1.5. Calculating Equivalent Annual Cost for Year 1

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 𝟎.𝟏𝟕(𝟏+𝟎.𝟏𝟓)𝟑 USCRF = 0.4380 (𝟑𝟓𝟎𝟎𝟐𝟏𝟎,𝟏𝟓,𝟑) (𝟏+𝒊)𝒏−𝟏 (𝟏+𝟎.𝟏𝟓)𝟑−𝟏 EAC = 0.4380 × 35,00,000 = 15,33,000 rupees

To calculate the Equivalent Annual Cost (EAC) of the purchase price for Year 1, you first need to determine the Uniform Series Capital Recovery Factor (USCRF). For Year 3, with an interest rate (i) of 15% and a purchase price of ₹35,00,000, the USCRF is calculated as 0.4380. This factor is then multiplied by the purchase price to find the EAC. By performing this multiplication, you find that the EAC for the third year amounts to ₹15,33,000.

Think of the EAC as the monthly payment on a loan. If you took a ₹35,00,000 loan to buy a house, the bank would tell you your monthly payment based on the interest rate. Similarly, the EAC tells you how much, on average, it costs you per year to own that investment.

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. Once you find the present worth of 1,13,200 then you can find it is equivalent annual cost using uniform series capital recovery factor.

To find the equivalent annual cost (EAC) of operating and maintenance (O&M) costs, we first need to determine the present worth of these costs at year 1, which is ₹1,13,200. The present worth factor is used to convert future costs into today's value (t = 0). In this case, you will multiply the known future cost of ₹1,13,200 by the present worth factor for Year 1, which is 0.8696, resulting in a present worth of ₹98,438.72.

Imagine you want to plan your expenses for the next year. If you know you will spend ₹1,13,200 on maintenance, you would want to know how much that is worth in today's money to understand your budget. By calculating the present worth, you can figure out how much money you really need today to cover that expense in the future.

So, now we are going to find the A, equivalent A for this P, so how to do that? USCRF = 1.15 EAC of O&M cost = 1.15 × 98,438.72 = 1,13,204.53 rupees

Once we have the present worth of O&M costs, we can calculate the EAC for these costs. We use the Uniform Series Capital Recovery Factor (USCRF), which for Year 1 is 1.15. We multiply the present worth of the O&M costs (₹98,438.72) by the USCRF (1.15). The result is the EAC for these costs, which sums up to ₹1,13,204.53 for Year 1.

Think of it like dividing your total annual expenses over the months. If you want to ensure you set aside enough money each month for maintenance, you would use the EAC to determine how much that should be. This way, you can manage your monthly budget effectively.

So, like this you are going to calculate the present worth of all the operating and maintenance cost. Now you add the cumulative, so find the cumulative operating and maintenance cost. So, now, next thing is we are going to find the equivalent annual cost of the present worth of the operating and maintenance cost.

After calculating the EAC for the first year's O&M costs, you will continue to calculate for subsequent years. You will sum up all previous EACs to generate a cumulative total. This total will then be used when calculating the overall equivalent annual cost of the investment, incorporating purchase price, O&M costs, and considering any salvage value.

This process is akin to saving money each month. If you know that certain costs will reoccur, you want to calculate how much you'll accumulate over the years. This way, you have a clearer picture of your financial situation and can make better planning and spending decisions.

--