4.3 - New Estimates and Remaining Life Considerations
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Calculating EAC for Purchase Price
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Today, we’re going to calculate the equivalent annual cost for an initial purchase price of a piece of equipment. If we have a purchase price of 3,500,000 and we want to calculate this over three years at a 15% interest rate, what are the steps?
We would use the Uniform Series Capital Recovery Factor formula, right?
Exactly! The EAC can be found using the formula: EAC = USCRF × Purchase Price. So, what’s the USCRF for our given values?
It’s 0.4380 for three years.
Correct! So, we multiply 0.4380 by 3,500,000 to get the EAC.
That would give us 1,533,000, right?
Yes! Always remember, EAC tells us how much we would pay yearly based on a one-time purchase. Great job!
Operating and Maintenance Costs
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Now, let’s move to operating and maintenance costs. How do we convert an operating cost into present worth and then into EAC?
We would first find the present worth using the present worth factor.
Exactly! For an operating cost of 113,200 at the end of Year 1, what’s the present worth?
Using a present worth factor of 0.8696, it becomes about 98,438.72.
Right! And how do we proceed to convert this to EAC?
We multiply the present worth by the USCRF for Year 1, which is 1.15!
Perfect! Now, what does that give us as the EAC for Year 1?
About 113,204.53...
Exactly! This calculation helps us understand annualized costs.
Resale Value Considerations
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Next, let’s discuss how resale value plays into our calculations. Why is it important to consider?
Because it can offset costs when calculating EAC!
Right! If we project a resale value at the end of Year 1, say 31,500,000. How do we find the present worth?
We multiply it by the present worth factor for Year 1, which is 0.8696.
Great! What’s the resale value present worth?
It’s roughly 27,39,240.
Yes! But how does this affect our total EAC?
We subtract it from overall costs since it's cash inflow, right?
Exactly! This approach helps us keep track of our net costs.
Determining Economic Life
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Lastly, let’s discuss determining the economic life. How do we find the optimal replacement point using EAC?
We track the EAC on a graph and look for the lowest point, right?
Correct! This lowest point gives us our economic life. If that happens around Year 3, what do we interpret?
That’s when we should consider replacing the equipment!
Yes! It’s vital for optimal operational efficiency.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The focus here is on understanding how to derive equivalent annual costs (EAC) for the purchase price, operating costs, and maintenance costs over time, along with adjustments for resale values and consideration of remaining life due to equipment depreciation and usage.
Detailed
New Estimates and Remaining Life Considerations
In this section, we explore the process of calculating the Equivalent Annual Cost (EAC) for various components of equipment expenses, including the initial purchase price and ongoing operating and maintenance costs. The EAC provides insights into the annualized costs over the equipment's useful life.
Key Calculations and Concepts
- Initial Purchase Price: The EAC can be evaluated by applying formulas involving the Uniform Series Capital Recovery Factor (USCRF). For example, to find EAC for a purchase price of 3,500,000 over a period of three years at an interest rate of 15%, the formula:
$$ EAC = USCRF imes Purchase Price $$
results in a calculated EAC of 1,533,000.
- Operating and Maintenance Costs: The assessment of ongoing costs begins with determining the present worth of future operating costs (e.g., 113,200 at the end of Year 1). Steps include calculating these amounts into present value using the present worth factor, followed by deriving their EAC similarly using the USCRF. For example, multiply present worth by the USCRF at the desired year to convert values back into annual equivalents.
- Cumulative Costs and Resale Value: It is essential to note that as equipment ages, the estimated resale value can be factored back into EAC calculations. The article illustrates deriving EACs for various years while adjusting costs based on depreciation and operational demand, factoring in the impact of resale value on overall cost assessments, calculating future cash flows based on present worth factors and uniform series capital recovery factors relevant to each designated year.
- Economic Life Determination: Key to optimizing financial outcomes is determining when the equivalent annual cost reaches its minimum, indicating an optimal replacement point for the equipment.
This meticulous examination allows users to optimize machinery utilization, operational expenses, and overall investments, ensuring informed economic decisions through equivalent annual cost analysis.
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Equivalent Annual Cost Calculation for Year 3
Chapter 1 of 5
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So, now we have to find the equivalent annual cost for the third year of the purchase price 3500000 for year 3,
\[
A = rac{i(1+i)^n}{(1+i)^n-1} ext{ USCRF} = 0.4380 ext{ (3500000, 0.15, 3)} \
\]
EAC = 0.4380 × 3500000 = 1533000 rupees.
Detailed Explanation
To calculate the Equivalent Annual Cost (EAC) for the purchase price of 3,500,000 in year 3, we first determine the Uniform Series Capital Recovery Factor (USCRF). The formula for USCRF involves the interest rate (0.15) and the number of years (3). After calculating this factor to be 0.4380, we can find the EAC by multiplying the purchase price by this factor, resulting in an EAC of 1,533,000 rupees.
