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Interactive Audio Lesson
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Initial Cost and Equivalent Annual Cost
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Today we are going to learn about how to convert the initial costs of machinery into equivalent annual costs using the capital recovery factor. Can someone tell me why it’s important to estimate such costs?
Is it to manage budgets effectively?
Exactly! By calculating annual costs, companies can understand their recurring expenses better. The formula we use is: \( EAC = I \times \frac{i(1+i)^n}{(1+i)^n-1} \), where EAC is Equivalent Annual Cost, I is Initial Cost, i is the interest rate, and n is the number of years.
Can you give an example using this formula?
Sure! For an initial cost of ₹2,89,00,000 with an interest rate of 8% over 12.5 years, we would find EAC to be approximately ₹37,41,844.41 per year.
What does this number represent?
This number represents the annualized cost that the company needs to budget each year to recover the initial investment. Remember it as EAC for future reference.
Salvage Value Calculation
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Now, let’s shift our focus to the salvage value. Who can tell me what salvage value is?
Is it the estimated resale value of equipment at the end of its useful life?
Right on target! Now, to calculate the annual equivalent of this salvage value, we use a similar approach. Can anyone remind us of the formula?
Are we using the sinking fund factor?
Exactly! The annual cost of the salvage is calculated as: \( SV_{annual} = SV \times \frac{i}{(1+i)^n - 1} \). With a salvage value of 20% of the initial cost, we can calculate this easily.
Can we do the calculation together?
Sure! If the initial cost is ₹2,89,00,000, the salvage value becomes ₹57,80,000, and using the sink fund factor gives us an annualized salvage value of approximately ₹2,85,968.88.
Hourly Depreciation
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Next, we will calculate hourly depreciation. Can anyone explain how we determine this?
Is it the difference between the initial and salvage value divided by the number of operational hours?
Exactly! We calculate it as: \( Hourly\ Depreciation = \frac{Annualized\ Initial\ Cost - Annualized\ Salvage\ Value}{Annual\ Usage} \).
What’s the result if we have 1,600 operational hours?
We would find the hourly depreciation to be around ₹2,159.92. Great job, everyone! Remember this formula for future calculations.
Total Ownership Cost
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We’ve calculated depreciation and salvage; now let’s look at other ownership costs, like insurance and taxes. Who can tell me how we might calculate these?
Are they percentages of the initial cost?
Correct! For example, if the insurance is 2% of the initial cost, we calculate it as: \( Insurance = \frac{2.0}{100} \times \frac{Initial\ Cost}{Annual\ Usage} \). So, for our cost…
The insurance would be ₹361.25 per hour, right?
Exactly! And if we add taxes and the accumulated costs, we find our total ownership cost of around ₹3,063.05/hr.
Total Operating Cost Calculation
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Finally, let’s compile everything into our total operating cost. What elements do we need to consider here?
We need to include ownership costs, operating costs, fuel and consumables as well.
Correct! Our fuel cost, if calculated properly, adds up to ₹1,137.50, among others, so adding all together gives us a final total operating cost of ₹5,759.20 per hour.
What is the implication of knowing this total cost?
Knowing this total cost is crucial for budgeting, project planning, and understanding the financial implications of ongoing operations. Great job today, everyone!
Introduction & Overview
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Quick Overview
Standard
This section details the estimation of operating costs using methods such as the capital recovery factor and sinking fund factor. It elaborates on how to derive annualized costs from initial investment and salvage values, and explains additional costs like depreciation, insurance, taxes, and operational resource consumption.
Detailed
Operating Cost Estimation
In this section, we explore the estimation of operating costs associated with machinery and equipment. The focus is on using financial concepts to convert initial costs and potential salvage values into expected annual costs, facilitating more accurate budgeting for operations.
Capital Recovery Factor
The section begins with the calculation of equivalent uniform annual costs of the initial investment using the uniform series capital recovery factor formula. For example, given an initial cost of ₹2,89,00,000 and an interest rate of 8% over 12.5 years, we derive an annualized cost of ₹37,41,844.41.
