Question

Given the financial data for four mutually exclusive alternatives in the table below,

	A	B	C	D
First cost	$18,000	$40,000	$21,200	45,000
O &M Cost/ year	2,600	5,000	3,900	11,000
Benefit/year	7,500	16,000	11,500	25,000
Salvage value	2,000	6,000	6,000	12,000
Life in years	4

Use a Rate of Return Analysis to solve for the following:

• Which alternative should be chosen using an MARR of 9%? Mathematical solution
• Create a choice table from 0 – 25%.
• Create a graphical solution to the problem indicating which alternative should be chosen for interest rates from 0 – 20%. Make sure your graph has all proper labels including the appropriate choices for the Rate of Returns shown in the graph. The graph should be on its own page and not embedded.  

Answer 1

Statement showing Net Present Value from each alternative Alternative A Alternative B Alternative C Alternative D PV Factor Present Present Present Present Particulars Years Amount Amount Amount Amount at 9% Value Value Value Value Cash outflow: 18000 18 First Cost 0 1.00 18000 40000 400002 2120021200 45000 45000 Total (A) 18000 40000 21200 45000 Cash Inflow: Net Benefit 1-4 3.9481 4900 19345.91 1100043429.67600 30005.90 14000 55274.03 Salvage Value 4 0.7084 1416.85 6000 4250.55 6000 4250.55 12000 8501.10 Total (B) 20762.76 47680.15 34256.45 63775.1:3 Net Present Value 2762.76 7680.15 13056.45 18775.13 B-A using a MARR at 9%, Project D should be selected since it is having the highest Net Present Value Consider the interest rate at 10% and 20% for analysing that which alternative is better

a) At the interest rate of 10% Statement showing Net Present Value from each alternative Alternative A Alternative B Alternative C Alternative D PV Factor Present Present Present Present Particulars Years Amount Amount Amount Amount at 10% Value Value Value Value Cash outflow: First Cost 0 1.00 1800018000 40000 40000 21200 21200 45000 45000 Total (A) 18000 40000 21200 45000 Cash Inflow: Net Benefit 1-4 3.8529 4900 18879.11 1100042381.67 7600 29281.88 14000 53940.30 Salvage Value 4 0.6830 2000 1366.027 6000 4098.08 6000 4098.08 120008196.16 Total (B) 20245.13 46479.75 33379.96 62136.47 Net Present Value 2245.13 6479.75 12179.96 17136.47 B-A

b) At the interest rate of 20% Statement showing Net Present Value from each alternative Alternative A Alternative B Alternative C Alternative D PV Factor | at 20% Present Present Present Present Years Particulars Amount Amount Amount Amount Value Value Value Value Cash outflow: 18000 18 400002 2120021200 45000 First Cost 0 1.00 18000 40000 Total (A) 18000 21200 45000 Cash Inflow: Net Benefit 3.0710 1-4 4900 15047.84 1100033780.86 7600 23339.51 14000 42993.83 Salvage Value 4 0.4823 2000 964.5062 60002893.52 6000 2893.52 12000 5787.04 Total (B) 16012.35 36674.38 26233.02 48780.86 Net Present Value 1987.65 3325.62 5033.02 3780.86 B-A Therefore from the above calculations, Alternative D is better to be selected at interest rate of 10% whereas Alternative C is better to be selected at interest rate of 20% Data for Chart Graph Selected Interest Rate Alternative 9% 10% 20% Interest Rate