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Interactive Audio Lesson
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Understanding Equivalent Annual Cost (EAC)
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Today we're going to talk about Equivalent Annual Cost or EAC. Can anyone tell me why it's important?
Is it used to compare the costs of different investments over time?
Exactly! EAC helps us make fair comparisons by spreading out total costs across the lifespan of an asset. It makes future costs comparable.
So, how do we actually calculate EAC?
Great question! We use the formula EAC = USCRF × Total Cost. Here, USCRF stands for Uniform Series Capital Recovery Factor. It's a way to convert the total cost into an annual figure.
Calculating Present Worth of Costs
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Now, moving on, let's find out how we calculate the present worth of operating and maintenance costs. Who can explain what the first step is?
Do we need to find the present value of future costs?
Exactly! For instance, if the operating cost is 113,200 at the end of Year 1, we'd calculate its present worth using the formula P.W = F × P.W Factor.
And then we multiply that by the capital recovery factor to get the EAC, right?
That's right! You've got it.
Understanding Sunk Costs
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Let's talk about sunk costs. Who knows what this term means?
It's the money already spent that can't be recovered, right?
Correct! And why should we ignore these costs when making decisions?
Because they don't impact future cash flows. We should focus on future costs instead.
Exactly! Always remember: past costs shouldn’t influence your future decisions.
Cumulative Operating and Maintenance Costs
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Next, let's calculate the cumulative operating and maintenance costs. Why is this step important?
It's important because we need to consider total costs over multiple years.
Exactly! Once we have that cumulative figure, we can determine the EAC for these costs.
And those are added to the initial purchase price.
Right! Finally, we factor in resale value to find the net cost. Keep that in mind!
Introduction & Overview
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Quick Overview
Standard
The section delves into the process of calculating equivalent annual costs (EAC) using uniform series capital recovery factors, focusing on operating, maintenance costs, and understanding sunk costs as irrelevant in decision-making.
Detailed
In this section, we provide a comprehensive guide to calculating equivalent annual costs (EAC) for various financial considerations, such as purchase prices, operating and maintenance costs, and salvage values. The section illustrates the use of the uniform series capital recovery factor (USCRF) to convert future costs into present values and then into annual costs. Additionally, a critical examination of sunk costs highlights their irrelevance in replacement analysis, emphasizing that past investments should not influence future financial decisions.
Audio Book
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Calculating Equivalent Annual Cost for Year 3
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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 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.
Detailed Explanation
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.
Examples & Analogies
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.
Calculating Present Worth of Operating and Maintenance Costs
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Finding Present Worth Factors
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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
𝟏𝟏𝟑𝟐𝟎𝟎,𝟎.𝟏𝟓,𝟏 (𝟏+𝟎.𝟏𝟓)𝟏
Present worth value = 0.8696 × 1,13,200 = 98,438.72 rupees.
Detailed Explanation
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.
Examples & Analogies
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.
Cumulative Operating and Maintenance Cost
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Calculating Total Costs
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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.
Detailed Explanation
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.
Examples & Analogies
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).
Summary of Equivalent Annual Costs
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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.
Detailed Explanation
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.
Examples & Analogies
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.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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EAC: Essential for comparing different investment alternatives by converting total costs into an annual figure.
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USCRF: A crucial factor that aids in transforming lump sum costs into equal annual costs.
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Sunk Cost: Should be ignored in decision-making as they do not affect future cash flows.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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If you purchase machinery for $100,000 and expect it to last 10 years, the EAC would help you understand the annual cost of that machinery.
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When considering replacing a machine, if the total sunk cost is $200,000, this amount should not impact the decision since it cannot be recovered.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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EAC, EAC, costs spread out you see, make decisions wisely, and set your finances free.
📖 Fascinating Stories
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Once in a business, a manager spent so much on a failed project but learned that focusing on future profits was key - that's how they avoided the sunk cost trap.
🧠 Other Memory Gems
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For EAC remember: E - Equally spread, A - Annual costs, C - Compare wisely.
🎯 Super Acronyms
SUNK
- S: - Spent
- U: - Unrecoverable
- N: - Never let it influence
- K: - Keep looking forward.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Equivalent Annual Cost (EAC)
Definition:
A method of calculating the total cost of an investment spread out over its useful life.
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Term: Uniform Series Capital Recovery Factor (USCRF)
Definition:
A factor used to convert total costs into equivalent annual payments.
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Term: Sunk Cost
Definition:
Costs that have already been incurred and cannot be recovered; should not factor into future decisions.
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Term: Present Worth Factor
Definition:
A factor used to convert future cash flows into their present value.