Value of Flexibility in Irrigation Projects

ANJULI JAIN FIGUEROADEC 7, 2010

ESD. 710

Value of Flexibility in Irrigation Projects

1

Outline

Big PictureAP6 Scope and AssumptionsDeterministicAccounting For UncertaintyIncorporating Flexibility

2

The Big Picture

• Nile Basin Initiative: 10 countries disputing Nile waters

• Ethiopia vs. Egypt

• Ethiopian Irrigation Drainage Project -feasibility study for an 80,000ha irrigation plan

Goal: mutually beneficial solution >> food security, drought prevention, agricultural productivity

3Nile Basin-

http://www.ess.co.at/WATERWARE/NILE/background.html

Project Scope4

Variable/Stochastic

Water Flow

Crop Yield

Crop Price

Reservoir

Irrigation Plot

Key

Flexible

20,000 ha x4

Inflexible

80,000 ha

Deterministic

80,000 ha

Compare big and small irrigations projects on basis of ENPV, P(<0), range, 5% and 95% and B/C ratio

Simplifying Assumptions5

Irrigation Project CostsLand Lease $8.15/haFixed Irrigation System Cost $419.90/haO&M Irrigation System $30.88/haCost of Crop Production $40/ha

Crop CornTime horizon 20 yearsDiscount rate 12%

*If the average change in water level in the past 2 years is negative then thecorn yield will decrease at a rate of 0.9% for every 1% decrease in water level

*Uncertainties sampled from historical data’s fitted distributions

6

Deterministic

80,000 ha

Deterministic InputsAverage corn price $116/MT

Average demand1558 MT/ha

Average flow4805 MCM

Average corn production 1.4 MT/haDeterministic OutputNPV $19.92 MillionP(<=0) 0

Deterministic

Accounting For Uncertainty-Forecasting by Sampling

Distributions-7

WATER INPUT

CROP PRICE

CORN DEMAND

CORN YIELD

INFLEXIBLE DESIGN

8

Water Input

42

00

44

00

46

00

48

00

50

00

52

00

54

00

56

00

58

00

60

00

62

00

64

00

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035Nile Average Mehr (Feb-Jun) Seasonal Flow

@RISK Student VersionFor Academic Use Only

3500

3700

3900

4100

4300

4500

4700

4900

5100

5300

Figure 13: Average Historical Flow for Mehr (Feb-Jun) Crop

Season and two Scenario Sample Predictions

"Historical Prediction

Mill

ion

Cub

ic M

eter

s

Mean 4806

St Dev. 142

Sample from Log logistic Distribution

9

Sample from Log logistic Distribution

Mean 116St Dev. 27.8

5010

015

020

025

030

035

040

045

050

0

0.000

0.005

0.010

0.015

0.020

0.025Yearly Average Corn Price


1980 1990 2000 2010 2020 20300

50

100

150

200

250

Average Yearly Historical Corn Price

"historical""prediction" prediction2

US

Dol

lars

Crop Price

10

Mean 1558St Dev. 882

1960 1970 1980 1990 2000 2010 2020 20300

500000

1000000

1500000

2000000

2500000

3000000

3500000

4000000

Demand for Ethiopian Corn Histor-ical & Example Prediction

Historical Prediction

1000

MT

Corn

Corn Demand 01

23

45

67

8

Values in Thousands

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012Corn Demand


Sample from Exponential Distribution

* Ignored trend

11

Corn Production Yield

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.000.050.100.150.200.250.300.350.40

Production Yield


1960 1970 1980 1990 2000 2010 2020 20300

0.5

1

1.5

2

2.5

3

Figure 11: Corn Yield Historical andTwo Scenario Sample Predictions

Historical Prediction prediction2

MT

Cor/

ha

Sample from Uniform Distribution

Mean 1.4St Dev. 0.8

12

1877959.3419

766497.8517

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Cash Flow / 1Values in Millions

Yearly Average Corn Price

Production Yield

Cash Flow / 1-FlexRegression - Mapped Values


7511848.0653

3065991.4068

-10

12

34

56

78

Cash Flow/1 InflexValues in Millions

Yearly Average Corn Price

Production Yield

Regression - Mapped Values


Input SensitivityWhen the input changes by +1 standard deviation, the output will change by the X-axis value associated with the length of the bar

St Dev. Price $/MT 27.8

St Dev. Yield MT/ha

0.8

13

Inflexible

80,000 ha

Inflexible OutputENPV $20.12 MillionP(<=0) 10.54%Min $-31.14 MillionMax $125.65 Million

10,000 sims

Inflexible

Incorporating Flexibility

14

EXPANSION RULES

FLEXIBLE DESIGN

COMPARISONS

VALUE OF FLEXIBILITY

Expansion Rules15

Start with 20,000 ha instead of 80,000 ha*Assume no additional upfront cost or cost to exercise flexibility

IF:1. Price of corn is greater than $63 and,

(in deterministic model this price gives NPV of 0)

2. Demand this year is greater than last year and,(increasing demand)

3. Change in water level in last two years is greater than 0, and (increasing water level)

4. Land size has not reached capacity of 80,000 ha

THEN:Expand by 20,000 ha

16

Flexible OutputENPV $16.76 MillionP(<=0) 1%Min $-9.28 MillionMax $74.38 Million

10,000 sims

Flexible

20,000 ha x4

Flexible

Comparisons

17

ENPV

PROBABILITY OF LOSING MONEY

RANGE

5 T H AND 95 T H PERCENTILES

B/C RATIO

18

-60

-40

-20

020

4060

8010

012

0

Values in Millions ($)

0.0

0.2

0.4

0.6

0.8

1.0Comparing ENPV


ENPV P(<=0) Min Max 5% 95%

Det. ---- $19.92M - - - - -Inflex

. ---- $20.12M 10.54% $-

31.14M$125.65

M $-6.3M $47.62M

Flex. ---- $16.76M 1% $-9.28M $74.38M $2.79M $33.88M

ENPV Comparisons

19

5.0% 90.0% 5.0%31.7% 68.3% 0.0%

1.35 5.10

-20

24

68

10

12

14

0.0

0.2

0.4

0.6

0.8

1.0

B/C (profitability index) Comparison

B/C (profitability index) Flex / 1

Minimum 0.2868Maximum12.7217Mean 2.9826Std Dev 1.1564Values 10000

B/C (profitability index) Inflex / 1

Minimum-0.0256Maximum 5.1184Mean 1.5969Std Dev 0.4882Values 10000

B/C det / 1

Minimum 1.5929Maximum 1.5929Mean 1.5929Std Dev 0.0000Values 10000


B/C Comparisons

No “all-time” best

“Best Project” depends on the evaluation metric used and risk tolerance of project manager.

If a plan is made on a deterministic basis, there may be a lot of surprises.

Conclusions20

Inflexible FlexibleENPV X

P(<=0) XMin XMax X 5% X95% X B/C X

http://www.google.com/imgres?imgurl=http://agricultureguide.org...

QUESTIONS?21

http://www.themillionairesecrets.net/4-questions-that-will-lead-you-to-success/

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Value of Flexibility in Irrigation Projects