Question

A machine purchased 1 year ago for $1055,000 costs more to operate than anticipated. When purchased, the machine was expected to be used for 10 years with annual maintenance costs of $32,000 and a $10,000 salvage value. However, last year, it cost the company $38,000 to maintain it, and these costs are expected to escalate to $40,000 this year and increase by $2,000 each year thereafter. The market value is now estimated to be $105,000 − $15,000k, where k is the number of years since the machine was purchased. It is now estimated that this machine will be useful for a maximum of 5 more years. A replacement study is to be performed now. Determine the value the first cost of this defender to be used in replacement analysis. Assume i = 10% per year.

Answer 1

The value of the machine at the beginning of year 1 needs to be considered.

Initial Investment = 1,055,000. This will not be discounted

Operating Costs = 38,000 in year 1, 40000 in year 2, 42000 in year 3, 44000 in year 4, 46000 in year 5 and 48000 in year 6.

6th year will be the last year that the machine can be used, since it has already been 1 year and it will last for 5 more years

The Market Value of the machine after 6 years = 105000 - 15000 * 6 = 15,000. This will be the salvage value

So the PV of the project is

PV = -1055000 - 38000 / 1.1 - 40000/1.1^2 - 42000 / 1.1^3 - 44000 / 1.1^4 - 46000 / 1.^5 - 48000 / 1.1^6 + 15000 / 1.1^6

PV = -1055000 - 34545.45 - 33057.85 - 31555.22 - 30052.59 - 28562.38 - 27094.75 + 8467.11

PV = -1231401.13

So the present first cost of this project is 1231401.13.

If the machine is to be replaced at the end of year 6, the comparision will be done at the end of year 6.

So First cost of the machine at end of year 6 = 1231401.13 * 1.1^6 = 2,181,502.22.

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