1. Sum of the Years Digit Method

So, here, how do you calculate the depreciation for the first year when you calculate the number of years left in the recovery period is say n = 9. So, number of years left in the recovery period is 9 divided by the sum of the years in the useful life 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 multiplied by initial cost minus the salvage value minus tire cost.

To calculate the depreciation for the first year using the Sum of the Years Digit method, you first identify the remaining recovery period, which is denoted by 'n'. In this case, 'n' is 9, meaning there are 9 years left in the asset's useful life. Next, you calculate the sum of the digits from 1 to 9, which equals 45. The formula for the first year’s depreciation is then:

$D = \frac{n}{1+2+3+...+n} \times (\text{initial cost} - \text{salvage value} - \text{tire cost})$

Here, the initial cost is the value at which the asset was purchased, the salvage value is the expected residual value at the end of its useful life, and the tire cost is considered separately. Substituting the respective values allows you to find the first year's depreciation amount.

Imagine buying a car for ₹8,200,000, with an expected salvage value of ₹600,000 and tire replacement costs of ₹1,200,000. Think of the Sum of the Years Digit method as deciding how much value your car loses each year based on how old it is. In the first year, because your car has a lot of its value still intact, it depreciates a significant amount. By the 9th year, less of its value is left, thus resulting in a smaller depreciation amount.

Similarly, depreciation for the second year number of years left in the recovery period is nothing but number of years left in the recovery period from the beginning of the second year to the end of the useful life of the machine is 8 year. So divided by the sum of the years in the useful life multiply by a initial cost minus tire cost minus salvage value.

For the second year, you adjust 'n' to reflect the new number of years remaining in the useful life, which is now 8. The formula remains the same, but this time it uses the updated 'n' value:

$D = \frac{8}{1+2+3+...+9} \times (\text{initial cost} - \text{tire cost} - \text{salvage value})$

This means you are evaluating how much depreciation to apply based on the fact that the asset is now older, and thus has less value to lose. You substitute into the formula to calculate the depreciation for the second year.

Continuing with the same car example, think of it as if your car is now 1 year old. It has lost some of its initial value from the first year and will continue to lose value more gradually during the second year. Now, rather than losing a lot of value like on the first anniversary, it loses a bit less this time around.

Say for the example depreciation for the 9th year it should be number of years left in recovery period will be 1 divided by 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 multiplied by initial cost minus salvage value.

When you reach the 9th year, only 1 year is left in the recovery period. You apply the same formula:

$D = \frac{1}{1+2+3+...+9} \times (\text{initial cost} - \text{salvage value})$

This reflects that the car is nearing the end of its useful life, and therefore its value drops significantly less compared to the earlier years. The pattern shows a gradual slowing down of depreciation as the asset ages.

Think about your car as it approaches its last year before it's worth that salvage price. By this last year, the depreciation amount is minimal compared to previous years because most of its value has already decreased over time. You can picture it as reaching the final stretch of a marathon run, where the last part is slower and steadier.

So, this is all the estimated depreciation using sum of the years digit method.

In summary, the Sum of the Years Digit method calculates depreciation based on the asset’s declining value over its useful life. The method produces larger depreciation expenses in the earlier years and smaller expenses as time goes on, aligning the depreciation with the asset's actual loss of value. This method serves businesses well by matching depreciation expense to revenues more accurately, particularly in industries where the asset wears down quickly.

Think of it like a new truck used by a delivery company. Early on, it loses value rapidly due to wear and tear from lots of use. However, towards the end of its life, the same truck may be used less, and thus, it doesn't lose value as quickly. This method accurately represents that scenario.

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