diagrams (Please note 5 points and explain the eproblems. Show the details in so
ID: 2594592 • Letter: D
Question
diagrams (Please note 5 points and explain the eproblems. Show the details in solving the rade 10 e Test and if you answer the 5h question you sarefully Please draw the cash nowW odgrm) ai solving will be deducted from every questi steps that you are going to approach to solve the problems problems. Please write l on if you do not draw cash etherwise there is a deduction from your Question -20 Points Consider four Alternatives (in table below) that each has an eigh t-year useful life Cost Uniform Annual Benefits$12.2 Salvage Value $50 $12.2 0 $100 $80 $12.0 $50.0 $60 $9.7 $50.0 $75.0 If MARR is 8% which alternative should be selected? Solve the problem by 1) Benefit-cost ratio analysis. 2) Net Present Value 3) Are the two Analysis give you the same answer?Explanation / Answer
Question 1). Solution :- Benefit-cost ratio = Present value of cash inflows / Present value of cash outflow.
Alternative A
Present value of cash inflows = 12.20 * [ 1 - (1.08)-8 ] / 0.08 + 75 / (1.08)8
= 12.20 * [ 1 - 0.5403 ] / 0.08 + 75 / 1.8509
= 12.20 * 0.4597 / 0.08 + 75 / 1.8509
= 70.10425 + 40.52083
= $ 110.62508 (Rounded off to $ 110.63)
Present value of cash outflow = $ 100.
Benefit-cost ratio of Alternative A = 110.63 / 100 = 1.1063 (Rounded off to 1.11)
Alternative B
Present value of cash inflows = 12.0 * [ 1 - (1.08)-8 ] / 0.08 + 50 / (1.08)8
= 12.0 * [ 1 - 0.5403 ] / 0.08 + 50 / 1.8509
= 12.0 * 0.4597 / 0.08 + 50 / 1.8509
= 68.955 + 27.014
= $ 95.969 (Rounded off to $ 95.97)
Present value of cash outflow = $ 80.
Benefit-cost ratio of Alternative B = 95.97 / 80 = 1.199625 (Rounded off to 1.20)
Alternative C
Present value of cash inflows = 9.7 * [ 1 - (1.08)-8 ] / 0.08 + 50 / (1.08)8
= 9.7 * [ 1 - 0.5403 ] / 0.08 + 50 / 1.8509
= 9.7 * 0.4597 / 0.08 + 50 / 1.8509
= 55.7386 + 27.0139
= $ 82.7525 (Rounded off to $ 82.75)
Present value of cash outflow = $ 60.
Benefit-cost ratio of Alternative C = 82.75 / 60 = 1.37917 (Rounded off to 1.38)
Alternative D
Present value of cash inflows = 12.2 * [ 1 - (1.08)-8 ] / 0.08
= 12.2 * [ 1 - 0.5403 ] / 0.08
= 12.2 * 0.4597 / 0.08
= 70.10425 (Rounded off to $ 70.10)
Present value of cash outflow = $ 50.
Benefit-cost ratio of Alternative D = 70.10 / 50 = 1.402 (Rounded off to 1.40)
Conclusion :-
Alternative D should be selected because the benefit-cost ratio of alternative D is the highest.
Question 2). Solution :- Net present value = Present value of cash inflows - Present value of cash outflow.
Alternative A :- Net present value = 110.63 - 100 = $ 10.63
Alternative B :- Net present value = 95.97 - 80 = $ 15.97
Alternative C :- Net present value = 82.75 - 60 = $ 22.75
Alternative D :- Net present value = 70.10 - 50 = $ 20.10
Conclusion :-
Alternative C should be selected using the net present value (NPV) approach because the net present value of alternative C is the highest.
Question 3). Answer :- No, the benefit-cost ratio analysis and net present value approach do not give the same answer. Alternative D should be selected using the benefit-cost ratio because the benefit-cost ratio of alternative D is the highest whereas the Alternative C should be selected using the net present value (NPV) approach because the net present value of alternative C is the highest.
Particulars Alternative A Alternative B Alternative C Alternative D Benefit-cost ratio 1.11 1.20 1.38 1.40Related Questions
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