1.3. Depreciation Calculation for the Ninth Year

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, identify the total number of years for which the asset will be useful. In this case, it is 9 years. You need to divide the remaining years (which is 9 in the first year) by the sum of all the years in the useful life (1 through 9). The sum of these numbers is 45 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45). Then, subtract the salvage value and tire cost from the initial cost and multiply by the fraction calculated. This will yield the depreciation amount for the first year.

Imagine you bought a car for ₹8,200,000. You can expect it to be useful for 9 years. During each year, the value of the car declines. In the first year, you look at how long you’ll use it (9 years) and calculate how much it should lose in value by spreading the total expected loss over the timeframe. By the first year, you're estimating that it will lose ₹1,280,000 of its value.

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.

For the second year, you again use the sum of the years digit method. Now, the number of years left in the recovery period is 8 (since one year has passed). You apply the same formula: divide 8 by the total sum of the years (still 45) and multiply the initial cost minus tire cost and salvage value by this fraction. The calculation will provide the depreciation amount for the second year.

Returning to our car example, by the second year, the car isn’t as new. The valuation drop continues, so you calculate the loss in value for that year just like before, but now you have 8 years left instead of 9, which affects how much you say it lost this year.

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.

For the ninth year, you are left with just 1 year of utilization. Using the sum of years digit method, the fraction is 1 divided by the sum of years, which is still 45. The formula remains the same where you subtract the salvage value and tire cost from the initial cost and multiply by this new fraction. This calculation provides the depreciation for the last year of the machine's useful life.

It’s akin to the final stretch in a marathon. As you approach the end, your energy (value) diminishes less dramatically than it did at the start. For your car, now it’s just one last year of value loss you’re calculating as you watch its worth dwindle closer to what you’d get if you sold it.

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

The sum of the years digit method allows for a structured, declining depreciation while recognizing that assets lose value more rapidly in their early years. By constantly recalculating based on remaining useful life, this method keeps depreciation amounts relevant to the current state and expected performance of the asset.

Think of a new smartphone that loses a lot of value within the first year as new models come out; its depreciation aligns more closely with how quickly it loses worth initially rather than uniformly every year. This method mimics that pattern.

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