Question

Use the NPV method to determine whether Hawkins Products should invest in the

following projects:

• Project A: Costs \(285,000 and offers seven annual net cash inflows of \)55,000. Hawkins Products requires an annual return of 14% on investments of this nature.

• Project B: Costs \(395,000 and offers 10 annual net cash inflows of \)77,000. Hawkins Products demands an annual return of 12% on investments of this nature.

Requirements

1. What is the NPV of each project? Assume neither project has a residual value. Round to two decimal places.

2. What is the maximum acceptable price to pay for each project?

3. What is the profitability index of each project? Round to two decimal places.

Short answer

NPV Project A: $235,840

NPV Project B: $435,065

PI Project A: 0.83

PI Project B: 1.10

Step-by-step solution

Computation of NPV

For project A

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

For project B

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

Maximum project price

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

Profitability Index

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