# Depreciation:

Depreciation simply means a decrease in the value/worth of an asset. Most of the assets are depreciated with time. For example, if you buy a cell phone worth $500 today and after one year of use, you want to sell your cell phone. Now the worth of your cell phone will not be $500, the reason is that you have used it for one year, it will not look, work and facilitate as a new phone. Therefore, the price will be less than the purchase price. This decrease in the worth of cell phone is termed as depreciation.

For example, the price of that cell phone after one year of usage is $250. If you sell this phone after two years, then the price will be depreciated more, maybe $125. This means that the asset depreciates with time, its value decreases with time. At one point, this cell phone will not be able to work, then the price of it will be $1 or nothing. We will see the methods of depreciation to know the price of the asset at any time instant. But before that, we will see the causes of Depreciation.

## Causes of Depreciation:

There are many causes of depreciation but some of the major and important causes are given below.

### 1) Physical Depreciation (Wear and Tear):

All the machines and appliances etc are subjected to wear and tear. We cannot eliminate it, it reduces the cost of the asset. Due to wear and tear the asset loses its original performance. Its ability to perform a certain task decreases with time. We can minimize the depreciation by proper maintenance and care.

### 2) Technological Depreciation (Obsolescence):

This is also the main factor, old technologies obsolete due to new technology. This is because new technology is cost-effective, more efficient and more effective. This will depreciate the old technology rapidly. Today new computers have a microprocessor and the old computers had vacuum tubes. No one will buy a vacuum tube computer today as the new technology is better than the old one.

### 3) Damage/Failure of Asset:

The assets may be damaged due to misuse and natural disasters as well. For example, if your cell phone is dropped from a certain height and is unable to work again. This reason can cause depreciation at a high rate. A light bulb may burn out due to excess voltage after that the light bulb will be of no use.

### 4) Depletion:

This depreciation occurs in natural resources. These resources deplete with time such as coal mines and oil wells etc. Hence due to the depletion of the valuable product, the asset value is decreased.

### 5) Effusion of Time:

The value of an asset decreases with time whether we use it or not. The reason is with the advancement the technology and wear and tear etc. Therefore, the old asset does not worth it as its beginning.

## Useful Terms:

### Initial Basis or First Cost:

It includes the cost of purchase, shipping, and installation.

### Purchase Price:

The price at which an asset is purchased. Sometimes the purchase price and the first cost mean the same thing.

### Book Value:

The remaining undepreciated value of the asset after intervals is termed as Book Value. For example, it can be the value of an asset after three years of use or five years of use. It is found by subtracting the depreciated amount from the first cost or purchase value. Initially, the book value of an asset when depreciation has not occurred is equal to the Purchase Price or the First Cost.

### Useful Life:

It is the life of the asset till which it can give the performance and can be beneficial for the owner. After completion of useful life, the asset is not economically feasible to use.

### Salvage Value:

The value of an asset after its useful life is termed as Salvage value. It is the value of an asset at its disposal. It can be zero, positive and negative as well. The negative value means that we need more money to dispose it. For example, if you have machinery fitted and after its useful life, it is of no use. You must spend for dismantling the machinery and transport cost as well.

## Methods of Deprecation:

There are many methods of depreciation, but we will cover the most commonly used methods. The methods in consideration are,

- Straight Line Depreciation Method
- Declining Balance Depreciation Method
- SOYD Depreciation Method
- MACRS (Modified Accelerated Cost Recovery System)

### a) Straight Line Depreciation Method:

It is the simplest method of depreciation. In this method, the annual depreciation remains the same throughout the useful life. For example, if the depreciation in the first year is $1000 then it will be as same as in the fifth year as well. The depreciation is constant.

The annual depreciation charge can be given as,

The book value at nth interval can be given as,

Where,

DC = Depreciation Charge

BV = Book Value

P = First Cost

S = Salvage Value

N = Intervals of Useful Life

n = No of intervals passed

#### Example 1:

A person has purchased machinery for the cost of $100,000. The useful life of the machinery is said to be 20 years. The salvage value will be $0. Calculate the Annual depreciation charge and the book value at each interval using the Straight Line Depreciation Method.

#### Solution:

The Annual Depreciation Charge can be found as,

This means the value of the asset will be depreciated by $5000 after each year.

Hence the book value of the asset after one year can be found as,

The book value of the asset after three years can be found as,

Similarly, the Book value at each year can be found.

Notice that the value at the book value at the end of useful life is $0 which is Salvage Value.

#### Example 2:

An asset is purchased at a cost of $15,000. It has a useful life of 7 years and has a salvage value of $1000. Calculate the Annual depreciation charge and the book value at each interval using the Straight Line Depreciation Method.

#### Solution:

The Annual Depreciation Charge can be found as,

This means the value of the asset will be depreciated by $2000 after each year.

Hence the book value of the asset after one year can be found as,

The other value can be found in a similar fashion as,

The Book value at after useful life is $1,000 which is the salvage value.

