Engineering Economics By R. Panneerselvam – PDF Free Download Engineering Economics By R. Panneerselvam. Download Links. Designed as a text book for undergraduate students in various engineering this comprehensive and well-organized book shows how complex economic. Designed as a textbook for undergraduate students in various engineering disciplines—Mechanical, Civil, Industrial Engineering, Electronics.
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Rent and save from the world's largest eBookstore. Read ENGINEERING ECONOMICS. Front Cover · R. PANNEERSELVAM. PHI Learning Pvt. Ltd., Jan 1, - Business & Economics - pages . Author, R. PANNEERSELVAM. Designed as a text book for undergraduate students in various engineering disciplines - mechanical, civil and industrial engineering - and for. eBook features: Highlight, take notes, and search in the book; Length: pages; Enhanced Typesetting: Enabled; Page Flip: Enabled; Due to its large file size.
Deals with different types of cost estimating models, index numbers and capital allowance. Covers the basics of nondeterministic decision making. Describes the meaning of cash flows with probability distributions and decision making, and selection of alternatives using simulation.
Discusses the basic concepts of Accounting. This book, which is profusely illustrated with worked-out examples and a number of diagrams and tables, should prove extremely useful not only as a text but also as a reference for those offering courses in such areas as Project Management, Production Management, and Financial Management. Introduction 3. Interest Formulas and Their Applications 4. Present Worth Method of Comparison 5.
Future Worth Method 7. Rate of Return Method 8. Replacement and Maintenance Analysis 9. Depreciation In the long run, this would give more yield in terms of tonnes of billet produced. In this exercise, there is no extra cost involved. The only task is the relocation of the billet-making facility which involves an insignificant cost. Decreased input for the same output.
In this strategy, the input is decreased to produce the same output. Let us assume that there exists a substitute raw material to manufacture a product and it is available at a lower price.
If we can identify such a material and use it for manufacturing the product, then certainly it will reduce the input. In this exercise, the job of the download department is to identify an alternate substitute material.
The process of identification does not involve any extra cost. So, the productivity ratio will increase because of the decreased input by way of using cheaper raw materials to produce the same output. Less proportionate increase in output is more than that of the input. Consider the example of introducing a new product into the existing product mix of an organization.
If the new product is taken up for production, it will lead to an increase in the revenue of the organization by way of selling the new product in addition to the existing product mix and. If we examine these two increases closely, the proportionate increase in the revenue will be more than the proportionate increase in the input cost.
Hence, there will be a net increase in the productivity ratio. When proportionate decrease in input is more than that of the output. Let us consider the converse of the previous example, i. This will result in the following: A decrease in the revenue of the organization A decrease in the material cost, and operation and maintenance cost of machinery If we closely examine these two decreases, we will see that the proportionate decrease in the input cost will be more than the proportionate decrease in the revenue.
Simultaneous increase in output and decrease in input. Let us assume that there are advanced automated technologies like robots and automated guided vehicle system AGVS , available in the market which can be employed in the organization we are interested in. If we employ these modern tools, then: There will be a drastic reduction in the operation cost. Initially, the cost on equipment would be very high. But, in the long run, the reduction in the operation cost would break-even the high initial investment and offer more savings on the input.
These advanced facilities would help in producing more products because they do not experience fatigue. The increased production will yield more revenue. In this example, in the long run, there is an increase in the revenue and a decrease in the input. Hence, the productivity ratio will increase at a faster rate.
In the process of managing organizations, the managers at different levels should take appropriate economic decisions which will help in minimizing investment, operating and maintenance expenditures besides increasing the revenue, savings and other related gains of the organization. Scope The issues that are covered in this book are elementary economic analysis, interest formulae, bases for comparing alternatives, present worth method, future worth method, annual equivalent method, rate of return method, replacement analysis, depreciation, evaluation of public alternatives, inflation adjusted investment decisions, make or download decisions, inventory control, project management, value engineering, and linear programming.
Variable cost varies with the volume of production while overhead cost is fixed, irrespective of the production volume. Variable cost can be further classified into direct material cost, direct labour cost, and direct expenses. The overhead cost can be classified into factory overhead, administration overhead, selling overhead, and distribution overhead. Direct material costs are those costs of materials that are used to produce the product. Direct labour cost is the amount of wages paid to the direct labour involved in the production activities.
