Lecture no44 real options analysis

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Real Options Analysis

Lecture No 44

Chapter 13

Contemporary Engineering Economics

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Contemporary Engineering Economics, 6th edition

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What Is Real About “Real” Options?

o Concept : Any corporate investment decision to invest and or divest real assets is simply an

option, giving the option holder a right to make an investment decision without any obligation to act

o At Issue : Can we apply the same logic used pricing financial options to value the real assets?

• Financial options analysis is mostly used in trading

• Real options analysis generally is used for valuing the real assets and strategic decision making.

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Decision Tree vs Real Options

Inve st

Goo d ne ws

Bad new s

Don’t

Goo d ne ws

Bad ne ws

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Real Option Premium

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Real Options: A New Math in Action

 Step 1, evaluate each stage of the project separately

 Step 2, understand your options

 Step 3, reevaluate the project, using an options mind-set

 Step 4, go figure

From “Exploiting Uncertainty—The ‘Real-Options’ Revolution in Decision-Making,” BusinessWeek, June 7, 1999, p.119.

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The Analogy Between a Call Option on a Stock and a Real Option

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Types of Real Options

In general, six real options exist in the decision-making process.

1. The option to postpone (or delay) the investment decision

2. The growth option to scale up an initial project if events are favorable

3. The option to abandon a project if events are unfavorable

4. The option to scale back (or contract) an initial project if events become unfavorable

5. The option to switch strategies once an initial strategy has been selected

6. The option to invest contingently (i.e invest a little now; if events are favorable invest a little more, or if not abandon.)

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Delay Option

o Uncertainty in market demand

o Uncertainty in market timing

o Uncertainty in market input/output prices

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Example 13.9: Delaying Investment: Value of Waiting

Do not wait: conventional NPW

 Given: Financial data

o Product life: 5 years

o Launch cost after 2 years:

$60.5M

o Is it worth waiting for 2 years? By

waiting, what do you gain?

o How much would it worth if you

were given the opportunity to

$50

PW(12%) = $12(P/A,12%,5) - $50

=-$6.74 < 0

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Real-Options Approach

 Given: V0 = $34.49, I = $60.5, T = 2 years,

r = 6%, and σ = 50%

 Find: ROP

 Conclusion: Since ROP > 0, it is worth

retaining the delay option as long as the cost

of this option does not exceed $11.5M.

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Economic Interpretation

What exactly does the $4.76 M delay value imply?

Assume the firm has 10 projects One of these 10 projects is this digital phone investment Assume the other

9 projects have a net present value of $100 M

Standard NPV: The value of the firm using standard NPV would still be $100 M including the digital phone project because the project has a negative NPV today and would not be accepted.

Delay Option: If the option to invest in the digital phones is included in the firm evaluation, then the value of the firm is $104.76 M Therefore, the delay option that the firm possesses is worth an additional $4.76 M.

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o The amount of loss from the initial investment represents the call option premium

o Investing in the initial investment provides the option to invest in any follow-on opportunities

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Example 13.11: Valuation of a Growth Option

Cash flow associated with two investment opportunities

 Given : Two different markets

o Years 0–3: Market the product

locally.

o Years 4–7: Expand the market

regionally, if events are favorable.

 Find : Value of the growth option $10 $12 $14 $16 $18

$20 $20

A small scale investment

A large scale investment

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NPV Analysis

Let the risk-adjusted discount rate (MARR) = 12% and the r = 6%.

The present value of the investments are:

o NPVSmall[0] (12%) = −$1.54 M [in year 0]

o NPVLarge[3] (12%) = −$60 + $55.58 = −$4.42 M [in year 3]

Therefore,

o NPVTotal[0] (12%) = −$1.54 − $4.42/1.12 3 = −$4.68 M < 0

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Real Options Decision Framework

o After investing in the small-scale project, the firm is not obligated to invest in the large-scale phase—hence, it is an option

o The value of these two investment opportunities is:

ENPV = NPVSmall + OptionExpand Large

Where ENPV = Expanded Net Present Value

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The Value of the Option

o The option to expand can be valued as a European call option using the B-S equation.

o The option inputs are:

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Economic Interpretation

Therefore, the total value of the two investment opportunities is:

FNPV = NPVSmall + OptionExpandLarge

FNPV = −$1.54 + $7.54 = $6 M

[Compared with the standard NPV = −$4.68 M]

Conclusion: Because the FNPV > 0, the two investment opportunities have positive value and should be pursued Even though the initial investment in the local market will lose money, the benefits of the large-scale investment offset any initial losses.

