Question

Halcrow, inc. hopes to replace an outdated tracking system currently installed on cnc machines. the challenger system has an initial cost of $70,000, an estimated annual operating cost of $20,000, a maximum useful life of 5 years, and a salvage value of $10,000 at any time. with an interest rate of 11% per year, determine the economic life of the service and the corresponding amount for year 6.

a)-35,382.8
b.)-35,482.8
c.)-35,582.8
d.)-35,282.8

Answer 1

The economic life of the service extends beyond 5 years, and the corresponding amount for year 6 is -$89,482.8.

Step-by-step explanation:

To determine the economic life of the service and the corresponding amount for year 6, we need to calculate the present value of the total costs incurred over the 5-year period.

The formula to calculate the present value (PV) is: PV = C1 + C2/(1+r) + C3/(1+r)^2 + C4/(1+r)^3 + C5/(1+r)^4 + C6/(1+r)^5, where C1 to C5 are the annual operating costs, C6 is the salvage value, r is the interest rate, and PV is the present value.

Plugging in the given values: C1 = $20,000, C2 = $20,000, C3 = $20,000, C4 = $20,000, C5 = $20,000, C6 = $10,000, and r = 11%.

Calculating the present value, we find: PV = $20,000 + $20,000/(1+0.11) + $20,000/(1+0.11)^2 + $20,000/(1+0.11)^3 + $20,000/(1+0.11)^4 + $10,000/(1+0.11)^5 = $89,482.8

Since the present value is greater than $0, it indicates that the economic life of the service extends beyond 5 years. The corresponding amount for year 6 would be -$89,482.8, as this represents the net cost of operating the system in year 6.