### b) Declining Balance Depreciation Method:

In this method, the asset is depreciated faster in its early life. In other words, depreciation is higher in the early life of an asset than ending life. The annual depreciation is found by taking the percentage of the book value at the start of the year. A fixed percentage value is set throughout the useful life.

The annual depreciation at interval ‘n’ can be found as,

The Book Value at the end of each year can be found as,

Where,

DC = Depreciation Charge

BV = Book Value

X% = Depreciation rate per year

n = No of intervals passed

Notice that we do not need the salvage value in this method.

#### Example 3:

An asset has purchase cost/first cost $10,000 and it has an estimated useful life of five years. The deprecation rate per year is 20%. Calculate the Annual Depreciation and Book value of each year by the Declining Balance Method.

#### Solution:

The Depreciation Charge for the first year can be found as,

We know that BV_{0} = Purchase Price, therefore,

The Book value can be found as,

Now the Depreciation Charge for the Second year can be found as,

The Book Value for the second year will be,

Similarly, we can find the book values and deprecation charges for other years as well.

The Salvage value of the asset is found to be $ 3,276.6

### Switching of the Declining Balance Method to Straight Line Method:

The asset depreciates faster in its early life in Declining Balance method which is beneficial because an asset has the best performance in its early life. Due to the best performance in early life, the asset can produce more profit and recover more. Near to the end of useful life, the asset can recover less, therefore, there should be lesser depreciation in the end. The Straight Line method lacks this feature of fast depreciation in early life. The problem with the Declining Balance method is that it does not includes Salvage Value. Therefore, the obtained salvage value is usually not equal to the estimated salvage value. The problem arises when the estimated salvage value is zero and by using the declining method we end up having salvage value greater than zero. Let’s see this with an example.

#### Example 4:

An asset is purchased at a cost of $5,000. The asset has a useful life of 7 years and the estimated salvage value is zero. The depreciation rate per year is 30%. Calculate the Book Value at the end of each year by the Declining Balance Method.

#### Solution:

The salvage value is found to be $411.7715 but the expected was zero. This is a drawback of this method. In Straight Line depreciation, we include salvage value and the salvage value is always equal to the expected one.

Hence both the methods have one drawback. The Straight Line is good for the ending life and the Declining method is good for starting life. Therefore, to overcome this problem we use both the methods together.

We will use the Declining Balance Method for the early years of useful life and Straight-Line method in the ending years of useful life. There will be switching between these two methods. The interval where we will switch can be determined easily be calculating depreciation by both the methods. When the depreciation by the Declining Method is less than the Straight-Line method, we will switch.

**Switching Condition: Deprecation by Declining Balance < Depreciation by Straight Line**

#### Example 5:

We will consider example 4 and switch the method at the required interval.

#### Solution:

You can see at the 5^{th} interval the Straight-Line Depreciation is more than the Declining Balance. Hence this is the switching point. We will do the same example to achieve zero salvage value as,

Hence, we have switched from Declining Balance to Straight Line and the salvage value is zero approximately.

### c) SOYD Depreciation Method:

SOYD means Sum of year digits. This method uses the fractional value of the Purchase Value for depreciation. The denominator of the fraction is the sum of the year and the numerator is the value of years in the in descending order. If the useful life is 10 years then, the sum of the year digits (SOYD) will be 1+2+3+4+5+6+7+8+9+10=55. The annual depreciation fractions will be as 10/55, 9/55, 8/55,… ., 10/55. This method takes care of Salvage Value as well.

The Depreciation Charge can be given as,

The Book Value can be given as,

#### Example 6:

An asset costs $10,000 and it has a useful life of 10 years. The salvage value is $1,000. Calculate book value after each year using SOYD Method.

#### Solution:

In this method, the obtained Salvage Value is as same as the estimated one.

### d) MACRS (Modified Accelerated Cost Recovery System)

In MACRS there are certain rules for all types of property and assets according to their useful life and we are not going to discuss those. This method can follow the Declining Balance Method in which the switching occurs to Straight Line Depreciation. Here we are going to discuss the MACRS by using recovery percentages provided by Internal Service Revenue (ISR). There is no difference in the result whether you use the Declining method or the percentages provided by ISR. But using percentage is an easier method to do so. The percentages are obtained from the Declining Balance Method and tabulated to make work easier. The table is given below,

There are percentages given for each year and these are multiplied with the First Cost every time. You can notice that the number of percentages is one more than the year. This is due to the half-year convention. In this convention, the asset is depreciated for a half year in the first year and the remaining is depreciated in the last year.

#### Classification of Property/Assets:

The assets are classified and standardized for specific useful life. Here some important assets are listed only.

#### Example 7:

A person purchased a car for $10,000. After its useful life, its value will be zero. Calculate the book value at the end of each year.

#### Solution:

Car is classified as 5-year property. Using the table, we can calculate annual depreciation and book values.

## Endnote:

We have discussed all the basic types of depreciation that are used. This is one of the most important topics in Engineering Economics. Depreciation is regulated by Governments for Tax as well. We have just discussed the methods and examples. Feel free to ask a question and share this article if you found this helpful.