3.2. Book Value Comparison

So, next is a 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.

In this chunk, we are discussing the sum of the years digit method for calculating depreciation. To calculate the depreciation for the first year, you first determine the total number of years of useful life left (n), which in this case is 9 years. Then, you calculate the sum of the years from 1 to n (which equals 45), and use this sum in the formula to find the depreciation expense for the first year by multiplying the initial cost of the asset, subtracting the salvage value and tire cost, and dividing by the total of the years.

Think of it like a cake: if you have 9 slices to share with your friends, and you want to give a bigger slice to the first friend because they are the most excited, you determine the size of each slice based on how many friends are left to share. The more friends you have left, the smaller the next slice will be.

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, the number of years left in the recovery period is now 8. This means that as time goes on, the depreciation expense decreases because you are dividing by a smaller fraction of the total years. The same formula applies: subtract the tire cost and salvage value from the initial cost, and multiply this by the fraction of the years left to the total sum of the years.

Continuing with the cake analogy, after you've given a larger slice to the first friend, the cake has less to give for the next friend, who might get a slightly smaller piece because there are fewer slices left to share.

Now, let us move on to the double declining balance method. In double declining balance method it is totally different from the earlier method as I told you here, we are not using salvage value in the estimation of the depreciation of the machine.

The double declining balance method accelerates depreciation by using a fixed percentage multiplied by the reducing book value at the start of the year. Unlike the sum of years' method, it does not take salvage value into account when calculating depreciation. Instead, it focuses on how much the asset devalues in the very first years of its useful life, allowing for larger tax deductions.

Imagine if your brand new car loses its value much faster in the first few years due to technology becoming outdated, similar to how some electronics drop rapidly in value. The double declining balance method captures this rapid loss by applying a consistent, higher depreciation rate during the initial years.

Now, let us compare the depreciation estimated using 3 different methods you can say straight line method depreciation is always same every year. So, when you compare sum of the years as well as the double declining method, you can see that the double declining method is giving accelerated depreciation.

When comparing three methods—straight line, sum of years, and double declining—you notice that the straight-line method provides the same expense amount each year, while the other two methods, particularly double declining balance, yield higher depreciation in the earlier years. This is critical for businesses looking to maximize tax benefits in the initial phases of an asset’s life.

Consider a student who studies intensively during the first two years of an academic program and then slacks off. Similarly, the double declining balance method allows for a steeper learning curve (or depreciation expenses) at the start, which is beneficial for immediate results, while straight-line keeps things evenly paced.

Another important factor which we are going to discuss today is about switching between different depreciation methods, this is very important as I told you, DDB stands for double declining balance the depreciation method, so, DDB method does not automatically produce a book value equal to the salvage value at the end of the recovery period.

Switching between methods, especially from double declining balance to straight-line, may be necessary when the estimated book value of an asset falls below its salvage value. Companies often need to ensure their reported values align with reality, so they must adapt by switching methodologies when the calculations dictate. This approach might also help manage tax liabilities effectively by enabling a shift to a method that provides more favorable results.

Think of a business trying to stay agile in an ever-changing market; if one strategy isn't yielding the results expected, they may pivot to a different approach that suits their goals better. Similarly, businesses can switch between depreciation methods to maintain accurate financial representation.

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