5. Summary of Methods

So, depreciation for the first year is nothing but 0.4 into book value. D = 0.4 × 28,00,000 = 11,20,000 rupees

In the first year, to calculate the depreciation of an asset, you multiply the depreciation rate by the book value of the asset. Here, the book value of the machine is ₹28,00,000, and the depreciation rate is 40% or 0.4. By performing the calculation 0.4 multiplied by ₹28,00,000, you get a depreciation amount of ₹11,20,000. This reduction reflects the wear and tear or decrease in value of the machine over the year.

Imagine you buy a new smartphone for ₹28,000. If it depreciates by 40% in the first year, it would mean that over the year, your phone loses ₹11,200 in value due to factors like wear, outdated technology, or market trends. At the end of the year, it is worth ₹16,800.

So, now you calculate the book value at the end of the first year, so what is the book value at the beginning of the year that is nothing but your purchase price of the machine 28 lakh minus the depreciation for the first year. That is nothing but 11,20,000, that gives you the book value at the end of the first year as 16,80,000.

To determine the book value at the end of the first year, you take the initial purchase price of the machine, which is ₹28,00,000, and subtract the depreciation calculated for the first year, ₹11,20,000. This calculation shows how much value the machine retains after one year of use, resulting in a book value of ₹16,80,000.

Consider the smartphone again, which started at ₹28,000 and lost ₹11,200 in value. Now, after one year, the book value of your phone is ₹16,800, signifying how much you would get if you sold it today.

So, for the second year the depreciation is nothing but D2 is 0.4 into book value the end of first year, D = 0.4 × 16,80,000 = 6,72,000 rupees

For the second year, you compute the depreciation again using the same rate of 40%. This time, you apply it to the new book value, which is ₹16,80,000. Thus, you multiply ₹16,80,000 by 0.4 to find that the second-year depreciation is ₹6,72,000. This shows that depreciation can vary from year to year based on the asset's current value.

Using the phone example, after one year it’s now worth ₹16,800. If it depreciates again by 40%, it loses another ₹6,720 in value this year, indicating that the loss of value continues as the phone ages.

Now calculate the book value at the end of the second year, it is nothing but book value at the end of the first year minus the depreciation for the second year. So, what is the book value at the end of the first year? It is nothing but 16,80,000 minus your depreciation for the second year is 6,72,000 that gives me the book value at the end of second year as 10,8000.

At the end of the second year, to find the new book value, you subtract the second-year depreciation from the book value at the end of the first year. With the first-year book value at ₹16,80,000, and the depreciation being ₹6,72,000, the calculation results in a final book value of ₹10,80,000 for the end of the second year.

In our smartphone example, after the first year, your phone was worth ₹16,800. By the end of the second year, losing another ₹6,720 means it is now valued at ₹10,080 — illustrating how quickly devices can lose value.

So, let us work it for the second year. So, like this you calculate the depreciation for all the years and the corresponding book values also you have to estimate. Now you can estimate the annual cost by adding the operating and the maintenance cost as the depreciation.

To estimate the annual costs of the machine, one would add the depreciation calculated earlier to both the operating costs and maintenance costs. Doing this for each subsequent year helps keep a clear picture of total expenses associated with operating the machine. This annual cost informs budgetary considerations and guides financial planning.

Think of the running costs of your smartphone, which include maintenance (like screen protectors or cases) and its depreciation. By keeping track of these costs each year, you can understand the total expense of owning the phone over time.

Then you can calculate the cumulative cost, then find the average annual cumulative cost. So, like we did for the earlier old loader or the current loader or the defender.

Cumulative costs represent the total costs incurred up to a certain year, including depreciation and operating costs. To find the average annual cumulative cost, you divide the cumulative cost by the cumulative usage or the number of years. This gives a per-year average that helps in analyzing long-term costs against usage.

Similar to budgeting for your monthly expenses, where you aggregate previous months' spending and find an average. If the cumulative total for your phone expenses is ₹60,000 over three years, your average annual cost would be ₹20,000 per year.

So, can you see here? So, you can see, here it is 17,99,000, here it is 17,47,000. So, it justifies the replacement of your proposed loader with the old loader because the minimum average annual cumulative cost for the challenger is lesser when compared to the old loader which is higher.

The comparison of average annual cumulative costs between the old loader and the proposed loader indicates that the proposed loader has a lower costs ratio, suggesting financial efficiency. Consequently, it justifies a decision to replace the old loader with the new proposed loader to optimize costs.

Consider replacing an old car with a new model; if the new car’s annual operating costs are substantially lower than the old car’s, it shows you would save money over time, making it a wise financial decision.

So, the decision to replace the equipment is made when the estimated annual cost of the current machine for the next year exceeds the minimum average annual cumulative cost of the proposed machine.

Following Dr. James Douglas's guidelines, replacement decisions are made based on cost-effectiveness. If the projected costs of maintaining the existing machine rise above the average costs calculated for the proposed new machine, then it indicates that the old machine should be replaced.

This is akin to deciding whether to continue repairing an aging vehicle. If repair costs surpass what you would pay for a more reliable new vehicle, the sensible decision is to purchase the new one to avoid ongoing high costs.

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