Abril 2015

Café de Conocimiento:

Ejemplos de Análisis Probabilista

de Costo-Beneficio

Use of CBA in DRR

0

5

10

15

20

25

30

35

40

High Income Med Income Low Income

Yes No (not indicated)

• CBA are increasingly being used in DRR investment appraisal but

barriers remain.

• Out of 99 countries who provided

responses to HFA monitoring over

2011-2013, 37 countries (37%) have conducted economic

appraisals on DRR investment. For

LICs, Bangladesh, Burkina Faso,

Ethiopia Malawi and Mozambique

• CBA for DRR investment is seen as

effective ways of evaluating and illustrating the gains that can be

made. (e.g. Fiji, St Lucia, British

Virgin Islands calls for the use of

CBA).

Figure: # of countries that have conducted economic appraisal based on HFA monitor (ODI 2014)

What’s probabilistic CBA?

• CBA that takes probabilistic benefits of risk reduction.

• Non-probabilistic CBA: what is the cost and benefit of sea wall construction given that a 50 year cyclone occurs?

• Probabilistic CBA: what is the cost and benefit of sea wall construction given that cyclones of different sizes occur stochastically with different return periods?

Why should we use probabilistic CBA?

ReturnPeriod EP Losses (A)

Losses (B)

5 0.2 2,000 1,000

10 0.1 6,000 6,000

50 0.02 10,000 50,000

100 0.01 12,000 80,0000

0.05

0.1

0.15

0.2

0.25

0 20,000 40,000 60,000 80,000 100,000

• Gives decision-makers full information about potential

benefits of DRR investment. (e.g. avoids under-funding for

catastrophic risk when we know costs of rare events are high in

advance).

• Possible to construct a portfolio of DRR measures tailored to

specific risks of varying intensity and frequency.

Forward-looking vs. backward-looking assessment

More accurate, but skills, time and

data intensive.

Rougher estimate, but more realistic for

contexts with lower capacity

Do you have hazard, exposure

vulnerability information?

Backward Looking Assessment:

Do you have more than

four credible data points of

past losses?

Non-

ProbabilisticCBA or CEA

Backward CBA

possible

Forward-Looking Assessment

No Yes

YesNo

Forward-looking or backward-looking assessment?

CAVEATS: scope of DRR benefits covered in CBA

CAVEATS: Limitation of Probabilistic CBA

• Due to inherent design of probabilistic CBA

Probabilistic CBA often assumes risk neutrality: it undervalues the benefit in case of ‘extreme events’(intensive risk)

The use of single measure such as B/C ratio, NPV masks inherent value conflicts (e.g. differences in time preference (discount rate) also risk aversion etc).

• Due to misuse of CBA

Probabilistic CBA often lacks incorporation of intangibles and distributional consequences

• Alternatives or complements to CBA include:

Cost Effectiveness Analysis (CEA)

Multi-criteria analysis (MCA)

Robust Decision Making Approach (RDMA)

• Economic assessment such as CBA should be used as part of wider decision-making process involving multiple stakeholders

Probabilistic CBA: Key terms and concepts

• Understanding key risk terms: annual average loss(AAL), exceedance probability(EP), risk layers, etc.

• Understanding key CBA terms: Benefit-Cost (B/C) ratio, Net present value (NPV), discount rate

• Understanding how risk-based information for probabilistic CBA are generated using both forward-looking and backward-looking methods and how different DRR investments reduce different layers of risks

• Understanding how a stream of benefits and costs of DRR investments accruing over-time can be assessed in a single framework (CBA).

• Understanding key strengths and weaknesses of probabilistic CBA.

Forward looking

Probabilistic Approach

• Requires a Probabilistic risk analysis software platform (such as CAPRA, EqCAT, CatSIM , R-Fonden or commercial insurance systems)

• Requires a comprehensive and detailed enough set of data:

Data files used for analysis

Exposure Georeferenced data points of

physical structures in Study area

shape file (shp format)

Hazard Possible hazard intensity (in

Capra is the Ame format)

Vulnerability Containing information on

vulnerability functions

Risk = H x E x V

• Hazard: cyclone intensity

• Exposure: locations of buildings

• Vulnerability: structural robustness

of buildings

-> Vulnerability function:

Relationship between % of damage

and wind-speed

Risk Analysis

General Probabilistic CBA

Process• Basic principle:

A DRR measure is reflected as a change in the vulnerability functions of the assets in questions. Benefits are estimated based on how these DRR measures (example: cyclone retrofit) will shift risk curves, and thus the expected losses.

• Tasks:

i) estimate risk curve and AAL before DRR and

ii) estimate risk curve and AAL after DRR

• Example Scenario:

Earthquake retrofitting of unreinforced masonry residential buildings which

change vulnerability from low design quality to high design quality

(reinforced masonry)

Backward looking CBA:

method and tasks• Method:

i) Risk curves and statistics such as annual average loss (AAL) are calculated using backward methodology

ii) Calculate how AAL will change due to DRR investment usingbackward methodology

iii) Compare costs and benefits of DRR intervention using an appropriate discount rate

iv) Estimate how different discount rate/project duration assumptions affect B/C ratio, NPV, etc/

• Tasks:

i) estimate risk curve and AAL before DRR and

ii) estimate risk curve and AAL after DRR

iii) Calculate B/C ratio, NPV and conduct sensitivity analysis

Calculating Annual Average

Loss in BLCBA• The expected annual loss is estimated using an application

of the Simson rule.

