Suppose a business purchases equipment for ​$17 comma 000 and depreciates it over 5 years with the​ straight-line method until it reaches its salvage value of ​$2000 ​(see the figure​ below). Assuming that the depreciation can be for any part of a​ year, answer the questions to the right.

Question

Years
Dollars
minus5000minus10 comma 000minus15 comma 000|2|4|6font size decreased by 2 17 comma 000font size decreased by 2 14 comma 000font size decreased by 2 11 comma 000font size decreased by 2 8000font size decreased by 2 5000font size decreased by 2 2000minus20 comma 000
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A coordinate system has a horizontal axis labeled Years from 0 to 6 in increments of 2 and a vertical axis labeled Dollars from 0 to 20000 in increments of 5000. A line segment falls from left to right from the plotted point (0, 17,000) to the plotted point (5, 2000) passing through the plotted points (1, 14,000), (2, 11,000), (3, 8000), and (4, 5000). Each point is labeled with its vertical coordinate.
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Answer 1

To understand the depreciation of the equipment using the straight-line method, we can break down the calculation and analyze the results step-by-step.

1. Initial Cost of Equipment: $17,000

2. Salvage Value: $2,000

3. Depreciable Amount: This is calculated as: \[ \text{Depreciable Amount} = \text{Initial Cost} - \text{Salvage Value} = 17,000 - 2,000 = 15,000 \]

4. Useful Life of Equipment: 5 years

5. Annual Depreciation Expense: This is calculated by dividing the depreciable amount by the useful life: \[ \text{Annual Depreciation} = \frac{\text{Depreciable Amount}}{\text{Useful Life}} = \frac{15,000}{5} = 3,000 \]

Now that we have the annual depreciation, we can summarize how much the equipment will be worth at the end of each year:

• At the End of Year 0:

  • Value = $17,000

• At the End of Year 1:

  • Value = $17,000 - $3,000 = $14,000

• At the End of Year 2:

  • Value = $14,000 - $3,000 = $11,000

• At the End of Year 3:

  • Value = $11,000 - $3,000 = $8,000

• At the End of Year 4:

  • Value = $8,000 - $3,000 = $5,000

• At the End of Year 5:

  • Value = $5,000 - $3,000 = $2,000 (this is the salvage value)

Now we can summarize the points for each year, which aligns with the figures you provided:

• Year 0: $17,000
• Year 1: $14,000
• Year 2: $11,000
• Year 3: $8,000
• Year 4: $5,000
• Year 5: $2,000

To answer related questions:

1. Description of the Plot: The line segment you described on the graph starts at the point (0, 17,000) and moves downward to (5, 2,000), representing the depreciation of the asset over time.

2. Interpretation of Depreciation: The depreciation expense reduces the book value of the asset evenly each year until it reaches its salvage value.

3. Impact of Partial Years: If the business were to sell or reassess the equipment value at any point before the end of year 5, the depreciation for the number of months used beyond the last complete year could be calculated proportionally. For example, if the equipment was used for 6 months into year 6, an additional depreciation expense of $1,500 (half of $3,000) would apply, making the ending value $0.

If you have specific questions related to this situation, please let me know!