3.3. Determining Economic Life Based on Profit

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 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 so hope you can understand. So, let us work it for the second year.

In the first year, we calculate depreciation using the formula Depreciation (D) = Depreciation Rate × Book Value. Here, the depreciation rate is 0.4 (or 40%), and the book value at the start is 28,00,000 rupees. Therefore, the calculation is D = 0.4 × 28,00,000 = 11,20,000 rupees. Next, to find the book value at the end of the first year, we subtract the depreciation from the purchase price: Book Value = Purchase Price - Depreciation. Thus, Book Value = 28,00,000 - 11,20,000 = 16,80,000 rupees.

Think of a new car that costs ₹28,00,000. After one year, it might lose ₹11,20,000 in value due to depreciation. So, if you were to sell it after a year, you could expect it to be worth around ₹16,80,000.

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 the second year, it is nothing but the 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 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.

In the second year, we again use the same method to calculate the depreciation. This time, the book value at the beginning of the year is now 16,80,000 rupees, so the depreciation for the second year is D2 = 0.4 × 16,80,000 = 6,72,000 rupees. Subsequently, we calculate the book value at the end of the second year by subtracting this depreciation from the book value at the end of the first year: Book Value = 16,80,000 - 6,72,000 = 10,80,000 rupees.

Imagine your car is now worth ₹16,80,000 after the first year. In the second year, it loses ₹6,72,000 in value. If you check after two years, you would find the car is now worth ₹10,80,000.

Then you can estimate the annual cost by adding the operating and the 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 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. Annual cost of second year = 6,72,000 + 12,60,000 = 19,32,000 rupees.

To determine the total annual cost of operating the machine, you add all relevant expenses, including depreciation, operating costs, and maintenance costs. For the first year, the combined operating and maintenance cost is 12 lakh rupees, and the depreciation is 11,20,000 rupees. Thus, the total annual cost for the first year is 11,20,000 + 12,00,000 = 23,20,000 rupees. In the second year, if the operating and maintenance costs rise to 12,60,000 rupees, adding the second year's depreciation (6,72,000 rupees) gives us an annual cost of 6,72,000 + 12,60,000 = 19,32,000 rupees.

Think of your monthly budget for your car. If you spend ₹12,00,000 in maintenance and it loses ₹11,20,000 in value the first year, your total cost of having the car for that year is the depreciation plus the maintenance expenses, giving you ₹23,20,000 as a big picture of cost.

So, like this you keep calculating for all the years with every year you can calculate the annual cost. 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 the cumulative cost divided by the cumulative usage of the machine.

The average annual cumulative cost is calculated by taking the cumulative costs incurred over a period and dividing that by the total usage time of the machine. This helps to spread out the costs over all the years the machine has been in operation, giving a single, understandable figure of costs per year. For example, if after two years the cumulative cost is 42,52,000 rupees, dividing this by the total machine usage (2 years in this case) gives you the average annual cumulative cost.

Consider a restaurant using a delivery van. If the total operating cost and depreciation for the van over three years amount to ₹6,00,000, then the average cost per year, when you hand over that vehicle to qualification, would be ₹2,00,000.

So, basically here 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. You can see the average annual cumulative costs minimum is 17,99,541.

The economic life of a machine refers to the period during which it is most cost-effective to operate it. In this case, it has been determined that the minimum cumulative cost occurs in the 9th year for the proposed loader and the 8th year for the old loader. This means that if the proposed loader is used until the 9th year, it provides the best cost-to-benefit ratio. Comparing these numbers provides insight into which loader to keep in operation longer.

Think of it like a mobile phone. If the best value for its performance and cost occurs after three years of use, then that's when it provides you the most benefit before you should consider upgrading to a newer model.

So, can you see here? So, you can see, here it is 17,99,000, here it is 17,47,000. 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.

When comparing the minimum average cumulative costs of the proposed loader (17,47,000 rupees) with that of the old loader (17,99,000 rupees), we find that the proposed loader offers lower costs over the same period. This significant difference justifies replacing the old loader with the new one, as it will provide savings in operational costs.

Imagine if you're considering two brands of coffee machines. One costs more upfront but less per cup of coffee over its lifetime. Comparatively, if the expensive model saves you money in the long run on coffee costs, it's worth the investment.

So, Dr. James Douglas has given a guideline for this minimum cost approach to decide when to replace the old machine with the new machine. 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.

Dr. Douglas's guideline recommends assessing when to replace a machine based on its estimated future costs. If the expected annual cost of the current machine exceeds the calculated minimum average costs of the proposed machine, then it is a clear signal to switch to the new machine. This ensures that you’re always operating under the most cost-effective conditions.

Think of replacing a car; if your current car's annual repairs and maintenance costs go past what you would pay in maintenance for a newer model that has lower operational costs, it's time to trade up for the better deal.

So, now let us compare as per Dr. James Douglas guideline the estimated annual cost of the machine for the next year. So, next year is nothing but because you are the loaders are already 1 year old. The current loader is 1 year old, so we are finding the estimated annual cost for the second year. Second year the value is 19,04,000, you compare it with the minimum average annual cumulative cost of the proposed loader.

For applying Dr. Douglas's guideline, you need to calculate the estimated annual cost for the current loader for the next year. Since the current loader is now 1 year old, and we've found that its estimated cost next year would be 19,04,000 rupees, you compare this with the minimum average annual cumulative cost of the challenger, which is previously determined. If the current loader’s expected annual cost is higher, it indicates the need for replacement.

If you calculated that next year your phone’s operating cost, like bills and repairs, hits ₹19,04,000, comparing it with a newer model’s running costs can help you realize which phone to keep and which to upgrade.

