4.1. Defender vs. Challenger Overview

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 (𝟑𝟓𝟎𝟎𝟎𝟎𝟏,𝟏𝟓,𝟑) (𝟏+𝒊)𝒏−𝟏 (𝟏+𝟎.𝟏𝟓)𝟑−𝟏 EAC = 0.4380 × 35,00,000 = 15,33,000 rupees

To determine the Equivalent Annual Cost (EAC) for the purchase price for the third year, we use a formula that involves calculating the Uniform Series Capital Recovery Factor (USCRF). The USCRF is calculated using the interest rate and the time period, in this case, for year 3. We find a value of 0.4380, which is then multiplied by the total purchase price of 3,500,000 rupees, giving us an EAC of 1,533,000 rupees for that year. This signifies the annual cost associated with the purchase price over its lifespan.

Think of it like spreading the cost of a car over its useful life instead of paying it all at once. If you buy a car for 3,500,000 rupees, you may plan to keep it for 10 years. Each year, you'll have to account for a part of that purchase price in your budget. This process directly helps in understanding how much you’re effectively 'paying' per year just to own the car.

So, how to find the equivalent annual cost of the operating and maintenance cost. 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 calculate the equivalent annual cost of the operating and maintenance expenses, we need to first determine their present value at the time of purchase (time t = 0). For this, we take the operating cost for year 1, which is 113,200 rupees, and find its present worth using a present worth factor. This factor accounts for the time value of money and reflects how much future cash flows are worth today. After determining the present worth, we can apply the USCRF to find the EAC of these costs.

Imagine you plan to pay a subscription of 113,200 rupees for a service every year. If you were to consider how much you'd need in hand right now to cover those payments into the future, you'd need to compute today’s value of that future payment. This is similar to putting aside a certain amount today that will cover your future costs.

So, like this you are going to calculate the present worth of all the operating and maintenance costs. So, let us compute it 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 𝟐𝟖𝟑𝟓𝟎𝟎,𝟎.𝟏𝟓,𝟐 (𝟏+𝟎.𝟏𝟓)𝟐 Present worth value = 0.7561 × 2,83,500 = 2,14,354 rupees

Continuing from our previous calculation of operating and maintenance costs, we now find the present worth of another cost, 283,500 rupees. Using the relevant present worth factor for year 2 which is 0.7561, we calculate that the present worth is 214,354 rupees. This approach allows us to aggregate all present values of future costs to understand the total burden today.

Think of this as calculating the total of all your future bills today. If you expect to pay 283,500 rupees next year while taking into account how money grows over time, the ability to compute a present value gives you a clear view of your current financial obligations.

So, you have supposed to find the equivalent annual cost of the purchase price and the operating and maintenance cost, your salvage value is in flow 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 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

When calculating the total equivalent annual cost (EAC), we must account for the purchase price, the annual operating and maintenance costs, and deduct the salvage value (which is considered a cash inflow). For instance, in year 1, if the EAC for the purchase price is 40,25,000 rupees and the EAC of the operating and maintenance cost is 1,13,204.53 rupees, while the salvage value is 31,50,126 rupees, the total equivalent annual cost sums up to 9,88,078.53 rupees.

Consider this like balancing your budget. If you have income from selling something (like a salvage value), you balance that against your new expenses and purchase costs to arrive at your net annual outlay—the remaining amount you need to manage each year.

--