One method used to analyze the uncertainty and risk involved in natural disaster decision makings is to choose the best alternative base on the lowest expected cost. In the following example, you can practice this method.

### Example 6-7:

A company is planning to build a new plant. The plant requires water for its production process and needs to be built near a river. But the location has the probability of being flooded and building levees around the plant is necessary to protect the facility. There are four possible sizes of levee that have different costs, maintenance, and level of protection, as displayed in following table. Calculate the expected annualized cost for each levee, considering minimum ROR of 12% and 18 years project life. Then explain which levee has the lowest expected annualized cost for the company.

Levee size | Levee Cost | Probability that levee fails | Expected Damage | Annual maintenance |
---|---|---|---|---|

1 | $150,000 | 0.25 | $100,000 | $3,000 |

2 | $180,000 | 0.15 | $130,000 | $4,500 |

3 | $200,000 | 0.08 | $140,000 | $5,000 |

4 | $220,000 | 0.04 | $180,000 | $7,000 |

Probability of levee failure: Probability of a flood exceeding levee size during the year

Expected Damage: Expected damage if flood exceeds levee size

In order to calculate expected annualized cost for each levee size, we need to convert all the costs into annual base. Then:

$$\text{Expectedannualcost=equivalentannualleveecost+expecteddamageperyear+annualmaintenance}$$From Table 1-12, equivalent annualized levee cost can be calculated as:

$$\left(Levee\text{}Cost\right)*\left(A/{P}_{12\%}{,}_{18}\right)=\left(Levee\text{}Cost\right)*0.13794$$

Expected damage per year is the multiplication of Probability of levee fails by Expected Damage

Expected annualized cost for different sizes of levee can be calculated as:

Levee size | Annual Levee Cost | Expected damage per year | Annual maintenance | Expected annual cost |
---|---|---|---|---|

1 | $20690.59 | $25,000 | $3000 | $48,690.59 |

2 | $24828.72 | $19,500 | $4500 | $48,828.72 |

3 | $27587.46 | $11,200 | $5000 | $43,787.46 |

4 | $30346.21 | $7,200 | $7000 | $44,546.21 |

Results show that the third levee has the lowest expected annualized cost; therefore, it is the best alternative.