Chapter 6, Problem 1P

An oil refinery finds that it is necessary to treat the waste liquids from a new process before discharging them into a stream. The treatment will cost $30,000 the first year, but process improvements will allow the costs to decline by $3,000 each year. As an alternative, an outside company will process the wastes for the fixed price of $15,000/year throughout the 10-year period, payable at the beginning of each year. Either way, there is no need to treat the wastes after 10 years. Use the annual worth method to determine how the wastes should be processed. The company’s MARR is 10%. (6.2)

To determine

Calculate the annual worth.

Explanation of Solution

Time period is denoted by n and the interest is denoted by i. Annual worth (AWA) of A can be calculated as follows.

$\begin{array}{c}\text{AWA}=-{\text{Cost}}_{\text{First year}}+\text{Decreasing cost}\left(\frac{1}{\text{i}}-\frac{\text{n}}{{\left(1+\text{i}\right)}^{\text{n}}}\right)\\ =-30,000+3,000\left(\frac{1}{\text{0}\text{.1}}-\frac{\text{10}}{{\left(1+\text{0}\text{.1}\right)}^{\text{n}}}\right)\\ =-18,824\end{array}$

Annual worth is -$16,500.

Annual worth (AWB) of B can be calculated as follows.

$\begin{array}{c}\text{AWB}=-\text{Fixed price}\left(\frac{1}{{\left(1+\text{i}\right)}^{10}}\right)\\ =-15,000\left(\frac{1}{{\left(1+\text{0}\text{.1}\right)}^{10}}\right)\\ =-16,500\end{array}$

Annual worth is -$16,500. Since the present worth of the cost is lower for  option B, select the option B.