Salvage Value
Following the initial costs, the section explains how to convert the future salvage value into a yearly cost equivalent, demonstrating this with a salvage value of 20% of the initial cost, leading to an annualized salvage value of ₹2,85,968.88.
Hourly Depreciation
Furthermore, it details how to calculate the hourly depreciation of equipment by using the annualized costs and operational hours, resulting in a value of ₹2,159.92 per hour.
Ownership Costs
The section emphasizes other ownership components such as insurance, taxes, and maintenance costs, calculated as percentages of the initial cost to derive an overall hourly ownership cost of ₹3,063.05.
Fuel and Consumable Costs
Operating costs include fuel, lubricants, and repair costs. For instance, by determining operational factors and adjusting fuel consumption rates, we conclude the hourly fuel cost as ₹1,137.50.
The estimated total hourly cost combines all these components, leading to a comprehensive operating cost figure necessary for financial planning and budgeting in project management.
Audio Book
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Annualized Initial Cost
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The initial cost is converted into equivalent uniform annual cost, annualized cost we call it as annualized initial cost using uniform series capital recovery factor. The initial cost is nothing but your 2,89,00,000 what you have determine just now after deducting the tire cost, 2,89,00,000 lakh multiplied by your uniform series capital recovery factor which is nothing but I into 1 + i whole power n by 1 + i whole power n - 1. The interest rate you know it is nothing but 8 percent and n is 12.5 years. So you can get the annualized initial cost as 37,41,844.41 per year.
Detailed Explanation
To convert an initial cost into an annual cost, we use the uniform series capital recovery factor formula. For this case, the initial cost of the equipment is ₹28900000. The formula considers the interest rate (i) of 8% and an estimated lifespan (n) of 12.5 years. Using these values, we calculate an annual cost of ₹3741844.41. This conversion helps in budgeting and financial planning by expressing initial investment over its useful life as a yearly expense.
Examples & Analogies
Consider you buy a car for ₹2,89,00,000. Instead of thinking about the total amount paid upfront, you might spread this cost over several years (like paying for a car monthly). Similarly, businesses convert large initial expenses (like equipment) into annual costs for easier financial management.
Salvage Value
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Now I need to convert the future salvage value into equivalent uniform annual cost. Salvage value will be converted into equivalent uniform annual cost. Equivalent uniform annual cost of salvage value = Salvage value ×[i/(1+i)^n -1]. Salvage value is nothing but 20% of the initial cost minus the tire cost. Now you substitute the value the interest rate and the useful life of the machine n = 12.5 you will get the annualized salvage value as 2,85,968.88 per year.
Detailed Explanation
The salvage value represents the estimated resale value of the equipment after its useful life. To transform this future value into a yearly cost, we multiply the salvage value (20% of the initial cost) by a factor that accounts for time value of money. After plugging in the proper formulas and values, we find the annualized salvage value as ₹2,85,968.88. This process is crucial for businesses to consider potential revenue when the equipment is sold.
Examples & Analogies
Imagine selling your used laptop after a few years for 20% of its original price. Just like calculating what you will get back later helps you understand the effective cost of ownership, businesses do the same for their equipment, considering what they will sell it for at the end of its use.
Hourly Depreciation Calculation
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Hourly depreciation is nothing but the difference between the initial cost minus the salvage value divided by the annual use of the machine in hours. Hourly Depreciation = (Annualized Initial Cost - Annualized Salvage Value) / Annual Use in Hours = ₹ 2159.92/hr.
Detailed Explanation
Hourly depreciation quantifies how much the equipment loses value over time while it is in use. We take the annualized initial cost of ₹37,41,844.41, subtract the annualized salvage value of ₹2,85,968.88, and then divides the result by the hours the equipment is utilized in a year (1600 hours). This results in a depreciation cost of ₹2159.92 per hour used, which helps businesses understand the cost of using their equipment.
Examples & Analogies
Think of it like a phone losing its value as time goes on. If you bought a phone for ₹37,41,844.41 and sold it for ₹2,85,968.88 years later, you could calculate how much it lost value for every hour you used it. This helps you see how much each hour of use costs you.
