Chapter 10, Problem 1P

The Adams Construction Company is bidding on a project to install a large flood drainage culvert from Dandridge to a distant lake. If they bid $2,000,000 for the job, what is the benefit-cost ratio in view of the following data? The MARR is 6% per year, and the project’s life is 30 years.

To determine

Calculate the benefit cost ratio.

Explanation of Solution

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

$\begin{array}{c}\text{BC}=\frac{\text{Annual benefit}}{\text{Bid}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)+{\text{Cost}}_{\text{Upkeep for 6 year}}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)+{\text{Cost}}_{\text{Maintenance}}}\\ =\frac{\text{135,000}}{\text{200,000}\left(\frac{\text{0}\text{.06}{\left(1+\text{0}\text{.06}\right)}^{\text{30}}}{{\left(1+\text{0}\text{.06}\right)}^{\text{30}}-1}\right)+\text{50,000}\left(\frac{\text{0}\text{.06}{\left(1+\text{0}\text{.06}\right)}^{\text{6}}}{{\left(1+\text{0}\text{.06}\right)}^{\text{6}}-1}\right)+\text{30,000}}\\ =0.728\end{array}$

Benefit cost ratio is 0.72. Since the benefit cost ratio is less than 1, it is not acceptable 1. To make the acceptable project, the bid price need to decrease. The new maximum bid amount to accept the project (B) can be calculated as follows.

$\begin{array}{c}\text{Benefit}=\text{B}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)+{\text{Cost}}_{\text{Upkeep for 6 year}}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)+{\text{Cost}}_{\text{Maintenance}}\\ \text{135,000}=\text{B}\left(\frac{\text{0}\text{.06}{\left(1+\text{0}\text{.06}\right)}^{\text{30}}}{{\left(1+\text{0}\text{.06}\right)}^{\text{30}}-1}\right)+\text{50,000}\left(\frac{\text{0}\text{.06}{\left(1+\text{0}\text{.06}\right)}^{\text{6}}}{{\left(1+\text{0}\text{.06}\right)}^{\text{6}}-1}\right)+\text{30,000}\\ \text{B}=1,306,198\end{array}$

Maximum amount bid is $1,306,198.