2.3. Book Value and Salvage Value Considerations

So, 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 the salvage value minus tire cost. So, this will give you the depreciation for the first year.

$D = \frac{n}{1 + 2 + 3 + \ldots + n} \times (\text{Initial Cost} - \text{Salvage Value} - \text{Tire Cost})$

For example: $D = \frac{9}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9} \times (8200000 - 600000 - 1200000) = ₹ 12,80,000$

In this chunk, we see how the depreciation for the first year is calculated using the 'sum of the years' digit method. This method involves dividing the number of years left (which is 9 in this case) by the total sum of years in the asset's useful life (1 through 9). This calculation helps to distribute depreciation over the years based on the asset's remaining usable life, factoring in the initial cost, salvage value, and any costs associated with the asset (like tire costs).

Imagine you buy a car worth ₹8,200,000 with a potential resale value (salvage value) of ₹1,200,000 after 9 years. The car's condition and usefulness decrease over time. Just as you wouldn't expect to sell a nearly used-up asset for the same price you bought it, vehicles lose value more quickly early in their life. The number '9' represents the ‘value’ left in years, showing how much of the car you've used compared to its lifespan.

Similarly, depreciation for the second year calculates the 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, which is 8 years. Thus, this is divided by the sum of years multiplied by the initial cost minus the tire cost minus the salvage value.

$D = \frac{8}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9} \times (8200000 - 600000 - 1200000) = ₹ 11,37,777.78$

In the second year, the available depreciation is calculated similarly but now only considers 8 years of the useful life left. The formula remains the same, but you substitute 'n' with 8. This illustrates how the depreciation decreases over time since fewer years are left for the asset’s recovery over its lifecycle, hence it generates less depreciation than the first year.

Think of your car's value decreasing each year. If in the first year you could claim a large portion of its initial value, by the second year, as the car ages and depreciates more slowly, the amount you can claim gets smaller, reflecting its diminished value and usability.

Now, let us move on to the double declining balance method, which is different from the earlier method as salvage value is not used in estimating depreciation. For the first year, the book value is ₹76 lakh (initial cost of ₹82 lakh minus tire cost of ₹6 lakh). Calculate the depreciation for the first year as follows:

$D = \frac{2}{n} \times \text{Book Value}$

Thus for first year: $D = \frac{2}{9} \times 76,00,000 = ₹ 16,88,888$

This method accelerates depreciation by allowing you to claim a higher initial depreciation in the early years of an asset's life compared to linear methods. Instead of factoring in the salvage value, it focuses on the book value at the start of each year. This approach is especially beneficial for assets like machinery that lose value quickly after purchase. The equation uses '2/n' where 'n' is the total lifespan of the asset, focusing on the calculated book value.

Visualize your smartphone: Before it hits the market, its value plummets. If you bought a new iPhone for ₹76,00,000, in the first year of usage, the depreciation hits harder. In subsequent years, while it continues to lose value, it generally doesn’t drop as drastically as in the first year. The double declining method takes into account that steep loss in that first year.

An important thing to note here is that often, the estimated book value can go below the salvage value. For example, after the 8th year, if the estimated depreciation brings the book value down to ₹10,17,789 but the salvage value is ₹12 lakh, this is unacceptable. You then back-calculate by adjusting the book value back to the salvage value before continuing with the calculations.

The significance of salvage value is that once the asset reaches its end of life, it shouldn’t be recorded at a value lower than what it can feasibly be sold for. This means if the double declining balance method brings down the book value too low, adjustments must be made to ensure book value reflects the salvage value to comply with accounting standards.

Imagine you own a vintage car that's worth ₹12 lakh as a salvage. If depreciation calculations showed it fetching only ₹10 lakh, you would likely feel it's undervalued and not sell it at that much. Thus, adjustments are equivalent to ensuring you don’t sell that vintage gem for less than its worth!

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