Direct expenses are those expenses that vary in relation to the production volume, other than the direct material costs and direct labour costs.
Overhead cost is the aggregate of indirect material costs, indirect labour costs and indirect expenses. Administration overhead includes all the costs that are incurred in administering the business. Selling overhead is the total expense that is incurred in the promotional activities and the expenses relating to sales force. Distribution overhead is the total cost of shipping the items from the factory site to the customer sites. The selling price of a product is derived as shown below: Marginal cost Marginal revenue Sunk cost Opportunity cost.
Marginal cost of a product is the cost of producing an additional unit of that product. Let the cost of producing 20 units of a product be Rs.
Then the marginal cost of producing the 21st unit is Rs. Marginal revenue of a product is the incremental revenue of selling an additional unit of that product.
Let, the revenue of selling 20 units of a product be Rs. Then, the marginal revenue of selling the 21st unit is Rs. Let us assume that an equipment has been downloadd for Rs.
If it is considered for replacement, then its present value is not Rs. Instead, its present market value should be taken as the present value of the equipment for further analysis. So, the download value of the equipment in the past is known as its sunk cost. The sunk cost should not be considered for any analysis done from nowonwards. If the same money is invested in some other alternative Y , it may fetch some return.
Since the money is invested in the selected alternative X , one has to forego the return from the other alternative Y. The amount that is foregone by not investing in the other alternative Y is known as the opportunity cost of the selected alternative X. So the opportunity cost of an alternative is the return that will be foregone by not investing the same money in another alternative. Consider that a person has invested a sum of Rs. Let the expected annual return by this alternative be Rs.
If the same amount is. Then, the corresponding total return per year for the investment in the bank is Rs. This return is greater than the return from shares. The foregone excess return of Rs.
The intersection point of the total sales revenue line and the total cost line is called Sales S. The corresponding volume of production on the X-axis is known as the break-even sales quantity. At the intersection point, the total cost is equal to the total revenue.
This point is also called the no-loss or no-gain situation. For any production quantity which is less than the break-even quantity, the total cost is more than the total revenue. Hence, the firm will be making loss. For any production quantity which is more than the break-even quantity, the total revenue will be more than the total cost.
Hence, the firm will be making profit. The contribution is the difference between the sales and the variable costs. The margin of safety M.
The following formula helps us find the M. Define economics. Also discuss the flow of goods, services, resources and money payments in a simple economy with the help of a suitable diagram. Illustrate the effect of price on demand and supply; illustrate with the help of a diagram.
Discuss the factors which influence demand and supply. Distinguish between technical efficiency and economic efficiency by giving examples. What are the ways by which the economic efficiency can be improved?
Give the definition and scope of engineering economics. Clearly explain the method of deriving the selling price of a product. Define the following costs with examples: Define break-even point. Draw a break-even chart and explain its components. Krishna Company Ltd. Consider the following data of a company for the year One can manage many of these decision problems by using simple economic analysis. For example, an industry can source its raw materials from a nearby place or from a far-off place.
In this problem, the following factors will affect the decision: Price of the raw material Transportation cost of the raw material Availability of the raw material Quality of the raw material Consider the alternative of sourcing raw materials from a nearby place with the following characteristics: The raw material is more costly in the nearby area.
The availability of the raw material is not sufficient enough to support the operation of the industry throughout the year. The raw material requires pre-processing before it is used in the production process.
This would certainly add cost to the product. The cost of transportation is minimal under this alternative. On the other hand, consider another alternative of sourcing the raw materials from a far-off place with the following characteristics: The raw material is less costly at the far off place.
The cost of transportation is very high. The availability of the raw material at this site is abundant and it can support the plant throughout the year. The raw material from this site does not require any pre-processing before using it for production. Under such a situation, the procurement of the raw material should be decided in such a way that the overall cost is minimized. The above example clearly highlights the various components of cost that are involved in each of the alternatives of the decision-making process as well as a method of taking a suitable decision.
The cost of a product can be reduced greatly by substitution of the raw materials. Among various elements of cost, raw material cost is most significant and it forms a major portion of the total cost of any product. So, any attempt to find a suitable raw material will bring a reduction in the total cost in any one or combinations of the following ways: In this process, if the new raw material provides any additional benefit, then it should be treated as its welcoming feature.
