2.1. Adding Purchase Price and Operating Costs

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 = \frac{0.15(1+0.15)^{3}}{(1+i)^{n}-1} = 0.4380

EAC = 0.4380 × 35,00,000 = 15,33,000 rupees

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

In this chunk, we are calculating the equivalent annual cost (EAC) of a purchase price of 3,500,000 for the third year. We use the formula for the Uniform Series Capital Recovery Factor (USCRF), which helps to determine how much of the total cost we need to account for on an annual basis. Here, we calculate the USCRF for year 3 with an interest rate of 15%, yielding a factor of 0.4380. We then multiply this factor by the purchase price of 3,500,000 to find that the EAC for the third year is 1,533,000 rupees. This process needs to be repeated for all years to understand their financial implications.

Imagine you bought a car for 3,500,000 rupees. If you want to understand how much you need to save annually to cover the cost of the car over its lifespan (let’s say 10 years), you'd use similar calculations. By deciphering how much you're 'spending' each year, you can better manage your finances, just like understanding the EAC helps in budgeting for your purchases.

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.

This chunk introduces how to calculate the present worth of operating and maintenance costs, starting with identifying an operating cost of 113,200 rupees at the end of year 1. The first step is to convert this future cash flow into present value (P), which allows us to assess its worth in today's terms. To do this, we apply the present worth factor, which is calculated based on the interest rate and time period until year 1. By establishing this present worth, we can then use it to calculate its equivalent annual cost.

Think of when you have to service your car. If a service costs you 113,200 rupees after one year, you need to consider how much you should set aside today to pay for that service later. Just as you'd figure out savings for the car service cost in advance, this financial analysis does the same for operating 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{P}{(1+i)^{n}} = 0.8696 Present worth value = 0.8696 × 1,13,200 = 98,438.72 rupees

In this chunk, we calculate the present worth (PW) of the operating cost of 113,200 rupees for the first year. We determine the present worth factor given the future value, interest rate (15%), and period (1 year), resulting in a factor of 0.8696. By multiplying this factor with the future cost, we determine the present worth value to be 98,438.72 rupees. This conversion is crucial as it standardizes future costs to today’s value, making it easier to budget and plan financially.

Consider saving for a vacation. If you plan to spend 113,200 rupees next year, you'd need to think about how much you should save today, considering the interest you could earn from that amount. This is akin to finding present worth; it helps in understanding the current equivalence of future expenses.

EAC of O&M cost = 1.15 × 98,438.72 = 1,13,204.53 rupees So, this is an equivalent annual cost of the present worth of operating and maintenance cost for the year 1.

This chunk focuses on converting the present worth of the operating and maintenance cost, calculated earlier, back into an annual format. We use the Uniform Series Capital Recovery Factor again; the equivalent annual cost for year 1 is calculated to be 113,204.53 rupees. This step transforms the present worth value into a yearly cost that can be budgeted and compared against the EAC of other expenses like the initial purchase price, allowing for comprehensive financial analysis.

Imagine that the present worth of your vacation expenses turns out to be 98,438.72 rupees. By figuring out how much you need to save each year to reach that total, you can effectively budget for your dream vacation just like figuring out the equivalent annual maintenance cost helps in financial planning for the machine.

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