Question

You are considering purchasing a dump truck. The truck will cost $62,000 and have operating and maintenance costs that start at $11,000 the first year and increases by $2,100 per year. Assume that the salvage value at the end of five years is $17,000 and interest rate is 7%. What is the equivalent annual cost of owning and operating the truck for five years? Click the icon to view the interest factors for discrete compounding when i = 7% per year. The equivalent annual cost of owning and operating the truck is $(Round to the nearest dollar.)

Answer 1

Truck cost = $62,000

Operation cost per year = $11,000 in the first year which increases by $2,100 per year

Salvage value = $17,000

Interest rate (r) = 7%

Life (n) = 5 years

Equivalent annual cost is calculated as: Net Present Value / {[1 - (1 + r)^^-n] / r}

Present value of operation cost is calculated as: [Operation Cost / (1 + r)^^Year]

Year	Operation Cost	Present value
1	11,000.00	10,280.37
2	13,100.00	11,442.05
3	15,200.00	12,407.73
4	17,300.00	13,198.09
5	19,400.00	13,831.93
		61,160.17

Present value of salvage after 5 years = [17,000 / (1 + 0.07)^⁵] = 12,120.76

Net present value of truck = Cost of truck + Present value of operation cost - Present value of salvage = 62,000 + 61,160.17 - 12,120.76 = 111,039.40

Equivalent annual cost = 111,039.40 / {[1 - (1 + 0.07)^^-5] / 0.07} = 27,081.48 or 27,081