Economics for Engineers PDF

Economics for Engineers 2023 Economics for Engineers Module I  Introduction to Economics Economics Lionel Robbins defined Economics as a science which studies human behavior as a relationship between ends and scarce means which have alternative uses. – Th...

Economics for Engineers 2023 Economics for Engineers Module I  Introduction to Economics Economics Lionel Robbins defined Economics as a science which studies human behavior as a relationship between ends and scarce means which have alternative uses. – Thus Economics focuses attention on the influence of scarcity on human behavior. The principle (and problem) of economics is that human beings occupy a world of unlimited wants and limited means. In a resource-constrained world, available resources are insufficient to satisfy all wants and needs. – Economics is the science of choice.  Macro and Microeconomics Macroeconomics deals with the economy as a whole; it examines the behavior of economic aggregates such as aggregate income, consumption, investment, and the overall level of prices. – Aggregate behavior refers to the behavior of all households and firms together. Microeconomics examines the behavior of individual decision-making units—business firms and households. – The branch of economics that analyzes the behavior of individual consumers and firms in an attempt to understand the decision-making process of firms and households. – It is concerned with the interaction between individual buyers and sellers and the factors that influence the choices made by buyers and sellers.  Engineering Engineering is defined as: “The profession in which a knowledge of the mathematical and natural sciences gained by study, experience, and practice is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind” Scientists discover the world that exists, while engineers create the world that never was.  Engineering There are a few qualifiers in the definitions – a) Utilize the scientific knowledge and resources – b) Economically – c) For the benefit of the mankind Economically is an important qualifier in the definition of engineering. A successfully engineered solution is one that not only works from a technical perspective, but also from an economic one. An economical solution is one that makes efficient use of resources.  Engineering Economics In a business decision making process, the role of engineering economics analysis includes 1.Define/Understand the problem. 2.Generate alternate technical solutions that are technically feasible 3.Use tools of engineering economics to cull the solutions or options that aren’t economically feasible. 4.Use professional judgment to select the preferred solution. 5.Monitor performance of solution selected. Use feedback to calibrate decision making process.  Engineering Economics – Perspectives MARR It’s not enough for benefits to simply exceed costs, the economic benefits have to exceed the Minimum Acceptable (Average) Rate of Return or MARR. – There is an alternative of doing nothing, or more precisely, take the money and invest in a secured return by buying a Certificate of Deposit earning the prevailing interest rate. Time Value of Money Different proposals often have different cash-flow streams. When money is coming and going at different times, how to make a meaningful comparison between two or more options? – Economic formulas needed to convert cash-flow streams into equivalent cash- flow instances at a common point in time and then compare instances. Thus economic analysis of alternate solutions to be looked at for different perspectives.  Microeconomics to Managerial Economics Managerial Economics This applies microeconomic analysis to specific decisions in business firms or other management units. – It attempts to optimize business decisions, including unit-cost minimization and profit maximization, given the firm's objectives and constraints imposed by technology and market conditions  Managerial Economics Managerial Economics is “the application of economic theory and methodology to business administration practice.” It is “the integration of economic theory with business practice for the purpose of facilitating decision making and forward plan- ning by management.” It is a branch of economics that applies microeconomic analysis to decision making.  Engineering Economics Engineers must decide if the benefits of a project exceed its costs, and must make this comparison in a unified framework. The framework within which to make this comparison is the field of engineering economics, which strives to answer exactly these questions, and perhaps more. In the final evaluation of most ventures, economic efficiency (cost-benefit ratio) takes precedence over physical efficiency (system output(s) which is = (𝑆𝑦𝑠𝑡𝑒𝑚 𝑜𝑢𝑡𝑝𝑢𝑡 𝑆𝑦𝑠𝑡𝑒𝑚 𝑖𝑛𝑝𝑢𝑡𝑠 ). – This makes the projects unacceptable, regardless of their physical efficiency.  