Advanced Electrical Insulator Company is considering replacing a broken inspection machine, which has been used to test the mechanical strength of electrical insulators with a newer and more efficient one. If repaired, the old machine can be used for another five years although the firm does not expect to realize any salvage value from scrapping it in five years. Alternatively, the firm can sell the machine to another firm in the industry now for $5,000. If the machine is kept, it will require an immediate $1,200 overhaul to restore it to operable condition. The overhaul will neither extend the service life originally estimated nor increase the value of the inspection machine. The operating costs are estimated at $2,000 during the first year and are expected to increase by $1,500 per year thereafter. Future market values are expected to decline by $1,000 per year. The new machine costs $10,000 and will have operating costs of $2,000 in the first year, increasing by $800 per year thereafter. The expected salvage value is $6,000 after one year and will decline 15% each following year. The company requires a rate of return of 15%. Find the economic life for each option and determine when the defender should be replaced.

Respuesta :

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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