Chapter 10, Problem 1P

To determine

Calculate the Benefit cos ratio.

Explanation of Solution

Time period is denoted by n and the interest is denoted by i. Benefit cost ratio (BC)can be calculated as follows.

$\begin{array}{c}\text{BC}=\frac{\text{Annual receipt}-\text{Annual expense}}{\text{Investment}\left(\frac{\text{i}{\left(\text{1}+\text{i}\right)}^{\text{n}}}{{\left(\text{1}+\text{i}\right)}^{\text{n}}-1}\right)-\text{Salvage value}\left(\frac{\text{i}}{{\left(\text{1}+\text{i}\right)}^{\text{n}}-1}\right)}\\ =\frac{100,000-50,000}{\text{200,000}\left(\frac{\text{0}\text{.15}{\left(\text{1}+\text{0}\text{.15}\right)}^{\text{10}}}{{\left(\text{1}+\text{0}\text{.15}\right)}^{\text{10}}-1}\right)-\text{10,000}\left(\frac{\text{0}\text{.15}}{{\left(\text{1}+\text{.15}\right)}^{\text{10}}-1}\right)}\\ =1.27\end{array}$   

The benefit cost ratio is 1.27. Since the BC value is greater than 1, it is acceptable project.