berk chapter 22: real options

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Chapter 22

Real Options

Copyright © 2011 Pearson Prentice Hall. All rights reserved.22-2

Chapter Outline

22.1 Real Versus Financial Options

22.2 Decision Tree Analysis

22.3 The Option to Delay an Investment Opportunity

22.4 Growth and Abandonment Options

22.5 Applications to Multiple Projects

22.6 Rules of Thumb

22.7 Key Insights from Real Options


Learning Objectives

1. Define the term “real option.” 2. Draw decision trees to represent alternative

decisions and potential outcomes in an uncertain economy.

3. Describe three types of real options—timing, growth, and abandonment—and explain why it is important to consider those options when evaluating projects.

4. Illustrate how, given the option to wait, an investment that currently has a negative NPV can have a positive value.


Learning Objectives

5. Describe situations in which the option to wait is most valuable.

6. Choose between investments of different lives by evaluating the option to replace or extend the shorter-lived project at the end of its original life.

7. Discuss the situation in which equivalent annual benefit method results in optimal decision making.

8. Describe the types of investments that should be done first in a multi-stage investment decision, and calculate project rankings according to Eq. 22.3.

9. Define and use the profitability index and the hurdle rate rules of thumb.


22.1 Real Versus Financial Options

• Real Option

– The right to make a particular business decision, such as a capital investment

– A key distinction between real options and financial options is that real options, and the underlying assets on which they are based, are often not traded in competitive markets.


22.2 Decision Tree Analysis

• Decision Tree

– A graphical representation of future decisions and uncertainty resolution


22.2 Decision Tree Analysis (cont'd)

• Assume Megan is financing part of her MBA education by running a small business. She purchases goods on eBay and resells them at swap meets.

– Swap meets typically charge her $500 in advance to set up her small booth. Ignoring the cost of the booth, if she goes to every meet, her average profit on the goods that she sells is $1100 per meet.


22.2 Decision Tree Analysis (cont'd)

• The decision tree showing Megan’s options looks like the one on the following slide.

– Because the NPV of setting up a booth is $600, the optimal decision (shown in blue) would be to set up the booth.

• $1100 – $500 = $600


Figure 22.1 Megan’s Choices


Mapping Uncertainties on a Decision Tree

• Megan is aware that attendance at swap meets is weather dependent. – In good weather her profits are $1500.

– In bad weather, she will incur a loss of $100.• There is a 25% chance of bad weather.

• This adds another element of uncertainty for Megan to consider.


Figure 22.2 Effect of the Weather on Megan’s Options


Mapping Uncertainties on a Decision Tree (cont'd)

• Decision Nodes– A node on a decision tree at which a decision is

made

– Corresponds to a real option

• Information Nodes– A type of node on a decision tree indicating

uncertainty that is out of the control of the decision maker



• In Megan’s case

– The square node represents the decision to pay the fee and go to the swap meet or do nothing.

– The round node represents the uncertain state of nature, sunshine versus rain.

• In this case, Megan must commit to going to the meet before she knows what the weather will be.



• In reality, Megan does not have to commit to going to the swap meet before she knows the weather conditions.

– Megan understands that the $500 loss for the booth is unavoidable, but in bad weather she can simply stay home and not incur the additional $100 loss at the meet.


Figure 22.3 Megan’s Decision Tree When She Can Observe the Weather Before She Makes the Decision to Go to the Meet


Real Options

• Megan’s option to wait until she finds out what the weather is like before she decides whether she should go to the meet is a real option.

– This flexibility has value to Megan.


Real Options (cont'd)

• Assume Megan is risk neutral about the risk from the weather.

– The value of the real option can be computed by comparing her expected profit without the real option to wait until the weather is revealed to the value with the option to wait.



• If Megan commits to go regardless of the weather, her expected profit is $1100.– 0.75 × $1500 + 0.25 × (–$100) = $1100

• However, if she goes only when the weather is good, her expected profit is $1125.– 0.75 × $1500 + 0.25 × $0 = $1125

• The value of the real option is the difference, $25.



• If Megan has to pay for the booth only the day before the meet, the NPV of paying for the booth (ignoring discounting for one day) is $625.

– $1125 – $500 = $625• Since the NPV is positive, Megan should always pay

for the booth.



• Corporations face similar options.

– The option to delay an investment opportunity

– The option to grow

– The option to abandon an investment opportunity


22.3 The Option to Delay an Investment Opportunity

• In Megan’s case, once the booth is paid for, there is no cost to waiting to find out about the weather.

