Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Calculating Equivalent Annual Cost (EAC)
Unlock Audio Lesson
Today we'll start with calculating the equivalent annual cost for our machine's purchase price. Who remembers the formula we use for this?
Is it using the USCRF?
Exactly right! The formula is EAC = USCRF times the purchase price. In our case, we’re using a purchase price of 3,500,000.
And what does USCRF stand for?
Good question! It stands for Uniform Series Capital Recovery Factor. It's important since it helps us convert future costs into equal annual costs. Let’s see if anyone can calculate the USCRF for us!
The USCRF for our case is 0.4380!
Perfect! Now, multiplying 0.4380 by 3,500,000 gives us our equivalent annual cost.
That would be around 1,533,000 rupees!
Yes! Now we have a better understanding of what the EAC tells us about our machine's financials. Remember, EAC helps in making better equipment replacement decisions.
Present Worth of Operating Costs
Unlock Audio Lesson
Now let’s talk about operating costs! Why is it important to calculate the present worth of operating costs?
So we can understand their impact over time?
Exactly! It helps in comparing initial costs with future expenses. So, how do we find the present worth of an operating cost of 113,200?
We use the present worth factor, right?
Correct! For an interest rate of 15% over one year, the present worth factor is 0.8696. Can someone calculate the present worth for me?
It will be approximately 98,438.72 rupees!
Excellent! This present worth will help us compute the equivalent annual cost for the operating costs.
And then we continue for different years, right?
Exactly! Each year’s operating cost is analyzed similarly.
Evaluating Salvage Value
Unlock Audio Lesson
Let’s look into salvage value. Why do you think the salvage value is considered in our calculations?
Because it’s a future cash inflow?
Right! It offsets some costs. When calculating the salvage value, how do we begin?
We find its present worth using the same present worth factor?
Exactly! For a resale value of 3,150,000, applying the present worth factor of 0.8696 gives us a present worth of about 2,739,240.
Then we find EAC for salvage value too?
Correct! We convert that into EAC just like other costs.
Calculating Total Equivalent Annual Cost
Unlock Audio Lesson
Finally, let’s compute the total EAC. Can anyone tell me how we calculate the overall total?
We add the EAC of purchase price with operating costs and subtract salvage value EAC.
Yes! So if our values are 4,025,000 for purchase price EAC, 1,13,204.53 for operating costs, and 3,150,126 for salvage value, what do we get?
It should be around 988,078.53 rupees!
Right! And can someone summarize why we do this?
To determine the optimal cost for maintaining our machine, while knowing when to replace it!
Great summary! Understanding these costs is crucial for effective management of our assets.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In this section, we learn how to compute the equivalent annual cost for both the purchase price of a machine and its operating costs using present worth factors and uniform series capital recovery factors. It emphasizes the importance of understanding these calculations for evaluating the economic life and optimal replacement time of equipment.
Detailed
Detailed Summary
This section provides a comprehensive overview of calculating the equivalent annual cost (EAC) of the purchase price and operating costs for a machine over its useful life. It begins by introducing the formula to calculate EAC based on the purchase price, using examples to demonstrate how to derive the values. The calculations involve different rates and years, applying the Uniform Series Capital Recovery Factor (USCRF) to convert future cash flows into present worth.
Important steps include:
1. Calculate EAC for the Purchase Price: Using the formula with the USCRF to determine the annual cost attributable to the purchase price.
2. Determine Present Worth of Operating Costs: This involves converting future operational expenses into present value, utilizing present worth factors.
3. Establish Equivalent Annual Costs for Different Years: By applying the USCRF on the present worth values of operating costs over their respective years.
4. Estimate Resale Value: Analyze the salvage value by calculating its present worth and converting it to an equivalent annual cost, considering the cash inflow.
5. Total Cost Computation: Summarize all costs to derive the total EAC, helping in decision-making about asset management in terms of economical efficiency.
The significance of this section lies in its practical application to real-world scenarios in asset management and equipment evaluation, ultimately aiding in determining the optimal time for equipment replacement.
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Calculating Equivalent Annual Cost (EAC) for Purchase Price
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
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 \USCRF = \frac{0.15(1+0.15)^{3}}{(1+i)^{n}-1} = 0.4380
EAC = 0.4380 × 35,00,000 = 15,33,000 rupees
So like this you are going to calculate for all the years.
Detailed Explanation
In this chunk, we are calculating the equivalent annual cost (EAC) of a purchase price of 3,500,000 for the third year. We use the formula for the Uniform Series Capital Recovery Factor (USCRF), which helps to determine how much of the total cost we need to account for on an annual basis. Here, we calculate the USCRF for year 3 with an interest rate of 15%, yielding a factor of 0.4380. We then multiply this factor by the purchase price of 3,500,000 to find that the EAC for the third year is 1,533,000 rupees. This process needs to be repeated for all years to understand their financial implications.