Problem analysis vs. Decision Making Problem analysis is done first and the information gathered in that process may be used towards decision making. Problem analysis – Analyze performance; what is against what it should be. – Problems are deviations from performance standards (should be). – Problem must be clearly identified and described – Causes to problems can be deducted from relevant changes found in analyzing the problem – Most likely cause to a problem is the one that exactly explains all the facts Decision making – Objectives must first be established – Objectives must be classified and placed in order of importance – Alternative actions are developed – The alternatives are evaluated against all the objectives – The alternative that is able to achieve the objectives best is the tentative decision – The tentative decision is evaluated. – The result in a decision model is used to determine an optimal production plan. – In a situation featuring conflict, role-playing is helpful for predicting decisions to be made by involved parties.  Economic Decisions Making Overview, Problems, Role, Decision making process: Six step process for Decision making that can be used to make all kinds of decisions. They are – Define the problem – Develop criteria and a ranking system – Identify possible alternatives – Evaluate alternatives against the criteria – Make a Decision that suits the best (Economic decision). – Evaluate the results (Control mechanism)  Various models of decision-making Various views and theories of decision-making may be found in the literature. The following list of views, supporting theories and models is based upon categorizations provided by Keen and Scott Morton (1978), Huber (1981), and Das and Teng (1999). The rational model The rational manager view assumes a rational and completely informed decision-maker who is an “economic man”. He takes decisions to maximize gains (profit) or to minimize loss (cost). The process of rational decision-making comprises a number of steps. They are : Intelligence: finding occasions for making a decision; Design: inventing, developing and analyzing possible alternative courses of action; Choice: selecting a particular course of action from those available; and Review: assessing past choices.  The Rational Model contd.. In classical or perfect rationality, methods of decision analysis are used to attach numerical values or utilities to each of the alternatives during the “choice” phase. The alternative with the highest utility (or maximum subjective expected utility) is selected. When using the rational model in this fashion, it is assumed that managers know of : all possible alternatives; the consequences of implementing each alternative; have a well organized set of preferences for these consequences; and have the computational ability to compare consequences and to determine which is preferred  The model of bounded rationality The “satisficing,” process-oriented view is based primarily on bounded rationality, admitting that the rational manager does not always have complete information, and that optimal choices are not always required. He wants to satisfy the minimum requirements to achieve his goal Bounded rationality is characterized by the activities of searching and satisficing. Alternatives are searched for and evaluated sequentially. – If an alternative satisfies certain implicitly or explicitly stated minimum criteria, it is said to “satisfice” and the search is terminated. The process of searching might be made easier by the identification of regularities in the task environment. “Good Enough” Lacks versus Complete Optimizing Information Bounded Rationality Cannot Cannot Assess All Weigh Alternatives All Criteria  The political view The political view sees decision-making as a personalized bargaining process, driven by the agendas of participants rather than rational processes. People differ on the organization’s goals, values and the relevance of information. The decision-making process never ends, but remains a continuous battle between different coalitions. Influence and power is wielded in a deliberate manner and to further self-interest. The goals of the coalitions are defined by self-interest rather than by what is good for the organization as a whole.  Managerial Decision The garbage can model The garbage can model tried to expand organizational decision theory into the uncharted field of organizational anarchy. which is characterized by "problematic preferences", "unclear technology" and "fluid participation". It disconnects problems, solutions and decision makers from each other, unlike traditional decision theory. Specific decisions do not follow an orderly process from problem to solution, but are outcomes of several relatively independent stream of events within the organization." Organizations operate on the basis of inconsistent and ill- defined preferences; their own processes are not understood by their members; they operate by trial and error; their boundaries are uncertain and changing; decision-makers for any particular choice change capriciously.  