1. and Cross-Border Investment Strategy
Chapter 16 Real Options
and Cross-Border Investment Strategy
Learning objectives
 Real options and corporate investment
– Definitions, terminology, concepts…
 The value of flexibility in an uncertain world
– Market entry as a simple real option
– Market entry as a compound real option
 Real options and NPV as complements

2. The blunders are all there on the board, waiting to be made.
16.1 Real Options
and the Theory and Practice of Investment
The blunders are all there on the board, waiting to be made.
Savielly Tartakower
(Chess grandmaster)

3. and the Theory and Practice of Investment
16.1 Real Options
and the Theory and Practice of Investment
The conventional theory of investment
Discount expected future cash flows at an appropriate risk-adjusted discount rate:
NPV = St [E[CFt] / (1+i)t]
Include only incremental cash flows.
Include all opportunity costs.
Oft-neglected opportunity costs include the option to invest (or disinvest) at a different time or in a different form.

4. and the Theory and Practice of Investment
16.1 Real Options
and the Theory and Practice of Investment
Options on real assets
A real option is an option on a real asset.
Real options derive their value from managerial flexibility in a changing and uncertain world:
Options to invest or abandon
Options to expand or contract
Options to speed up or defer
Pursuing one investment option necessarily involves forgoing other investment options.

5. and the Theory and Practice of Investment
16.1 Real Options
and the Theory and Practice of Investment
Option terminology
Simple options
Call versus put options
European versus American options
Compound option
A compound option is an option on an option.
Special case: An alternating sequence of calls and puts is called a switching option.
Rainbow option
Multiple sources of uncertainty

6. 16.2 Market Entry as a Simple Real Option
Market entry and the option to invest
Investing today means forgoing the opportunity to invest at some future date, so that projects must be compared against similar future projects.
A puzzle: Firms often use inflated hurdle rates:
Because of the value of waiting for more information, hurdle rates on investments in uncertain environments are often set above investors’ required returns.

7. 16.2 Market Entry as a Simple Real Option
An example of the option to invest
Investment I0 = PV(I1) = $20 million
The present value of investment is $20 million regardless of when investment is made
Price of oil P = $70 or $90 with equal probability
Þ E[P] = $80
Variable production cost V = $68 per barrel
E[production] = Q = 200,000 barrels/year
Discount rate i = 10%

8. 16.2 Market Entry as a Simple Real Option
The option to invest as a now-or-never decision
NPV(invest today)
= [ ($80-$68) (200,000) / 0.1 ] – $20 million
= $4 million > $0
Þ invest today (?)

9. 16.2 Market Entry as a Simple Real Option
Invest today or wait for more information

10. 16.2 Market Entry as a Simple Real Option
The option to wait one year before deciding
NPV = [ (E[P]-V) Q / i ] / (1+i) - I0
In this example, waiting one year reveals the future price of oil.

11. 16.2 Market Entry as a Simple Real Option
The investment timing option
NPV(wait 1 year½P = $90)
= (($90 – $68)(200,000) / 0.1) / (1.1) – $20,000,000
= $20,000,000 > $0
Þ invest if P = $90
NPV(wait 1 year½P = $70)
= (($70 – $68)(200,000) / 0.1) / (1.1) – $20,000,000
= –$16,363,636 < $0
Þ do not invest if P = $70
Þ NPV(wait 1 year½P = $70) = $0

12. 16.2 Market Entry as a Simple Real Option
The investment timing option
NPV(wait 1 year)
= Probability(P = $70) (NPV$70)
+ Probability(P = $90) (NPV$90)
= ½ ($0) + ½ ($20,000,000)
= $10,000,000 > $0
Þ wait one year before deciding whether to invest

13. When you see a good move, look for a better one.
16.2 Market Entry as a Simple Real Option
When you see a good move, look for a better one.
Emanuel Lasker
(Chess grandmaster)

14. 16.2 Market Entry as a Simple Real Option
Option value = Intrinsic value + Time value
Intrinsic value
= value if exercised immediately
Time value
= additional value if left unexercised

15. 16.2 Market Entry as a Simple Real Option
The opportunity cost of investing today
Option Value
= Intrinsic Value + Time Value
NPV (wait 1 year)
= Value if exercised + Additional value
immediately from waiting
$10,000,000
= $4,000,000 + $6,000,000

16. 16.2 Market Entry as a Simple Real Option
The value of BP’s option to invest 15
Option value
prior to expiration 10
Time value 5
Intrinsic value
at expiration 5 10 15 20 25 30
Value of an oil well

17. 16.2 Market Entry as a Simple Real Option
A resolution of a puzzle: Inflated hurdle rates
Managers facing this type of uncertainty have four choices:
Ignore the timing option (?!).
Estimate the value of the timing option using option pricing methods.
Adjust the cash flows with a decision tree that captures possible future states of the world.
Inflate the hurdle rate (apply a “fudge factor”) to compensate for high uncertainty.