• In the real world, there is often a cost to delaying an investment decision.


22.3 The Option to Delay an Investment Opportunity (cont'd)

• By choosing to wait for more information the firm gives up any profits the project might generate in the interim. In addition, a competitor could use the delay to develop a competing product.

– The decision to wait therefore involves a tradeoff between these costs and the benefit of remaining flexible.


Investment as a Call Option

• Assume you have negotiated a deal with a major restaurant chain to open one of its restaurants in your hometown.

– The terms of the contract specify that you must open the restaurant either immediately or in exactly one year.

• If you do neither, you lose the right to open the restaurant at all.


Figure 22.4 Restaurant Investment Opportunity


Investment as a Call Option (cont'd)

• How much you should pay for this opportunity?

– It will cost $5 million to open the restaurant, whether you open it now or in one year.

– If you open the restaurant immediately, you expect it to generate $600,000 in free cash flow the first year.

• Future cash flows are expected to grow at a rate of 2% per year.

– The cost of capital for this investment is 12%.



• If the restaurant were to open today, its value would be:

– This would give an NPV of $1 million.• $6 million – $5 million = $1 million

• Given the flexibility you have to delay opening for one year, what should you be willing to pay?

• When should you open the restaurant?

$600,000 $6 million

12% 2%V



• The payoff if you delay is equivalent to the payoff of a one-year European call option on the restaurant with a strike price of $5 million.

– Assume

• The risk-free interest rate is 5%.

• The volatility is 40%.

• If you wait to open the restaurant you have an opportunity cost of $600,000 (the free cash flow in the first year).

– In terms of a financial option, the free cash flow is equivalent to a dividend paid by a stock. The holder of a call option does not receive the dividend until the option is exercised.


Table 22.1 Black-Scholes Option Value Parameters for Evaluating a Real Option to Invest



• The current value of the asset without the “dividends” that will be missed is:

• The present value of the cost to open the restaurant in one year is:

$0.6 million ( ) $6 million $5.46 million

1.12xS S PV Div

$5 million( ) $4.76 million

1.05PV K



• The current value of the call option to open the restaurant is:

1

2 1

ln[ / ( )] ln(5.46 / 4.76) 0.20 0.543

2 0.40

0.543 0.40 0.143

xS PV K Td

T

d d T

1 2 ( ) ( ) ( )

($5.46 million) (0.706) ($4.76 million) (0.557)

$1.20 million

xC S N d PV K N d



• The value today from waiting to invest in the restaurant next year (and only opening it if it is profitable to do so) is $1.20 million.

– This exceeds the NPV of $1 million from opening the restaurant today. Thus, you are better off waiting to invest, and the value of the contract is $1.20 million.



• What is the advantage of waiting in this case?

– If you wait, you will learn more about the likely success of the business.

– Because the investment in the restaurant is not yet committed, you can cancel your plans if the popularity of the restaurant should decline. By opening the restaurant today, you give up this option to “walk away.”



• Whether it is optimal to invest today or in one year will depend on the magnitude of any lost profits from the first year, compared to the benefit of preserving your right to change your decision.


Figure 22.5 The Decision to Invest in the Restaurant


Factors Affecting the Timing of Investment

• When you have the option of deciding when to invest, it is usually optimal to invest only when the NPV is substantially greater than zero.

– You should invest today only if the NPV of investing today exceeds the value of the option of waiting.

– Given the option to wait, an investment that currently has a negative NPV can have a positive one.


Factors Affecting the Timing of Investment (cont'd)

• Other factors affecting the decision to wait

– Volatility• The option to wait is most valuable when there is a

great deal of uncertainty.

– Dividends• Absent dividends, it is not optimal to exercise a call

option early. • In the real option context, it is always better to wait

unless there is a cost to doing so. The greater the cost, the less attractive the option to delay becomes.


Textbook Example 22.1


Textbook Example 22.1 (cont'd)


Alternative Example 22.1

• Problem

– Assume:• Your company is considering a new project at a cost

of $12 million.

• The project may begin today or in exactly one year.

• You expect the project to generate $1,500,000 in free cash flow the first year if you begin the project today.

• Free cash flow is expected to grow at a rate of 3% per year.



• Problem (continued)

– Assume:• The risk-free rate is 4%

• The appropriate cost of capital for this investment is 11%.