Management Decision Making The process of responding to a problem by searching for and selecting a solution or course of action that will create value for organizational stake holders. There are basically two kinds of decisions that managers called upon to make – Programmed and – Non-programmed  Types of Problems and Decisions Programmed Decision Structured Problems – Involved goals that has clarity – Are familiar(that has occurred before) – Are easily and completely defined – information about that problem is available and complete Programmed Decisions – A repetitive problem that can be handled by a routine approach  Non-Programmed Decision Unstructured Problems – Problems that are new or unusual and for which the information is ambiguous or incomplete – Problems that will require custom made solution Non programmed Decision – Decisions that are unique or nonrecurring – Decisions that generate unique responses  Programmed vs. Non-Programmed Decisions Characteristics Programmed Decisions Non-programmed Decisions Type of problem Structured Unstructured Managerial level Lower level Upper level Frequency Repetitive New, Unusual Information Readily available Ambiguous, or incomplete Time frame for solution Short Relatively long Solution relies on Procedure, Rules and Judgment and creativity policies TYPES OF PROBLEMS, TYPES OF DECISIONS, AND LEVEL IN THE ORGANIZATION Poorly structured Top Non-programmed Type of Decisions Level in Problem Organization Programmed Decisions Well structured Lower © 2003 Pearson Education Canada Inc.  Decision Making Criteria Classifying decision-making criteria – Decision making under certainty. The future state-of-nature is assumed known. Typically for structured problems with short time horizons – Decision making under risk. There is some knowledge of the probability of the states of nature occurring. Decision maker must consider several possible outcomes for each alternative, each with a given probability of occurrence Calculate the expected value of each alternative Selecting the alternative with the best expected value. – Decision making under uncertainty. There is no knowledge about the probability of the states of nature occurring, and the decision maker does not know, or cannot estimate, the probability of occurrence of the possible outcomes. Tries to maximize profit or minimize cost. 25  DECISION MAKING Process Decisions – Choices from two or more alternatives – All organizational members make decisions Decision-Making Process – Step 1 - Identifying a Problem problem - discrepancy between an existing and a desired state of affairs 6.4 DECISION MAKING (continued) Decision-Making Process (continued) – Step 2 - Identifying Decision Criteria decision criteria - what’s relevant in making a decision – Step 3 - Allocating Weights to the Criteria must weight the criteria to give them appropriate priority in the decision – Step 4 - Developing Alternatives list the viable alternatives that could resolve the problem without evaluating them 6.5 DECISION MAKING (continued) Decision-Making Process (continued) – Step 5 - Analyzing Alternatives each alternative is evaluated against the criteria – Step 6 - Selecting an Alternative choosing the best alternative from among those considered – Step 7 - Implementing the Decision implementation - conveying the decision to those affected by it and getting their commitment to it – Step 8 - Evaluating Decision Effectiveness determine whether the problem is resolved 6.6 THE DECISION-MAKING PROCESS -Example Identifying a My sales Problem representatives need new computers. 6.3 Identifying Price Manufacturer and model the Decision Warranties Criteria Support Reliability Repair Record Allocating Reliability 10 Weights Service 8 To Criteria Warranty Period 5 On-site Service 5 Price 4 Case Style 3 Developing Alternatives Compaq Fujitsu AST NEC Exhibit 6.1 (continued) Sharp IBM HP TI Compaq Reliability Fujitsu Analyzing Service Alternatives NEC Warranty Period IBM AST On-site Service Sharp Price HP TI Case Style Selecting an Alternative The Fujitsu is the best. Implementing Decision Evaluation of Decision Effectiveness  Decision Making Example- EVALUATION OF LAPTOP COMPUTER ALTERNATIVES AGAINST CRITERIA AND WEIGHTS © 2003 Pearson Education Canada Inc. Engineering Decisions- normally under uncertainty For a small number of real world systems there will be complete knowledge, where all facts/information and their relationships, judgments and predictive behavior become a certainty. For most systems, however, even after all of the data that can be bought to bear on it has been considered, some areas of uncertainty are likely to remain. If a decision must be made, these areas of uncertainty must be bridged by consideration of non-quantitative data/information, such as common sense, judgment and so forth. Decisions among system alternatives should be made on the basis of their