Examples & Analogies
Imagine you bought a car for 3,500,000 rupees. If you want to understand how much you need to save annually to cover the cost of the car over its lifespan (let’s say 10 years), you'd use similar calculations. By deciphering how much you're 'spending' each year, you can better manage your finances, just like understanding the EAC helps in budgeting for your purchases.
Calculating Present Worth of Operating and Maintenance Costs
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
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.
Detailed Explanation
This chunk introduces how to calculate the present worth of operating and maintenance costs, starting with identifying an operating cost of 113,200 rupees at the end of year 1. The first step is to convert this future cash flow into present value (P), which allows us to assess its worth in today's terms. To do this, we apply the present worth factor, which is calculated based on the interest rate and time period until year 1. By establishing this present worth, we can then use it to calculate its equivalent annual cost.
Examples & Analogies
Think of when you have to service your car. If a service costs you 113,200 rupees after one year, you need to consider how much you should set aside today to pay for that service later. Just as you'd figure out savings for the car service cost in advance, this financial analysis does the same for operating costs.
Using Present Worth Factors to Calculate Costs
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
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.W = \frac{P}{(1+i)^{n}} = 0.8696
Present worth value = 0.8696 × 1,13,200 = 98,438.72 rupees
Detailed Explanation
In this chunk, we calculate the present worth (PW) of the operating cost of 113,200 rupees for the first year. We determine the present worth factor given the future value, interest rate (15%), and period (1 year), resulting in a factor of 0.8696. By multiplying this factor with the future cost, we determine the present worth value to be 98,438.72 rupees. This conversion is crucial as it standardizes future costs to today’s value, making it easier to budget and plan financially.
Examples & Analogies
Consider saving for a vacation. If you plan to spend 113,200 rupees next year, you'd need to think about how much you should save today, considering the interest you could earn from that amount. This is akin to finding present worth; it helps in understanding the current equivalence of future expenses.
Calculating Equivalent Annual Cost for Maintenance for Subsequent Years
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
EAC of O&M cost = 1.15 × 98,438.72 = 1,13,204.53 rupees
So, this is an equivalent annual cost of the present worth of operating and maintenance cost for the year 1.
Detailed Explanation
This chunk focuses on converting the present worth of the operating and maintenance cost, calculated earlier, back into an annual format. We use the Uniform Series Capital Recovery Factor again; the equivalent annual cost for year 1 is calculated to be 113,204.53 rupees. This step transforms the present worth value into a yearly cost that can be budgeted and compared against the EAC of other expenses like the initial purchase price, allowing for comprehensive financial analysis.
Examples & Analogies
Imagine that the present worth of your vacation expenses turns out to be 98,438.72 rupees. By figuring out how much you need to save each year to reach that total, you can effectively budget for your dream vacation just like figuring out the equivalent annual maintenance cost helps in financial planning for the machine.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
EAC: A yearly cost that integrates multiple factors for efficient asset management.
-
USCRF: The key factor for converting future costs into equivalent annual costs, facilitating comparisons.
-
Present Worth: Allows future costs to be translated into present values for analysis.
-
Salvage Value: Represents potential financial inflow at the end of an asset's life, affecting total cost calculations.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Calculating EAC for a machine with a purchase price of 3,500,000 leads to an annual cost of approximately 1,533,000 rupees.
-
Converting an operating cost of 113,200 using present worth factor of 0.8696 gives a present worth of about 98,438.72 rupees.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
If you want costs to show, convert them with care, EAC is what you'll compare!
📖 Fascinating Stories
-
Imagine a factory deciding whether to keep a machine or buy a new one. They calculate all costs to find the true cost of keeping old equipment versus the new investment.
🧠 Other Memory Gems
-
Remember PERSIST - Purchase price, Interest, Resale value, Simplifications, Time - to calculate EAC!
🎯 Super Acronyms
EAC = Expenses | Annual | Calculated - Use these terms to remember what EAC means!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: EAC (Equivalent Annual Cost)
Definition:
A method to compute the yearly cost of owning an asset, factoring in purchase price, operating costs, and salvage value.
-
Term: USCRF (Uniform Series Capital Recovery Factor)
Definition:
A factor used to convert future amounts of money into an equal annual cost over a specified period and interest rate.
-
Term: Present Worth Factor
Definition:
A factor used to calculate present value of future cash flows.
-
Term: Salvage Value
Definition:
The estimated resale value of an asset at the end of its useful life.
-
Term: Operating and Maintenance Cost
Definition:
Ongoing costs incurred for running and maintaining an asset.