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# Depreciation Study Notes for Chemical Engineering

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In the field of chemical engineering, understanding the concept of depreciation and its implications is essential for effective financial management. These study notes are designed specifically for chemical engineering students, providing in-depth knowledge and practical insights into depreciation methods and their application in the industry.

**Depreciation Study Notes for Chemical Engineering** cover a wide range of essential topics, including depreciation types, calculation methods, and their significance in assessing asset value over time. By studying these notes, you will gain a thorough understanding of how depreciation impacts financial statements, investment decisions, and tax considerations in the chemical engineering sector. These study notes will equip you with the necessary skills to accurately account for asset depreciation, plan for future asset replacements, and optimize financial performance within the dynamic chemical engineering landscape.

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Table of content

**Depreciation**

Depreciation represents the reduction in the market value of an asset due to age, wear and tear and obsolescence. The physical deterioration of the asset occurs due to wear and tear with the passage of time. Obsolescence occurs due to the availability of new technology or new product in the market that is superior to the old one and the new one replaces the old one even though the old one is still in working condition. Examples of tangible assets for which the depreciation analysis is carried out are construction equipment, buildings, machinery, vehicles, etc. The depreciation amount for an asset is usually calculated on a yearly basis. Depreciation is considered an expenditure in the cash flow of the asset, although there is no physical cash outflow. Depreciation affects the income tax to be paid by an individual or a firm as it is considered an allowable deduction in calculating the taxable income. Generally, the income tax is paid on taxable income which is equal to gross income less the allowable deductions (expenditures). Depreciation reduces the taxable income and hence results in lowering the income tax to be paid.

**Types of Depreciation**

The causes of depreciation may be physical or functional. Physical depreciation is the term given to the measure of the decrease in value due to changes in the physical aspects of the property. Wear and tear, corrosion, accidents, and deterioration due to age or the elements are all causes of physical depreciation. With this type of depreciation, the serviceability of the property is reduced because of physical changes. Depreciation due to all other causes is known as functional depreciation.

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**Depletion**

Capacity loss due to materials actually consumed is measured as **depletion.** Depletion cost equals the initial cost times the ratio of the amount of material used to the original amount of material purchased. This type of depreciation is particularly applicable to natural resources, such as stands of timber or mineral and oil deposits.

**Salvage Value**

Salvage value is the net amount of money obtainable from the sale of used property over and above any charges involved in removal and sale. If a property is capable of further service, its salvage value may be high. This is not

necessarily true, however, because other factors, such as the location of the property, existing price levels, market supply and demand, and difficulty of dismantling, may have an effect. The term salvage **value **implies that the asset can give some type of further service and is worth more than merely its scrap or junk value.

If the property cannot be disposed of as a useful unit, it can often be dismantled and sold as junk to be used again as a manufacturing raw material. The profit obtainable from this type of disposal is known as the **scrap, **or **junk, **value.

**Present Value**

The present value of an asset may be defined as the value of the asset in its condition at the time of valuation. There are several different types of present values, and the standard meanings of the various types should be distinguished.

### Book Value, or Unamortized Cost

The difference between the original cost of a property, and all the depreciation charges made to date is defined as the book value (sometimes called unamortized cost). It represents the worth of the property as shown on the owner’s accounting records.

**Market Value**

The price which could be obtained for an asset if it were placed on sale in the open market is designated as the market value. The use of this term conveys the idea that the asset is in good condition and that a buyer is readily available.

### Replacement Value

The cost is necessary to replace an existing property at any given time with one at least equally capable of rendering the same service is known as the replacement value.

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### Methods of Determining Depreciation

The commonly used depreciation methods are the straight-line depreciation method, declining balance method, sum-of-years-digits method and sinking fund method.

** Straight-line (SL) depreciation method**

It is the simplest method of depreciation. In this method, it is assumed that the book value of an asset will decrease by the same amount every year over its useful life till its salvage value is reached. In other words, the book value of the asset decreases at a linear rate with the time period.

The expression for annual depreciation in a given year ‘ m ‘ is presented as follows;

In equation (3.1), 1/n is the constant annual depreciation rate which is denoted by the term ‘d_{m}‘.