Ownership Cost Calculation
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Now let us calculate the total hourly ownership cost including depreciation, insurance, and taxes. Total Hourly Ownership Cost = Hourly Depreciation + Insurance + Taxes = ₹ 3063.05/hr.
Detailed Explanation
Total hourly ownership cost includes all the costs associated with owning the equipment—not just the depreciation. We add hourly costs for insurance (₹361.25) and taxes (₹541.88) to the hourly depreciation (₹2159.92) to find the total cost. This comprehensive calculation enables better budgeting and cost assessment over time for the assets owned by the business.
Examples & Analogies
Think of owning a car. The total cost of ownership includes not just the price you paid (depreciation) but also recurring expenses like insurance and taxes. Knowing the total cost helps you understand how much you truly spend on owning your car every hour you drive it.
Estimating Fuel Costs
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So this fuel consumption factor is given for a standard condition for maximum output. Fuel consumed per hour = Operating factor x Rated power x Fuel consumption factor. = 0.50 x 250 x 0.14 = 17.50 litres. Hourly cost of fuel = Hourly fuel consumption x unit cost of fuel = 17.50 lit x ₹65/lit = ₹ 1137.50/hour.
Detailed Explanation
Fuel costs are estimated based on how much fuel the equipment consumes per hour during operation. The fuel consumption factor measures how many liters of fuel are used per horsepower. This factor needs to be adjusted for actual working conditions, like operating efficiency and load. By calculating the hourly consumption and multiplying by the fuel price, we find that operating the machinery costs ₹1137.50 per hour for fuel.
Examples & Analogies
Imagine your vehicle's efficiency changes based on how much weight it's carrying or the terrain you're driving on. Just as you might fill up more frequently when hauling heavy loads, machinery operators must calculate fuel costs based on real-world conditions, adjusting for factors like weight and use to manage budgets efficiently.
Total Operating Cost Calculation
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Total hourly operating cost = Fuel Cost + FOG Cost + Tire Cost + Repair & Maintenance Cost + Total Hourly Ownership Cost + Operator Wages. Total cost of equipment = ₹ 5759.2/h.
Detailed Explanation
Total hourly operating cost sums up all the costs incurred in operating machinery, including daily use, repairs, maintenance, and operator wages. By adding these components together, we can see the complete picture of what it costs to operate the equipment per hour. This thorough understanding ensures businesses can plan and allocate budgets effectively.
Examples & Analogies
Running a small business has similar costs. You would sum all expenses—like inventory, utilities, employee wages, and ongoing maintenance—to see how much you are truly spending. This helps in decision-making and planning, just as it does for equipment operations.
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): The annual payment required to recover an initial investment.
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Salvage Value: The estimated resale value at the end of the asset's life.
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Depreciation: A measure of how much an asset loses value over time.
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Sinking Fund: A method used to determine how much to save each year to fund a future expense.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Calculating the annualized initial cost using a capital recovery factor for an initial investment of ₹2,89,00,000.
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Determining annualized salvage value by applying a sinking fund factor for a salvage value of 20% of the initial cost.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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EAC every year, keep your costs near, salvage at the end, that’s how we’ll spend!
📖 Fascinating Stories
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Imagine a business starting with a new machine. They invest a big sum, but over the years, it might break down. By understanding depreciation, they save, and when it’s time to sell, they gather salvage value to recover.
🧠 Other Memory Gems
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E.A.C. - Estimate All Costs.
🎯 Super Acronyms
C.R.E.E.P. - Costs Recoverable Every End of Project.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Operating Cost
Definition:
The total cost incurred in operating and maintaining machinery or equipment.
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Term: Equivalent Annual Cost (EAC)
Definition:
The annualized cost of an initial investment, including interest and depreciation.
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Term: Salvage Value
Definition:
The estimated resale value of an asset at the end of its useful life.
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Term: Depreciation
Definition:
The reduction in the value of an asset over time, commonly used for accounting and tax purposes.
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Term: Sinking Fund Factor
Definition:
A method used to determine how much money must be set aside annually to fund a future payment.