• It requires three or more loss data points to be accurate

• The expected loss up to a N year event is the cumulative

probability of the N year event minus the cumulative

probability of the M year event multiplied by the average

loss between the M and N year events.

Case of Orosi Project

Loss

Estimated Damage

and Loss (USD)

Reconstruction and rehabilitation for 8

months 431,707

Shortage in drinking water for over

500,000 people and resulting decrease

in revenue from the provision of

drinking water for 18 hours 91,500

Total 523,207

The total economic losses of the 2010 flood are reported to be USD 523,200, and result from both reconstruction and rehabilitation costs, as well losses in revenue from lack of drinking water provision to over 500,000 people for a period of 18 hours (Table 1).

Return period of the disaster (!!?)

• While reports suggest the overall damage from storm

Tomas in 2010 due to widespread flooding and landslides

was very large, (losses at over USD 280 million) (GFDRR,

2010), the reported monthly daily maximum rainfall from

Liberia station suggests the amount of daily maximum

precipitation observed for November 2010 is by no means

extreme (with an estimated return period of less than 1

year (0.6 year)). Using this information, the economic

losses caused by flooding to the Orosi aqueduct resulting

from Storm Tomas was also estimated to have less than 1

year return period.

• CAVEAT: no closer stations were found to provide better

rainfall data.

Return period of the disaster (!!?)

rainfall (< or =)

cumulative

observations

# of

observat

ions frequency

Monthly exc

%

return period

months

return period

years

1

0 34 34 0.110 0.890 1.123 0.094

200 112 78 0.252 0.639 1.566 0.130

500 213 101 0.326 0.313 3.196 0.266

820 268 55 0.177 0.135 7.381 0.615

1000 287 19 0.061 0.074 13.478 1.123

1500 302 15 0.048 0.026 38.750 3.229

2000 307 5 0.016 0.010 103.333 8.611

4000 309 2 0.006 0.003 310.000 25.833

7025 310 1 0.003 50.000

date 2010/10

rainfall 820

return 0.615

Maximum rainfall recorded for November, 2010 (Storm Thomas)

Estimation of curve based on past

losses points

• It is important to keep in mind that risk curve estimation

generally requires more than 3 credible data points of past

disaster events (Mechler 2005), and the use of single data

point with the probability of first loss estimate adopted here

cannot give an accurate loss estimate as recommended.

Despite this data limitation, we have estimated a risk curve

based on estimated exceedance probabilities to perform

illustrative probabilistic CBA.

• CAVEAT: no other (representative) loss data points were

found (DesInventar?)

Estimation of curve based on past

losses points

• “Using this precipitation and loss data, the annual average

loss (AAL) was estimated (Table 2). The expected annual

loss is estimated using an application of the Simpson rule.

For example, based on the return periods identified, the

expected loss up to a 10 year event is the exceedence

probability of the 5 year event (0.2) minus the exceedence

probability of the a 10 year event (0.1) multiplied by the

average loss between the 5 and 10 year events. In

numerical terms:”

EL(5-10 years)= (0.2-.01)*((1,617,974+2,261,959)/2)= 193,997

•

Estimation of curve based on past

losses points

• This process is then repeated for all other intervals. For the

last interval, it is assumed for this CBA that losses

associated with events of more than a 200 year return

period will result in the same losses as the 200 year event.

return period

exceedance

probability Loss expected loss

1 1 699,968 699,968

2 0.5 1,026,400 431,592

5 0.2 1,617,974 396,656

10 0.1 2,261,959 193,997

25 0.04 4,510,318 203,168

50 0.02 8,566,946 130,773

100 0.01 15,729,186 121,481

200 0.005 30,053,666 114,457

>200 114,457

AAL 2,406,549

Estimation of Benefits

• To assess the benefits of the proposed aqueduct project, we

must estimate the amount of economic losses that would be

reduced as a result of the project. There is no clear data on the

expected amount of loss reduction resulting from the aqueduct

project. However, since the proposal was made in response to

the damaging 2010 Tropical Storm Tomas, it is assumed that

the aqueduct would be designed to protect against all

damages caused by a 1-year event. Events with larger return

periods would have damages reduced, but not eliminated

(Table 3). As the actual reduction in damages is not known,

particularly for extreme events, these numbers must be

interpreted with caution and are to serve an illustrative purpose

only.

