3. Depreciation Calculation

The initial cost is converted into equivalent uniform annual cost, annualized cost we call it as annualized initial cost using uniform series capital recovery factor.

To convert the initial cost of an asset into an annual cost, we use a formula called the uniform series capital recovery factor. This factor takes into account the initial investment amount, interest rate, and the lifespan of the asset. For example, if the initial cost is ₹2,89,00,000, and the interest rate is 8% with a lifespan of 12.5 years, the annualized initial cost can be calculated. The formula used is:

$𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 ext{ Annual Cost} = \text{Initial Cost} \times \frac{i(1+i)^n}{(1+i)^n - 1}$

This results in an annual cost of ₹37,41,844.41.

Imagine you buy a car for ₹2,89,00,000. Instead of thinking about this as a one-time purchase, you could think about how much that car 'costs' you each year. Using the formula helps you spread the cost over the years you'll use it and take into account the interest you'd be paying if you financed it.

Now I need to convert the future salvage value into equivalent uniform annual cost using uniform series sinking fund factor.

The salvage value of an asset is the estimated residual value at the end of its useful life. To find its equivalent annual cost, we use the sinking fund factor formula, which is:

$𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 ext{ Annual Salvage Cost} = \text{Salvage Value} \times \frac{i}{(1+i)^n - 1}$

If the salvage value is 20% of the initial cost of the asset, it can be calculated and annualized similarly to the initial cost. For instance, this calculation results in an annualized salvage value of ₹2,85,968.88.

Think of when you sell an old appliance. You might sell it for a lower price than what you paid. This 'salvage value' can be thought of in a way like a trade-in value on a car. Understanding its annualized value helps you to see how much you gain from it each year as you use the appliance.

Hourly depreciation is calculated as the difference between the annualized initial cost and the annualized salvage value divided by the annual use of the machine in hours.

To determine how much value an asset loses per hour of usage, start by calculating the depreciation:

$\text{Hourly Depreciation} = \frac{ \text{Annualized Initial Cost} - \text{Annualized Salvage Value} }{\text{Annual Usage Hours}}$

For this example, with an annualized initial cost of ₹37,41,844.41 and an annualized salvage value of ₹2,85,968.88, if the machine is used for 1600 hours a year, the hourly depreciation comes to ₹2,159.92.

Imagine you're using a rental bike. Each time you ride, the bike loses a little value. If you ride for hours and know how much the bike costs, you can calculate how much it 'depreciates' each hour of use.

Other components of the ownership cost, such as insurance and taxes, are calculated as a percentage of the initial cost minus the tire cost.

Insurance and tax costs associated with the asset are often calculated as a percentage of its initial cost, which in this case is 2% for insurance and 3% for taxes. These costs are then divided by the annual usage to find the hourly equivalents:

$\text{Insurance} = \frac{2\% \times (\text{Initial Cost} -\text{Tire Cost})}{\text{Annual Usage in Hours}}$

$\text{Taxes} = \frac{3\% \times (\text{Initial Cost} -\text{Tire Cost})}{\text{Annual Usage in Hours}}$

This results in insurance of ₹361.25/hour and taxes of ₹541.88/hour.

Just like you pay for insurance and taxes on your house or car, you also have similar costs for equipment. By understanding and splitting these costs into hourly rates, it’s easier to see how much you’re truly spending.

Now, calculating the total hourly ownership cost involves adding hourly depreciation, insurance, and taxes together.

Total hourly ownership cost aggregates all costs including hourly depreciation, insurance, and taxes:

$\text{Total Hourly Ownership Cost} = \text{Hourly Depreciation} + \text{Insurance} + \text{Taxes}$

From the previous calculations, if hourly depreciation is ₹2,159.92, insurance is ₹361.25, and taxes are ₹541.88, the total hourly ownership cost will sum to ₹3,063.05.

It’s like calculating the total cost of owning a vehicle. You don’t just think about the monthly payment, but you also add in fuel, insurance, and maintenance. By considering all these costs, you get a clearer picture of your spending.

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