A machine costs $500,000 new.It has a useful life of 20 years,at the end of which it can be sold for $S.Maintenance costs are $15,000 at the end of each year.If the cost of capital is j₁ = 12%,the capitalized cost of the machine is $675,000.What is the value of S?

Question

Quizplus · Accepted Answer

The capitalized cost of the machine is the present value of all its costs, including the initial price, maintenance costs, and salvage value. We know that the capitalized cost is $675,000 and the cost of capital is 12%.

Using the formula for present value of an annuity, we can find the present value of the 20 yearly maintenance costs of $15,000:

PV = $15,000 x [(1 - (1/1.12^20))/0.12] = $161,771

Therefore, the present value of the initial cost and salvage value is:

$675,000 - $161,771 = $513,229

We know that the initial cost is $500,000, so the salvage value must be:

$513,229 - $500,000 = $13,229

Therefore, the value of S is:

$13,229 x 1.12^20 = $79,940

The closest answer choice is C: at least $65,000, but less than $80,000.

A Machine Costs $500,000 New