Examples & Analogies
Think of EAC like spreading the cost of a new car over its useful life. Instead of paying for the car all at once, you can think about how much it costs annually, helping you budget better for that purchase.
Calculating Present Worth of Operating and Maintenance Costs
Chapter 2 of 5
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Now let us find the equivalent annual cost of the operating and the 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. 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.
P.W = \[ P = \frac{1}{(1+i)^n} = 0.8696 ext{ (113200, 0.15, 1)} \]
Present worth value = 0.8696 × 113200 = 98,438.72 rupees.
Detailed Explanation
To find the equivalent annual cost for operating and maintenance costs, we start by calculating the present worth of the cost incurred at the end of year 1 (113,200 rupees). Using the present worth formula, we find that it equates to about 98,438.72 rupees. This initial step is crucial as it gives us a basis for calculating equivalent costs in a consistent time period.
Examples & Analogies
Imagine planning a vacation. If you pay for various things (like flights and hotels) at different times, finding out how much you should save every month for that vacation helps you budget better. Similarly, we break down costs here to understand the total in today's terms.
Calculating Equivalent Annual Costs for Years 2 and 3
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EAC of O&M cost = \[ A = i(1+i)^n = 1.15\text{ (98438.72, 0.15, 1)} \]
EAC of O&M = 1.15 × 98,438.72 = 113,204.53 rupees.
Detailed Explanation
For year 2, the equivalent annual cost of operating and maintenance is derived from the present worth calculated for the previous year. Using the uniform series capital recovery factor for year 2 (which is calculated similarly), we estimate future costs based on the present worth we calculated earlier. Continuing this for each year helps us understand the evolving cost structure.
Examples & Analogies
If you have a yearly subscription for a service, knowing the upfront cost lets you break it down into monthly payments, ensuring you can plan your budget accurately each month.
Considering Salvage Value and Total Cost Calculation
Chapter 4 of 5
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So, now let us find the equivalent annual cost of the resale value, that is your salvage value... So, first calculate the present value of the resale value, present value of your resale value 31,50,000, so use the present worth factor...
EAC of resale value for year 1 = 1.15 × 27,39,240 = 31,50,126 rupees.
Detailed Explanation
When considering the salvage value, we apply the same principles we used before. By calculating the present worth of the resale value of 31,500,000, we convert this into an equivalent annual cost, ultimately arriving at the EAC of the resale value for year 1 as 31,50,126 rupees. This process highlights the importance of also considering what you can recover from an asset after its useful life.
Examples & Analogies
Consider selling your old phone after buying a new one. The amount you can recover from selling the old phone should factor into the total cost of owning the new one. Just like evaluating asset resale value helps in making financially sound decisions.
Summary of Total Costs and Cost Analysis
Chapter 5 of 5
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So, now you can find the total cost... EAC of purchase price, O&M, salvage value=40,25,000+1,13,204.53–31,50,126 = 9,88,078.53.
Detailed Explanation
To derive the total cost of owning and maintaining the machine, we combine the equivalent annual costs from the purchase price and operating costs and account for the salvage value, – that is, what we expect to recover when we sell the asset. This summation gives a clear view of the financial commitment over the machine's life.
Examples & Analogies
It’s similar to deciding whether to keep a gym membership. You’d sum up the yearly cost of the membership, add in what you might 'recover' through benefits like improved health or fitness and subtract the value of any old memberships or sessions you might have left. This gives you a clearer idea of whether it’s worth continuing.
Key Concepts
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EAC Calculation: Method to find yearly costs from one-time expenses.
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USCRF: Factor converting present values to annual costs.
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Resale Value: Impact on total EAC through adjustments.
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Economic Life Determination: Identifying optimal replacement points.
Examples & Applications
Calculating EAC for Purchase Price: If the purchase price is 3,500,000, the EAC for 3 years at 15% is 1,533,000.
Operating Cost Analysis: For an operating cost of 113,200, the present worth and EAC calculations yield annual costs for ongoing expenses.
Memory Aids
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Rhymes
To find the cost that's fair, consider how much you share, EAC will lead the way, keeping thrifty, day by day.
Stories
Imagine a farmer deciding when to sell his old tractor based on repair costs and his savings from resale. The wise farmer keeps records of his tractor's performance until he finds the best time to sell, ensuring he maximizes his profit and keeps his budget intact.
Memory Tools
Use the acronym EAC to remind you: E - Evaluate, A - Annualize, C - Costs.
Acronyms
Remember the term REMS for Resale, EAC, Maintenance, and Sunk costs to categorize calculations.
Flash Cards
Glossary
- Equivalent Annual Cost (EAC)
A method to evaluate the annualized cost of owning and operating equipment over its useful life.
- Uniform Series Capital Recovery Factor (USCRF)
A factor used in financial math to convert present worth of a series of payments into equivalent annual payments.
- Present Worth Factor
A factor used to calculate the present value of a future cash flow based on a specific interest rate.
- Salvage Value
The estimated resale value of equipment at the end of its useful life.
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