18. 16.2 Market Exit as a Simple Real Option
Market exit and the option to abandon
Abandoning today means forgoing the opportunity to abandon at some future date, so that abandonment today must be compared to future abandonment.
Another puzzle: Failure to abandon losing ventures
Because of the value of waiting for additional information, hurdle rates on corporate abandonment decisions are often set above investors’ required return.

19. 16.2 Market Exit as a Simple Real Option
An example of the option to abandon
Cost of disinvestment I0 = PV(I1) = $2 million
The present value of abandonment is $2 million regardless of when abandonment is made.
Price of oil P = $65 or $75 with equal probability
Þ E[P] = $70
Variable production cost V = $72 per barrel
E[production] = Q = 200,000 barrels/year
Discount rate i = 10%

20. 16.2 Market Exit as a Simple Real Option
Abandon today or wait for more information

21. 16.2 Market Exit as a Simple Real Option
The abandonment option as a now-or-never decision.
NPV(abandon today)
= –($70 – $72) (200,000) / 0.1 – $2 million
= $2 million > $0
Þ abandon today (?)

22. 16.2 Market Exit as a Simple Real Option
The abandonment timing option
NPV(wait 1 year½P = $65)
= –(($65-$72)(200,000) / 0.1) / (1.1) – $2 million
= $10,727,273 > $0
Þ abandon if P = $65
NPV(wait 1 year½P = $75)
= –(($75 – $72)(200,000) / 0.1) / (1.1) – $2 million
= –$7,454,545 < $0
Þ do not abandon if P = $75

23. 16.2 Market Exit as a Simple Real Option
The abandonment timing option
NPV(wait 1 year)
= Probability(P=$65) (NPV$65)
+ Probability(P=$75) (NPV$75)
= ½ ($10,727,273) + ½ ($0)
= $5,363,636 > $0
Þ wait one year before deciding to abandon

24. 16.2 Market Exit as a Simple Real Option
Opportunity cost of abandoning today
Option Value
= Intrinsic value + Time value
NPV(wait 1 year)
= NPV(abandon today) + Additional value
from waiting 1 year
$5,363,636
= $2,000,000 + $3,363,636

25. 16.3 Uncertainty and the Value of Real Options
The determinants of call option values
Relation to
call option BP
Option value determinant value example
Value of the underlying asset P + $24 million
Exercise price of the option K – $20 million
Risk-free rate of interest rF + 10%
Time to expiration of the option T + 1 year
Volatility of the underlying asset sP + ($3.6m or $40m)
Time value = f ( P, K, T, rF, sP )

26. 16.3 Uncertainty and the Value of Real Options
Volatility and option value
Option value
Exercise price
Value of the underlying asset

27. 16.3 Uncertainty and the Value of Real Options
Exogenous price uncertainty
Exogenous uncertainty is outside the influence or control of the firm.
Oil price example
P1 = $65 or $95 with equal probability
Þ E[P1] = $80/bbl
NPV(invest today)
= (($80 – $68)(200,000) / 0.1) – $20 million
= $4,000,000 > $0
Þ invest today?

28. 16.3 Uncertainty and the Value of Real Options
Exogenous price uncertainty
NPV(wait 1 year½P1=$95)
= (($95 – $68)200,000 / 0.1) / 1.1 – $20 million
= $29,090,909 > $0
Þ invest if P1 = $95
NPV(wait 1 year½P1 = $65)
= (($65-$68)(200,000) / 0.1) / 1.1 – $20 million
= –$25,454,545 < $0
Þ do not invest if P1 = $65

29. 16.3 Uncertainty and the Value of Real Options
Exogenous price uncertainty
NPV(wait one year)
= (½)($0) + (½)($29,090,909)
= $14,545,455 > $0
Þ wait one year before deciding to invest

30. 16.3 Uncertainty and the Value of Real Options
Time value & exogenous uncertainty
Option value = Intrinsic value + Time value
±$70
$10,000,000 = $4,000,000 + $6,000,000
±$15
$14,545,455 = $4,000,000 + $10,545,455
The time value of a real option increases with exogenous price uncertainty.

31. 16.3 Uncertainty and the Value of Real Options
Compound real options
Real options are compound rainbow options:
A compound option is an option on an option.
A rainbow option has multiple sources of uncertainty.
Project valuation and investment strategy is difficult because most investment alternatives are compound rainbow options.

32. 16.4 Market Entry as a Compound Real Option
Another puzzle:
Negative-NPV entry into emerging markets
Firms often make investments into emerging markets even though investment does not seem warranted according to the NPV decision rule.
An exploratory (perhaps negative-NPV) investment can reveal information about the value of subsequent investments.