Since the depreciation amount is same every year, D_{1} = D_{2 }= D_{3 }= D_{4 }= ……… = D_{m}

The book value at the end of 1^{st} year is equal to the initial cost less the depreciation in the 1^{st} year and is given by;

BV |
(3.2) |

Book value at the end of 2^{nd} year is equal to book value at the beginning of 2^{nd} year (i.e. book value at the end of 1^{st} year) less the depreciation in 2^{nd} year and is expressed as follows;

BV |
(3.3) |

As already stated depreciation amount is the same in every year.

Now putting the expression of ‘BV_{1}‘ from equation (3.2) in equation (3.3);

BV |
(3.4) |

Similarly, the book value at the end of 3^{rd} year is equal to the book value at the beginning of 3^{rd} year (i.e. book value at the end of 2^{nd} year) less the depreciation in 3^{rd} year and is given by;

BV BV |
(3.5) (3.6) |

In the same manner the generalized expression for book value at the end of any given year ‘ m ‘ can be written as follows;

BV |
(3.7) |

**Declining balance (DB) depreciation method**

It is an accelerated depreciation method. In this method, the annual depreciation is expressed as a fixed percentage of the book value at the beginning of the year and is calculated by multiplying the book value at the beginning of each year with a fixed percentage. Thus this method is also sometimes known as the fixed percentage method of depreciation. The ratio of depreciation amount in a given year to the book value at the beginning of that year is constant for all the years of the useful life of the asset. When this ratio is twice the straight-line depreciation rate i.e., the method is known as the double-declining balance (DDB) method. In other words, the depreciation rate is 200% of the straight-line depreciation rate. Double-declining balance (DDB) method is the most commonly used declining balance method.

The depreciation in 1^{st} year is calculated by multiplying the initial cost (i.e. book value at the beginning) with the depreciation rate and is given by;

Now putting the expression of ‘ D 1 ‘from the above equation (3.8) in the above expression;

The depreciation in 2^{nd} year i.e. ‘ D_{2}‘ is calculated by multiplying the book value at the beginning of 2^{nd} year (i.e. book value at the end of 1^{st} year) with the depreciation rate ‘ d_{m}‘ and is given as follows;

Now putting the expression of ‘BV_{1}‘ from equation (3.9) in equation (3.10) results in the following;

Book value at the end of 2^{nd} year is equal to book value at the beginning of 2^{nd} year (i.e. book value at the end of 1^{st} year) less the depreciation in 2^{nd} year and is expressed as follows;

Now putting the expressions of ‘BV_{1}‘ and ‘D_{2}‘ from equation (3.9) and equation (3.11) respectively in the above expression results in the following;

Similarly the depreciation in 3^{rd} year i.e. ‘D_{3}‘ is calculated as follows;

Now putting the expression of ‘BV_{2}‘ from equation (3.12) in equation (3.13);

…..3.14

Book value at the end of 3^{rd} year is calculated as follows;

(3.15) |

In the same manner the generalized expression for depreciation in any given year ‘m ‘ can be written as follows (referring to equations (3.8), (3.11) and (3.14));

(3.16) |

Similarly the generalized expression for book value at the end of any year ‘m’ is given as follows (referring to equations (3.9), (3.12) and (3.15));

(3.17) |

The book value at the end of useful life i.e. at the end of ‘n ‘ years is given by;

(3.18) |

The book value at the end of useful life is theoretically equal to the salvage value of the asset. Thus equating the salvage value (SV) of the asset to its book value (BV_{n}) at the end of useful life results in the following;

(3.19) |

Thus for calculating the depreciation of an asset using the declining balance method, equation (3.19) can be used to find out the constant annual depreciation rate, if it is not stated for the asset. From equation (3.19), the expression for constant annual depreciation rate ‘d_{m}‘ from known values of initial cost ‘ P ‘ and salvage value (SV > 0) is obtained as follows;

(3.20) |

In the double-declining balance (DDB) method, for calculating annual depreciation amount and book value at the end of different years, the value of constant annual depreciation rate ‘d_{m}‘ is replaced by ‘2/n ‘ in the above-mentioned equations.

**Illustration -1**

The initial cost of a piece of construction equipment is Rs.3500000. It has a useful life of 10 years. The estimated salvage value of the equipment at the end of its useful life is Rs.500000. Calculate the annual depreciation and book value of the construction equipment using the straight-line method and double-declining balance method.

**Solution: **

The initial cost of the construction equipment = P = Rs.3500000

Estimated salvage value = SV = Rs.500000

Useful life = n = 10 years

**For the straight-line method**, the depreciation amount for a given year is calculated using equation (3.1).

The book value at the end of a given year is calculated by subtracting the annual depreciation amount from the previous year’s book value.

