6.1. Upcoming Lecture Focus on Time Value

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 learn how to calculate depreciation using the given formula. The depreciation for the first year is calculated by multiplying the depreciation rate (40% or 0.4) by the book value of the asset (in this case, a machine worth 28 lakh rupees). So, by multiplying 0.4 by 28,00,000, we find that the depreciation for the first year is 11,20,000 rupees.

Imagine you bought a car for 28,00,000 rupees, and every year, it loses 40% of its value due to wear and tear. In the first year, it loses 11,20,000 rupees in value. This helps you understand how much value your car loses each year.

Now you calculate the book value at the end of the 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 find the book value of the machine at the end of the first year, we begin with the purchase price of 28 lakh rupees. We then subtract the depreciation for that year (11,20,000 rupees) from the original value. The calculation is as follows: 28,00,000 - 11,20,000 = 16,80,000 rupees. This value represents what the machine is worth after accounting for depreciation.

Continuing with the car example, if your car originally cost 28,00,000 rupees and lost 11,20,000 rupees in value, its new worth or book value would be 16,80,000 rupees after one year.

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, we use the new book value (16,80,000 rupees) to calculate the depreciation again at the same rate of 40%. By multiplying 0.4 by 16,80,000, we find that the depreciation for the second year will be 6,72,000 rupees.

Think of it like continuing to age your car. In the second year, its value has dropped to 16,80,000 rupees, so it will lose 40% of this new value. The car's depreciation continues each year, just like all assets do as they get older.

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 10,80,000.

Similar to the previous year, we find the book value at the end of the second year by taking the book value from the end of the first year (16,80,000 rupees) and subtracting the depreciation calculated for the second year (6,72,000 rupees). The calculation becomes: 16,80,000 - 6,72,000 = 10,80,000 rupees.

As the car continues to age, the value drops again. If at the beginning of the second year it was valued at 16,80,000 rupees, after losing another 6,72,000 rupees in value, it is now worth 10,80,000 rupees.

You can estimate the annual cost by adding the operating and maintenance cost as the depreciation. When you add column 2 and the column 3 you will get the annual costs for every year. So, what is the annual cost for the first year? Your operating and 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.

To find the annual cost of owning and operating the machine, we add the annual depreciation to the operating and maintenance costs. For the first year, the operating cost was 12 lakh and depreciation was 11,20,000. Adding these amounts gives us an annual cost of 23,20,000 rupees.

If you think about your car, you have yearly expenses like maintenance, insurance, and how much it depreciates. If maintenance costs are 12 lakh rupees and the car depreciates by 11,20,000 rupees, your total cost of owning and operating the car for that year would be 23,20,000 rupees.

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 you can see it is increasing. So, basically here the economic life of the machine is 9th year for the proposed loader, because the cost is minimum the 9th year.

As costs are calculated over the years, we typically observe a pattern where the costs are initially high, then decrease to a low point before starting to rise again. The 'economic life' of a machine refers to the year in which its costs are the lowest—in this case, it is identified as the 9th year for the proposed loader.

Think of how cars depreciate in value over time. Initially, they cost a lot due to purchase and maintenance, but over time, they can become less and less expensive to maintain until they are very old and start costing more again for repairs, which can be seen as the economic life of the asset.

Now you can compare the average annual cumulative cost of the proposed loader and the old loader. You can see the average annual cumulative costs minimum is 17,99,541.

Comparison between the costs of the proposed loader and the old loader helps in assessing the economic viability of replacing the older model. If the average annual cumulative cost of the new loader is substantially lower than that of the old loader (17,47,975 versus 17,99,541), this indicates a financial advantage for the new loader.

Consider if replacing an old car with a new one would save you money on maintenance and fuel efficiency. If the new car costs you less in the long run, it is better to switch. Similarly, the loaders' costs comparison helps determine the better economic 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.

The time to replace equipment is determined by comparing the estimated annual cost of continuing to use the current machine against the minimum average annual cumulative costs of a newer machine. When the costs of the current machine rise above the threshold, it is advisable to replace it.

If your old phone starts costing you more to maintain due to repairs and battery replacements compared to a new model with a warranty, it’s more economical to buy the new one. This decision-making principle applies to machines as well.

As per Dr. James Douglas' guideline the estimated annual cost of the machine for the next year is calculated. Since your annual cost of the current loader for the next year is 19,04,000, you compare this with the minimum average annual cumulative costs of the proposed loader.

Following Dr. James Douglas' guidelines, we assess the estimated annual cost for the next year against the proposed loader's costs. As the costs for the current loader are estimated to be 19,04,000 rupees, which exceeds the minimum cumulative cost of the new machine, it suggests replacing the old one is financially sound.

It’s akin to realizing that keeping your current phone—while it has high maintenance costs— means it would be better financially to switch to a new phone with lower overall costs. The point of comparison is crucial in making this economic decision.

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