33. 16.4 Market Entry as a Compound Real Option
Growth options and project value
VAsset = VAsset-in-place + VGrowth options
Real options derive their value from flexibility in responding to an uncertain world, so this equation can alternatively be stated as:
VAsset = VAsset-in-place with no flexibility
+ VFlexibility

34. 16.4 Market Entry as a Compound Real Option
Consider a negative-NPV investment
Initial investment I0 = PV(I1) = $20 million
The present value of investment is $20 million regardless of when investment is made.
Price of Oil P = $70 or $90 with equal probability
Þ E[P] = $80
Variable production cost V = $72 per barrel
E[production] = Q = 200,000 barrels/year
Discount rate i = 10%

35. 16.4 Market Entry as a Compound Real Option
The option to invest as a now-or-never decision
NPV(invest today)
= ($80 – $72) (200,000) / 0.1 – $20,000,000
= –$4 million < $0
Þ do not invest today (?)

36. 16.4 Market Entry as a Compound Real Option
Endogenous price uncertainty
Uncertainty is endogenous when the act of investing reveals information about the value of an investment.
Suppose this oil well is the first of 10 identical wells that BP might drill
and that the quality and hence price of oil from these wells cannot be revealed without drilling a well.

37. 16.4 Market Entry as a Compound Real Option
Invest today in order to reveal information about future investments.
Investing today
E[P] = $80/bbl
P = $90/bbl
reveals information
P = $70/bbl

38. 16.4 Market Entry as a Compound Real Option
The investment timing option
NPV(wait 1 year½P = $90)
= (($90 – $72)(200,000) / 0.1) / (1.1) – $20,000,000
= $12,727,273 > $0
Þ invest if P = $90
NPV(wait 1 year½P = $70)
= (($70 – $72)(200,000) / 0.1) / (1.1) – $20,000,000
= –$23,636,363 < $0
Þ do not invest if P = $70

39. 16.4 Market Entry as a Compound Real Option
A compound option in the presence of endogenous uncertainty.
NPV(invest in an exploratory well)
= NPV(one now-or-never well today)
+ Prob($90) (NPV of 9 more wells$90)
= –$4,000,000 + ½ (9) ($12,727,273)
= $53,272,727 > $0
Þ invest in an exploratory oil well and then
reconsider further investment in one year.

40. 16.4 Market Entry as a Compound Real Option
Market entry and the value of growth options
Negative-NPV investments into emerging markets are often out-of-the-money call options entitling the firm to make further investments should conditions prove to be favorable:
If conditions are unfavorable, the firm can forego further investment.
If conditions are good, the firm can expand its investment.

41. 16.4 Market Entry as a Compound Real Option
Competitors’ actions influence investment decisions, and vice versa
When exit costs are zero, the effect of a shared investment opportunity is spread across all firms in an industry and results in a lower value to each firm.
When there are exit costs, competitive response to uncertainty is asymmetric and firms must be more cautious in their investment decisions.
As with hysteresis, firms might stay invested in unprofitable situations in the hope that other less-profitable firms will exit first.

42. 16.5 Real Options as a Complement to NPV
Why DCF fails
Option value
Exercise price
-3s
-2s
-1s
+1s
+2s
+3s
Value of the underlying asset

43. 16.5 Real Options as a Complement to NPV
Why DCF fails
Nonnormality
Returns on options are not normally distributed even if returns to the underlying asset are normal.
Option volatility
Options are inherently more volatile than the underlying asset on which they are based.
Changing option volatility
Option volatility changes with changes in the value of the underlying asset.

44. 16.5 Real Options as a Complement to NPV
The option pricing alternative
Option pricing methods construct a replicating portfolio that mimics the payoffs on the option.
Costless arbitrage then ensures that the value of the option equals the value of the replicating portfolio.

45. 16.5 Real Options as a Complement to NPV
Pricing financial options
Underlying asset values are observable
An example is the price of a share of stock.
Low transactions costs allow arbitrage
Most financial assets are liquid.
A single source of uncertainty
Contractual exercise prices and expiration dates result in a single source of uncertainty.
Exogenous uncertain
Most financial options are side bets that don’t directly involve the firm, so uncertainty is exogenous.

46. 16.5 Real Options as a Complement to NPV
Pricing real options
Underlying asset values are unobservable
What is the value a manufacturing plant?
High transactions costs impede arbitrage
Real assets are illiquid.
Multiple sources of uncertainty
e.g., exercise prices can vary over time.
e.g., exercise dates are seldom known.
Endogenous uncertain
Investing reveals information.

47. To get anywhere, or even to live a long time,
16.6 Summary
To get anywhere, or even to live a long time,
a man has to guess, and guess right,
over and over again,
without enough data for a logical answer.
Robert Heinlein
Time Enough for Love