Book value at the end of 1^{st} year = Rs 3500000-Rs 300000 = Rs 3200000

Book value at the end of 2nd year = Rs 3200000-Rs 300000 = Rs 2900000

Similarly, the book values at the end of other years have been calculated in the same manner. The annual depreciation amount and book values at the end of the years using the straight-line depreciation method are presented in Table 3.1. For the straight-line method, the book value at the end of different years can also be calculated by using equation (3.7). For example, the book value at the end of 2^{nd} year is given by;

BV_{2} = Rs 3500000-2*300000 = Rs 2900000

**For the double-declining balance method**, the constant annual depreciation rate ‘d_{m}‘ is given by;

The book value at the end of a given year is calculated by subtracting the annual depreciation amount from the previous year’s book value.

Similarly, the annual depreciation and book value at the end of other years have been calculated in the same manner and are presented in Table 3.1.

The book value at the end of different years can also be calculated by using equation (3.17). Using this equation, the book value at the end of 2^{nd} year is given by;

**Table 3.1 Depreciation and book value of the construction equipment using the straight-line method and double-declining balance method**

**Sum-of-years-digits (SOYD) depreciation method**

It is also an accelerated depreciation method. In this method, the annual depreciation rate for any year is calculated by dividing the number of years left (from the beginning of that year for which the depreciation is calculated) in the useful life of the asset by the sum of years over the useful life.

The depreciation rate ‘d_{m}‘ for any year ‘m’ is given by;

(3.21) |

Where n = useful life of the asset as stated earlier

SOY = sum of years’ digits over the useful life =

Rewriting equation (3.21);

(3.22) |

The depreciation amount in any year is calculated by multiplying the depreciation rate for that year with the total depreciation amount (i.e. the difference between initial cost ‘P’ and salvage value ‘SV ‘) over the useful life.

Thus the expression for depreciation amount in any year ‘m ‘ is represented by;

(3.23) |

Putting the value of ‘d_{m}‘ from equation (3.21) in equation (3.23) results in the following;

(3.24) |

The depreciation in 1^{st} year i.e. ‘D_{1}‘ is obtained by putting ‘m ‘ equal to ‘1’ in equation (3.24) and is given by;

(3.25) |

The book value at the end of 1^{st} year is equal to the initial cost less the depreciation in the 1^{st} year and is given by;

Now putting the expression of ‘D_{1}‘ from equation (3.25) in the above expression results in the following;

(3.26) |

The depreciation in 2^{nd} year i.e. ‘D_{2}‘ is given by;

(3.27) |

Book value at the end of 2^{nd} year is equal to book value at the beginning of 2^{nd} year (i.e. book value at the end of 1^{st} year) less the depreciation in 2^{nd} year and is given by;

Now putting the expressions of ‘BV_{1}‘ and ‘D_{2}‘ from equation (3.26) and equation (3.27) respectively in the above expression results in the following;

(3.28) |

Similarly, the expressions for depreciation and book value for 3^{rd} year are presented below.

(3.29) |

(3.30) |

The expressions for depreciation and book value for 4^{th} year are given by;

(3.31) |

(3.32) |

Similarly, the expressions for depreciation and book value for 5^{th} year are given by;

(3.33) |

(3.34) |

The expressions for book value in different years are presented above to find out the generalized expression for book value at the end of any given year. Now referring to the expressions of book values BV_{1}, BV_{2}, BV_{3}, BV_{4}, and BV_{5 }in above mentioned equations, it is observed that the variable terms are ‘n ‘, ‘(2n- 1)’, ‘(3n -3)’, ‘(4n-6)’ and ‘(5n-10)’ respectively. These variable terms can also be written ‘(n +1- **1 **)’, ‘(2n+1 – **2 **)’, ‘(3n +1- **4 **)’, ‘(4n+1- **7 **)’ and ‘(5n+1- **11 **)’ respectively. The numbers 1, 2, 4, 7, and 11 in these variable terms follow a series and it is observed that the value of each term is equal to the value of the previous term plus the difference in the values of the current term and the previous term. On this note, the general expression for the value of ‘ term of this series is given by;

(3.35) |

Now the generalized expression for book value for any year ‘m ‘ is given by;

(3.36) |

In this method also, the annual depreciation during the early years is more as compared to that in the later years of the asset’s useful life.