$1.$ ABC Manufacturing Corp is considering investing in new equipment to improve its production efficiency. The company has two options:

Option A: Purchase new state$-$of$-$the$-$art equipment for $$1,000,000.$ This equipment is expected to generate cash flows of $$400,000$ per year for five years.

Option B: Lease the equipment for an annual payment of $$300,000$ for five years. The lease includes maintenance and support services.

The company's cost of capital is $10\%.$

$1.$ Calculate the Net Present Value $($NPV$)$ for both options.

$2.$ Use the Payback Period and Profitability Index to supplement the NPV analysis.

$3.$ Provide a recommendation to ABC Manufacturing Corp on whether to purchase or lease the equipment, considering all evaluation criteria.