This concept is demonstrated with two numerical problems. Either material will provide equal service, but the aluminium casting will weigh 1. The aluminium can be cast for Rs. The cost of machining per unit is Rs. Every kilogram of excess weight is associated with a penalty of Rs. Which material should be specified and what is the economic advantage of the selection per unit? Solution a Cost of using aluminium metal for the jet engine part: Hence, aluminium is suggested for making the jet engine part.
The different materials used to manufacture the tables and their costs are given in Table 2. Table 2. In view of the growing awareness towards deforestation and environmental conservation, the company feels that the use of wood should be minimal.
The wooden top therefore could be replaced with a granite top. This would require additional wood for the frame and legs to take the extra weight of the granite top. The materials and labour requirements along with cost details to manufacture a table with granite top are given in Table 2. Engineering Economics Table 2. If the cost of the dining table with a granite top works out to be lesser than that of the table with wooden top, the company is willing to manufacture dining tables with granite tops.
Compute the cost of manufacture of the table under each of the alternatives described above and suggest the best alternative. Also, find the economic advantage of the best alternative.
The cost of a table with granite top works out to be less than that of a table with a wooden top. Hence, the table with granite top should be selected by the manufacturer. Design is an important factor which decides the cost of the product for a specified level of performance of that product. The elementary economic analysis applied to the selection of design for a product is illustrated with two example problems. Either design will serve the purpose and will involve the same material and manufacturing cost except for the lathe and grinder operations.
Design A will require 16 hours of lathe time and 4. Design B will require 7 hours of lathe time and 12 hours of grinder time per 1, units. The operating cost of the lathe including labour is Rs. The operating cost of the grinder including labour is Rs. Which design should be adopted if 1,00, units are required per year and what is the economic advantage of the best alternative? Hence, design B is recommended for making the tapered fastening pin. The chief engineer of refinery operations is not satisfied with the preliminary design for storage tanks to be used as part of a plant expansion programme.
The engineer who submitted the design was called in and asked to reconsider the overall dimensions in the light of an article in the Chemical Engineer, entitled How to size future process vessels? The original design submitted called for 4 tanks 5. From a graph of the article, the engineer found that the present ratio of height to diameter of 1. The cost for the tank design as originally submitted was estimated to be Rs.
What are the optimum tank dimensions if the volume remains the same as for the original design? What total savings may be expected through the redesign? As discussed in the introduction to this chapter, the sourcing of raw materials will have a significant effect on the cost of any product.
Hence, it is assumed that the price of raw material is location dependent. While sourcing a raw material, the cost of transportation is to be considered in conjunction with the price of the raw material. This concept is demonstrated with a numerical example. Either steel or aluminium window frames will satisfy the design criteria.
Because of the remote location of the building site and lack of building materials in Alpha State, the window frames will be downloadd in Beta State and transported for a distance of 2, km to the site.
The price of window frames of the type required is Rs. The weight of steel window frames is 75 kg each and that of aluminium window frame is 28 kg each.
The shipping rate is Re 1 per kg per km. Which design should be specified and what is the economic advantage of the selection? Hence, aluminium window frame is recommended. The process sequence of a component which has been planned in the past is not static.
It is always subject to modification with a view to minimize the cost of manufacturing the component. The steps in process planning are as follows: Analyze the part drawing to get an overall picture of what is required. Make recommendations to or consult with product engineers on product design changes.
List the basic operations required to produce the part to the drawing or specifications. Determine the most practical and economical manufacturing method and the form or tooling required for each operation.
Devise the best way to combine the operations and put them in sequence. Specify the gauging required for the process. Steps 35 aim to determine the most practical and economical sequence of operations to produce a component. This concept is demonstrated with a numerical problem. The details of processing times of the component for various operations and their machine hour rates are summarized in Table 2.
Find the most economical sequence of operations to manufacture the component. Solution a Cost of component using process sequence 1. Turning Milling Shaping Drilling The calculations for the cost of the above process sequence are summarized in Table 2. Turning Milling Drilling. The process sequence 3 of the component is as follows: Only CNC operations The calculations for the cost of the above process sequence are summarized in Table 2.
The process sequence 2 has the least cost. Therefore, it should be selected for manufacturing the component. List and explain the different situations deserving elementary economic analysis.
Explain the steps in the process planning. In the design of an aircraft jet engine part, the designer has a choice of specifying either an aluminium alloy casting or a steel casting.
