4.2. Current Value and Sunk Cost Analysis

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 (𝟑𝟓𝟎𝟎𝟐𝟐𝟏𝟑,𝟎.𝟏𝟓,𝟑) (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, we use the formula that incorporates the purchase price and the Uniform Series Capital Recovery Factor (USCRF). In this case, for a purchase price of 3,500,000 rupees over a period with an interest rate of 15%, the USCRF gives a factor of 0.4380. By multiplying this factor by the total purchase price, we find the EAC for year 3 is 1,533,000 rupees.

Think of it like spreading out the cost of a car over its useful life. If the car costs you 3,500,000 rupees and you know it will last you 3 years, you'd want to estimate how much that costs you to keep it each year. The calculated EAC tells you that you'll be spending 1,533,000 rupees every year to account for its purchase.

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. 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 find the equivalent annual cost of operating and maintenance costs, we first need to determine their present worth at time t = 0. This involves using the formula for present worth (P.W) based on future cash flows (here, 113,200 rupees) discounted back to the present value as of year 0. Once we find this present worth using the appropriate factor, we can calculate the EAC using the USCRF.

Imagine you have a subscription service that charges you every month. To understand the cost today, you calculate how much you’d need to set aside now to make those future payments. By calculating the present worth of 113,200 rupees (equivalent to all your future payments), you can figure out how much that costs you every year.

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 Present worth value = 0.8696 × 1,13,200 = 98,438.72 rupees.

Here's where we specifically calculate the present worth factor for the operating costs. Using the formula for present worth (P.W) based on the future cash flow amount of 113,200 rupees, interest rate, and time period, we derive a present worth factor of 0.8696. By multiplying this factor by the future cash flow, we arrive at a present worth of 98,438.72 rupees.

Suppose you plan to pay off a debt in the future. To figure out how much you’d need to save today to cover that debt amount, you would apply a similar method: discounting it back to present value which tells you how much to set aside based on future payment expectations.

So, like this you are going to calculate the present worth of all the operating and maintenance cost. So, let us workout for one more trial, so that you will understand better. EAC of O&M cost = 1.15 × 98,438.72 = 1,13,204.53 rupees.

To estimate the cumulative operating and maintenance costs over multiple years, we need to calculate each year's present worth similarly, sum them up, and then determine their equivalent annual costs. For the first year, from our findings, it translates to 113,204.53 rupees. This process continues for subsequent years to maintain a complete cost forecast.

Think of managing a household budget, where you keep track of your monthly spending. Each month you calculate how much you need to allocate for bills, groceries, etc. As months go by, you sum these costs to get a total, which ultimately lets you know if you are within your budget or need to adjust.

So, you are supposed to add the purchase price and the operating and maintenance cost, your salvage value is in flow cash inflow, so you subtract it.

To find the total cost related to the asset, we tally the equivalent annual costs from the purchase price and operating and maintenance costs while deducting the salvage value—the cash inflow expected from selling the asset at the end of its useful life. The final figure represents the total cost of ownership per year.

Consider it like calculating the total cost of owning a pet. You'd add the initial purchase price of your pet (buying the pet), plus yearly expenses like food and healthcare (operating and maintenance costs), but you would subtract any money you might recoup if you decided to sell them or if they have a future value (salvage value).

So now you can find the total cost. So how to find the total cost? ... economic life of this machine is third year, the optimum replacement time of this machine is third year.

The summary emphasizes the comprehensive analysis performed throughout the section to reach a conclusion about the economic life of the machine. By calculating and comparing all relevant costs, we conclude that the optimal time to replace the machine is in the third year based on the lowest total equivalent annual cost.

Imagine deciding when to replace your old smartphone. You evaluate how much it costs you each year—repairs, lost opportunities for newer features, battery issues, etc. After tracking these for a few years, you identify that after year three, those costs become unreasonable compared to what a new phone would incur, guiding you to replace it then.

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