Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume straight line depreciation method is used. $($Future Value of $$1,$ Present Value of $$1,$ Future Value Annuity of $$1,$ Present Value Annuity of $$1.)($Use appropriate factor$($s$)$ from the tables provided.$)$

Project $1$: Retooling Manufacturing Facility

This project would require an initial investment of $$5,040,000.$ It would generate $$1,036,000$ in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $$1,990,000.$

Project $2$: Purchase Patent for New Product

The patent would cost $$4,065,000,$ which would be fully amortized over five years. Production of this product would generate $$894,300$ additional annual net income for Hearne.

Project $3$: Purchase a New Fleet of Delivery Trucks

Hearne could purchase $25$ new delivery trucks at a cost of $$187,200$ each. The fleet would have a useful life of $10$ years, and each truck would have a salvage value of $$6,900.$ Purchasing the fleet would allow Hearne to expand its customer territory resulting in $$246,000$ of additional net income per year.

Required:

$1.$ Determine each project's accounting rate of return.

$2.$ Determine each project's payback period.

$3.$ Using a discount rate of $10$ percent, calculate the net present value of each project.

$4.$ Determine the profitability index of each project and prioritize the projects for Hearne.