Either material will provide equal service, but the aluminium casting will weigh 5 kg as compared with 7 kg for the steel casting. The aluminium part can be cast for Rs. Two alternatives are under consideration for a hexagonal bolt fastening pin.
Either design will serve equally well and will involve the same material and manufacturing cost except for the lathe and grinder operations. Design A will require 20 hours of lathe time and 8 hours of grinder time per 10, units. Design B will require 10 hours of lathe time and 22 hours of grinder time per 10, units. Which design should be adopted if 10,00, units are required per year and what is the economic advantage of the best alternative?
A building contractor can source door frames from either a nearby shop or a far-off forest area. The cost details are as summarized in the following table. The total requirement of wood for the construction work is 75 tons. Find the best alternative for downloading the wooden frames. Also find the economic advantage of the best decision. Consider Example 2. Rework this example if the ratio of the height to diameter corresponding to the minimum cost is 6: The process planning engineer of a firm listed down the sequences of operations, as shown in the following table to produce a component: The details of process time for the components for various operations and their machine hour rates are tabulated now.
Operation Machine hour rate Rs. It represents the growth of capital per unit period. The period may be a month, a quarter, semiannual or a year. So, the total amount at the end of the first year will be Rs. Hence the total amount at the end of the second year will be Rs. The process will continue thus till the specified number of years.
If an investor invests a sum of Rs. Table 3. The maturity value at the end of the fifth year is Rs. This means that the amount Rs. This is diagrammatically shown in Fig. This explanation assumes that the inflation is at zero percentage. Alternatively, the above concept may be discussed as follows: If we want Rs.
A detailed working is shown in Table 3. From Table 3. Similarly, if we want Rs. Also, this concept can be stated as follows: A person has received a prize from a finance company during the recent festival contest. But the prize will be given in either of the following two modes:. Spot payment of Rs. If this option is followed, the equivalent amount for Rs. This example clearly demonstrates the time value of money. To simplify all these computations, it is extremely important to know how to use interest formulas more effectively.
Before discussing the effective application of the interest formulas for investment-decision making, the various interest formulas are presented first. Interest rate can be classified into simple interest rate and compound interest rate. In simple interest, the interest is calculated, based on the initial deposit for every interest period.
In this case, calculation of interest on interest is not applicable. In compound interest, the interest for the current period is computed based on the amount principal plus interest up to the end of the previous period at the beginning of the current period. The notations which are used in various interest formulae are as follows: The cash flow diagram of this situation is shown in Fig.
Find the maturity value after 10 years. The maturity value of Rs. Here, the objective is to find the present worth amount P of a single future sum F which will be received after n periods at an interest rate of i compounded at the end of every interest period.
The corresponding cash flow diagram is shown in Fig. What is the single-payment that he should deposit now so that he gets the desired amount after 10 years? The person has to invest Rs. In Fig. He plans to invest an equal sum of Rs. Find the maturity value of his account when he is 60 years old. Find the equivalent amount that must be deposited at the end of every year for the next 15 years. Find the single-payment that must be made now as the reserve amount.
The corresponding cash flow diagram is illustrated in Fig. The objective of this mode of investment is to find the annual equivalent amount A which is to be recovered at the end of every interest period for n interest periods for a loan P which is sanctioned now at an interest rate of i compounded at the end of every interest period see Fig.
This amount should be repaid in 15 yearly equal installments. Find the installment amount that the company has to pay to the bank. He has 10 more years.
Find the total amount at the end of the 10th year of the above series. The future worth sum of this revised series at the end of the 10th year is obtained as follows: He has 10 more years of service.
He would like to deposit Rs. The cash flow diagram is shown in Fig. This is equivalent to paying an equivalent amount of Rs. But, in practice, the compounding may occur less than a year.
For example, compounding may be monthly, quarterly, or semi-annually. Compounding monthly means that the interest is computed at the end of every month. There are 12 interest periods in. The compounding is quarterly. Find the maturity amount of the deposit after 10 years. Let us assume that an organization has a huge sum of money for potential investment and there are three different projects whose initial outlay and annual revenues during their lives are known. The executive has to select the best alternative among these three competing projects.
There are several bases for comparing the worthiness of the projects. These bases are: Present worth method Future worth method Annual equivalent method Rate of return method. Explain the time value of money. Give practical applications of various interest formulas.
