even if his signal is

L. (NPV is positive, no matter what signal C received, and eventhough B may have flipped a coin.)

























Let’s focus on first case: A and B both invested, and thus Cinvested even if his signal is L. Now, what will D do?

D will invest, no matter what signal she receives.

Likewise, E, F, etc. will all invest.

We now have an informational cascade. It is possible that A,and only A, received a signal of H, and all others received signalsof L. Yet all will invest.

If D, E, etc., could have observed that B and C received signalsof L, they would not have invested. But they only observeactions of others.

Everyone is acting rationally (expected NPVs are positive) eventhough no new information is being produced.











































Suppose in fact V = −1. Then how does this end? Perhapssome investors seek and obtain information – signals of L. Theystart to sell. Others observe these actions and — quite rationally— also sell. Price plummets!

What to Do? Doesn’t mean you should not invest. (ExpectedNPVs are positive.) But understand how little information yourdecision is based on.

Remember: Rational decisions based on actions of others involvemuch more risk than decisions based on accumulation offundamental information.












LECTURES ON REAL OPTIONS: PART I — BASIC · PDF fileLECTURES ON REAL OPTIONS: PART I — BASIC CONCEPTS Robert S. Pindyck Massachusetts Institute of Technology Cambridge, MA 02142

Documents