Problem 15 - Accounting

Question

A building with a cost of \( 750,000\) has an estimated residual value of \( 300,000\), 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 \(\$ 200,000\), what is the depreciation expense for each of the remaining 20 years?

Step-by-Step Solution

Answer

(a) $12,500 per year; (b) $500,000; (c) $15,000 per year.

Step 1: Understanding Straight-Line Depreciation

Straight-line depreciation spreads the cost of an asset evenly over its useful life. The formula to calculate annual depreciation is: \[ \text{Annual Depreciation} = \frac{\text{Cost of Asset} - \text{Residual Value}}{\text{Useful Life}} \] Here, the cost is \(750,000, the residual value is \)300,000, and the useful life is 36 years.

Step 2: Calculating Annual Depreciation

Using the formula: \[ \text{Annual Depreciation} = \frac{750,000 - 300,000}{36} = \frac{450,000}{36} \] This results in an annual depreciation of \(12,500\).

Step 3: Calculating Book Value After 20 Years

The book value is calculated by subtracting the accumulated depreciation from the original cost. After 20 years, the accumulated depreciation is: \[ 20 \times 12,500 = 250,000 \] The book value is then: \[ 750,000 - 250,000 = 500,000 \]

Step 4: Adjusting for Revised Useful Life and Residual Value

At the start of the 21st year, the remaining book value needs to be depreciated over the new estimated useful life. The new residual value is \(200,000 and the remaining life is now 20 years. The book value at the start of the 21st year is \)500,000. Calculate the depreciation: \[ \text{New Annual Depreciation} = \frac{500,000 - 200,000}{20} = \frac{300,000}{20} \] Results in a new annual depreciation of \(15,000\).

Key Concepts

Residual Value

Residual value, often known as salvage value, is the estimated amount that an asset is expected to be worth at the end of its useful life. It is an important consideration in depreciation calculations. When determining an asset's straight-line depreciation, the residual value is subtracted from the original cost to calculate how much of the asset's value will be depreciated over its useful life.
In our example, the building costs \( 750,000 \) and has a residual value of \( 300,000 \). This means the asset's depreciable amount is \( 450,000 \), which is calculated by subtracting the residual value from the total cost. This depreciable amount represents the total value that will be spread out and depreciated over the years.

Useful Life

The useful life of an asset is the span of time over which the asset is expected to be usable, with the efficiency and performance it was intended to offer. The useful life is a key component in calculating depreciation and helps in planning for asset replacement.
In our scenario, the building has a useful life of 36 years. This means that over the span of these 36 years, the gradual reduction in the building’s value, due to wear and tear or obsolescence, will be accounted for each year until it reaches the residual value.

Book Value

The book value of an asset represents its net value on the balance sheet after accounting for depreciation. It provides an estimate of the asset's value after depreciation has been deducted from its original cost over a certain period.
Calculating the book value involves subtracting accumulated depreciation from the cost of the asset. For example, after 20 years, the building's accumulated depreciation is \( 250,000 \), and so the book value is calculated as \( 750,000 - 250,000 = 500,000 \). This figure reflects how much of the original cost is deemed to still hold economic worth after 20 years of use.

Annual Depreciation Calculation

Annual depreciation calculation is the process of determining the amount to depreciate an asset every year. In straight-line depreciation, this is a constant amount each year.
For our building, the annual depreciation calculation is determined using the formula:

• Initial Computation: \[ \text{Annual Depreciation} = \frac{\text{Cost of Asset} - \text{Residual Value}}{\text{Useful Life}} \]

Plugging in the values, we have \( \frac{450,000}{36} = 12,500 \) as the annual depreciation before any changes are made to useful life or residual value.
When either the residual value or the useful life changes, as in the 21st year scenario, the depreciation needs to be recalculated to account for accurate financial reporting. The updated computation results in an annual depreciation of \( 15,000 \). This adjustment ensures that the asset's value is appropriately recorded according to the latest estimates of future utility and salvage potential.