1. Cost-Benefit Analysis
March 2, 2017
MSSM Program
Columbia University
Satyajit Bose

2. Monte Carlo Questions
What is the 90% confidence interval for Project NPV?
Given the Monte Carlo distribution of project cost, in what percentage of cases will the Project NPV be less than $0?

3. Monte Carlo Example 2 Consider requiring recycling of paper in a town:
Town population 164,250 in 39,050 households
Benefit: revenue from paper sales, avoided tipping fees
Costs: specialized equipment, household containers, sorting facility, inconvenience etc.
Horizon: 8 years (life of specialized equipment).
Uncertainty in: waste paper price, waste quantity increase and % paper recovery.

4. Option Price
Expected Surplus = Expected Net Benefit = probability-weighted average of surpluses across all outcomes
Option Price = Ex Ante WTP = maximum amount an individual would pay for a policy prior to knowing which outcome will result after that policy is implemented

5. Option Value
Option value is the difference between option price and expected surplus: the maximum amount beyond expected benefits that individuals are willing to pay to reduce risk.
Can be positive or negative (depending on impact on income risk).
Option value must be calculated in risk-reducing (or increasing) projects.

6. Example: OV of building a Dam
Temporary Dam that provides water for irrigation
Two contingencies: wet or dry weather
Farmer Income under different scenarios:
Dam
No Dam
Wet
110
100
Dry 50

7. Example: OV of building a Dam
Farmer Income under different scenarios:
Compute expected value
Compute variance
Dam
No Dam
Wet
110
100
Dry 50

8. Example: OV of building a Dam
Farmer Income under different scenarios:
Compute expected surplus
Compute option price
Compute option value
Dam
No Dam
Wet
110
100
Dry 50

9. Example: OV of building a Dam

10. Utility Function of Sole Beneficiary

11. Real Option
The right, but not the obligation, to take an action (e.g. investing in a project) at a predetermined price (exercise price) for a predetermined period of time (the life of the option).

12. Example Real Option Analysis
The government is auctioning lease rights on some of its timber-rich lands. You are bidding for the lease rights.
If you win and do not develop the land within 5 years, the lease rights revert to the government.
You estimate the NPV of the cash flows using expected future timber prices, growth rates, management costs and development costs. Estimated NPV = $21 million, assuming you develop right away.

13. Example Real Option Analysis
You could estimate the NPV of the cash flows, assuming the development decision could be deferred 1, year, 2 years, 3 years up to 5 years. Estimated NPV in those cases range from $19 million to $24 million.
How might you use real option analysis to model the value of flexibility differently?

14. Question
What factors make it likely that real option analysis will add value to the investment decision (over and above NPV analysis)?
When NPV is close to zero (it is not obvious whether trigger should be pulled or not)
When there is high uncertainty about the future AND we are likely to receive new information over time AND that information has value i.e. can affect decision

15. Terminology
A call option is the right to buy the underlying asset by paying the exercise price.
A put option is the right to sell the underlying asset for the exercise price.
An option which would make an immediate profit upon exercise is said to be in-the-money.

16. Real Options The option to make follow-on investments (long call)
The option to abandon a project before all project costs are incurred (long put)
The option to wait and learn before investing (long call)
The option to switch production processes (portfolio of options)

17. Determinants of Option Value
Financial Option variable
Real Option variable
Impact on Value
level of the value of the underlying asset
expected PV of the cash flows from the project 
Exercise price
Investment cost 
Time to expiry
Life of the option
Standard deviation of the level of the value of the underlying asset
Uncertainty about the expected PV of the cash flows from the project
Risk-free interest rate
Cash flows available upon exercise (dividends)
Cash flows lost to competitors who have fully committed

18. Questions
Why would a long term option be more valuable than a short-term option?
Why does an increase in uncertainty or volatility increase option values?

19. Concluding Remarks on ROA
Real application is in ex-ante individual projects rather than in ex-post macro-economic explanations
Monte Carlo methods provide a novice with an entry point to apply the techniques in her particular decision problem
ROA is probably always used but rarely spelled out

20. Measurement Fallacy Measure what you can. (Obvious)
Ignore what you cannot measure. (Misleading)
Assume that what you cannot measure is irrelevant. (Lamppost Syndrome)
Assume what cannot be measured really doesn’t exist. (Suicide)

21. Value of Information Three (interrelated) sources of value:
Reducing uncertainty affects decisions, which has economic consequences.
Reducing uncertainty affects choices of others, which has economic consequences.
Information can be sold.
Information is not valued at production cost.

22. Value of Information
By how much would the information increase the expected value of playing the game?
Value of information =
E(NB) of the optimal choice in the game with information
MINUS
E(NB) of the optimal choice in the game without information.

23. Value of Information
If information does not impact optimal action, then value of information = 0.
Example: may not be worth investing in larger sample size if sample size is sufficiently large that additional observations will have minimal impact.

24. Example: Corn Speculation
Drought
No Drought
Investor
Buy futures
$10,000
-$2,000
Buy fertilizer company stock
$4,000 $0
Investor’s opponent is Nature (i.e. whether there will be a drought or not)

25. Example
Suppose the investor’s subjective probabilities over the events is pr(Drought) = .9 and pr(No Drought) = .1
Suppose the investor’s wealth is $90,000 and he has the utility function U = -e W
What is the utility value of information that tells the investor whether the drought will happen for sure?

26. Example
With imperfect information, investor prefers to buy corn futures:
EU(Buy corn futures) = .9×U($100,000) + .1×U($88,000) = see spreadsheet
EU(Buy fertilizer company) = .9×U($94,000) + .1×U($90,000) = see spreadsheet

27. Example: Demand Forecasts
On Thurs evening, the manager of a car rental agency branch has 6 cars on hand for rental the next day. She can request delivery of additional cars from the regional depot at $20 each. Each car rented produces an expected profit of $40. She finds that on previous Fridays, the cars requested were: 7, 9, 8, 7, 10, 8, 7, 8 , 9, 10, 7, 6, 8, 9, 8, 8, 6, 7, 7, 9. How many cars should she order? What is the expected value of perfect information?

28. Value of Information
Attempting to understand the value of information prevents us from falling into the trap of measuring only that which is easily measured.
Direct investment in learning towards resolving the uncertainty with the highest value.

29. Quasi-Option Value
Quasi-option value is the gain in the expected value of information due to delaying an irreversible decision.
Requires multi-period decision modeling
Exogenous learning: learning is revealed no matter what option is taken. (No activity often optimal)
Endogenous learning: information is generated only through the activity itself. (Limited activity) often optimal.

30. Quasi-Option Value
Example: Waiting 2 years to invest in a new solar plant with a 30 year life, because a new technology may improve efficiencies.