1.4. Present Worth of Operating and Maintenance Cost Calculation

So, now we have to find the equivalent annual cost for the third year of the purchase price 3500000 for year 3,

USCRF = \frac{A  \cdot i(1+i)^n}{(1+i)^n - 1} = \frac{0.15(1+0.15)^3}{(1+0.15)^3 - 1} = 0.4380
EAC = 0.4380 \times 3500000 = 15,33,000 rupees

So like this you are going to calculate for all the years.

In this section, we are calculating the Equivalent Annual Cost (EAC) for the third year of an asset with a purchase price of 3,500,000 rupees. The EAC helps in understanding the annualized version of the total cost of the asset.

First, we compute the Uniform Series Capital Recovery Factor (USCRF) using the formula provided. Here, the interest rate is 15% (0.15) and the time period is 3 years. Using the calculation, we get the USCRF value of 0.4380.

Next, we multiply the USCRF by the total purchase price (3,500,000 rupees) to find the EAC for year 3, which is 15,33,000 rupees. This EAC could be applied for annual budgeting or comparative analyses with other costs over time.

Think of buying a car for 3,500,000 rupees. To determine how much that car 'costs' you annually, you would want to consider not just the initial payment but also financing costs (interest), insurance, and maintenance. Similarly, the EAC method gives you a yearly figure that reflects the real cost of owning the asset, making it easier to compare against future expenses.

Now let us find the equivalent annual cost of the operating and the maintenance cost. So, how to find the equivalent annual cost let us go back to the cash flow diagram. So, this 1,13,200 is operating and maintenance cost at the end of year 1. Now you convert it into t = 0, how to convert it into t = 0, find the present worth? So, find the present worth of 1,13,200, so that is a first step.

In this step, we are finding the present worth of the operating and maintenance costs that are incurred at the end of year 1, which is 113,200 rupees. To do this, we need to calculate its present value as of time t = 0 (the present time).

This is typically done using the present worth factor, which discounts future cash flows back to their value today. After finding the present worth of 113,200 rupees through this factor, we can then calculate the equivalent annual cost (EAC) using the previously discussed USCRF.

Imagine you are considering a payment you will make in the future, like college tuition due in a year. To determine its value today (for your savings decision), you would calculate its present worth, as inflation and saving rates would change how you view that amount. Thus, present worth helps in determining today’s value of future costs.

So, we are going to find the present worth of 1,13,200 that is your operating cost. So, you need to find P for the known F, i, n,

P.W = \frac{1}{(1 + i)^n} = \frac{1}{(1 + 0.15)^1} = 0.8696

This present worth factor you multiply it by the operating and maintenance cost Present worth value = 0.8696 \times 1,13,200 = 98,438.72 rupees.

This chunk describes how to find the Present Worth factor associated with our future operating costs. With an interest rate of 15% (0.15) and for one period (n=1), we first calculate the Present Worth (P.W) factor, resulting in 0.8696.

When we multiply this factor by the future cost of 1,13,200 rupees expected at the end of year 1, we obtain a present worth value of 98,438.72 rupees. This means if you wanted to have the equivalent value today that you will pay in the future, you would need to have 98,438.72 rupees today.

Think of it this way: if you plan to buy a piece of equipment next year for 1,13,200 rupees, how much money would you need to invest today at 15% interest to afford that payment? The present worth calculation helps you understand this value in today’s terms.

So, like this you are going to calculate the present worth of all the operating and maintenance cost. So, let us workout for one more trial, so that you will understand better.

So, this is your operating and maintenance cost, we are going to find the present worth of 2,83,500,

P.W = \frac{1}{(1 + i)^n} = \frac{1}{(1 + 0.15)^2} = 0.7561
Present worth value = 0.7561 \times 2,83,500 = 2,14,354 rupees.

In this chunk, we calculate the present worth of another operating and maintenance cost, which is 283,500 rupees, expected at the end of year 2. Using the present worth factor for two years at the same interest rate (0.15), we compute a factor of 0.7561. This represents the discounting necessary to find the current worth of that future cost.

We multiply this factor with the future cost (283,500 rupees) to find a present worth of 214,354 rupees. This process is repeated for all applicable operating and maintenance costs to accumulate the total present worth.

Consider planning a large event with expenses accumulated yearly. To gauge how much money you'd need today in savings to cover those future costs, you'd calculate the present worth of each year's expenses. Here, we're doing that for machine operational costs in the same systematic manner.

Now your present value of your operating and maintenance cost, you are going to find the A for the given P, i, n,

USCRF = \frac{A  \cdot i(1+i)^n}{(1+i)^n - 1} = \frac{0.15(1+0.15)^1}{(1+0.15)^{1-1}} = 1.15.

EAC of O&M cost = 1.15 \times 98,438.72 = 1,13,204.53 rupees.

Here we take the present value of the operating and maintenance costs we calculated earlier (98,438.72 rupees). To derive the equivalent annual cost (EAC) from the present value, we compute the USCRF, which for year 1 results in a value of 1.15 (using a rate of 0.15). This factor allows us to convert a lump sum present value into an annual series of costs.

Multiplying the present worth value by this factor yields an annual equivalent of 1,13,204.53 rupees, which signifies what must be budgeted annually for these costs over the asset’s lifespan.

Imagine you have a fixed amount of debt that you’d like to pay off through regular annual payments. The annual amount you’d pay, considering interest, represents how you’d convert a lump sum into more manageable yearly payments. In business, the EAC helps budget for future expenses consistently.

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