91Ó°ÊÓ

For project A

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{cash}\mathrm{inflow}& =& \mathrm{Annual}\mathrm{inflow}×\left[\frac{1-{\displaystyle \frac{1}{{\left(1+\mathrm{r}\right)}^{\mathrm{n}}}}}{\mathrm{r}}\right]\\ & =& \$55,000×\left[\frac{1-{\displaystyle \frac{1}{{\left(1+0.14\right)}^7}}}{0.14}\right]\\ & =& \$235,840\\ & & \\ \mathrm{NPV}& =& \mathrm{Present}\mathrm{value}-\mathrm{Cost}\\ & =& \$235,840-\$285,000\\ & =& -\$49,160\end{array}$

For project B

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{cash}\mathrm{inflow}& =& \mathrm{Annual}\mathrm{inflow}×\left[\frac{1-{\displaystyle \frac{1}{{\left(1+\mathrm{r}\right)}^{\mathrm{n}}}}}{\mathrm{r}}\right]\\ & =& \$77,000×\left[\frac{1-{\displaystyle \frac{1}{{\left(1+0.12\right)}^{10}}}}{0.12}\right]\\ & =& \$435,065\\ & & \\ \mathrm{NPV}& =& \mathrm{Present}\mathrm{value}-\mathrm{Cost}\\ & =& \$435,065-\$395,000\\ & =& \$40,065\end{array}$

The maximum price of the projects is the value at which there is neither any profit nor any loss. This would be possible when the net present value of each project would be equal to its initial investment value.

Based on this,

The maximum price for project A = $235,840

The maximum price for project B = $435,265

$\begin{array}{rcl}\mathrm{Profitability}\mathrm{index}\mathrm{for}\mathrm{project}\mathrm{A}& =& \frac{\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{project}\mathrm{A}}{\mathrm{Initial}\mathrm{investment}\mathrm{value}\mathrm{for}\mathrm{project}\mathrm{A}}\\ & =& \frac{\$235,840}{\$285,000}\\ & =& 0.83\\ & & \\ \mathrm{Profitability}\mathrm{index}\mathrm{for}\mathrm{project}\mathrm{B}& =& \frac{\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{project}\mathrm{B}}{\mathrm{Initial}\mathrm{investment}\mathrm{value}\mathrm{for}\mathrm{project}\mathrm{B}}\\ & =& \frac{\$435,265}{\$395,000}\\ & =& 1.10\end{array}$