Estimation of Benefits

Before Aqueduct After Aqueduct

return

period

exceedance

probability loss expected loss Loss reduction expected loss

1 1 699,968 699,968 1 0

2 0.5 1,026,400 431,592 0.50 215,796

5 0.2 1,617,974 396,656 0.20 297,492

10 0.1 2,261,959 193,997 0.10 174,597

25 0.04 4,510,318 203,168 0.04 195,042

50 0.02 8,566,946 130,773 0.02 128,157

100 0.01 15,729,186 121,481 0.01 120,266

200 0.005 30,053,666 114,457 0.005 113,885

>200 114,457 0.000 114,457

AAL Before

DRR 2,406,549 AAL After DRR 1,359,692

Benefit in

terms of AAL

Reduction 1,046,857

Estimation of Benefits

0

500000

1000000

1500000

2000000

2500000

3000000

0 1 2 3 4 5 6 7 8 9 10

Eco

no

mic

Lo

ss (

US

D)

Return Period (years)

Loss Return Period Curve: Orosi Aqueduct

Orosi Aqueduct

Baseline, No DRR

Costs

The cost of the Orosi Aqueduct is USD 5.56 million, plus maintenance costs. The maintenance costs are separated between annual maintenance (USD 1,835) and, maintenance that is required on a five-year basis (USD 64,220). The breakdown of the costs, which come directly from the project report, are seen in Table 4 below.

Table 4: Costs of the proposed project

Time Factors

VI.1 Discount rate. There has been no official social discount rate in Costa Rica. However, literature suggests a social discount rate in Costa Rica to be between 9-10% (Aylward, Porras, 1998). Therefore, we start with initial assumption of 10%, but apply different rates as a means of sensitivity analysis.

VI.2 Increase in Exposed AssetsAs the project is assumed to last and protect against flooding for a period of 50 years, it is assumed that the amount of exposed assets in the region, as well as the number of people who will be provided with drinking water from the aqueduct, will increase in a yearly basis. The GNP per capita has increased by an average of 8% annually of the last decade, and the population has grown at an average of 1.5% per year over the same period (World bank development indicators 2014). For a baseline level, an increase of 1.5% of exposed assets per year will be applied to the analysis. This will be represented as an annual increase of 1.5% to the annual benefits.

Cost Benefit results

Using the data, provided information, and assumptions described to this

point, we are able to conduct an illustrative cost-benefit analysis for the

project. Table 5 below shows the net present value of the project with a 50-

year lifespan, a 10% discount rate, and an annual increase in exposed

assets of 1.5%.

In this scenario, the results of the CBA suggest the project to be cost-

efficient with a net present value (NPV) of USD 6,328,984, and a Benefit –

Cost ratio (B/C) of 2.1.

Tables 6 and 7 below show sensitivity analysis with regards to the discount

rate and the increase in exposed assets.

Cost Benefit results

YearCalendar

YearCosts USD Benefits

Net benefits:

benefits-costsDiscounted costs

Discounted

benefits

Discounted net

benefits

1 2013 5,563,396 0 -5,563,396 5,563,396 0 -5,563,396

2 2014 1,835 1,046,857 1,045,022 1,668 951,688 950,020

3 2015 1,835 1,062,560 1,060,725 1,517 878,149 876,632

4 2016 1,835 1,078,498 1,076,663 1,379 810,292 808,913

5 2017 1,835 1,094,676 1,092,841 1,253 747,678 746,425

6 2018 64,220 1,111,096 1,046,876 39,876 689,903 650,027

7 2019 1,835 1,127,762 1,125,927 1,036 636,592 635,557

8 2020 1,835 1,144,679 1,142,844 942 587,401 586,459

9 2021 1,835 1,161,849 1,160,014 856 542,011 541,155

10 2022 1,835 1,179,277 1,177,442 778 500,128 499,350

11 2023 64,220 1,196,966 1,132,746 24,760 461,482 436,722

12 2024 1,835 1,214,920 1,213,085 643 425,822 425,179

13 2025 1,835 1,233,144 1,231,309 585 392,918 392,333

14 2026 1,835 1,251,641 1,249,806 532 362,556 362,024

15 2027 1,835 1,270,416 1,268,581 483 334,540 334,057

16 2028 64,220 1,289,472 1,225,252 15,374 308,689 293,316

17 2029 1,835 1,308,814 1,306,979 399 284,836 284,437

18 2030 1,835 1,328,446 1,326,611 363 262,826 262,463

19 2031 1,835 1,348,373 1,346,538 330 242,517 242,187

20 2032 1,835 1,368,599 1,366,764 300 223,777 223,477

21 2033 64,220 1,389,128 1,324,908 9,546 206,485 196,939

22 2034 1,835 1,409,964 1,408,129 248 190,529 190,281

23 2035 1,835 1,431,114 1,429,279 225 175,807 175,581

24 2036 1,835 1,452,581 1,450,746 205 162,222 162,017

25 2037 1,835 1,474,369 1,472,534 186 149,686 149,500

26 2038 64,220 1,496,485 1,432,265 5,927 138,120 132,192

27 2039 1,835 1,518,932 1,517,097 154 127,447 127,293

28 2040 1,835 1,541,716 1,539,881 140 117,599 117,459

29 2041 1,835 1,564,842 1,563,007 127 108,511 108,384

30 2042 1,835 1,588,314 1,586,479 116 100,126 100,011

31 2043 64,220 1,612,139 1,547,919 3,680 92,389 88,709