• The standard deviation of the project’s value is 30%.

– Should you begin the project today or wait one year?



• Solution

– Thus, the NPV of the project today is:• $18,750,000 − $12,000,000 = $6,750,000

– The current value of the project without the “dividend” that will be missed is:

$1,500,000$18,750,000

11% 3%TodayV

$1,500,000( ) $18,750,000 $17,398,649

1.11xS S PV Div



• Solution (continued)

– The present value of the cost to begin the project in one year is:

$12,000,000( ) $11,538,462

1.04PV K




(1.4868) 0.9315 (1.1868) 0.8823N N

1

2

ln[$17,398,649 /$11,650,485] .30 11.4868

2.30 1

1.4868 .30 1 1.1868

d

d

$17,398,649 0.9315 $11,650,485 0.8823

$5,927,619

C




– The value of waiting one year to start the project is $5,927,619.

– The NPV of starting the project is $6,750,000.• Thus, it is optimal to begin the project today rather

than wait.


22.4 Growth and Abandonment Options

• Growth Option

– A real option to invest in the future

• Abandonment Option

– The option to disinvest

• Because these options have value, they contribute to the value of any firm that has future possible investment opportunities.


Valuing Growth Potential

• Future growth opportunities can be thought of as a collection of real call options on potential projects.

– This can explain why young firms tend to have higher returns than older, established firms.


Valuing Growth Potential (cont'd)

• Assume StartUp Incorporated is a new company whose only asset is a patent on a new drug.

– If produced, the drug will generate certain profits of $1 million per year for 17 years (after then, competition will drive profits to zero).

– It will cost $10 million today to produce the drug.

– The yield on a 17-year risk-free annuity is currently 8% per year.



• What is the value of the patent?

– The NPV of investing in the drug today is:

– Given today’s interest rates, it does not make sense to invest in the drug today.

– What if interest rates permanently fall (rise) to 5% (10%) in one year?

17

1 1 1 10,000,000 $878,362

0.08 1.08NPV



– If rates rise to 10%, the NPV is still negative and it does not make sense to invest in the drug today.

– If rates fall to 5%, the NPV of investing in the drug today is:

• If rates fall to 5%, the NPV is positive and it makes sense to invest in the drug today.

16

1 1 1 10,000,000 $837,770

0.05 1.05NPV


Figure 22.6 Start Up’s Decision to Invest in the Drug



• Recall that to find risk-neutral probabilities, the probabilities that set the value of a financial asset today equal to the present value of its future cash flows must be solved for.

– In this case, a 17-year risk-free annuity that pays $1000 per year is used.



• The value of the annuity today is:

17

1000 1 1 $9122

0.08 1.08S



• If interest rates rise to 10% in one year, the value of the annuity will be:

16

1000 1 1000 1 $8824

0.1 1.1uS



• If interest rates fall to 5% in one year, the value of the annuity will be:

16

1000 1 1000 1 $11,838

0.05 1.05dS



• Recall that the risk-neutral probability of interest rates increasing to 10%, , is the probability such that the expected return of the annuity is equal to the risk-free rate of 6%.

(1 ) 1.06 9122 11,838 71.95%

8824 11,838f d

u d

r S S

S S



• The value today of the investment opportunity is the present value of the expected cash flows (using risk-neutral probabilities) discounted at the risk-free rate:

837,770 (1 0.7195) 0 0.7195 $221,693

1.06PV



• In this example, even though the cash flows of the project are known with certainty, the uncertainty regarding future interest rates creates substantial option value for the firm.

– The firm’s ability to use the patent and grow should interest rates fall is worth $221,693.


The Option to Expand

• Consider an investment opportunity with an option to grow that requires a $10 million investment today.

– In one year you will find out whether the project is successful.

• The risk neutral probability that the project will generate $1 million per year in perpetuity is 50%, otherwise, the project will generate nothing.

– At any time we can double the size of the project on the

original terms.


Figure 22.7 Staged Investment Opportunity


The Option to Expand (cont'd)

• By investing today, the expected annual cash flows are $500,000 (ignoring the option to double the size of the project).

– $1 million × 0.5 = $500,000



• Computing the NPV gives:

– The negative NPV suggests that you should not take on the project today.

– However, this means you will never find out whether the project is successful.

without growth option

500,000 10,000,000 $1.667 million

0.06NPV



• Now consider undertaking the project and exercising the growth option to double the size in a year if the product takes off.

