In this article, we explain method of calculating depreciation like sinking fund method, straight line method, constant percentage method with solved examples.

Table of Contents

**What is Depreciation?**

Depreciation is the gradual exhaustion of the usefulness of a property. This is defined as the **decrease in the value of property structural deterioration use, life wear and tear, decay, and obsolescence.**

The value of property decreases every year till the life of property due to depreciation.

The rate of depreciation is depends on following condition.

- Initial Condition
- Quality of Maintenance
- Mode of Use

**The annual decrease of value of property **due to decayed, damaged, wear & tear deterioration, obsolescence, etc., **is known as annual depreciation.**

**Also Check: ****How to Calculate Quantity of Concrete | Concrete Quantity Calcula**tor

**Method of calculating depreciation**

Method of calculating depreciation are as follows

- Straight Line method
- Constant percentage method
- Sinking Fund Method
- Quantity Survey Method

**1. Straight Line Method:**

In straight line method it is assumed that the property loses its value by the same amount every year.

A Fixed amount of the original cost is deducted every year, so that at the of the utility period only the scrap value is left.

The formula for finding depreciation using straight line method is given below.

**Annual depreciation (D) = (Original cost – Scrap value) / (Life in year)**

= (C – S) / n

Where,

- C = original cost
- S = scrape value
- n = life of property in years
- D = annual depreciation

**The book value after the number of years = original cost – (Number of year × depreciation)**

**Example of Straight line method:**

The present value of machine is Rs. 2,50,000 workout the depreciated cost at the end of 7 year if the salvage value is Rs. 20,000. Assume the life of machine 18 years. Use straight line method for finding depreciation.

**Solution:**

- C = 2,50,000 Rs.
- S = 20,000 Rs.
- n = 18 years

Using straight line method,

**Annual depreciation,**

= (C – S) / n

= ( 250000 – 20000 ) / 18

= 12778 Rs.

**Total depreciation after 7 year**

= 7 × 12778

= 89446 Rs.

**Depreciated cost after 7 years**

= 250000 – 89446

= 160554 Rs.

**Also Check: Brickwork Calculator**

**2. Constant Percentage Method:**

Constant percentage method is also known as Declining balance method.

In this method, it is assumed that the property will lose its value by a constant percentage of its value at the beginning of every year.

The formula of finding annual depreciation using Constant percentage method is given below.

**Annual depreciation (D) = 1 – (S/C) ^{1/n}**

Where,

- C = original cost
- S = scrape value
- n = life of property in years
- D = annual depreciation

The value of the property of the depreciated cost at the end of the** first year, (C _{1}) = C – DC**

The value of the property at the end of the **second year (C _{2}) = C_{1} – DC_{1}**

The value of the property or the depreciated cost at the** end of the m years = C × (S/C) ^{m/n}**

The formula will fail when S=0, when the ratio S/C is very small, the depreciation for the first year will be considerable.

**Example of Constant percentage method:**

Using above example data,

- C = 2,50,000 Rs.
- S = 20,000 Rs.
- m = 7 years
- n = 18 years

**Depreciated cost after 7 years**

= C × (S/C)^{m/n}

= 250000 × (20000 / 250000)^{(7/18)}

= 93600 Rs

**Depreciated cost after 7 years**

= 250000 – 93600

=156400 Rs.

**Also Check: Different Rate analysis sheets of Civil Engineering**

**3. Sinking Fund Method:**

In the sinking fund method, the depreciation of property is assumed to be equal to the annual sinking fund plus the interest on the fund for that year, which is supposed to be invested on interest-bearing investment.

If A is the annual sinking fund and b, c, d, etc., represent interest on the sinking fund for the subsequent year, and C = total original cost.

At the end of | Depreciation for the year | Total Depreciation | Book Value |
---|---|---|---|

1st year | A | A | C – A |

2nd year | A+b | 2A+b | C – (2A +b) |

3rd year | A+b+c | 3A+b+c | C – (3A+b+c) |

4th year | A+d | 4A+b+c+d | C – (4A+b+c+d) |

**Example of Sinking Fund method:**

Find out present value of building, which was constructed 15 years before at a cost of 500000/-. Assuming life of building is 50 years, rate of interest 10% and scrap value 8% of construction cost.

**Solution:**

C = 500000 Rs.

S = 0.08 × 500000

= 40000 Rs.

**Total amount of sinking fund required**

( C – S ) = 500000 – 40000

= 460000 Rs.

**Sinking Fund coefficient for 50 years:**

P = (i) / (1+ i)^{n} – 1

= 0.10 / (1+0.10)^{50} – 1

= 0.000859

Q = ((1+ i)^{n} – 1) / (i)

= ((1+0.10)^{15} – 1) / 0.10

= 31.77

Therefore,

**Rate of depreciation in 15 years**

= P × Q

= 0.000859 × 31.77

= 0.02729

**Total depreciation in 15 years**

= 0.02729 × 460000

= 12553 Rs.

**Present value of building**

= 500000 – 12553

= 487447 Rs.

**Also read: What is estimate? Different types of estimates in civil engineering**

**4. Quantity Survey Method:**

In quantity survey method the property is studied in details and loss in value due to life, wear and tear, decay, obsolescence, etc., worked out.

Each and every step is based on some logical ground without any fixed percentage of the cost of the property.

An only experienced valuer can work out the amount of depreciation and the present value of the property by this method.