Question

your manager has asked you to analyze the purchase of some dump trucks. each truck will cost 45000$ and have an operating and maintenance cost starting 15000$ the first year and increase by 2000$ per year. assume the salvage value at the end of 5 years is 9000$ and interest rate 12% . what is the equivalent annual cost of each truck

Answer 1

Initial cost of Each truck is = $45,000

Operating and Maintenance cost is starting in year 1 which is $15,000 and it will increase by $2,000 in each year thereafter

Salvage value at the end 5 years is $9,000.

The equivalent annual cost of each truck has to calculate at 12% interest rate and the useful life of truck is 5 years.

Annual Equivalent Cost (AEW) of each truck is -

[$45,000 + $15,000(P/A, 5, 12%) + $2,000(P/G, 12%, 5) - $9,000(P/F, 12%, 5)]*[(A/P, 12%, 5)]

=[$45,000 + $15,000{(1+0.12)^5 - 1}/0.12(1+0.12)^5} + $2,000*[{1+0.12)^5 - 1}/{0.12^2*(1+0.12)^5} - {5/(1+0.12)^5}] - $9,000/(1+0.12)^5]*[{(0.12(1+0.12)^5}/{(1+0.12)^5 - 1}]

= [$45,000 + $15,000*3.60477 + $2,000*6.397 - $9,000/1.76234]*(0.2774)

= [$45,000 + $54,071.55 + $12,794 - $5106.84]*(0.2774)

= $106,758.71*0.2774

= $29,614.86

= $29,615. (Approx).

Therefore, Equivalent annual cost of each truck is $29,615. (Answer).