Falcon Industries Ltd$.,$ a leading manufacturer of specialized parts for the aerospace industry, isconsidering the acquisition of a new piece of machinery, the Precision Automated Lathe $($PAL$).$The company believes that the PAL could help streamline operations and enhance productivity.However, the decision to invest is not straightforward due to the significant costs involved andthe potential impact on the company's financial position.The management has narrowed down their choices to two options for the PAL:Option $1$: A brand$-$new PAL machine with advanced features costing $$1,280,000.$ It has a usefullife of $8$ years with no salvage value. Annual maintenance and operating costs are estimated at$$45,000.$Option $2$: A refurbished PAL machine with a cost of $$980,000.$ It has a useful life of $6$ years witha salvage value of $$50,000$ at the end of its life. Annual maintenance and operating costs areestimated at $$52,000.$For both options, Falcon's management expects that the machine can increase annual revenuesby $$480,000$ due to its superior precision and speed. Additionally, the PAL is expected to reducelabor costs by $$65,000$ annually. The company uses a discount rate of $10\%$ for capital budgetingdecisions.Other relevant data:$-$ Current annual sales: $$5,800,000-$ Gross margin: $40\%-$ Current annual labor costs: $$1,500,000-$ Expected growth rate without PAL: $3\%$ annuallyBased on the above, answer the following questions:$1.$ Calculate the net present value $($NPV$)$ of acquiring the PAL for both options$\mathrm{.}2.$ Determine the internal rate of return $($IRR$)$ for each option$\mathrm{.}3.$ Calculate the payback period for both options$\mathrm{.}4.$ Based on your calculations, which option should Falcon Industries Ltd$.$ choose? Consider boththe quantitative and qualitative benefits and drawbacks of each option$\mathrm{.}5.$ How would the decision change if the expected annual revenue increase was only $$400,000$for both Options?