Question

The following three mutually exclusive alternative proposals are being considered for flood proofing a factory building that is located in an area subject to occasional flooding by a nearby river.

1. Do nothing: Damage to the building in a moderate flood is $11,000 and in a severe flood it is $24,000.
2. Protect the building with a one-time initial expenditure of $20,000 so that the building can withstand moderate flooding without any damage and withstand severe flooding with only a $12,000 damage.
3. Protect the building with a one-time initial expenditure of $30,000 so that the building can withstand any flooding with no damage at all. In any year, there is a 21% probability of moderate flooding and a 9% probability of severe flooding. Using a MARR of 12% per year and a service life of 16 years, determine which of the three alternatives is the most economical.

Answer 1

To determine which of the three flood proofing alternatives is the most economical, we need to calculate the present worth of each alternative. The present worth is the sum of the initial expenditure and the present worth of the annual damages. Alternative 2 is the most economical, as it has the lowest present worth.

Step-by-step explanation:

To determine which of the three flood proofing alternatives is the most economical, we need to calculate the present worth of each alternative. The present worth is the sum of the initial expenditure and the present worth of the annual damages. For alternative 1, the present worth is $11,000 + ($24,000 * (1 + 0.12)^{-16}) = $11,000 + ($24,000 * 0.069) = $11,000 + $1,656 = $12,656. For alternative 2, the present worth is $20,000 + ($12,000 * (1 + 0.12)^{-16}) = $20,000 + ($12,000 * 0.069) = $20,000 + $828 = $20,828. For alternative 3, the present worth is $30,000 + ($0 * (1 + 0.12)^{-16}) = $30,000 + ($0 * 0.069) = $30,000. Therefore, alternative 2 is the most economical, as it has the lowest present worth.