In what method of computing depreciation where it assumes that the loss in value is directly proportional to the age of the equipment or assets?

This article throws light upon the top six methods for calculating depreciation of an asset. The methods are: 1. Straight Line Method 2. Diminishing Balance Method 3. The Sum of Years Digit Method 4. Sinking Fund Method 5. Annuity Charging Method and 6. Machine Hour Basis Method.

1. The Straight Line Method:

This is the simplest of all the methods available for calculation of depreciation cost. This method provides depreciation by means of equal periodic charges over the assumed useful life of the asset.

The method assumes that the equipment/machine will wear out at the same rate over its economic life. It means one should deduct the scrap value of the asset from its original value and divide the remainder by the number of years of its economic life which gives annual depreciation charges.

Let Ci = initial cost of a machine.

Cs = scrap value of the machine.

N = number of years of economic or useful life of the machine.

D = depreciation charges per year.

Then D = Rs Ci/Cs/N

Advantages:

(i) The method is simple and easily understandable.

(ii) It recognises the fact that usage of asset with time is a major factor in depreciation calculations and the decline in value of an asset is directly proportional to its age.

(iii) The method requires little efforts for depreciation calculations.

Limitations:

(i) The method is unrealistic since the assets do not wear out at same rate during their life.

(iii) The repair and maintenance costs tend to increase during the later life of the asset/equipment so it is better to charge higher rates of depreciation during earlier life of the machine.

Example 1:

A furnace was purchased for Rs. 500000 and Rs. 50000 more were spent on its erection and commissioning. The estimated salvage value after ten years was Rs. 5000.

(ii) Calculate the annual rate of depreciation.

(ii) Determine the depreciation fund collected at the end of six years after the purchase of the furnace.

Solution:

Using the equation:

D (depreciation charges per year) = Ci – Cs/N

2. Diminishing Balance Method:

This is also called “Reducing Balance” method. In most of the cases, the cost of repair and maintenance of an equipment/machine or a fixed asset increases towards the end of its active life. Therefore, it is sometimes considered desirable to calculate depreciation costs in such a way that these charges asset decreases rate.

The rate of depreciation in this method in neither constant nor linear but curvilinear because the depreciation is calculated by taking a certain percentage of current book value of the asset. Therefore this method is also known as “percentage on book value” depreciation model.

Let N = Economical life of the asset in years.

Ci = initial cost of the asset in rupees

p = Fixed percent depreciation.

Cs= Scrap value at the end of N year so depreciation in the first year.

Example 2:

A computer has been purchased for Rs. 60000and its useful life is estimated to be 10 years. Its scrap value at the end of 10 years is estimated as Rs.12000.

(i) The percentage by which the value of computer is reducing every year.

(ii) Depreciation in first two years and last two years of computer life.

Solution: Given

3. The Sum of Years Digit Method:

The effect of the method is to charge deprecation at a decreasing rate each year. After an asset or equipment has been installed, the reduction in its value will be greater initially and it will go on decreasing gradually. Taking cognizance of this fact, greater amount of deprecation is made during early years of life if as the asset decreases.

If N is the estimated useful life of an equipment in years the rate is calculated for each year as a fraction in which the denominator is always sum of the series 1, 2, 3..N and the numerator for first year is N, for the second years N-1 and foe the third Years and for the Years N-2 and so on .The following example will illustrate the sum of years digit method.

Example 3:

A lathe machine has been purchased for Rs. 65000/-.Its estimated use full life is 5 years. Calculate the depreciation at the end of each year if its scrap value is Rs. 5000/- use sum of years Digit Method.

4. The Sinking Fund Method:

This method is based on the assumption of setting up, a sinking fund in which money is accumulated to replace the existing equipment/ machine asset at the proper time. In this model of depreciation, a fund equal to the actual loss in the value of the equipment/asset is estimated taking into account the interest on the depreciation is charged every year throughout the on the so accumulated fund.

An identical rate is charged every year throughout the useful life of the asset/equipment. This is the only technique which provides cash for the replacement of the equipment/asset at the end of the useful life estimated for it

The mathematical relation used to calculate annual rate of depreciation i.e. R.O.D. is

where i = rate of interest on accumulated fund in fraction number charged throughout the life of the asset.

An industrial plant with initial value of Rs. 220000 and the salvage value of Rs. 40000 at the end of 20 years is sold for Rs. 195000 at the end of one year. What is profit or loss if sinking found depreciation method at 8% compounded annually was adopted

5. The Annuity Charging Method of Depreciation:

This method considers original cost and rate of interest on the written down value of the equipment/ machine or assest. In this technique we consider the purchase of equipment/machine as an investment on which interest is earned.

Therefore the investment for the purpose of calculation of depreciation cost is the written down or book value of the asset plus interest earned to date. Thus in this method the rate of depreciation is constant every year.

Advantages:

(i) Money invested in the equipment asset is not idle but earning interest.

Limitations:

(i) The modernization and developments taking place in the equipment/machines and other assets sometimes make the application of annuity method difficult.

(ii) In some cases in view of the performance of the unit/plant interest never materialises.

6. Machine Hour Basis Method of Depreciation:

This method provides for depreciation by means of a fixed rate per hour of production. In this method depreciation is calculated by considering the total number of productive machine hours or the number

of hours the machine is run per year. Rate of depreciation will be equal to value of the equipment/asset (difference of initial cost and scrap value) divided by number of productive machine hours. The method will be clear with following example.

Example 4:

A machine costing Rs. 90000 has a scrap value of Rs. 10000 at the end of 10 years of its useful life. If the machine runs for 16 hours daily without weekly rest calculate the rate of depreciation charged annually under machine hour basis method.

Solution:

Here N = 10 years C, = 90000 Cs = 10000

Life of the machine in hours = 10 x 365 x 16 = 58400

Depreciation/hr = (90000-10000)/58400 = 80000/58400 = 1.37 Rs./hr.

Rate of Depreciation/year = (800/584) X 365 X 16 = Rs. 8000