5.1. Intuitive Method and its Comparison

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 this chunk, we calculate the depreciation expense for the first year of a machine. Depreciation indicates how much value the machine loses over time due to wear and tear. To find the depreciation for the first year, we multiply the book value by the depreciation rate of 40% (0.4). In this case, the initial book value of the machine is 28,00,000 rupees, leading to a depreciation of 11,20,000 rupees for the first year.

Consider a new car, which you buy for a specific price. Over the first year, because of usage, the car's value decreases. Similar to how a car loses value, machines also depreciate in value over time, and this depreciation can be calculated using a fixed percentage of its value.

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.

To calculate the book value at the end of the first year, we start with the original purchase price of the machine, which is 28,00,000 rupees. We then subtract the depreciation from this amount: 28,00,000 - 11,20,000 = 16,80,000 rupees. This final amount represents how much the machine is worth at the end of the first year.

Imagine buying a new laptop. If you bought it for $1,000 and it loses$400 in value during the first year (like depreciation), you would consider it to be worth $600 at the end of the year. Similarly, the book value of the machine decreases as it ages.

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

For the second year, we calculate depreciation again, using the new book value we just calculated (16,80,000 rupees). We multiply this book value by the depreciation rate of 40%: D = 0.4 × 16,80,000 = 6,72,000 rupees. This means that in the second year, the machine loses a value of 6,72,000 rupees.

Think of a smartphone. As it gets older, not only does it lose value but it also depreciates faster in the earlier years. In the first year, it might lose $100, but in the second year, it might only lose$80. This gradual decrease illustrates how the depreciation varies with time.

Now calculate the book value at the end of second year, it is nothing but book value at the end of first year minus the depreciation for the second year. So, what is the book value at the end of 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 10,08,000.

To find the book value at the end of the second year, we take the book value from the end of the first year, which is 16,80,000 rupees, and subtract the depreciation for the second year, 6,72,000 rupees. This calculation shows how the value of the machine continues to decline over its lifespan: 16,80,000 - 6,72,000 = 10,08,000 rupees.

Continuing with the laptop example, if after one year, it was worth $600 and it loses another$240 in value during its second year, it would be worth $360 at the end of the second year. This mirrors the calculation of book values through depreciation.

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.

After calculating depreciation for several years, you need to consider both operating costs and maintenance costs to estimate the total annual costs. The annual cost combines these elements and gives a complete picture of the machine's economic impact over time.

When owning a car, annual costs aren't just the price of fuel; they include maintenance like oil changes and repairs. Similarly, calculating a machine's annual costs requires considering all factors contributing to its running expenses.

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

To find the average annual cumulative cost, you start with the total cumulative cost accumulated over the years and divide it by how many years you've used the machine. This gives you a per-year cost, helping you evaluate the machine's efficiency over time.

Think of calculating the average cost of a subscription service over some months. If you spent $60 for six months, your average monthly cost is$10. This calculation helps in assessing how much you're actually spending over time.

So, the same way you can see the trend here, here also the initially the cost is high then it starts reducing, it reaches a minimum point here, after that it starts increasing. So, basically here the economic life of the machine is 9th year for the proposed loader, because the cost is minimum 9th year.

The trend indicates that the costs associated with the machine rise and fall over time, eventually showing a peak and subsequent increase. The point at which costs are lowest indicates the optimal time to replace the machine—here identified as during the 9th year of usage.

Consider a refrigerator that runs efficiently for a certain number of years. After that, it requires more frequent repairs and higher energy bills. Finding that 'sweet spot' for replacement before costs increase significantly mirrors the analysis conducted here.

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