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Interactive Audio Lesson
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Introduction to Equivalent Annual Cost (EAC)
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Today, we will learn about Equivalent Annual Costs or EAC. This is a crucial concept because it helps us compare costs effectively over different time periods.
Why is it important to calculate the equivalent annual cost?
Great question! Calculating EAC allows us to assess the annual cost impact of a purchase over its lifespan, making future financial planning more manageable.
Can you give us an example?
Sure! For example, if we buy a machine for 3,500,000 rupees, understanding its EAC can help us decide if we should keep it or replace it.
Calculating Present Worth Factors
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Let’s dive into calculating present worth factors. For a cash flow in year 3, we need to understand the formula: P.W = F / (1+i)^n.
What does each variable represent?
Good question! 'F' is the future cash flow, 'i' is the interest rate, and 'n' is the number of years until the cash flow occurs.
How do we apply this to our calculations for resale value?
Exactly! We use the future cash flow of the resale value and apply it over the time period to find its present worth.
Calculating Equivalent Annual Cost for Operating Costs
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Now let’s calculate the EAC of operating costs. Suppose our operating cost is 113,200 rupees; we first find its present worth.
What’s the process to find this present worth?
You would use the present worth factor, and multiply it by the operating costs to convert these future cash flows to today’s value.
So it’s similar to how we calculated the resale value?
Exactly! After finding the present worth, we then convert that to EAC using the uniform series capital recovery factor.
Integration of Resale Values into Total Costs
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Let's now discuss how resale values impact our total costs. When calculating total EAC, we need to subtract the resale value from our total expenditures.
How does this affect our decision to keep or replace equipment?
Excellent point! Understanding the net cost after factoring the resale value can help us determine the economic feasibility of machine replacement.
So, can we see the financial benefits of replacing an older machine?
Exactly, by evaluating the EAC including resale values, we can make more informed replacement decisions.
Introduction & Overview
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Quick Overview
Standard
The chapter delves into the methodology for determining the equivalent annual cost associated with the purchase price of a machine, including calculations for operating and maintenance costs. It emphasizes how to find present worth values and subsequently convert them into equivalent annual costs using uniform series capital recovery factors.
Detailed
In this section, we examine the conversion of future cash flows, like resale values and operating costs, into present worth factors to understand their economic implications. Starting with the example of a machine purchased for 3,500,000 rupees, the teacher leads students through the calculation of equivalent annual costs (EAC) for both purchase and operating costs based on a specified interest rate. The section reinforces concepts such as the uniform series capital recovery factor (USCRF) and the methods for assessing the present worth of costs incurred over time. Examples illustrate the calculations for operating and maintenance costs, culminating in a discussion on the cumulative total costs and their implications for replacement decisions. This analysis is crucial for making informed financial decisions regarding machinery and operations.
Audio Book
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Finding Present Worth of Operating Costs
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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
Detailed Explanation
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.
Examples & Analogies
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.
Calculating Present Worth for Down the Line Costs
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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
Detailed Explanation
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.
Examples & Analogies
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.
Equivalent Annual Cost Calculation
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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
Detailed Explanation
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.
Examples & Analogies
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.
Present Worth of Resale Value
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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
Detailed Explanation
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.
Examples & Analogies
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.
Calculating Equivalent Annual Cost of Resale Value
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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
Detailed Explanation
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.
Examples & Analogies
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.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Equivalent Annual Cost (EAC): A method to determine the annualized cost of owning and operating an asset.
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Present Worth Factor: A crucial calculation in converting future cash values into present-day equivalents.
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Uniform Series Capital Recovery Factor: A key factor in determining the annual recovery amount for an investment.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example of EAC Calculation: If a machine costs 3,500,000 rupees, and the USCRF for the first year at 15% is 1.15, EAC can be calculated as 3,500,000 * 1.15.
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Calculating Present Worth for an Operating Cost of 113,200: Using a 15% interest rate, if the present worth factor is 0.8696, the present worth will be 113,200 * 0.8696.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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EAC you see, is the cost for me, to know how much I pay, to keep the machine at bay!
📖 Fascinating Stories
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Imagine a factory manager named Alex, who always calculated costs wrong. One day, he discovered EAC, and his budgeting became strong. Now, with each machine's cost in hand, he can make the best decisions in demand!
🧠 Other Memory Gems
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EASy - Equivalent Annual Series: Convert now to make future money clear!
🎯 Super Acronyms
PWFP - Present Worth Factor is Powerful for understanding investments.
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Equivalent Annual Cost (EAC)
Definition:
The fixed annual cost associated with owning and operating an asset over its useful life.
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Term: Present Worth Factor
Definition:
A ratio that converts future cash flows into their equivalent present value based on a specific interest rate.
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Term: Uniform Series Capital Recovery Factor (USCRF)
Definition:
A factor used to determine the annual payment required to recover the cost of an investment made at a specific interest rate over a predetermined period.