Eight years ago, Ohio Valley Trucking purchased a large-capacity dump truck for $124,000 to provide short-haul earth-moving services. The company sold it today for $45,000. Operating and maintenance costs averaged $11,300 per year. A complete overhaul at the end of year 3 costs an extra $3600.

Calculate the annual cost of the truck at i = 8% per year. (Include a minus sign if necessary).

The annual cost of the truck is $

We can calculate the annual cost of the truck using the **Equivalent Uniform Annual Cost (EUAC)** method. Here's how the calculation proceeds:

### Step 1: Calculate the Present Value (PV) of the truck's initial purchase
The truck was purchased for $124,000 eight years ago. The salvage value today is $45,000.

The **net initial cost** of the truck (without considering operating and maintenance costs) can be computed as the difference between the present worth of the initial investment and the present worth of the salvage value. Both must be discounted over 8 years at 8% interest.

#### Present Value of the purchase:
The purchase cost is already at present value, so no adjustment is needed:
\[
\text{PV of purchase} = 124,000
\]

#### Present Value of the salvage value:
The salvage value is $45,000 after 8 years. We discount it back to the present using the formula:
\[
\text{PV of salvage value} = \frac{45,000}{(1 + 0.08)^8}
\]
\[
\text{PV of salvage value} = \frac{45,000}{1.85093} \approx 24,311.78
\]

#### Net Present Value (NPV) of truck's cost:
\[
\text{NPV} = 124,000 - 24,311.78 = 99,688.22
\]

### Step 2: Convert NPV to Equivalent Uniform Annual Cost (EUAC)
We now convert the NPV into an annual cost using the **capital recovery factor** (CRF). The formula for CRF is:
\[
\text{CRF} = \frac{i(1 + i)^n}{(1 + i)^n - 1}
\]
where:
- $i = 0.08$
- $n = 8$ years

\[
\text{CRF} = \frac{0.08(1.08)^8}{(1.08)^8 - 1} = \frac{0.08 \times 1.85093}{1.85093 - 1} = \frac{0.14807}{0.85093} \approx 0.17395
\]

So, the annual cost for the capital investment:
\[
\text{Annual capital cost} = 99,688.22 \times 0.17395 \approx 17,334.93
\]

### Step 3: Add Operating and Maintenance Costs
The annual operating and maintenance costs are $11,300 per year. In addition, there was an overhaul at the end of year 3 costing $3,600. We need to annualize this overhaul cost as well.

#### Present Value of the overhaul:
The overhaul happened in year 3, so we discount it back to the present:
\[
\text{PV of overhaul} = \frac{3,600}{(1.08)^3} = \frac{3,600}{1.25971} \approx 2,857.31
\]

Now, convert this present value into an annualized cost using the CRF from above:
\[
\text{Annual overhaul cost} = 2,857.31 \times 0.17395 \approx 497.01
\]

### Step 4: Total Annual Cost
Now, we sum up the annual capital cost, annual operating and maintenance cost, and annual overhaul cost to get the total annual cost:
\[
\text{Total annual cost} = 17,334.93 + 11,300 + 497.01 = 29,131.94
\]

Thus, the annual cost of the truck is approximately **$29,131.94**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does changing the interest rate affect the Equivalent Uniform Annual Cost?
2. What is the impact of the salvage value on the overall cost?
3. How would the EUAC change if the overhaul occurred at a different time?
4. Can the capital recovery factor formula be used in different financial contexts?
5. What happens to the EUAC if operating costs increase each year?

**Tip:** Always factor in future expenses (like overhauls) into today's costs using present value discounting methods for accurate financial planning.

Eight years ago, Ohio Valley Trucking purchased a large-capacity dump truck for $124,000 to provide short-haul earth-moving services. The company sold it today for $45,000. Operating and maintenance costs averaged $11,300 per year. A complete overhaul at the end of year 3 costs an extra $3600. Calculate the annual cost of the truck at i = 8% per year. (Include a minus sign if necessary).

Learn how to calculate the annual cost of a dump truck purchased for $124,000, sold for $45,000 after 8 years, and with maintenance and overhaul costs included. The solution covers Equivalent Uniform Annual Cost (EUAC) methods, capital recovery factor, and present value discounting. Suitable for college-level finance or engineering economics students.

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