Question

A truck acquired at a cost of $400,000 has an estimated residual value of $24,100, has an estimated useful life of 42,000 miles, and was driven 4,200 miles during the year. Determine the following. If required, round your answer for the depreciation rate to two decimal places.

Line Item Description Amount
(a) The depreciable cost $fill in the blank 1

(b) The depreciation rate $fill in the blank 2
per mile
(c) The units-of-activity depreciation for the year $fill in the blank 3

Answer 1

To determine the required amounts, we will go through the calculations step by step:

### (a) The Depreciable Cost
The depreciable cost is calculated as the acquisition cost minus the estimated residual value.

\[
\text{Depreciable Cost} = \text{Cost} - \text{Residual Value}
\]
\[
\text{Depreciable Cost} = 400,000 - 24,100 = 375,900
\]

### (b) The Depreciation Rate
The depreciation rate per mile is calculated by dividing the depreciable cost by the estimated useful life in miles.

\[
\text{Depreciation Rate} = \frac{\text{Depreciable Cost}}{\text{Estimated Useful Life}}
\]
\[
\text{Depreciation Rate} = \frac{375,900}{42,000} \approx 8.95
\]

### (c) The Units-of-Activity Depreciation for the Year
To find the units-of-activity depreciation for the year, multiply the depreciation rate by the number of miles driven during the year:

\[
\text{Units-of-Activity Depreciation} = \text{Depreciation Rate} \times \text{Miles Driven}
\]
\[
\text{Units-of-Activity Depreciation} = 8.95 \times 4,200 \approx 37,590
\]

### Summary of Results
- (a) The depreciable cost: **$375,900**
- (b) The depreciation rate: **$8.95 per mile**
- (c) The units-of-activity depreciation for the year: **$37,590**

Here are the answers summarized:
- **(a)** $375,900
- **(b)** $8.95
- **(c)** $37,590