1.2. Second Year Downtime Cost

Downtime cost per hour = 3% of equipment cost, where equipment cost is 900 rupees per hour.

Downtime cost per hour = rac{3}{100} \times 900 = 27 rupees per hour.

Yearly downtime cost = 27 x 2000 = 54,000 rupees.

The downtime cost per hour represents how much income is lost when machinery is not operational. For the first year, the equipment cost is defined as 900 rupees per hour. By calculating 3% of this cost, we find that the downtime cost is 27 rupees per hour. To determine the total downtime cost for the entire year, we multiply the downtime cost per hour by the total number of operational hours in a year, which is 2000. Thus, the yearly downtime cost becomes 54,000 rupees.

Imagine if a factory's machine costs 900 rupees an hour to operate but is down for repairs. During this downtime, the factory loses 27 rupees every hour, which adds up to 54,000 rupees over the year. This is akin to a shop being closed for repairs; each hour closed translates to lost sales.

In the second year, the downtime percentage is 6% of the equipment cost (900 rupees per hour).

Downtime cost per hour = rac{6}{100} \times 900 = 54 rupees per hour.

Downtime cost per year = 54 x 2000 = 1,08,000 rupees.

For the second year, the downtime cost increases to 6% of the equipment cost, which is now calculated to be 54 rupees per hour. This marks a significant increase from the first year. When we multiply this new hourly downtime cost by the total yearly operational hours (2000), we find that the total downtime cost for this year is 1,08,000 rupees.

Think of a delivery service that has a truck costing 900 rupees per hour to operate. If the truck is out of service for repairs, the cost increases to 54 rupees per hour in the second year of operation. This means, over the year, the service is losing out on potential revenue amounting to 1,08,000 rupees.

To find cumulative downtime cost:

Cumulative downtime cost = Previous total + Current year cost.

For the second year: Cumulative dowtime cost = 54,000 + 1,08,000 = 1,62,000 rupees.

Cumulative downtime cost is calculated by adding the downtime costs from each year together. In this example, we simply take the first year's downtime cost (54,000 rupees) and add it to the second year's cost (1,08,000 rupees), resulting in a cumulative cost of 1,62,000 rupees.

Picture a savings account where you add 54,000 rupees in the first year, and then another 1,08,000 rupees in the second year. By the end of the second year, you would have a total of 1,62,000 rupees saved. Similarly, the cumulative downtime cost accumulates over the years.

Cumulative cost per hour for first year = rac{54,000}{2000} = 27 rupees per hour.

For the second year: Cumulative cost per hour = rac{1,62,000}{4000} = 40.5 rupees per hour.

Cumulative cost per hour is determined by dividing the cumulative downtime cost by the total hours operated until that year. After the first year, with 2000 hours worked, the rate remains 27 rupees per hour. By the end of the second year, total operating hours increase to 4000, which raises the rate to 40.5 rupees per hour due to the cumulative downtime costs.

Think of a restaurant that measures its success in terms of hours it operates. If it spends 54,000 rupees on downtime in its first 2000 hours of operation, the cost per hour is 27 rupees. As it continues and operates for an additional 2000 hours, the cost per hour increases to 40.5 rupees due to earlier downtime expenses.

Downtime leads to loss in productivity, resulting in increased costs. When machinery is being repaired, productivity decreases.

To return productivity to original levels, costs increase as more machines or operators are needed.

When machines undergo repairs, their absence leads to a loss of productivity, which can have a snowball effect on overall operations. To compensate for this loss and meet production targets, businesses may need to hire additional workers or rent additional machinery, thus increasing costs further.

Imagine a bakery that relies heavily on a single oven. When the oven breaks down, the bakery can’t produce bread. To meet demand, they may need to borrow an additional oven from a neighbor and possibly hire extra help to keep up with orders, leading to higher operational costs.

For first year: Productivity adjusted cumulative cost = rac{1,62,000}{(2000 \times 1)} = 27 rupees/hour. In the second year, with productivity factor of 0.98: Productivity adjusted cumulative cost = rac{40.5}{0.98} = 41.33 rupees/hour.

To account for decreased productivity due to downtime, we must adjust the cumulative cost calculations. For the first year, the adjustment does not affect the cost, but in the second year, we observe a productivity loss, which means we will divide the cumulative cost by the productivity factor (0.98). This helps reflect the true cost per hour of operating, factoring in the lost productivity.

Think of your study time: if you intended to study for 10 hours but only managed 9 due to distractions, dividing your expected productivity by your actual productivity (9/10) would reflect how well you used your study time. Similarly, businesses need to calculate what their costs truly are when productivity slips.

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