Created byBogna SzykyThomas the only son, doctor

review by

Jack Bowwater

Based on research from

Cyprus T. *"Financial and Insurance Formulas"*(2006)

Last update:

February 2, 2023

- What is depreciation? — the definition of depreciation
- depreciation methods
- Residual value and depreciation
- car depreciation calculator
- How to use our depreciation calculator?
- fixed depreciation
- declining depreciation
- Sum of Digit Years Depreciation

The Depreciation Calculator uses three different methods to estimate how quickly an asset's value declines over time.

You can use it to compare three models:**Straight line depreciation**,**declining balance amortization**, you**the sum of the digits of the years of depreciation**- to decide which one suits you best. Keep reading to find answers to the following questions:

- What is depreciation and what does depreciation mean?
- What are the most common depreciation methods?
- What is residual value?
- How to calculate depreciation? especially how to calculate
**fixed depreciation**? how do you calculate it**declining balance amortization**and how to calculate**sum of digits of years depreciation**?

In this article, you'll learn how to calculate depreciation expense and how to calculate accumulated depreciation.

## What is depreciation? — the definition of depreciation

Imagine you bought a personal computer for a certain price. After a few months, you decide you'd like to sell it. The problem is, you're not sure how much you're worth right now. Hepresent valuecomputer is definitely less than the amount you bought a few months ago. An economist would say here that your computer has**depreciated**During the last few months. Thus, we can say that the fundamental concept of depreciation is to reflect the**decrease in value**of an asset over time due to factors such as wear and tear and the introduction of new and better products to the market.

The most formal definition of depreciation says that it is**the method of calculating the cost of an asset over its useful life**. In accounting, depreciation is understood as a method of reallocating the cost of a tangible asset over its useful life. To fully understand this approach, let's study the following situation.

When a company purchases a large-value tangible asset (for example, machinery or a vehicle), such a large expense can have a significant effect on the company's annual income statement. So, to ignore wild swings on the income statement, the purchase of expensive assets is smoothed out on the books by showing the asset as an expense over its useful life. This means that, each year, only a portion of an asset's value is recorded as a current expense. This approach allows the company to spread the cost evenly over the period of use.

## depreciation methods

In practice, various methods are used to calculate depreciation. These methods can be based on the passage of time or the degree of use of the asset. The following depreciation methods can be applied to different types of tangible assets:

- Fixed depreciation?
- declining balance method;
- double declining balance method.
- Annuity depreciation?
- Year digit sum method.
- Production unit depreciation method?
- Return time units?
- Depreciation group method? It is
- Compound depreciation method.

Remember that, at the end of an asset's useful life, the total amount of its depreciation will be the same, regardless of the depreciation method used. The only difference between the different amortization methods is time (the amount of money amortized over shorter periods).

In the next part of this text, we will focus on describing the three most commonly used types of depreciation: straight-line depreciation, declining-balance depreciation, and sum-of-years depreciation. We will see in particular the types of depreciation and the detailed explanation of how to calculate the amount of depreciation with each of them.

## Residual value and depreciation

As already mentioned, residual value (residual value) is an estimated amount of money that an asset will be worth after the planned number of years of use. Of course, in real life it is impossible to accurately predict the exact salvage value of an asset after a given number of years.

This means that residual value is only approximate. However, in accounting, this approach is just a kind of transition because when you sell an asset, if the cash received for it is greater than its net book value (original value minus accumulated depreciation), you must record a profit in sale. On the other hand, if you sell an asset below its net book value, you must record a loss on the sale.

Note here that if this number of years of use equals the lifespan of the product, then the residual value is zero.

## car depreciation calculator

Undoubtedly, one of the most interesting cases of depreciation is the loss of value of a motor vehicle. As you may know, the value of a new car drops dramatically when it leaves the dealership. Experts say that the value of a car is reduced to 91% of its original value at the time of purchase! In subsequent years, the value of the car decreases, until after several years (about 10-11) it becomes useless. Obviously, you will still be able to sell it. However, its market value will be very low. To avoid the hassle of selling a used car, many people preferrent a carthese days instead of buying one.

If you are interested in detailed car depreciation calculations, check out ourcar depreciation calculator. It uses a more car-specific template.

## How to use our depreciation calculator?

Smart Depreciation Calculator allows you to calculate annual depreciation and determine the value of an asset after a certain period of time. Annual depreciation is calculated using the three most widely used methods: straight-line depreciation, declining balance depreciation, and sum-of-years depreciation.

