Project $1$: Expansion of Production Facility Initial Investment: $$500,000$ Expected Annual Cash Flows:o Year $1$: $$100,000$o Year $2$: $$120,000$o Year $3$: $$140,000$o Year $4$: $$160,000$o Year $5$: $$180,000$o Year $6$: $$200,000$o Year $7$: $$220,000$o Year $8$: $$240,000$o Year $9$: $$260,000$o Year $10$: $$280,000$o Year $11$: $$300,000$o Year $12$: $$320,000$o Year $13$: $$340,000$o Year $14$: $$360,000$o Year $15$: $$380,000$ Project $2$: Launching a New Product Line Initial Investment: $$700,000$ Expected Annual Cash Flows:o Year $1$: $$90,000$o Year $2$: $$110,000$o Year $3$: $$130,000$o Year $4$: $$150,000$o Year $5$: $$170,000$o Year $6$: $$190,000$o Year $7$: $$210,000$o Year $8$: $$230,000$o Year $9$: $$250,000$o Year $10$: $$270,000$o Year $11$: $$290,000$o Year $12$: $$310,000$o Year $13$: $$330,000$o Year $14$: $$350,000$o Year $15$: $$370,000$ Project $3$: Acquisition of New Machinery Initial Investment: $$600,000$ Expected Annual Cash Flows:o Year $1$: $$80,000$o Year $2$: $$100,000$o Year $3$: $$120,000$o Year $4$: $$140,000$o Year $5$: $$160,000$o Year $6$: $$180,000$o Year $7$: $$200,000$o Year $8$: $$220,000$o Year $9$: $$240,000$o Year $10$: $$260,000$o Year $11$: $$280,000$o Year $12$: $$300,000$o Year $13$: $$320,000$o Year $14$: $$340,000$o Year $15$: $$360,000$ Assumptions: $-$ All projects have a useful life of fifteen years.$-$ The company's cost of capital is $10\%.-$ Depreciation and taxes are not considered in this analysis.$-$ The payback period cutoff is $3$ years. Your Task:$1.$ Evaluate each project using the following investment appraisal methods while showing your calculations:a$.$ Net Present Value $($NPV$)$b$.$ Payback Period $($cutoff at $3$ years$)$c$.$ Internal Rate of Return $($IRR$)$d$.$ Profitability Index $($PI$)2.$ Compare the outcomes obtained from each method. $3.$ Provide a recommendation on which project the company should invest in and justify your choice based on the analysis's results. Further Instructions: $-$ This will be a group assignment. Each group will consist of a maximum of $5$ students.$-$ The deadline for group members to inform the course lecturer of their group members is April $15$th$,2024.$ There is Microsoft form placed at the Moodle you can use that form to inform the group lecturer. If they fail to do so$,$ automatic grouping will occur.$-$ The assignment should have a cover page that includes the assignment title, group members' names and student numbers, and the course title.$-$ The assignment should be submitted in hard and soft copy. The soft copy submission is due on $28$th May $2024.$ The hard copy will also be collected on the final exam date $($Please do not forget to bring it to the exam venue$).$ Failing to submit both will result in an automatic zero grade.$-$ On the next page, you can find how your term assignment will be graded with a rubric. Assignment RubricCriteriaDescription$4-$ Excellent$3-$ Good$2-$ Satisfactory$1-$ Needs ImprovementAnalysis of Investment MethodsAccuracy and depth of analysis using NPV$,$ Payback Period, IRR, and PI methods.Thorough analysis of all investment appraisal methods with accurate calculations and insightful interpretations.Analysis covers all methods with mostly accurate calculations and clear interpretations.Analysis includes most methods with some inaccuracies in calculations and interpretations.Analysis lacks depth or contains significant errors in calculations and interpretations.Comparison of OutcomesComprehensive comparison of outcomes obtained from different methods and identification of their strengths and weaknesses.Thorough comparison provided, identifying strengths and weaknesses of each method effectively.Comparison is mostly comprehensive with minor omissions, and strengths and weaknesses are mostly identified.Some aspects of the comparison are missing, and identification of strengths and weaknesses is somewhat unclear.Comparison lacks depth and clarity, and strengths and weaknesses are not effectively identified.Recommendation and JustificationClarity of recommendation on the most suitable project for investment and well$-$supported justification based on the analysis's results.Recommendation is clear, and justification is well$-$supported, considering all appraisal methods and outcomes.Recommendation is mostly clear with minor omissions, and justification is mostly well$-$supported.Recommendation is somewhat unclear, and justification lacks depth, or some appraisal methods$/$outcomes are not adequately considered.Recommendation is unclear, and justification is weak or unsupported, lacking consideration of appraisal methods$/$outcomes$.$Presentation and OrganizationClarity of presentation, organization, and proper use of headings, subheadings, and formatting.Information is presented clearly and logically with proper organization and formatting.Presentation is mostly clear with minor organizational issues, and formatting is mostly appropriate.Some aspects of the presentation are unclear or disorganized, and formatting is inconsistent.Presentation lacks clarity and organization, and formatting is inadequate.