1.8. Calculating Equivalent Annual Cost of Resale Value

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 𝟎.𝟏𝟓(𝟏+𝟎.𝟏𝟓)𝟑 USCRF = = = = 0.4380 (𝟑𝟓𝟎𝟎𝟎𝟐𝟗,𝟎.𝟏𝟓,𝟑) (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) for the purchase price in the third year, we apply the formula using the uniform series capital recovery factor (USCRF). We find that the USCRF for year 3 is 0.4380. By multiplying this factor by the purchase price of 35,00,000 rupees, we determine the EAC for year 3 to be 15,33,000 rupees. This calculation converts the total cash outflow for the purchase price into an annual equivalent, making it easier to compare with other costs over time.

Imagine you bought a car for 35,00,000 rupees and want to understand how much that car costs you each year. By calculating the equivalent annual cost, you're essentially figuring out the yearly 'payment' if you had financed that entire purchase; in this case, 15,33,000 rupees. This way, you can easily see how this compares to your annual expenses related to fuel, maintenance, and insurance.

Now let us find the equivalent annual cost of the operating and 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.

To determine the equivalent annual cost of operating and maintenance costs, we first identify the costs and when they occur. For year 1, the operating and maintenance costs amount to 1,13,200 rupees. The next step involves converting these future costs into their present worth (value at time t=0) to account for the time value of money. This is necessary because money today is worth more than the same amount in the future due to inflation and interest.

Think of it as planning for a vacation. You know you’ll spend 1,13,200 rupees on your trip next year. If you want to set aside money today for that trip, you need to consider how much you could earn in interest on that money before your trip. The present worth is like figuring out how much to save today so you have exactly the right amount to spend next year for your vacation.

So, 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

Next, we calculate the present worth factor for the operating cost of 1,13,200 rupees using the formula for present worth. In this instance, the present worth factor (P.W) is calculated to be 0.8696, which reflects the value of the future cost in today's terms when considering an interest rate of 15%. By multiplying this factor with the annual operating cost, we can find the present worth value, which here turns out to be approximately 98,438.72 rupees.

Consider saving for a new phone that costs 1,13,200 rupees next year. If you deposit money into a savings account that earns 15% interest, you wouldn't need to save the full price today. Instead, by calculating the present worth, you discover that by saving 98,438.72 rupees today, you can manage to buy the phone next year using the interest earned.

So, now you have found the present value of your operating and maintenance cost, you have to find it is equivalent value, so go for the uniform series capital recovery factor. So, that means you are going to find A for the given P, i, n, what is a known P? P is nothing but your the present value is 98,438.72, interest rate is 0.15, n is 1.

After calculating the present worth, we now need to convert that present value back into an equivalent annual cost. This is achieved using the uniform series capital recovery factor. In our case, we use the present value of 98,438.72 rupees, at an interest rate of 15% over one year to find the equivalent annual cost.

Imagine you've saved 98,438.72 rupees today in your bank account and your bank gives you a 15% interest rate for one year. To understand what that money can provide you as an annual expenditure over the next year, you calculate its equivalent annual cost, revealing how much you can effectively use without depleting your savings.

Now let us find the equivalent annual cost of the resale value, that is your salvage value. So, let us go back to the cash flow diagram. So, now what you are going to do is, this is the salvage value which is occurring at the end of year 1.

Next, we calculate the equivalent annual cost of the resale value (or salvage value). This is a value that is expected to be received from the sale of the asset at the end of its useful life. Again, we can calculate this by converting the future resale value into present worth before figuring out its annual equivalent using the capital recovery factor. This process helps to standardize the value of future cash flows from selling the asset.

If you anticipate selling your car for a salvage value at the end of one year, this future amount isn't worth its full value today. For instance, if you expect to sell it for a certain price, this price needs to be converted to its present worth, much like figuring out what your car will really 'cost' you annually after considering how much you'll likely make when you sell it.

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