3) A small town at risk of periodic flooding is considering the option of buildi

Question

3) A small town at risk of periodic flooding is considering the option of building a levee to reduce flood risk. When a flood occurs, the average cost of damages is $300,000. The following tables provide information on the frequency of different floods and the cost of building levees of different heights. Assuming that a levee lasts 50 years and a MARR of 12%, should a levee be built? And if so, how high?

Flood Height Above River Bank (m)

Flood Frequency

2

Once every 3 years

2.5

Once every 8 years

3

Once every 25 years

3.5

Once every 50 years

4

Once every 100 years

Levee Height (m)

Cost

2

$100,000

2.5

$165,000

3

$300,000

3.5

$400,000

4

$550,000

Flood Height Above River Bank (m)

Flood Frequency

2

Once every 3 years

2.5

Once every 8 years

3

Once every 25 years

3.5

Once every 50 years

4

Once every 100 years

Explanation / Answer

Here we calculate the Net Present Value of all the damages saved by Levee during 50 years for period for all type of flood levels using the formula:

NPV= -Initial investment + [(Cash Inflow1)/(1+r)1] + [(Cash Inflow2)/(1+r)2] + [(Cash Inflow3)/(1+r)3]…..+ [(Cash Inflown)/(1+r)n]

We will select that levee which has highest NPV.

Calculation for 2 Meters:

NPV = -$100,000 + ($300,000/1.123) + ($300,000/1.126) + ($300,000/1.129) + ($300,000/1.1212) + ($300,000/1.1215) + ($300,000/1.1218) + ($300,000/1.1221) + ($300,000/1.1224) + ($300,000/1.1227) + ($300,000/1.1230) + ($300,000/1.1233) + ($300,000/1.1236) + ($300,000/1.1239) + ($300,000/1.1242) + ($300,000/1.1245) + ($300,000/1.1248) = $637,656.73

Calculation for 2.5 Meters:

NPV = -$165,000 + ($300,000/1.128) + ($300,000/1.1216) + ($300,000/1.1224) + ($300,000/1.1232) + ($300,000/1.1240) + ($300,000/1.1248) = -$83,790.09

Calculation for 3 Meters:

NPV = -$300,000 + ($300,000/1.1225) + ($300,000/1.1250) = -$281,314.95

Calculation for 3.5 Meters:

NPV = -$400,000 + ($300,000/1.1250) = -$398,961.95

Calculation for 4 Meters:

NPV = - [($550,000) + ($550,000/1.1251)] + ($300,000/1.12100) = -$551,695.60

We see that highest value is $637,656.73 which belongs to 2 meter Hence we will build 2 meter levee.

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