Depreciation using Sum of Years Digit Method

Introduction:
The Sum of Years Digit (SYD) method is a depreciation technique that allocates the cost of an asset over its useful life. It assumes that the asset is more valuable in its early years and loses value as time goes on. The method calculates depreciation by multiplying the depreciable cost of the asset by a fraction determined by the sum of the digits of the asset's useful life.

Given Information:
- Cost of motor car: Rs 200,000
- Scrap value: Rs 20,000
- Useful life: 4 years

Calculating the Digits:
To determine the fraction for each year, we need to calculate the sum of the digits of the useful life. In this case, the useful life is 4 years, so the digits are 1, 2, 3, and 4. The sum of these digits is 10 (1+2+3+4=10).

Calculating Depreciation for the First Year:
To calculate the depreciation for the first year using the SYD method, we use the following formula:

Depreciation = (Remaining useful life / Sum of digits) * (Cost - Scrap value)

In the first year, the remaining useful life is 4 years, and the sum of digits is 10. Substituting these values into the formula, we get:

Depreciation = (4/10) * (200,000 - 20,000)
Depreciation = (0.4) * (180,000)
Depreciation = 72,000

Explanation:
The depreciation amount for the first year using the Sum of Years Digit method is Rs 72,000. This means that the motor car will lose Rs 72,000 in value during the first year of its useful life. The remaining value of the motor car after the first year can be calculated as follows:

Remaining value = Cost - Depreciation
Remaining value = 200,000 - 72,000
Remaining value = 128,000

So, at the end of the first year, the motor car will have a remaining value of Rs 128,000. This process is repeated for subsequent years until the useful life of the motor car is reached.

Conclusion:
The Sum of Years Digit method is a useful technique for allocating the cost of an asset over its useful life. By calculating the sum of the digits of the useful life, we can determine the fraction for each year's depreciation. In the case of the motor car with a useful life of 4 years, the depreciation for the first year using the SYD method is Rs 72,000.