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Answer :
The equivalent annual cost of the lathe is $27,288.26. This is the annual cost that would make the purchase and operation of the lathe equivalent to a stream of equal payments over the 4-year period.
To calculate the equivalent annual cost of the lathe, we need to add up all the costs associated with it and convert them into an annual cost.
The cost of the lathe is $16,000 and it will last for 4 years. Therefore, the depreciation expense for the lathe can be calculated as:
Depreciation expense = Cost of lathe / Useful life of lathe
Depreciation expense = $16,000 / 4 years
Depreciation expense = $4,000 per year
In addition to the cost of the lathe, there is also an annual cost of $26,000 to operate and maintain it. Therefore, the total cost of the lathe for one year is:
Total cost = Depreciation expense + Operating and maintenance expense
Total cost = $4,000 + $26,000
Total cost = $30,000 per year
To calculate the equivalent annual cost of the lathe, we need to discount this cost over the 4-year period using the discount rate of 10%. The formula for calculating the present value of an annuity is:
Equivalent annual cost = (Total cost x Discount factor) / Present value of annuity factor
Where:
Discount factor = (1 - (1 + Discount rate)^-n) / Discount rate
n = Number of years
Present value of annuity factor = ((1 - (1 + Discount rate)^-n) / Discount rate) x (1 + Discount rate)
Substituting the values, we get:
Discount factor = (1 - (1 + 0.1)^-4) / 0.1
Discount factor = 3.16986
Present value of annuity factor = ((1 - (1 + 0.1)^-4) / 0.1) x (1 + 0.1)
Present value of annuity factor = 3.48685
Equivalent annual cost = ($30,000 x 3.16986) / 3.48685
Equivalent annual cost = $27,288.26
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