Problem 15 - Accounting

Question

A building with a cost of \(1,050,000 has an estimated residual value of \)420,000, has an estimated useful life of 36 years, and is depreciated by the straight-line method. (a) What is the amount of the annual depreciation? (b) What is the book value at the end of the twentieth year of use? (c) If at the start of the twenty-first year it is estimated that the remaining life is 20 years and that the residual value is $300,000, what is the depreciation expense for each of the remaining 20 years?

Step-by-Step Solution

Answer

(a) \(17,500\); (b) \(700,000\); (c) \(20,000\) per year.

Step 1: Calculate Initial Depreciation

To calculate the annual depreciation using the straight-line method, subtract the residual value from the cost of the building, then divide by the useful life. \[ \text{Annual Depreciation} = \frac{1,050,000 - 420,000}{36} = \frac{630,000}{36} = 17,500 \] The annual depreciation is \(17,500\).

Step 2: Calculate Book Value After 20 Years

To find the book value at the end of the 20th year, calculate the total depreciation for 20 years and subtract it from the initial cost.\[ \text{Total Depreciation for 20 Years} = 17,500 \times 20 = 350,000 \]\[ \text{Book Value at Year 20} = 1,050,000 - 350,000 = 700,000 \] The book value at the end of the 20th year is \(700,000\).

Step 3: Recalculate Depreciation for Remaining 20 Years

Starting the 21st year, the building has a new estimated useful life and residual value. Subtract the new residual value from the book value and divide by the remaining useful life.\[ \text{Annual Depreciation for Remaining Years} = \frac{700,000 - 300,000}{20} = \frac{400,000}{20} = 20,000 \]The depreciation expense for each of the remaining 20 years is \(20,000\).

Key Concepts

Straight-Line Depreciation

Straight-line depreciation is one of the most commonly used methods to account for the loss in value of an asset over time. It's popular because it's straightforward and easy to calculate. Here's how it works: subtract the asset's residual value from its initial cost, and then divide the result by the asset's useful life.

For example, if you purchase a building costing $1,050,000 with an estimated residual value of $420,000 and a useful life of 36 years, the annual depreciation expense can be calculated as follows:

• Subtract the residual value ( $420,000 ) from the cost ( $1,050,000 ), resulting in $630,000 .
• Divide $630,000 by 36, which totals to $17,500 .

Each year, the building would decrease in value by $17,500 , reflecting this consistent decline until the end of its useful life.

Residual Value

Residual value, also known as salvage value, is the estimated amount that an asset is expected to be worth at the end of its useful life. It plays a crucial role in calculating depreciation because it represents the portion of the asset cost that will not be depreciated.

In the exercise, the building's initial residual value was estimated at $420,000 after 36 years. This means that when the building reaches the end of its intended use, it should still have a worth of $420,000 in some capacity, be it in resale value or utility from parts.

Understanding residual value helps ensure that the asset’s depreciation reflects a realistic loss in value without overstating the decline, aiding in accurate financial reporting and planning.

Useful Life

Useful life is the duration over which an asset is expected to be functional and economically viable for its intended purposes within a company. This term helps determine the annual depreciation expense.

• It directly influences the straight-line depreciation calculation. A longer useful life means smaller annual depreciation expenses, spreading the cost of the asset over a prolonged period.
• Conversely, a shorter useful life increases the annual depreciation expense, with the asset cost being amortized more quickly.

For instance, the building in question had an original useful life of 36 years. However, useful life estimates can change. By the 21st year, it was estimated to have 20 more years of remaining life, necessitating a recalculated depreciation to accommodate changes in usage or expected longevity.

Book Value

Book value represents an asset's carrying value on a company's balance sheet and is calculated as the asset's original cost minus accumulated depreciation. It's an essential figure for understanding the real-time worth of an asset.

• After 20 years of use, the building in the exercise had its book value calculated by subtracting the total depreciation ( $350,000 ) from the original cost ( $1,050,000 ), resulting in a book value of $700,000 .

At any point, the book value reflects how much of the asset has been depreciated, indicating how much of its cost has been "used up" over the years. Adjustments to future depreciation based on changes in residual value or extended useful life further refine this measure to align it with ongoing business realities. This ensures that the book value is adjusted accordingly, providing accurate insights into the asset's current financial standing.