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1.1. Calculating the Equivalent Annual Cost for Year 3
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Today, we will discuss how to calculate the Equivalent Annual Cost or EAC. Can anyone tell me what EAC represents in cost analysis?
Isn't it the annual cost of owning and operating an asset?
Exactly! EAC helps us spread out all costs over the equipment's lifespan. Now, for the third year, we start with the purchase price—can you recall how much that was?
It's 3,500,000 rupees.
Great! Now, applying the USCRF for year 3 at 15%, which is 0.4380, we can calculate the EAC. Can anyone show me the calculation?
It's EAC equals 0.4380 multiplied by 3,500,000, which gives us 1,533,000 rupees!
Perfect! So the EAC for our purchase price in year 3 is 1,533,000 rupees.
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Let's now discuss operating costs. The first-year operating cost was given as 113,200 rupees. How do we find its present worth?
We use the present worth factor!
Correct! For year 1 with an interest rate of 15%, the present worth factor is 0.8696. Can someone calculate the present worth?
It's 98,438.72 rupees!
Excellent! Now, to find its EAC, which uniform series capital recovery factor do we use for year 1?
It’s 1.15!
So, how would we calculate the EAC for the operating cost?
We multiply 1.15 by 98,438.72.
Exactly! The calculation gives us approximately 113,204.53 rupees as the EAC of operating costs for year 1.
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Now let's find the EAC of the operating and maintenance cost for year 3. What do we do first?
We need to calculate the present worth of operating costs for year 3?
Correct! The given operating cost for year 3 is 538,315.57 rupees. What factor do we use?
The capital recovery factor for year 3, which is 0.4380!
Exactly. Can someone show how to arrive at the EAC for this operating and maintenance cost?
It’s 0.4380 times 538,315.57, which equals 235,782.22 rupees.
Great job! You've just calculated the EAC for operating and maintenance costs in year 3.
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Now that we have EAC for the purchase price and operating costs, how do we find the total equivalent annual cost?
We add the EAC of purchase price to the EAC of operating costs and then subtract the salvage value!
Exactly! So can anyone tell me what the total EAC would be if the salvage value is taken into account?
The total would be 1,533,000 plus 235,782.22 minus the resale value.
How do we find that resale value?
You would calculate it similarly by converting any future cash inflows of the salvage value into present value and then to EAC.
Oh! Got it! This helps to identify the economic life of the machine.
Exactly! That brings us to understanding the optimum time to replace the machine based on EAC calculations!
Overview
Short Summary
This section covers the process for calculating the equivalent annual cost (EAC) for the third year considering purchase, operating, and maintenance costs.
Medium Summary
This section explains how to calculate the Equivalent Annual Cost (EAC) for the purchase price, operating, and maintenance costs in the third year. It discusses steps to find each cost's present worth and uses uniform series capital recovery factors to convert these to EAC.
Detailed Summary
Detailed Summary
In this section, we detail the methodology for calculating the Equivalent Annual Cost (EAC) specifically for the third year, focusing on various cost components associated with a capital project. The process begins by determining the purchase price of 3,500,000 rupees and uses a uniform series capital recovery factor (USCRF) formula where
EAC = USCRF × Purchase Price.
Here, the calculated USCRF for year 3 at an interest rate of 15% is 0.4380, leading to an EAC of approximately 1,533,000 rupees.
Next, we transition to operational and maintenance costs. The initial operating and maintenance cost given is 113,200 rupees at the end of year 1, which is converted into present worth using the present worth factor and then expressed as an EAC through the USCRF. The process involves several steps: calculating present worth using the P.W factor, summing costs, and then converting it back to an EAC. For instance, for the year 1 operating cost, the present worth is calculated as 98,438.72 rupees.
Following through similar calculations for year 2 and year 3, we find that the EAC for O&M costs also remains consistent in methodology with various factors leading to different annual costs for subsequent years.
Lastly, after finding the recycle value or salvage value at year 3 using the same methodologies, students learn how to aggregate these determinations to assess total costs structured as cash inflows and outflows to reach a final equivalent annual cost which helps in making decisions about machine replacement and economic life estimation methods.
