Problem 44 - Elementary Algebra Within Reach

Question

A textile corporation buys equipment with an initial purchase price of \(\$ 750,000\). It is estimated that its useful life will be 3 years and at that time its value will be \(\$ 75,000\). The total depreciation is divided equally among the three years. (Depreciation is the difference between the initial price of an item and its current value.) What is the total amount of depreciation declared each year?

Step-by-Step Solution

Answer

The total amount of depreciation declared each year is $225,000.

Step 1: Identify given values

The initial price of the equipment is $750,000. The value of the equipment after 3 years will be $75,000. There is a 3-year period over which the depreciation occurs.

Step 2: Calculate Total Depreciation

We can calculate the total depreciation by subtracting the value of the equipment at the end of 3 years from its initial price. So, the total depreciation is \(750,000 - 75,000 = 675,000\). This is the total depreciation over 3 years.

Step 3: Calculate Annual Depreciation

We then divide total depreciation by the number of years (in this case, 3) to find the annual depreciation. \(\frac{675,000}{3} = 225,000\). So, the depreciation declared each year is $225,000.

Key Concepts

Initial Purchase Price

The initial purchase price is the amount spent to acquire an asset before it undergoes any depreciation. In our case, the textile corporation paid $750,000 to buy the equipment. This purchase price reflects the original value of the equipment to the company. It's crucial because it sets the base value from which depreciation will be calculated. Depreciation is essentially a method to allocate the cost of this initial price over the asset's useful life. This ensures that the expense is matched with the revenue it generates within a specific period.

Useful Life

Useful life refers to the period over which an asset is expected to remain usable and generate economic benefits for the company. For the equipment bought by the textile corporation, the useful life is estimated to be 3 years. During these 3 years, the equipment is expected to perform effectively before its value significantly decreases. Determining the useful life is important for calculating depreciation, as it determines over how many years the asset's cost will be spread. Keep in mind that the useful life can vary based on factors like usage intensity, maintenance, and technological advancements.

Annual Depreciation

Annual depreciation is the amount by which an asset's value decreases each year over its useful life. It shows how much of the asset's initial purchase price is expensed annually. To find this, we first calculate the total depreciation and then divide it by the useful life in years. For our equipment, the total depreciation is $675,000 over 3 years. When divided by 3, we get an annual depreciation of $225,000. This means the equipment's value reduces by $225,000 each year on financial statements. This systematic approach helps companies manage expenses related to asset wear and tear.

Total Depreciation

Total depreciation signifies the total reduction in asset value over its entire useful life. It is computed by subtracting the asset's value at the end of its useful life from the initial purchase price. In our scenario, the total depreciation for the equipment is calculated as $750,000 (initial price) minus $75,000 (end value), which equals $675,000. Total depreciation illustrates the overall decrease in the asset's value due to usage, wear, and obsolescence during the period it was useful to the company. This concept is pivotal for financial reporting and helps businesses understand asset utilization.