1.9. Conversion to Present Worth Factor for Resale Value

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 𝟏𝟑𝟐𝟎𝟎,𝟏𝟓,𝟏 (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 future operating costs, we first need to determine the present worth factor (P.W). In this case, the operating cost is 113,200 rupees at an interest rate of 15% over one year. Using the formula, we calculate the present worth factor as 0.8696. We then multiply this factor by the operating cost to find its present worth, leading us to a present worth value of approximately 98,438.72 rupees.

Imagine you plan to receive a payment of 113,200 rupees one year from now. However, if you were to invest that amount today with a 15% interest rate, you would effectively receive less today than the full amount next year. This concept is similar to understanding how much a future expense is actually worth in today’s money.

So, let us workout for one more trial, so that you will understand better.

So, this is your operating and maintenance cost. We are going to find the present worth of 2,83,500,

𝑷 𝟏 P.W = = = 0.7561 𝟐𝟖𝟑𝟓𝟎𝟎,𝟏𝟓,𝟐 (𝟏+𝟎.𝟏𝟓)𝟐

Present worth value = 0.7561 × 2,83,500 = 2,14,354 rupees

In this example, we are looking at another operating and maintenance cost amounting to 283,500 rupees over two years. We calculate the present worth factor for this time period and interest rate, yielding a value of 0.7561. We then multiply this factor by the future operating cost to arrive at a present worth value of 214,354 rupees, reflecting its value in today’s terms.

Think of planning a vacation that costs 283,500 rupees in two years. If you could invest this money instead at a 15% return, the amount you would need to save today would be less, represented by the present worth. This helps you plan better by showing the true cost of future expenses today.

So, now you have found the present value of your operating and maintenance cost, 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 the 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 (𝟗𝟖𝟒𝟑𝟖.𝟕𝟐,𝟏𝟓,𝟏) (𝟏+𝒊)𝒏−𝟏 (𝟏+𝒊)𝒏−𝟏

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

Having determined the present value of operating costs as 98,438.72 rupees, we now convert this present value into an equivalent annual cost (EAC). Using the uniform series capital recovery factor formula, we keep the interest rate of 15% and the period of 1 year in mind. Following calculations will guide us to an EAC of approximately 113,204.53 rupees, indicating the average annual cost of this expense.

Consider you need to budget for regular monthly expenses on a subscription service. Instead of paying a lump sum every year, you would like to understand how much you need to set aside each month. The EAC helps you think about expenses like a monthly bill, allowing for easier financial planning.

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. So, you can directly convert into an equivalent annual cost using the uniform series sinking fund factor or the another method is you find it is present value, you convert this future cash flow into t = 0, convert it into t = 0 using present worth factor.

Present value of your resale value 31,50,000, so use the present worth factor. 𝑷 𝟏 P.W = = = 0.8696 𝟑𝟏𝟓𝟎𝟎𝟏,𝟏𝟓,𝟏 (𝟏+𝟎.𝟏𝟓)𝟏 Present worth value = 0.8696 × 31,50,000 = 27,39,240 rupees

To assess the resale value, or salvage value, which is expected at the end of year 1, we can use the present value approach. In this case, if the salvage value is pegged at 31,50,000 rupees, we first apply the present worth factor, resulting in a present worth of 27,39,240 rupees reflecting today's value of that future amount.

When selling a car that you plan to trade in later, understanding its future value helps you decide how much to spend on a new purchase today. The resale value represents what you’ll get back if you part with the item, just as this formula helps calculate what that future income means in present terms.

So, equivalent annual cost of your present worth of the resale value is 27,39,240 for this we have to find the equivalent annual cost, so we need to find A for the given P, i, n.

𝑨 𝒊(𝟏+𝒊)𝒏 𝟎.𝟏𝟓(𝟏+𝟎.𝟏𝟓)𝟏 USCRF = = = = 1.15 (𝟐𝟕𝟑𝟗𝟐𝟒𝟎,𝟏𝟓,𝟏) (𝟏+𝒊)𝒏−𝟏 (𝟏+𝒊)𝒏−𝟏

EAC of resale value for year 1 = 1.15 × 27,39,240 = 31,50,126 rupees

Here, we compute the equivalent annual cost of the resale value we just obtained. This involves knowing the present worth of 27,39,240 rupees, applied with the uniform series capital recovery factor calculated earlier. We arrive at the equivalent annual cost for the resale value, approximately 31,50,126 rupees, providing perspective on the yearly value derived from an asset.

Consider if you invested in a gadget with a resale value that offers returns in the long run. You would analyze its long-term benefits similar to this calculation, allowing you to assess what you could earn every year from holding on to your investment.

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