Audio Book
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Create a free accountSo, 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 (𝟑𝟓𝟎𝟎𝟎𝟏𝟏𝟓,𝟎.𝟏𝟓,𝟑) (𝟏+𝒊)𝒏−𝟏 (𝟏+𝟎.𝟏𝟓)𝟑−𝟏 EAC = 0.4380 × 35,00,000 = 15,33,000 rupees.
Detailed Explanation
To find the equivalent annual cost (EAC) for the third year of purchasing an asset that cost 3,500,000 rupees, we use the Uniform Series Capital Recovery Factor (USCRF). The formula allows us to calculate the EAC by multiplying the USCRF by the original purchase price. We determined that the USCRF for year 3 at an interest rate of 15% is 0.4380. By multiplying this factor by the purchase price, we calculate that the EAC for year 3 is 1,533,000 rupees.
Examples & Analogies
Think of it like spreading the cost of a car over its useful life. If you buy a car for 3,500,000 rupees and want to understand how much it costs you annually over three years, you would use a similar approach to find out your yearly expense for just that vehicle. It helps you decide if keeping the car is still financially sound.
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Create a free accountSo like this you are going to calculate for all the years. 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
To find the equivalent annual cost of the operating and maintenance (O&M) costs, we need to calculate the present worth of these costs first. For instance, consider the operating and maintenance cost of 113,200 rupees occurring at the end of year 1. We convert this future cost into present value using the present worth factor for year 1, and then we can obtain the EAC using the uniform series capital recovery factor. This same process is applied to each year's O&M costs.
Examples & Analogies
Imagine each maintenance expense as a future bill you have to pay. You wouldn't want to miss the total cost over several years. By calculating how much those bills would cost in today’s terms, you can better understand the financial impact and prepare for expenses, much like budgeting for an upcoming vacation.
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Create a free accountSo, now you can find the total cost. So, how to find the total cost? So, you are supposed to add the purchase price and the operating and maintenance cost, your salvage value is in flow cash inflow...
Detailed Explanation
To find the total equivalent annual cost, we add the EAC of the purchase price with the EAC of the operating and maintenance costs and subtract the EAC of the salvage value since that is a cash inflow. This gives us a complete picture of the annual cost associated with keeping the machine and helps evaluate its economic viability over time.
Examples & Analogies
Consider it like calculating the total cost of owning a house. You sum up the mortgage payment (purchase price), the yearly maintenance costs, and then subtract any income you earn from renting part of the house (salvage value). It's essential to see the full financial landscape, just like ensuring you can afford all aspects of that house before buying it.
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Key concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
- Capital Recovery:
Refers to the method of recovering the initial investment cost over the useful life of an asset.
- Present Worth Factor:
A calculation used to determine how much future cash flows are worth today.
- Salvage Value:
The estimated resale value of an asset at the end of its useful life.
Examples
Step-by-step examples to apply the section's ideas and test your understanding.
If the initial purchase price is 5,000,000 rupees and the USCRF for year 4 is 0.3255, the EAC would be 5,000,000 x 0.3255 = 1,627,500 rupees.
A machine with an operating cost of 150,000 rupees will have its present worth calculated as 150,000 x 0.8696 to find EAC for year 1.
Memory aids
Once a machine was bought for much strife, finding EAC gave it new life, with costs all aligned, its future defined, through each year’s given financial knife.
P.O.S.S.E. - Present Worth, Operating cost, Salvage value, Sum, EAC helps with machine life.
Flash Cards
Glossary
Equivalent Annual Cost (EAC)
The annual cost of owning and operating an asset over its entire life.
Uniform Series Capital Recovery Factor (USCRF)
A factor used to convert present worth into annual payments.
Present Worth
The current worth of a cash flow that occurs in the future, discounted back to the present.
Operating Cost
Expenses related to the operation of an asset or equipment.
Maintenance Cost
Costs incurred to maintain an asset in working condition.