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Advanced Electrical Insulator Company is considering replacing a broken inspection machine, The defender should be replaced after the Fifth year.
What is economic life?
Generally, To compare the two options, we need to find the net present value (NPV) of each option. The NPV is the sum of the present values of the expected future cash flows, discounted at the required rate of return.
For the option to repair the old machine, the initial cost is the cost of the overhaul, which is $1,200. The expected cash flows from the old machine are the operating costs in each year. The present value of each year's operating cost can be calculated using the formula:
Present value = cash flow / (1 + r)^n
where r is the required rate of return and n is the number of years in the future.
The present value of the operating costs for the first year is:
$2,000 / (1 + 0.15)^1 = $1,739.73
The present value of the operating costs for the second year is:
$3,500 / (1 + 0.15)^2 = $2,924.53
The present value of the operating costs for the third year is:
$5,000 / (1 + 0.15)^3 = $3,928.61
The present value of the operating costs for the fourth year is:
$6,500 / (1 + 0.15)^4 = $4,701.24
The present value of the operating costs for the fifth year is:
$8,000 / (1 + 0.15)^5 = $5,169.47
The sum of the present values of the operating costs is $18,463.09.
The NPV of the option to repair the old machine is the sum of the initial cost and the present value of the operating costs:
NPV = $1,200 + $18,463.09 = $19,663.09
For the option to purchase the new machine, the initial cost is the cost of the machine, which is $10,000. The expected cash flows from the new machine are the operating costs in each year and the salvage value in each year.
The present value of the operating costs for the first year is:
$2,000 / (1 + 0.15)^1 = $1,739.73
The present value of the operating costs for the second year is:
$2,800 / (1 + 0.15)^2 = $2,319.49
The present value of the operating costs for the third year is:
$3,600 / (1 + 0.15)^3 = $2,738.34
The present value of the operating costs for the fourth year is:
$4,400 / (1 + 0.15)^4 = $3,051.91
The present value of the operating costs for the fifth year is:
$5,200 / (1 + 0.15)^5 = $3,241.48
The present value of the salvage value for the first year is:
$6,000 / (1 + 0.15)^1 = $5,217.39
The present value of the salvage value for the second year is:
$5,100 / (1 + 0.15)^2 = $4,115.93
The present value of the salvage value for the third year is:
$4,385 / (1 + 0.15)^3 = $3,235.73
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