– The NPV of doubling the size of the project in a year in this state is:

doubling after a year

1,000,000 10,000,000 $6.667 million

0.06NPV



• The risk-neutral probability that this state will occur is 50%, so the expected value of this growth option is $3.333 million. – 6.667 × 0.5 = $3.333

• The present value of this amount today is:

growth option

3.333 $3.145 million

1.06PV



• You have this option only if you choose to invest today, so the NPV of undertaking this investment is the NPV calculated above plus the value of the growth option we obtain by undertaking the project:

without growth option growth option

1.667 3.145 $1.478 million

NPV NPV PV



• This analysis shows that the NPV of the investment opportunity is positive and the firm should undertake it.

– It is optimal to undertake the investment today only because of the existence of the future expansion option.


The Option to Abandon

• Assume you are the CFO of a chain of gourmet food stores and you are considering opening a new store in the recently renovated Ferry Building in New York.

– If you do not sign the lease on the store today, someone else will, so you will not have the opportunity to open a store later.

– There is a clause in the lease that allows you to break the lease at no cost in two years.

– Including the lease payments, the new store will cost $10,000 per month to operate.


The Option to Abandon (cont'd)

• Because the building has just reopened, you do not know what the pedestrian traffic will be.

– If your customers are mainly limited to morning and evening commuters, you expect to generate $8000 per month in revenue in perpetuity.

– If, however, the building becomes a tourist attraction, you expect to generate $16000 per month in revenue in perpetuity.



• There is a 50% probability that the Ferry Building will become a tourist attraction.

• The costs to set up the store will be $400,000.

• The risk-free interest rate is constant at 7% per year (or 0.565% per month).



• The number of tourists visiting the New York Ferry Building represents idiosyncratic uncertainty. Since this is the kind of uncertainty investors in your company can costlessly diversify away, the appropriate cost of capital is the risk-free rate.



• If you were forced to operate the store under all circumstances, the expected revenue will be $12000.– $8000 × 0.5 + $16,000 × 0.5 = $12,000

• The NPV of the investment is:

– Given the negative NPV, it would not make sense to open the store.

12,000 10,000 400,000 $46,018

0.00565 0.00565NPV



• In reality, you would not have to keep operating the store. You have an option to get out of the lease after two years at no cost.– After the store is open, it will be immediately

obvious whether the Ferry Building is a tourist attraction. The decision tree is shown on the next slide.


Figure 22.8 Decision to Open a Store in the New York Ferry Building



• If the Ferry Building is a tourist attraction, the NPV of the investment opportunity is:

16,000 10,000 400,000 $661,947

0.00565 0.00565NPV



• If the Ferry Building does not become a tourist attraction, you will close the store after two years and the NPV of the investment opportunity is:

24 24

8000 1 10,000 1 1 1 400,000

0.00565 1.00565 0.00565 1.00565

$444,770

NPV



• There is an equal probability of each state.

• The NPV of opening the store is:

– By exercising the option to abandon the venture, you limit your losses and the NPV of undertaking the investment becomes positive. The value of the option to abandon is $154,607, the difference between the NPV with and without the option:

• $108,589 – (–46,018) = $154,607

$661,947 0.5 $444,770 0.5 $108,589


The Option to Abandon (cont’d)

• It is easy to ignore or understate the importance of the option to abandon.– Many times, abandoning an economically

unsuccessful venture can add more value than starting a new one.

– Managers often de-emphasize this alternative.



• Comparing Mutually Exclusive Investments with Different Lives– Consider Canadian Motors. Last year, an

engineering firm was asked to design a new machine for use in production.



– The firm has produced two designs• The cheaper design will cost $10 million to implement

and last five years.

• The more expensive design will cost $16 million and last 10 years.

• In both cases, the machines are expected to save Canadian Motors $3 million per year.

• If the cost of capital is 10%, which design should Canadian Motors approve?


Standalone NPV of Each Design

• The NPV of adopting the shorter-lived design is:

• The NPV of adopting the longer-lived design is:

– The NPV rule would suggest choosing the longer-lived project. However, NPV ignores the difference in the project’s life spans.

5

3 1 1 10 $1.37 million

0.1 1.1NPV

10

3 1 1 16 $2.43 million

0.1 1.1NPV


Standalone NPV of Each Design (cont’d)

• To truly compare the two options, we must consider what will happen once the shorter-lived equipment wears out.

