1.3. Present Worth Factor Calculation

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 (𝟑𝟖𝟓𝟎𝟎𝟎𝟎,𝟎.𝟏𝟓,𝟑) (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 third year of an asset that costs 3,500,000 rupees and has an interest rate of 15%, we first determine the Uniform Series Capital Recovery Factor (USCRF). The formula for USCRF is used to calculate how much each payment (EAC) is when you consider the interest rate and the duration of the loan (n). In this case, with i = 0.15 and n = 3, we calculate USCRF to be approximately 0.4380. Finally, by multiplying the USCRF by the original cost of the asset, we find that the EAC for the third year is 15,33,000 rupees.

Think of it like taking a car loan; when you take out a loan to buy a car, you want to know how much you'll pay each month. The USCRF helps us calculate that monthly payment by considering how long you'll pay it and the interest. Just like a loan, understanding how much you pay each year for an important purchase helps you budget for the future.

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 its equivalent annual cost using the uniform series capital recovery factor.

(Refer Slide Time: 25:26)

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 find the present worth of the operating and maintenance costs of 1,13,200 rupees occurring at the end of year 1, we use the present worth factor. We apply the formula for present worth, which incorporates the future cash flow, interest rate, and time. For i = 0.15 and n = 1, we calculate the present worth factor to be approximately 0.8696. Multiplying this factor by the operating cost gives us a present worth value of 98,438.72 rupees, which represents the worth of future costs in today’s terms.

Imagine you're making a commitment to pay for a gym membership. If the membership costs 1,13,200 rupees starting next year, you might wonder what that amount is worth today (how much you'd need to save today to have that amount next year after earning interest). The present worth calculation helps you understand how future expenses stack up against your current savings.

So, now you have found the present value of your operating and maintenance costs, you have to find its 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 present value is 98,438.72, interest rate is 0.15, n is 1.

A 𝒊(𝟏+𝒊)𝒏 𝟎.𝟏𝟓(𝟏+𝟎.𝟏𝟓)𝟏 USCRF = = = = 1.15 (𝟗𝟖𝟒𝟑𝟖.𝟕𝟐,𝟎.𝟏𝟓,𝟏) (𝟏+𝒊)𝒏−𝟏 (𝟏+𝒊)𝒏−𝟏

So, this factor you multiply it by the operating and the maintenance cost present value that is 98,438.72.

EAC of O&M cost = 1.15 × 98,438.72 = 1,13,204.53 rupees

After determining the present worth of 98,438.72 rupees for the operating and maintenance costs, we need to convert this present value into an annual cost. This is done using the uniform series capital recovery factor (USCRF). For our parameters, the USCRF calculation shows it to be 1.15 for a 15% interest rate over 1 year. Multiplying the present worth by this factor gives us the equivalent annual cost (EAC) of 1,13,204.53 rupees, providing a clear understanding of the annual cost of ongoing expenses.

Think of it as converting your savings into a monthly budget. If you have saved 98,438.72 rupees for a future expense, the EAC helps you figure out how much to set aside every month to cover that future cost, similar to determining a monthly rent from your one-time home purchase.

So, you are supposed to add the purchase price and the operating and maintenance cost, your salvage value is an inflow cash inflow, so you subtract it. So, what is your equivalent annual cost of the purchase price for the year 1? Equivalent annual cost of the purchase price is 40,25,000 you add it with the equivalent annual cost of the operating and maintenance cost.

EAC of purchase price, O&M, salvage value = 40,25,000 + 1,13,204.53 – 31,50,126 = 9,88,078.53

To find the total annual equivalent cost, we aggregate the various components: purchase price, operational costs, and any salvage value which is a cash inflow. Here, the EAC of the purchase price is given as 40,25,000 rupees, and the operational cost from previous calculations is 1,13,204.53 rupees. The salvage value received when selling the machine, 31,50,126 rupees, is subtracted from the total costs. Thus, we arrive at a total annual cost of 9,88,078.53 rupees.

This calculation is akin to managing a household budget. Suppose your monthly expenses include rent, groceries, and income from selling old items. You total your expenses but subtract any incoming cash from sales to find out how much you actually need to allocate each month, ensuring you stay on track with finances.

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