Question

You are considering purchasing a dump truck. The truck will cost $75000 and have operating and maintenance costs that start at $18000 the first year and increases by $2000 per year. Assume that the salvage value at the end of five years is $22000 and interest rate is 12%. What is the equivalent annual cost of owning and operating the truck?You are considering purchasing a dump truck. The truck will cost $75000 and have operating and maintenance costs that start at $18000 the first year and increases by $2000 per year. Assume that the salvage value at the end of five years is $22000 and interest rate is 12%. What is the equivalent annual cost of owning and operating the truck?

Answer 1

The equivalent annual cost of owning and operating the dump truck is approximately $51,967.91.

How to solve

Equivalent Annual Cost of Dump Truck

Step 1: Calculate Operating and Maintenance Costs:

Year 1: $18,000

Year 2: $20,000

Year 3: $22,000

Year 4: $24,000

Year 5: $26,000

Step 2: Calculate Present Value of Costs:

Present value of operating and maintenance costs:

PV = $18,000/(1 + 0.12)^1 + $20,000/(1 + 0.12)^2 + $22,000/(1 + 0.12)^3 + $24,000/(1 + 0.12)^4 + $26,000/(1 + 0.12)^5

PV ≈ $75,834.84

Step 3: Calculate Present Value of Salvage Value:

Present value of salvage value:

PV = $22,000/(1 + 0.12)^5

PV ≈ $12,662.32

Step 4: Calculate Equivalent Annual Cost (EAC):

EAC = (Initial Investment + PV of Operating Costs - PV of Salvage Value) / Capital Recovery Factor (CRF) at 12% and 5 years.

CRF = (1 - (1 + 0.12)^(-5)) / 0.12 ≈ 3.604772

EAC = ($75,000 + $75,834.84 - $12,662.32) / 3.604772

EAC ≈ $51,967.91

Therefore, the equivalent annual cost of owning and operating the dump truck is approximately $51,967.91.