A person deposits a sum of Rs. Find the future amount of the deposited money at the time of admitting his son in the professional course. A person needs a sum of Rs. A person who is just 30 years old is planning for his retired life. A company is planning to expand its business after 5 years from now. The expected money required for the expansion programme is Rs. The company can invest Rs. If not, find the difference in amounts for which the company should make some other arrangement after 5 years.
A financial institution introduces a plan to pay a sum of Rs. Find the annual equivalent amount that a person should invest at the end of every year for the next 10 years to receive Rs. The money required for the expansion programme is Rs. A company wants to set-up a reserve which will help it to have an annual equivalent amount of Rs.
Find the single-payment that must be made as the reserve amount now. An automobile company recently advertised its car for a down payment of Rs. Alternatively, the car can be taken home by customers without making any payment, but they have to pay an equal yearly amount of Rs. Suggest the best alternative to the customers.
A company takes a loan of Rs. Find the equal installment amount that should be paid for the next 20 years. A bank gives loan to a company to download an equipment which is worth of Rs. This amount should be repaid in 25 yearly equal installments.
A working woman is planning for her retired life. She has 20 more years of service. Find the total amount at the end of the 15th year of the above series.
Consider the following cash flow diagram. A person is planning for his retired life. A person invests a sum of Rs.
The compounding is monthly. Find the maturity amount of the deposit after 15 years. Then, depending on the type of decision, the best alternative will be selected by comparing the present worth amounts of the alternatives. The sign of various amounts at different points in time in a cash flow diagram is to be decided based on the type of the decision problem.
In a cost dominated cash flow diagram, the costs outflows will be assigned with positive sign and the profit, revenue, salvage value all inflows , etc. The costs outflows will be assigned with negative sign. In case the decision is to select the alternative with the minimum cost, then the alternative with the least present worth amount will be selected.
On the other hand, if the decision is to select the alternative with the maximum profit, then the alternative with the maximum present worth will be selected. S R1 R2 R3. Rj Rn. The interest rate is i, compounded annually. S is the salvage value at the end of the nth year. If we have some more alternatives which are to be compared with this alternative, then the corresponding present worth amounts are to be computed and compared.
Finally, the alternative with the maximum present worth amount should be selected as the best alternative. Finally, the alternative with the minimum present worth amount should be selected as the best alternative.
In this section, the concept of present worth method of comparison applied to the selection of the best alternative is demonstrated with several illustrations. It has identified three different technologies for meeting the goal.
The initial outlay and annual revenues with respect to each of the technologies are summarized in Table 4. Table 4. Technology 1 Technology 2 Technology 3 12,00, 20,00, 18,00, Annual revenue Rs. Solution In all the technologies, the initial outlay is assigned a negative sign and the annual revenues are assigned a positive sign.
From the above calculations, it is clear that the present worth of technology 2 is the highest among all the technologies. Therefore, technology 2 is suggested for implementation to expand the production. The details of the bids for the elevators are as follows: Bid Initial cost Rs. Alpha Elevator Inc. Beta Elevator Inc. Solution Bid 1: The cash flow diagram of bid 1 is shown in Fig.
The present worth of the above cash flow diagram is computed as follows: Hence, bid 1 is to be selected for implementation. That is, the elevator from Alpha Elevator Inc. Proposal 0 A Rs. Which proposal should be selected?
The cash flow diagram of the proposal B is shown in Fig. Therefore, select proposal B. If it is downloadd under down payment, the cost of the machine is Rs. Solution There are two alternatives available for the company: Down payment of Rs. Present worth calculation of the second alternative. The cash flow diagram of the second alternative is shown in Fig.
Hence, the company should select the second alternative to download the fully automated granite cutting machine. In plan 1, the company pays Rs. In plan 2, for every Rs. Solution Plan 1. The cash flow diagram for plan 1 is illustrated in Fig. The cash flow diagram for plan 2 is shown in Fig.
Therefore, plan 1 is the best plan from the investors point of view. Innovative Investment Ltd. Which is the best investment alternative? Solution Novel Investment Ltds plan. The cash flow diagram of Novel Investment Ltds plan is shown in Fig.
The cash flow diagram of the Innovative Investment Ltds plan is illustrated in Fig. Therefore, Innovative Investment Ltds plan is the best from investors point of view.
At the end of the life of the business, the salvage value is zero. A project involves an initial outlay of Rs. The salvage value at the end of the life of the project after five years is Rs.