To get results using our calculator, all you have to do is fill in four fields:

**initial cost**— the original value of the asset (purchase price).**residual dexterity**— an estimated amount of money an asset will be worth at the end of its useful life (generally assumed to be zero, for more information see sectionResidual value and depreciation).**Life**— The estimated number of years the asset is likely to remain in use.**Final book value after...**— In this field, you must indicate the year from which you intend to calculate the book value of the asset.

And that is! At one point, the depreciation calculator calculates three depreciation variances. If you are curious about how it works, you should familiarize yourself with the types of depreciation described in the following sections of the article. Each type uses the same set of symbols:

- $\text{OV}$VOis the original cost (value) of the asset,
- $\text{RV}$motor houseis the residual value of the asset,
- $norte$norteis the useful life of the asset,
- $subway$subwayis the number of years between the purchase of the asset and the date on which you intend to sell it, which corresponds to the
*Final book value after...*on the calculator.

## fixed depreciation

The least complicated depreciation model is straight-line depreciation. In this model, you must apply the following type of depreciation:

$\small\text{gaso anual} = \frac{\text{OV} -\text{RV}}{n}$annual expense=norteVO−motor house

In this model, the asset loses value at a constant rate. Each year, the depreciation expense is exactly the same. While this is not the most accurate description of depreciation, it is often used because of its simplicity.

If you want to calculate the final book value of your asset after a certain number of years, use this equation:

$\small\text{valor final em livros} \\ = \text{OV} - m \times \frac{\text{OV} - \text{RV}}{n}$final book value=VO−subway×norteVO−motor house

Keep in mind that you don't need to calculate this value manually. you can plug the amounts into this straight-line depreciation calculator and let it do the math for you.

## declining depreciation

The second model that describes depreciation is declining depreciation. Each year, the expense is calculated as a percentage of the asset's book value in the previous year. You can write it as

$\small \text{gaso anual} \\ = p\times\text{OV} \times (1 - p)^{m - 1}$annual expense=p×VO×(1−p)subway−1

where$p$pis the depreciation rate expressed as a percentage. This interest rate can be calculated for an asset with a known useful life and a residual value other than zero using:

$\small p = 1 - (\text{RV}/\text{OV})^{1/n}$p=1−(motor house/VO)1/norte

Our declining balance depreciation calculator can also figure out the final book value of your asset after a certain number of years. Use the following equation:

$\small \text{valor final contável} = \text{OV} \times (1 - p) ^ m$final book value=VO×(1−p)subway

This method gives results much closer to reality than when using the fixed depreciation model. However, it has its limits: the biggest problem with this method is its complexity.

## Sum of Digit Years Depreciation

The last method is an accelerated depreciation model which assumes that depreciation decreases with each passing year. Instead of a fixed depreciation rate, it allocates a fraction of the total depreciation cost over each year of the asset's useful life.

To use this model, you must calculate the depreciation base according to the formula.

$\small d = (\text{OV} - \text{RV})$No=(VO−motor house)

Then you need to divide it by the sum of the number of years before your salvage value reaches zero:

$\small D = d / (1 + 2 + 3 + ... + n)$No=No/(1+2+3+...+norte)

Number$(1 + 2 + 3 + ... + n)$(1+2+3+...+norte)is a sum of a finitenumerical sequenceand therefore can be calculated as

$\little 1 + 2 + 3 + ... + n \\ = (n + 1) \times \frac{n}{2}$1+2+3+...+norte=(norte+1)×2norte

After calculating your value$No$No, you can use the following depreciation formula to find the annual expense:

$\small \text{annual costs} \\ = D \times (n - m + 1)$annual expense=No×(norte−subway+1)

It means that if the useful life of your asset is equal to 5 years, in the first year the expense will be equal to$\frac{5}{15}$155of the depreciation base. In the second year, it will be equal to$\frac{4}{15}$154from the base, during the third to$\frac{3}{15}$153, etc. All these fractions must be added$1$1.

The Sum of Years Digits Calculator can also be used to find the final book value:

$\small \text{valor final em livros} \\ = \text{OV} - Dmn - \frac{D m \times (m - 1)}{2}$final book value=VO−NoMinnesota−2Nosubway×(subway−1)

If you use this method, your initial depreciation cost will be significantly higher than in later years. Also, keep in mind that most tax systems do not allow this model to be used.

Bogna SzykyThomas the only son, doctor