5.1. Fuel Cost Estimation

Using uniform series capital recovery factor to convert initial cost into equivalent uniform annual cost.

The formula is:

$A = I \times \frac{i(1+i)^n}{(1+i)^n - 1}$

Where:

• $I$ = Initial cost (₹2,89,00,000)
• $i$ = Interest rate (8%)
• $n$ = Useful life (12.5 years)

Annualized initial cost = ₹ 37,41,844.41/year

To calculate the annualized initial cost, we use the uniform series capital recovery factor. This factor allows us to take a one-time initial cost and spread it across multiple years, taking into account the interest rate.

1. The initial cost of the machine is ₹2,89,00,000.
2. We apply the formula that includes the interest rate of 8% and the lifespan of the machine, which is 12.5 years.
3. When we calculate it, we find that the annualized cost comes to approximately ₹37,41,844.41. This means each year, for 12.5 years, we would 'spend' that amount to represent the initial investment in our calculations.

Think of it like a mortgage on a house. When you buy a house, you can’t just pay the full price upfront if it’s expensive. Instead, you pay a certain amount each month over many years. The bank considers interest in this payment. Annualized costs work similarly; we’re spreading out the expense of the machine over its useful life just like monthly mortgage payments.

Converting future salvage value into equivalent uniform annual cost:

$A = S \times \frac{i}{(1+i)^n - 1}$

Where:

• $S$ = Salvage value (20% of initial cost)
• Salvage value = 0.2 × ₹2,89,00,000 = ₹57,80,000

Annualized salvage value = ₹ 2,85,968.88/year

The salvage value is the estimated resale value of the machine at the end of its useful life. To convert this future value into an annualized cost, we again use a formula similar to the one for the initial cost:

1. First, we determine the salvage value which is 20% of the initial cost, making it ₹57,80,000.
2. Then, we apply a formula that accounts for the interest and time. The result gives us about ₹2,85,968.88 annually.
3. This figure now represents the annual income we can expect from selling the machine at the end of its useful life in our calculations.

Imagine you buy a car worth ₹20 lakh, and after 10 years, you expect to sell it for ₹4 lakh. Instead of thinking of the ₹4 lakh as a one-time event, we can think of it as receiving a 'salary' of ₹40,000 every year over 10 years. Salvage value works the same; it helps to consider it in relation to annual costs.

Hourly depreciation is calculated as:

$Hourly Depreciation = \frac{(A - SV)}{Annual\ use\ in\ hours}$

Where:

• $A$ = Annualized initial cost = ₹37,41,844.41
• $SV$ = Annualized salvage value = ₹2,85,968.88
• Annual use = 1600 hours.

Hourly Depreciation = ₹ 2,159.92/hour

To find the hourly depreciation, we calculate the difference between the annualized initial cost and the annualized salvage value, then divide that by the total hours the machine will be used annually:

1. We take the annual cost from the first calculation (₹37,41,844.41) and subtract the annual salvage cost (₹2,85,968.88).
2. This gives us the total depreciation over the year.
3. Then, we divide this depreciation by the number of hours the machine will operate annually, which is 1600 hours. The result is ₹2,159.92 per hour, indicating how much value the machine loses each hour it's in use.

Think of it like a pizza. If you buy a pizza for ₹1,000 and it’s expected to be worth nothing after you eat it all, you can think of the 'value lost' for each slice. If you eat it over 10 slices, you 'lose' ₹100 of value for each slice you eat. In this scenario, each hour of machine usage is like eating a slice, losing its value.

Calculating total hourly ownership cost involves:

• Hourly depreciation = ₹2,159.92
• Insurance cost = ₹361.25/hour
• Taxes = ₹541.88/hour

Total hourly ownership cost = ₹ 3,063.05/hour

The total hourly ownership cost is found by adding together all the individual costs associated with owning and operating the machinery per hour:

1. Start with the hourly depreciation which we calculated earlier as ₹2,159.92.
2. We then add the insurance cost (₹361.25/hour) and the taxes (₹541.88/hour).
3. Adding these together gives us the total ownership cost of ₹3,063.05 per hour, which represents all fixed costs associated with owning the equipment.

Imagine you run a delivery business and need a van. You count all costs like the depreciation of the van, insurance for it, and the parking fees you pay. Just like calculating expenses for a single hour of owning and using the van, here we are summing everything up to see what it costs to own and operate the machine each hour.

Estimating fuel costs involves:

• Fuel consumption factor: 0.14 liters/horsepower/hour.
• Rated horsepower: 250.
• Adjusted hourly fuel consumption = Operating factor x Rated power x Fuel consumption factor = 17.5 liters/hour.

Hourly fuel cost = 17.50 liters x ₹65/liter = ₹ 1,137.50/hour.

To calculate the hourly fuel cost, we first identify how much fuel our machine uses:

1. The fuel consumption factor tells us that our machine uses 0.14 liters for every horsepower it has.
2. Since our machine has a power rating of 250 horsepower, we can calculate that it will use around 35 liters for its total capacity.
3. However, we also consider the 'operating factor' which accounts for real-world conditions and reduces this to 17.5 liters an hour.
4. Finally, we multiply this number by the price of fuel to get the hourly cost, which is ₹1,137.50.

Think of your car driving in a city; it consumes more fuel per kilometer than on a smooth highway due to stop-and-go traffic. Just like fuel consumption may vary based on conditions, in this calculation, we adjust for how the machine actually runs in a working environment to find out what it costs to keep it going.

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