2.1. Replacement Justification Based on Economic Life

So, depreciation for the first year is nothing but 0.4 into book value. D = 0.4 × 28,00,000 = 11,20,000 rupees. So, now you calculate the book value at the end of first year, so what is the book value at the beginning of 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 so hope you can understand.

In this first part, we learn how to calculate the depreciation of a machine for its first year of usage. The formula used is simple: multiply the depreciation rate (in this case 40%, or 0.4) by the book value of the machine (28,00,000 rupees). The calculation gives us a depreciation of 11,20,000 rupees. The next step involves adjusting the book value; we subtract the depreciation from the initial purchase price (28 lakh), resulting in a new book value of 16,80,000 rupees at the end of the first year.

Think of a car that you buy for 28 lakh rupees. Over the year, as you use it, its value decreases due to wear and tear, much like how the machine’s value is reduced each year through depreciation. If your car loses 11,20,000 rupees in value during the first year, it is like saying your car is now worth 16,80,000 rupees at the end of that year.

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. Now calculate the book value at the end of second year, it is nothing but book value at the end of the first year minus the depreciation for the second year.

Here, we perform a similar calculation for the second year. Again, we use the depreciation rate of 40%. This time, however, we apply it to the new book value of the machine at the end of the first year, which is 16,80,000 rupees. The resulting depreciation comes out to be 6,72,000 rupees. To find the end-of-year book value, we subtract this depreciation from the second-year beginning value, yielding 10,80,000 rupees as the book value at the end of the second year.

Continuing with our car analogy, let's say your car’s value after the first year is 16,80,000 rupees. If in the second year, it depreciates further by 6,72,000 rupees, it means after the second year, it’s worth only 10,80,000 rupees.

Now you can estimate the annual cost by adding the operating and the maintenance cost as the depreciation. When you add column 2 and column 3 you will get the annual costs for every year. So, what is the annual cost for the first year? Your operating in the maintenance cost for the first year is 12 lakh and your depreciation for the first year is 11,20,000, so your annual cost will be Annual cost of first year = 11,20,000 + 12,00,000 = 23,20,000 rupees.

In this section, we determine the annual cost of operating the machine, which combines both the maintenance costs and the depreciation. For example, for the first year, we have 12 lakh rupees in maintenance costs and 11,20,000 rupees in depreciation. Adding these figures gives us an annual cost of 23,20,000 rupees for that year.

Returning to our car example, if maintaining the car for the first year costs you 12 lakh rupees, and the loss in value (depreciation) is 11,20,000 rupees, then your total cost (or annual cost) for having the car is like saying you spent 23,20,000 rupees to keep it on the road that year.

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. So, now, how will you calculate the average annual cumulative cost? It is nothing but your the cumulative cost divided by the cumulative usage of the machine.

After determining the annual costs, we sum up these costs to find the cumulative cost over several years. To find the average annual cumulative cost, we divide the cumulative cost by the total number of years the machine is in use. This indicates the average cost incurred each year over its lifespan.

Think of this like budgeting for a family. If your total expenses over two years were, say, 60,000 rupees for groceries and other necessities, dividing that by the number of years (2) gives you the average expense per year, helping you plan your future budgets better.

So, the economic life of the machine is 9th year for the proposed loader, because the cost is minimum 9th year. So, the economic life of the proposed loader is 9th year but for the old loader the economic life is 8th year. Now you can compare the average annual cumulative cost of the proposed loader and the old loader.

The economic life of a machine refers to the year during which its average cost is the lowest. Here, the proposed loader's economic life is found to be the 9th year, while the existing machine’s economic life is the 8th year. By comparing the average costs of both loaders, we can justify replacing the old loader with the proposed one.

Imagine knowing that a smartphone you purchased becomes more economical to own after 9 years instead of 8 years for the older model. This means that after a certain point, the new smartphone not only performs better but also costs less per year in maintenance and use compared to the old one, encouraging users to upgrade.

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.

Dr. James Douglas provides a guideline for determining when to replace a machine. If the predicted costs for the existing machine in the upcoming year surpass the minimum average annual cumulative cost of the proposed machine, it is time to consider a replacement.

Think of this as looking at old tires on your car. If you realize that next year's cost of fixing those tires will be more expensive than the cost of investing in new tires, it would make sense to replace them before they incur even more costs over time.

Since your annual cost estimated for the current loader for the next year is much higher than the proposed loader. So, it implies that you have to replace immediately.

If the estimated costs for maintaining and operating the current loader in the next year are significantly higher than that of the new proposed loader, this signals the need for immediate replacement. The cost-benefit analysis shows that continuing with the old machine is more costly.

This can be likened to deciding whether to pay for ongoing repairs on an old car versus investing in a new one. If the repairs are costing you more than a new car payment, then it makes more sense financially to buy a new car.

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