• Consider three possibilities:– The technology is not replaced– It is replaced at the same terms– Technological advances allows it to be replaced

at improved terms


No Replacement

• If the shorter-lived technology is not replaced and the firm reverts to its old production process, there will be no benefit once the five-year life ends.– In that case, the original comparison is correct, and the

10-year machine will increase firm value by 2.43-1.37=$1.06 million more than the 5-year machine.

• One reason for not replacing the machine is if the cost is expected to increase. If the cost in five years is expected to be $11.37 million or higher, the NPV of the additional investment will be zero or less, so replacement will not be optimal.


Replacement at the Same Terms

• Suppose we expect the costs and benefits of the sorter-lived design to be the same in five years. In that case, the total NPV over the 10-year horizon will be:

• Since this NPV is still inferior to the $2.43 million for the 10-year design, we will still choose the longer-lived machine.

5 yr ,with replacement 5

1.37NPV 1.37 $2.22million

1.10


Replacement at Improved Terms

• In reality, the future cost of a machine is uncertain. If we expect technological advances to have caused the cost of the new technology to fall by $3 million at the end of five years, the NPV of the shorter-lived design will have increased to 3+1.37=$4.37 million.


Replacement at Improved Terms (cont’d)

5 yr ,with improved replacement 5

4.37NPV 1.37 $4.08million

1.10

• The NPV of the five-year design over a 10-year horizon will be:

• This improvement results in a higher NPV for the shorter-lived design, compared to $2.43 million for the 10-year machine.


Valuing the Replacement Option

• In order to compare the two designs correctly, we must determine the value of the replacement option, which will depend on the likelihood that the cost of the machine will increase or decrease.


Equivalent Annual Benefit Method

• Equivalent Annual Benefit Method

– A method of choosing between projects with different lives by selecting the project with the higher equivalent annual benefit

• It ignores the value of any real options because it assumes that both projects will be replaced on their original terms.


Textbook Example 22.2 (cont’d)


Staging Mutually Dependent Investments

• In some situations, we can choose the order of development stages.

• If so, how can we maximize the value of the real options we create?


An Example: Eclectic Motors

• Eclectic Motors is considering developing an electric car that would compete directly with gasoline-powered cars.

• They must overcome three technological hurdles:– Develop materials to significantly reduce the car’s body

weight.– Develop a method to rapidly recharge the batteries.– Advance battery technology to reduce weight and

increase storage capacity.

• As shown in Table 22.2 (next slide), each task requires further research and substantial risk.


Table 22.2 Required Time, Cost, and Likelihood of Success for Eclectic’s Project


An Example: Eclectic Motors (cont’d)

• Suppose: – All 3 risks are idiosyncratic, and the risk-free

rate is 6%– Given resources, the company can only work on

one technology at a time– By appropriately staging these investments,

they can enhance firm value

• Assuming it makes sense to proceed, in which order should they develop the technologies?


Mutually Dependent Investments

• This project represents a situation with mutually dependent investments, in which the value of one project depends on the outcome of the others.

• In this case, we assume all three challenges must be overcome, or there will be no benefit.


Investment Scale

• Consider first the materials and recharger technologies.

• If we begin with the materials technology, the expected cost to complete both is:

1100 0.50 400 $288.7million

1.06

Investment in materials

Probability materials technology succeeds

PV of delay

Investment in recharger


Investment Scale

• If we begin with the recharger technology, the expected cost to complete both is:

• Thus, Eclectic should begin with the materials technology. If it is unsuccessful, they will not waste money on the recharger technology.

1400 0.50 100 $447.2million

1.06

Investment in recharger

Probability recharger technology succeeds

PV of delay



Investment Time and Risk

• Now compare the materials and battery technologies. These two have the same cost, but the battery technology has a greater chance of failure and takes longer to develop.

• If we begin with the materials technology, it costs:

1100 0.50 100 $147.2million

1.06


Probability materials technology succeeds

PV of delay

Investment in battery


Investment Time and Risk

• If we begin with the battery technology, the expected cost to complete both is:

• Thus, Eclectic should work on the battery technology before working on the materials.

4

1100 0.25 100 $119.8million

1.06

Investment in battery

Probability battery technology succeeds

PV of delay



A General Rule

• Given its greater risk, the battery technology’s success will tell the firm more about the overall viability of the project than the other two.

• Given its longer time requirement, the investment in the second technology can be postponed, so the company benefits from the time value of the investment.