End of year 1 2 3 4 5 Maintenance and operating expense Rs. Find the present worth of the following cash flow series. End of year Cash flow Rs. Consider the following cash flow series over a year period.
End of year 0 1 2. The cost of erecting an oil well is Rs. The annual equivalent yield from the oil well is Rs. The salvage value after its useful life of 10 years is Rs.
The details of the feasibility report of a project are as shown below. You are asked to advise the best alternative for the customers based on the present worth method of comparison. The cash flows of two project proposals are as given below. Each of the project has an expected life of 10 years.
Initial outlay Rs. Project 1 Project 2 7,50, 9,50, Annual equivalent revenue Rs. A company has two alternatives for satisfying its daily travel requirements of its employees for the next five years:. Alternative 1: Renting a vehicle at a cost of Rs. Alternative 2: downloading a vehicle for Rs. The salvage value of the vehicle after five years is Rs. She would like to have an annual equivalent amount of Rs.
Find the single amount that should be deposited now so that she receives the above mentioned annual equivalent amount at the end of every year for 20 years after her retirement. Then, the alternative with the maximum future worth of net revenue or with the minimum future worth of net cost will be selected as the best alternative for implementation. If we have some more alternatives which are to be compared with this Finally, the alternative with the maximum future worth amount should be selected as the best alternative.
If we have some more alternatives which are to be compared with this alternative, then the corresponding future worth amounts are to be computed and compared. Finally, the alternative with the minimum future worth amount should be selected as the best alternative. In this section, several examples highlighting the applications of the future worth method of comparison are presented.
End of year Alternative A Rs. The future worth of alternative A is greater than that of alternative B. Thus, alternative A should be selected. He must decide which of the several alternatives to select in trying to obtain a desirable return on his investment.
After much study and calculation, he decides that the two best alternatives are as given in the following table: Build gas station First cost Rs. Annual property taxes Rs. Annual income Rs. Life of building years Salvage value Rs. Thus, building the gas station is the best alternative. Therefore, alternative 2 must be selected. Thus, none of the two alternatives should be selected.
It has received tenders from three different original manufacturers of annealing furnace. The details are as follows. Manufacturer 1 Initial cost Rs. Life years Annual operation and maintenance cost Rs. Salvage value after 12 years 80,00, 12 8,00, 5,00, 2 70,00, 12 9,00, 4,00, 3 90,00, 12 8,50, 7,00, Krishna castings should download the annealing furnace from manufacturer 2. A company must decide whether to download machine A or.
Initial cost Useful life, in years Salvage value at the end of machine life Annual maintenance cost. Use future worth method of comparison. The cash flow diagram of machine A is given in Fig.
The future worth function of Fig. The cash flow diagram of the machine B is illustrated in Fig. The future worth function of Fig 5. Therefore, machine A should be selected. A suburban taxi company is considering downloading taxis with diesel engines instead of petrol engines.
The cars average 50, km a year, with a useful life of three years for the taxi with the petrol engine and four years for the diesel taxi. Other comparative information are as follows: A motorcycle is sold for Rs. The motorcycle dealer is willing to sell it on the following terms: Consider the following two mutually exclusive alternatives. A Cost Uniform annual benefit Useful life years Rs. A company must decide whether to download machine A or machine B: Use the future worth method of comparison.
Due to increasing awareness of customers, two different television manufacturing companies started a marketing war. The details of advertisements of the companies are as follows: Alpha Finance Company is coming with an option of accepting Rs. Beta Finance Company is coming with a similar option of accepting Rs. An insurance company gives an endowment policy for a person aged 30 years. The yearly premium for an insured sum of Rs. The policy will mature after 25 years. Also, the person is entitled for a bonus of Rs.
If a person survives till the end of the 25th year: Then the alternative with the maximum annual equivalent revenue in the case of revenue-based comparison or with the minimum annual equivalent cost in the case of costbased comparison will be selected as the best alternative.
Rj Rn n. The first step is to find the net present worth of the cash flow diagram using the following expression for a given interest rate, i: In the second step, the annual equivalent revenue is computed using the following formula: If we have some more alternatives which are to be compared with this alternative, then the corresponding annual equivalent revenues are to be computed and compared. Finally, the alternative with the maximum annual equivalent revenue should be selected as the best alternative.
