Question

A factory building is located in an area subject to occasional flooding by a nearby river. You have been

brought in as a consultant to determine whether flood proofing of the building is economically justified.

The alternatives are as follows:

A. Do nothing. Damage in a moderate flood is $10,000 and in a severe flood, $25,000.

B. Alter the factory building at a cost of $15,000 to withstand moderate flooding without damage

and to withstand severe flooding with $10,000 damages.

C. Alter the factory building at a cost of $20,000 to withstand a severe flood without damage.

In any year the probability of flooding is as follows: 0.70, no flooding of the river; 0.20, moderate flooding;

and 0.10, severe flooding. If interest is 15% and a 15-year analysis period is used, what do you

recommend?

Answer 1

Solution:

A.). Expected damages = (10,000 $\times$ 0.20) + (25,000 $\times$ 0.10) = 2,000 + 2,500 = 4,500

Equivalent Annual Cost (EAC) = $\frac{Expected \; damages}{NPV}$

NPV = $(1-\frac{1}{1+0.15^{15} }) \div 0.15 = \frac{0.877}{0.15} = 5.85$

Equivalent Annual Cost (EAC) = $\frac{4,500}{5.85} = 769.23$

 

B.). Expected damages = (15,000 $\times$ 0.20) + (10,000 $\times$ 0.10) = 3,000 + 1,000 = 4,000

Equivalent Annual Cost (EAC) = $\frac{Expected \; damages}{NPV}$

NPV = $(1-\frac{1}{1+0.15^{15} }) \div 0.15 = \frac{0.877}{0.15} = 5.85$

Equivalent Annual Cost (EAC) = $\frac{4,000}{5.85} = 683.76$

 

C.). Expected damages = (20,000 $\times$ 0.10) = 2,000

Equivalent Annual Cost (EAC) = $\frac{Expected \; damages}{NPV}$

NPV = $(1-\frac{1}{1+0.15^{15} }) \div 0.15 = \frac{0.877}{0.15} = 5.85$

Equivalent Annual Cost (EAC) = $\frac{2,000}{5.85} = 341.88$

 

I recommend option C. Alter the factory building at a cost of $20,000 to withstand a severe flood without damage.

This is because option C has the lowest Equivalent Annual Cost.