Q$1.$ Problem: Modernized Farming Equipment Analysis $[6$ Marks$]$

The Green Valley Agricultural Co$-$op is considering investing in a new automated irrigation system to

improve efficiency on their farms. The system is priced at $$20,000.$ The automation will not increase

crop yields or sales revenues, but it is expected to decrease water usage and labor costs significantly.

The system requires annual maintenance to function correctly. The system is expected to be functional

for eight years, after which it will have no salvage value. The following table summarizes the

anticipated annual savings in water and labor costs and the annual maintenance cost over eight years.

Table $1$: Cost and Savings Summary Table

The costs represent the annual maintenance required, while the savings are from reduced water

consumption and labor. The net cash flow is the savings minus the costs each year.

Tasks:

Calculate the Net Present Value $($NPV$)$ of the investment using a discount rate of $8\%.[1\mathrm{.}5$

Mark$]$

Determine the Internal Rate of Return $($IRR$)$ for the project. $[1\mathrm{.}5$ Mark$]$

Perform a sensitivity analysis to assess how changes in the discount rate affect the NPV$.[1\mathrm{.}5$

Mark$]$

Provide a recommendation based on the NPV and IRR whether Green Valley Agricultural

Co$-$op should proceed with the investment in the new irrigation system. $[1\mathrm{.}5$ Mark$]$

PLEASE PROVIDE THE FORMULAS AND THE STEPS