Since your annual cost the estimated cost for the current loader for the next year is very much higher than the proposed loader. So it implies that you have to replace immediately. So you have to replace the current loader with the new loader as per the Dr. Douglas guidelines.

Once you determine that the estimated annual cost of the current loader (19,04,000 rupees) significantly exceeds the average annual cumulative cost of the proposed loader (17,47,975 rupees), it provides a clear justification for immediate replacement. Following these systematic guidelines assures minimizing operational costs and maximizing efficiency.

Suppose you realize your old laptop’s monthly expenses far exceed what you'd pay for a newer, more efficient one. By replacing it now, you save money and improve performance, just like in the loader analysis.

So, now let us look into the next approach given by Dr. Douglas, it is nothing but maximum profit method. So, this is based on maximizing the equipment profit, so here we are optimizing the prediction with respect to profit. So, how to defend economic life here, it is a time period when the average annual cumulative profit is maximum.

The maximum profit method shifts the focus from minimizing costs to maximizing profits. It defines economic life as the point in time when the average annual cumulative profit reaches its peak. This method is particularly useful for companies whose primary goal is profit generation, allowing decision-makers to evaluate if retaining equipment aligns with profit objectives.

Consider a business choosing between two products. One generates higher sales but has lower profit margins. By analyzing not just costs but also how much profit each product contributes, the business can decide whether to focus on high-revenue items or those that maximize profit.

So, now let us workout the same problem using maximum profit method. So, we are going to find the average annual cumulative profit of the current loader as well as the proposed loader. Now as given in the question, the revenue for the current loader is 28 lakh, it decreases by 70,000 every year.

In applying the maximum profit method, we need to understand revenue trends for the current loader. For the first year, revenue is 28,00,000, but it decreases by 70,000 each subsequent year, indicating the machine's performance and profitability decline over time. This decreasing revenue must be tracked to calculate actual profits accurately, providing insight into the loader's performance as it ages.

Imagine that every year you save a certain amount from your salary. Initially, you might earn a bonus. However, if you assume you’ll earn less each year, you need to monitor how quickly your savings grow or decline, much as we track the loader's revenue.

To start with for the first year it is 28 lakh then the revenue is decreasing by 70,000 every year. Annual profit of first year = 28,00,000-22,40,000 = 5,60,000 rupees. Annual profit of second year = 27,30,000-19,04,000 = 8,26,000 rupees.

To find yearly profits, subtract the total costs from the expected revenues. For example, if the first year's revenue is 28,00,000 and costs total 22,40,000, then the profit is 28,00,000 - 22,40,000 = 5,60,000 rupees. Repeat this method each year, ensuring accurate tracking of how the equipment's profitability changes over time.

Think of it as your monthly earnings; if you earn ₹28,000 but your expenses total ₹22,400, your profit each month is ₹5,600. Just like you would analyze your earnings versus expenses, we analyze the loader's revenue against its costs.

So, similarly, you have to find the cumulative profit by adding the profit of all the years you can get the cumulative profit. Now the average annual cumulative profit, so that is going to be the nothing but your cumulative profit divided by cumulative usage of the machine.

By adding the annual profits over the years, you can determine the cumulative profit. To derive the average annual cumulative profit, take this cumulative profit and divide it by the total years of usage. This provides a holistic view of how profitable a machine is over its operational life.

Consider a savings account where you earn interest each year. If you track how much total money you’ve made by the end of each year, then dividing by the number of years gives you an average annual gain—similar to calculating average profits from a loader.

So, you can see the trend here, here also the initially the profit 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 the 5th year for the current loader.

As we plot the average annual cumulative profits over usage time, we notice a trend: profit rises, peaks, and then declines. The economic life is identified as the point at which profit is maximized. In this case, the loader's economic life is determined to be the 5th year, suggesting optimal profitability during that period.

Think about how a business product might have its peak season. For instance, a winter clothing line might see high profits in winter, but as seasons change, sales drop. Understanding this cycle helps in determining the best time to maximize profit, much like evaluating the loader's economic life.

So, now you can compare the maximum average annual cumulative profits of the current loader and the proposed loader. So, the maximum profit we are getting at the 5th year. So, it means that if you are holding this machine for 5 years with you. So, for the first five years, the average annual profit for the past five years will be 8,20,435.

After calculating the average annual cumulative profits, we compare the current loader's maximum profit (8,20,435 rupees at the 5th year) against that of the proposed loader. This analysis indicates where profits are maximized and can serve as a guide for replacement decisions based on which machine offers the higher profitability.

Imagine you're running a lemonade stand. After 5 years, you notice that your earnings are maximized during summer. Recognizing this peak helps you decide whether to keep selling in winter or focus on the best season for profits, paralleling the profitability analysis for the loaders.

So, the decision to replace the equipment is made, when the estimated annual profit of the defender for the next year falls below the maximum average annual cumulative profit of the challenger.

According to Dr. Douglas's guidelines, a replacement decision should be made when the estimated annual profit from the current loader for the following year is projected to be lower than the average cumulative profit of the proposed loader. This method emphasizes switching to equipment that provides better profit margins to ensure ongoing business profitability.

If your old smartphone shows signs of poorer performance and lower app efficiency year after year compared to a new model, you’d understand the need to upgrade to maintain productivity—just as businesses should swap out less profitable equipment.

So, these are the references which I have referred for this lecture. So, you can go through this textbooks to prepare the topics related to this lecture, so let us meet in the next lecture, thank you.

This section concludes with a call to review the references used in this analysis and an encouragement to continue studying the material presented. Understanding these methods—minimum cost and maximum profit—provides a strong foundation for effective equipment replacement decisions, emphasizing a strategic approach to managing assets.

Just like a student reviewing textbooks before an exam to deepen understanding, staying informed on equipment methods and strategies allows business decision-makers to make informed choices and maximize profitability.

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