Note: Recall that NPVSmall also represents the option premium paid Therefore, the maximum loss on the NPVSmall should not exceed OptionExpandLarge This is equivalent to EVPI in decision tree analysis For example, if the estimated NPVSmall was negative $9 M, then these two investment opportunities should not be pursued all together.

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Scale-up Option

• A firm has the right to scale-up an investment if the initial project is favorable.

• A firm has the option to increase investment in a project, in return for

increased revenues.

• This is just a growth option, but will be valued on a binomial lattice

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Example 13.12: Scale-Up Option Using Binomial Lattice Approach

 Given:

o The project’s current value is V0 = $10M

o Anytime over the next three years, the firm can

invest an additional I = $3 M and receive an

expected 30% increase in net cash flows and

therefore, a 30% increase in project value

o The risk-free interest rate is 6% and the volatility

of the project’s value is 30%

 Find: Value of scale-up option

Lattice Evolution of the Project Value

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Process of Calculating Option Value

Lattice Evolution of the Underlying Value Process of Reaching a Decision at Node

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Valuation Lattice: Decision Tree for a Scale-Up Option

Option value = $11.23 − $10

= $1.23M

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Example: Scale-down Option

A project has been undertaken within a firm The firm has the option to sell some of its

equipment and facilities and sublet out the same project workload

o The projects current value is V0 = $10 M Anytime over the next 3 years, the firm can sell off $4 M in

resources but receive an expected 30% decrease in net cash flows (and therefore, a 30% decrease in project value)

o Let the r = 6% and the σ = 30% A binomial lattice will be used with a one-year time increment

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Binomial Lattice with Scale-Down Option

18.23 max(18.23*0.7 + 4, 18.22)=

18.22

Do not scale-down

24.60 max(0.7*24.6 + 4, 24.6)= 24.6

10 max(10*0.7 + 4, 10.78)=

11

Scale-down

13.5 max(0.7*13.5 + 4, 13.5)= 13.5

7.4 max(0.7*7.4 + 4, 7.4)= 9.18

Scale-down

5.48 max(5.48*0.7 + 4, 7.59)=

7.836

Scale-down 4.05

max(0.7*4.05 + 4, 4.05)= 6.835

0.94 0.53 24.6 0.47 13.5 $18.22

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Compound Options

later phases depend on the success of earlier phases.

• Invest a little, observe results; the option to invest more

Local, regional, national, international

Research & development

Growth opportunities

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Example 13.13: “A Real-World Way to Manage Real Options”

 Given:

design phase

over the following two years.

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Phases of Project

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Compound Option Framework

o Investing in permit/preparation (or Phase 0 ) provides option to invest in design phase ( Phase 1 ).

o Investing in design phase provides the option to invest in plant construction ( Phase 2 ).

o Therefore, investing in Phase 2 is contingent upon investing in Phase 1, which

is contingent upon the results of Phase 0.

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How to Calculate the Combined Option Value

Phase 2 Phase 1

Phase 0

Compound Real Options

Calculate the Phase 2 option first.

Calculate the Phase 1 option second.

Calculate the Phase 0 option last.

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(a) Traditional NPV Analysis

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(b) Real Options Analysis: Step 1

 The event tree that illustrates how

the project’s value changes over time

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Step 2: Valuing Phase 2 Options

 At Issue : Is it worth keeping the option open at Year

2, assuming that you were at node B?

 Keeping the option open

 Exercise (committing $800M):

$1,440M − $800M = $640M

 Conclusion: Keep the option open.

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Step 3: What to Do in Year 1

At Issue : Is it worth investing

$400M in design?

Decision: At year 1, if you find

yourself in node C, go ahead and

invest $400M If not, don’t invest and

get out of the project In that case,

your loss is limited to $60M that were

committed in year 0.

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Step 4: Standing at Year 0

At Issue : Is it worth spending

$60M today?

The value of having the compound

options is worth $71M (or exactly

$71.039M) Since it requires only

$60M now, it is desirable to proceed

for now

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