1.1. Depreciation Calculation for the First Year

So, next is a sum of the years digit method. 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? The 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 salvage value minus tire cost). So, this will give you the depreciation for the first year.

The sum of the years' digits method is used to calculate depreciation based on the idea that an asset loses value more rapidly in the early years of its useful life. In our example, if the useful life is 9 years (n = 9), we first need to determine the total of the years' digits, which is 1 + 2 + 3 + ... + 9 = 45. We then take the remaining life for the first year (9) and divide it by this total (45). This fraction gives us the portion of the total depreciable amount to allocate to the first year. After calculating the fraction, this value is then multiplied by the depreciable base, which is the initial cost of the asset minus any salvage value (final value after depreciation) and tire cost.

Imagine buying a new car for ₹8,200,000. You expect it to have a salvage value of ₹600,000 and some associated tire costs of ₹1,200,000. For the first year, using the sum of the years' digits method, you would determine the portion of depreciation to apply, reflecting how a car often loses more value in its first year. This could be likened to how a brand-new car loses its 'new' status dramatically when first driven off the lot, which is why it depreciates more at the start.

For the second year, the number of years left in the recovery period is 8. So, you divide by the sum of the years again and multiply by the initial cost minus tire cost minus salvage value. Similarly, we calculate the depreciation for every year.

As you progress to the second year of depreciation, the remaining life of the asset is now 8 years. To find the depreciation for the second year, you follow the same process: take 8 (remaining life) divided by the total sum of the years (still 45), and multiply it by the depreciable base (initial cost minus tire cost minus salvage value). This maintains the consistency of the method by allowing for a decreasing amount of depreciation each successive year according to its remaining useful life.

Continuing with the car example, as you enter the second year, the car's value might drop less dramatically than in the first year, reflecting how vehicles typically lose value slower as they age. Calculating depreciation annually using the same formula allows the car’s declining market value to be accurately represented financially.

For the example depreciation in the 9th year, the number of years left in recovery is 1 divided by 1 + 2 + 3 + ... + 9 multiplied by the initial cost minus salvage value. This is the estimated depreciation using the sum of the years digit method.

In the final year, the remaining life is reduced to 1 year. Therefore, the formula uses this single remaining year divided by the total number of years' digits. Importantly, at this point, the emphasis is on not allowing the depreciation to exceed the predetermined salvage value. The calculation ensures that the total depreciation does not surpass the initial cost minus the salvage value, sustaining accurate financial principles as the asset's life ends.

Think of it like holding onto your car for 9 years; by year 9, you can’t expect it to lose much value relative to its salvage value—this is like ensuring that the last year of depreciation doesn’t dip below a price that seems unreasonable based on the car's overall worth, allowing for realistic financial reporting.

Now, let us move on to the double declining balance method. In this method, we are not using salvage value in estimating the depreciation of the machine. For the first year, what is the book value at the beginning of the year? It is ₹76 lakh, obtained by subtracting tire cost from the initial cost. The depreciation for year 1 is calculated as 2/n multiplied by book value.

The double declining balance (DDB) method operates under a different principle than the sum of the years' digits. Here, it does not consider salvage value during calculations, focusing instead solely on the book value at the beginning of each year. To calculate depreciation, the formula applies 2 divided by the total lifespan (n) multiplied by the current book value. This approach allows for quicker depreciation initially, yielding tax benefits.

Imagine you’re watching a race where the car depreciates rapidly at first. This method mimics that sense of urgency—depreciating faster in the early years, giving you quick financial relief at tax time, much like receiving a fast cash return in a race from early performance.

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