Question

You are considering purchasing a dump truck. The truck will cost $45,000 and have an operating and maintenance cost that starts at $15,000 the first year and increases by $2,000 per year thereafter. Assume that the salvage value at the end of 5 years is $9,000 and interest rate is 12%. The equivalent annual cost of owning and operating the truck is most nearly:

Answer 1

The equivalent annual cost of owning and operating the dump truck is approximately $12,615.48.

Step-by-step explanation:

The equivalent annual cost of owning and operating the dump truck can be calculated using the formula for calculating annuities. First, we need to calculate the net cash flows for each year by subtracting the salvage value from the operating and maintenance cost. Then, we can use the formula:

Equivalent Annual Cost = [(Initial Cost - Salvage Value) + (Annual Operating and Maintenance Cost - Salvage Value) * (1 - (1 + Interest Rate)^-n)) / (Interest Rate)]

Plugging in the given values:

Initial Cost = $45,000

Operating and Maintenance Cost = $15,000 + ($2,000 * (n - 1))

Salvage Value = $9,000

Interest Rate = 0.12

n = 5

We can calculate the equivalent annual cost as:

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

Solving this equation gives a value of approximately $12,615.48.

Answer 2

The equivalent annual cost of owning and operating the truck is most nearly:

= $29,616.

Step-by-step explanation:

a) Data and Calculations:

Costs PV Factor Present Value

Year 0 Truck purchase $45,000 1 $45,000

Year 1 Operating &

maintenance cost 15,000 0.893 13,395

Year 2 O&M cost 17,000 0.797 13,549

Year 3 O&M cost 19,000 0.712 13,528

Year 4 O&M cost 21,000 0.636 13,356

Year 5 O&M costs 23,000 0.567 13,041

Year 5 Salvage value -9,000 0.567 -5,103

Total costs $106,766

Annuity factor at 12% after 5 years = 3.605

Equivalent annual cost = $29,616 ($106,766/3.605)