The first step is to find the net present worth of the cash flow diagram using the following relation for a given interest rate, i. Then, in the second step, the annual equivalent cost is computed using the following equation: As in the previous case, if we have some more alternatives which are to be compared with this alternative, then the corresponding annual equivalent costs are to be computed and compared.
Finally, the alternative with the minimum annual equivalent cost should be selected as the best alternative. Such procedure is to be applied to all the alternatives and finally, the best alternative is to be selected.
In each of the cases presented in Sections 6. In this section, the application of the annual equivalent method is demonstrated with several numerical examples.
The owner of the company is concerned about the increasing cost of petrol. The cost per litre of petrol for the first year of operation is Rs. He feels that the cost of petrol will be increasing by Re.
His experience with his company car indicates that it averages 9 km per litre of petrol. The executive expects to drive an average of 20, km each year for the next four years. What is the annual equivalent cost of fuel over this period of time?. If he is offered similar service with the same quality on rental basis at Rs. If the rental car is preferred, then the company car will find some other use within the company. The cash flow diagram for this situation is depicted in Fig. This amount is less than the annual rental value of Rs.
Therefore, the company should continue to provide its own car to its executive. Three original manufacturers have responded to its tender whose particulars are tabulated as follows: Manufacturer Down payment Rs. The annual equivalent cost of manufacturer 3 is less than that of manufacturer 1 and manufacturer 2.
Therefore, the company should download the advanced machine centre from manufacturer 3. The life of both alternatives is estimated to be 5 years with the following investments, annual returns and salvage values. Alternative A Investment Rs.
Annual equal return Rs. Salvage value Rs. The cash flow diagram for alternative A is shown in Fig. The annual equivalent revenue expression of the above cash flow diagram is as follows: Thus, the company should select alternative B. The following data are to be used in the analysis: Which machine would you choose?
Base your answer on annual equivalent cost. The cash flow diagram of machine X is illustrated in Fig. The cash flow diagram of machine Y is depicted in Fig. So, machine X is the more cost effective machine. Data on the routes are as follows: The cash flow diagram for this alternative is shown in Fig. Therefore, select the route around the lake for laying the power line. The cars average 60, km a year with a useful life of three years for the petrol taxi and four years for the diesel taxi.
Other comparative details are as follows: Diesel Vehicle cost Rs. Therefore, the taxi company should download cars with diesel engine. Comparison is done on common multiple lives of 12 years. He expects that he will be promoted to a supervisory job at the end of third year and so his concern now is to have a car for the three years he expects to be on the road.
The company will reimburse their salesman each month the fuel cost and maintenance cost. Ramu has decided to drive a low-priced automobile. He finds, however, that there are two different ways of obtaining the automobile. In either case, the fuel cost and maintenance cost are borne by the company. The monthly charge is Rs. At the end of the three-year period, the car is returned to the leasing company.
If the car could be sold for Rs. The monthly equivalent cost of alternative 1 is less than that of alternative 2. Hence, the salesman should download the car for cash. Machine B 6,00, 4 3,00, 0. She estimates that it will have a five year useful life and no salvage value at the end of equipment life.
The dealer, who is a friend has offered Jothi Lakshimi two alternative ways to pay for the equipment. Hence, Jothi Lakshimi should select alternative 2 for downloading the home equipment.
This is months. Therefore, the comparison is made on months basis. The annual equivalent cost of brand C is less than that of other brands. Hence, it should be used in the vehicles of the trucking company. It should be replaced four times during the month period. A company has three proposals for expanding its business operations. The details are as follows: Each alternative has insignificant salvage value at the end of its life. An automobile dealer has recently advertised for its new car. There are three alternatives of downloading the car which are explained below.
Alternative 1 The customer can take delivery of a car after making a down payment of Rs. The remaining money should be paid in 36 equal monthly installments of Rs. Alternative 2 The customer can take delivery of the car after making a down payment of Rs.
Alternative 3 The customer can take delivery of the car by making full payment of Rs. Use the annual equivalent method. A small-scale industry is in the process of downloading a milling machine. The download value of the milling machine is Rs. It has identified two banks for loan to download the milling machine. In Urban Bank, the loan is to be repaid in 60 equal monthly installments of Rs.
In State Bank, the loan is to be repaid in 40 equal monthly installments of Rs. Suggest the most economical loan scheme for the company, based on the annual equivalent method of comparison. There are two alternatives of replacing a machine.