Chapter 12, Problem 1P

To determine

Select the alternative.

Explanation of Solution

Time period is denoted by n and the interest is denoted by i. Equivalent annual cost (EUAC) of alternate nothing can be calculated as follows.

$\begin{array}{c}\text{EUAC}=\text{Cost}\times \left(\frac{{\text{Chance}}_{\text{Occurance}}}{\text{Total chance}}\right)\\ =1,000,000\times \frac{1}{100}\\ =10,000\end{array}$   

Equivalent annual cost of alternate nothing is $10,000.

Increasing rate is denoted by f. Equivalent annual cost (EUAC) of alternate culvert can be calculated as follows.

$\begin{array}{c}\text{EUAC}=\left(\text{Cost}+\frac{{\text{Cost}}_{\text{Maintenance}}\left(1-\left(\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\right){\left(1+\text{f}\right)}^{\text{n}}\right)}{\text{i}-\text{f}}\right)\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\\ =\left(\text{50,000}+\frac{\text{20,000}\left(1-\left(\frac{1}{{\left(1+\text{0}\text{.07}\right)}^{\text{20}}}\right){\left(1+\text{0}\text{.05}\right)}^{\text{20}}\right)}{0.07-0.05}\right)\left(\frac{0.07{\left(1+\text{0}\text{.07}\right)}^{\text{20}}}{{\left(1+\text{0}\text{.07}\right)}^{\text{20}}-1}\right)\\ =7,688\end{array}$   

Equivalent annual cost of alternate culvert is $7,688. The equivalent annual cost is lower for the alternate culvert. Thus, select alternate culvert.