1.7. Calculating Equivalent Annual Cost for Year 3 of O&M Cost

So, now we have to find the equivalent annual cost for the third year of the purchase price 3500000 for year 3, 𝑨 𝒊(𝟏+𝒊)𝒏 USCRF = 0.4380 (𝟑𝟖𝟎𝟓𝟙𝟐𝟎𝟐𝟓,𝟎.𝟏𝟓,𝟑) EAC = 0.4380 × 35,00,000 = 15,33,000 rupees So like this you are going to calculate for all the years.

To find the Equivalent Annual Cost (EAC) of the operating and maintenance (O&M) costs specifically for year 3, we use the Uniform Series Capital Recovery Factor (USCRF).

First, we need to identify the purchase price which is 3,500,000. Using the interest rate (0.15) and the year (3), we calculate the USCRF, which comes out to be 0.4380. This factor helps us recover the total cost over the specified period.

Next, we multiply the USCRF by the purchase price: 0.4380 * 3,500,000 = 15,33,000 rupees. This value represents the EAC for year 3.

Consider a student who willingly contributes 100 dollars every year to a scholarship fund for a duration of 3 years. The amount they contribute each year is similar to the EAC in a financial model. Using different interest rates, the total contribution that needs to be accounted each year can be derived in a similar manner, keeping the student's initial donation constant.

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?

The first step to finding the equivalent annual cost of O&M is converting future costs back to present value (t = 0).

For the O&M cost of 113,200 at the end of year 1, we use the present worth factor with the known future amount, interest rate, and the number of periods. After computing the present worth using the formula, we multiply by the present worth factor to determine how much this future expense is worth today.

Imagine you're planning a vacation next year that will cost you 1,200 dollars. If you were to save up today, you wouldn't have to save the full 1,200 dollars if you can put that money into a savings account earning interest. By finding the present worth, you learn how much less you would need to save today compared to the entire cost next year.

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 𝟏 P.W = 0.8696 𝟏𝟏𝟑𝟐𝟘𝟎,𝟎.𝟏𝟓,𝟏 (𝟏+𝟎.𝟏𝟓)𝟏 This present worth factor you multiply it by the operating and maintenance cost Present worth value = 0.8696 × 1,13,200 = 98,438.72 rupees

To calculate the present worth factor (P.W) of the operating cost, we need to input the known values for the future cash flow (F = 113,200), interest rate (i = 0.15), and the number of periods (n = 1).

Using the formula, we derive the present worth factor as 0.8696. Next, we use this value to determine the present worth of the 113,200 rupees by multiplying: 0.8696 * 113,200 = 98,438.72 rupees. This value represents how much the operating cost is worth today.

Think of it like buying a concert ticket: if a ticket costs 100 dollars today, but you want to attend the concert next year when it may cost more due to popularity, the present worth helps you decide how much you should set aside today compared to what you might need to pay next year.

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 trail, so that you will understand better.

To find the total cost of operations and maintenance over multiple years, the present worth needs to be calculated for each subsequent year using the same approach, adjusting the values of F, i, and n for each year. After calculating for each year, add these present worth values together for a cumulative total.

Picture saving for several goals at once, each with its own timeline. Each goal has different amounts to save (like the operating costs in different years). By treating each goal individually and summing them up, you’ll know your total savings target, just like adding up your present worths.

Now your column 8 will be equivalent annual cost of the present worth of the operating and maintenance cost, how to find that? You know the present value of your operating and maintenance cost, you multiply this column by the uniform series capital recovery factor.

To finalize the calculation for year 1, take the cumulative present worth calculated previously and apply the uniform series capital recovery factor to determine the equivalent annual cost. Essentially, you take the total present worth from the O&M costs and multiply it by the factor to convert it into an annualized format.

If you were to spread out a total vacation cost over several months as monthly payments, this step is like determining how much you'd need to set aside each month to pay for that vacation, similar to determining EAC for year 1.

So now we are going to calculate the equivalent annual cost of the present worth of operating and maintenance cost for year 2. EAC of O&M cost for year 2 = 0.6151 × 3,12,793.07 = 1,92,399.02 rupees

For year 2, we follow the same steps. After determining the present worth of the operating cost for year 2, we’ll apply the uniform series capital recovery factor, which in this case is 0.6151, to calculate the EAC. By multiplying this factor with the present worth gives us the EAC for year 2.

Continuing with the vacation analogy, just like you would determine how much to save monthly not just for one stretch but for another year as your expenses grow, you're applying a consistent method to ensure you're prepared for ongoing costs.

So, this is how you have to calculate for the third year. So, for the year 3, you know already the capital recovery factors for different years. EAC of O&M cost for year 3 = 0.4380 × 5,38,315.57 = 2,35,782.22 rupees

Here, we compute the EAC for year 3 in a similar manner as before. We utilize the uniform series capital recovery factor for year 3, which we found to be 0.4380, and multiply it by the present worth for year 3. This provides the EAC of 2,35,782.22 rupees.

Think about budgeting your monthly expenses again. Just as your expenses and income change from year to year, the EAC mirrors that variability by taking account of ongoing costs that might change as the years go on.

So like this you are going to calculate the equivalent annual cost for all for the entire useful life of the machine. By converting all cash flows into equivalent annual amounts, you can analyze and compare the annual operating costs focused around time.

Calculating the EAC for the entire life of the machine provides a clearer picture of the total costs incurred over time, enabling effective long-term planning. By understanding these costs consistently on an annual basis, it is easier to make financial decisions, such as whether to continue using or replace the machine.

Think of it as preparing for retirement: knowing exactly how much money you need to save or spend each year helps you make sound decisions about your financial future, just as EAC forecasts the operating costs related to specific machinery.

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