1 ine3 alternatives below all have infinite lives. Determine which alternative s
ID: 2795382 • Letter: 1
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1 ine3 alternatives below all have infinite lives. Determine which alternative should be selected using the Incremental rate of return method. The M 20% per year. ARR is Alternative A Alternative B Alternative C First Cost ($) Annual income (S/yr) Annual expenses ($/yr) 55,00028000 17,000 2,500 42,000 18,000 1,500 20,000 3,000 (i) Compare the alternatives based on the incremental capitalized cost. (ii) You must calculate each incremental rate of return to the nearest whole percent. Do not substitute the MARR of 20% per year into the equation but compare the incremental rate of return to make the decision. Since there is positive cash flow, start by comparing the least expensive alternative to the Do-Nothing (DN) alternative No credit is given if the analysis procedure or if the comparison made at any point in the solution is incorrect. The solution must be shown in logical order and must be appropriately documented. Clearly label each comparison made and the alternative selected in each case. Show all work, including factor notation, equations, values of factors etc., to demonstrate how the rate of return was determined. State which project is finally selected. (iii) (iv) (v)Explanation / Answer
Since, the alternatives have infinite lives therefore, the cash inflows for these projects will be perpetual or infinite as well.
The present value of all cash inflows for (alternative A) are PVa = (Income - Expense)/IRR
IRR is determined when NPV = 0, therefore,
NPVa = 0 = -55,000 + (20000 - 3000)/IRR = IRR
IRRa = 17000/55000 = 31%
NPVa = -55,000 + 17000/0.2 = 30,000 (Using 20% MARR as discount rate)
The present value of all cash inflows for (alternative B) are PVb = (Income - Expense)/IRR
IRR is determined when NPV = 0, therefore,
NPVb = 0 = -28,000 + (17000 - 2500)/IRR = IRR
IRRb = 14500/28000 = 52%
NPVb = -28,000 + 14500/0.2 = 44,500 (Using 20% MARR as discount rate)
The present value of all cash inflows for (alternative C) are PVc = (Income - Expense)/IRR
IRR is determined when NPV = 0, therefore,
NPVc = 0 = -42,000 + (18000 - 1500)/IRR = IRR
IRRc = 16500/42000 = 39%
NPVa = -42,000 + 16500/0.2 = 40,500 (Using 20% MARR as discount rate)
Though all the project has high IRR and based on the values from their NPV all alternatives are having positive NPV. But if we at all need to consider we should take take alternative B as it has maximum positive NPV using 20% MARR to measure. If the cost of capital is less than 20% then each of these projects will give positive cash flow but Alternative B will give maximum cash inflow. So compared to Do-Nothing (DN), the alternative B is the least expensive to execute.
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