• In general, it is beneficial to invest in riskier and lengthier projects first.


A General Rule

• In general, we can find the optimal order to stage mutually dependent projects by ranking each, from highest to lowest, according to:

• Where PV(success) is the value at the start of the project of receiving $1 if the project succeeds, which is the risk-neutral probability of success.

1 (success)

(investment)

PV

PV



• Problem– Matthews Company is considering the

development of a jet backpack that uses a rocket-propelled engine for personal transportation. The company will need to overcome three technological hurdles in order to be successful:

1. Develop new fabrics to use in the backpack and wearer coveralls to be light and fire-resistant.

2. Design a lightweight, practical engine for propulsion.

3. Develop a safe, effective fuel to use in the engine.


Alternative Example 22.3 (cont’d)

• Problem– The required time, cost, and likelihood of

success for each step of the project is below:

– The risks are idiosyncratic, and the risk-free rate is 5%. Use Eq. 22.3 to rank the stages of Matthews’ rocket-propelled skateboard project.

Technology Cost TimeProbability of

Success

Fabric $30 million 6 months 80%

Engine $80 million 1 year 30%

Fuel $60 million 2 years 25%


Alternative Example 22.3 (cont’d)

• Solution– Evaluating Eq. 22.3 for each stage, we have:

– Fabric: [1-(0.80/1.05.5)]/30= 0.007309– Engine: [1-(0.30/1.05)]/80= 0.008929– Fuel: [1-(0.25/1.05)2]/60=0.013643

– So, Matthews should develop the fuel first, then the engine, then the fabric.


22.6 Rules of Thumb

• One of the major drawbacks of using the above analysis is that is can be difficult to implement.

– Consequently, many firms resort to following rules of thumb.


The Profitability Index Rule

• Profitability Index Rule

– Recommends investment whenever the profitability index exceeds some predetermined number

• Recall, the profitability index is defined as:

• When there is an option to delay, a good rule of thumb is to invest only when the index is at least 1.

NPVProfitability Index

Initial Investment


The Hurdle Rate Rule

• Hurdle Rate Rule– Raises the discount rate by using a higher

discount rate than the cost of capital to compute the NPV, but then applies the regular NPV rule

• Hurdle Rate– A higher discount rate created by the hurdle

rate rule. – If a project can jump the hurdle with a positive

NPV at this higher discount rate, then it should be undertaken.


The Hurdle Rate Rule (cont'd)

• When the source of uncertainty that creates a motive to wait is interest rate uncertainty, the hurdle rate is calculated as:

• The callable annuity rate is the rate on a risk-free annuity that can be repaid at any time.

Callable Annuity RateHurdle Rate Cost of Capital

Risk-Free Rate


Textbook Example 22.5 (cont'd)


The Hurdle Rate Rule (cont'd)

• Using a hurdle rate rule is cost-effective, but does not provide an accurate measure of value.

• NPV using the appropriate cost of capital is an accurate measure of value.


22.7 Key Insights from Real Options

• Out-of-the-money real options have value– Even if an investment has a negative NPV, if there is a

chance it could be positive in the future, the opportunity is worth something today.

• In-the-money real options need not be exercised immediately– The option to delay may be worth more than the NPV of

undertaking the investment immediately.

• Waiting is valuable– By waiting for uncertainty to resolve you can make

better decisions.


22.7 Key Insights from Real Options (cont’d)

• Delay investment expenses as much as possible– Committing capital before it is absolutely

necessary gives up the option to make a better decision once uncertainty is resolved.

• Create value by exploiting real options– The firm must continually re-evaluate its

investment opportunities, including the options to delay or abandon projects, as well as to create or grow them.


Chapter Quiz

1. What is the difference between a real option and a financial option?

2. What is the difference between an information node and a decision node on a decision tree?

3. What makes a real option valuable?4. Why can a firm with no ongoing projects, and

investment opportunities that currently have negative NPVs, still be worth a positive amount?

5. Why is it sometimes optimal to invest in stages?


Chapter Quiz

6. How can an abandonment option add value to a project?

7. Why is it inappropriate to simply pick the higher NPV project when comparing mutually exclusive investment opportunities with different lives?

8. How can you decide the order of investment in a staged investment decision?

9. Explain the profitability index rule of thumb.10.What is the hurdle rate rule, and what

uncertainty does it reflect?

berk chapter 22: real options

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