differences. – Examples : Infrastructure expenditure decision Replace versus repair decisions Selection of inspection method Selection of a replacement for an equipment  Group Decision Making Groups can make better quality decisions. – There are a few assumptions that form the basis of this argument Groups are more vigilant than individual Groups can generate more ideas and more alternative solutions than individuals Groups can evaluate ideas more than the individual Decisions are more acceptable and easy to implement. Vroom and Yetton Model considers the style of Group decision making as follows A- stands for Autocratic C – stands for Consultative G – stands for Group  Vroom- Yetton Model- Group Decision Making The above styles are further classified as 1. A-Autocratic – A1 –The manager unilaterally makes the decision and his decision is based upon whatever information and facts are available to him/her. – A2- The manager makes the decision himself but gets all the necessary information needed personally from his subordinates. 2. C-Consultative – C1- Consult the subordinate who are expected to be involved with the outcome of the decision making – C2- Meet subordinates in a group 3. G- Group style – G1- Participative style  Group Decision Making Advantages of Group Decision making – Group members may have different specialties – Implementation of decision may be more effective – Eliminates bias – Builds up foundation as a training ground – Democratic in nature Disadvantages of Group Decision making – Time consuming – Social pressure – Own interests to protect – May not be in accord with the goals and objectives of the organization – Groupthink  Decision Making without Probabilities Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are: – Optimistic approach – Conservative approach – Minimax regret approach.  Optimistic Approach The optimistic approach would be used by an optimistic decision maker. The decision with the largest possible payoff is chosen. If the payoff table was in terms of costs, the decision with the lowest cost would be chosen.  Conservative Approach The conservative approach would be used by a conservative decision maker. For Gains – For each alternative decision the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected. (Hence, the minimum possible payoff is maximized.) For Cost – If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected. (Hence, the maximum possible cost is minimized.)  Mini-max Regret Approach The minimax regret approach requires the construction of a regret table or an opportunity loss table. – This is done by calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature. – Then, using this regret table, the maximum regret for each possible decision is listed. The decision chosen is the one corresponding to the minimum of the maximum regrets, i.e. opportunity loss  Example: CAL Heights Complex A developer must decide how large a luxury building complex to build – small, medium, or large. The profitability of this complex depends upon the future level of demand for the complex’s flats. Example deals with various options and with or without their probabilities, known. 40  CAL Heights: Elements of Decision Theory States of nature: The states of nature could be defined as low demand and high demand- Probability of demand (occurrence). Alternatives: CAL could decide to build a small, medium, or large housing complex. Payoffs: The profit for each alternative under each potential state of nature is going to be determined. We develop different models for this problem on the following slides. 41  CAL Heights: Payoff Table THIS IS A PROFIT PAYOFF TABLE States of Nature Alternatives Low demand High demand Small 8 8 Medium 5 15 Large -11 22 (payoffs in millions of Rs) 42  Decision Making without Probabilities Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are: – the optimistic approach – the conservative approach – the minimax regret approach. 43  Optimistic Approach The optimistic approach would be used by an optimistic decision maker. – The decision with the best possible payoff is chosen. – If the payoff table was in terms of costs, the decision with the lowest cost would be chosen. – If the payoff table was in terms of profits, the decision with the highest profit would be chosen. 44  CAL Heights: Optimistic Decision If the optimistic approach is selected: STATES OF NATURE BEST Alternatives Low High PROFIT demand demand Small 8 8 8 Medium 5 15 15 Large -11 22 22 Maximax Maximax decision payoff 45  Conservative Approach The conservative approach would be used by a conservative decision maker. For gains / profits – For each decision the worst payoff/ profit is listed and then the decision corresponding to the best of these worst payoffs is selected. (Hence, the worst possible profit/ payoff is maximized.) For costs – If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected. (Hence, the maximum possible cost is minimized.) 46  CAL Heights: Conservative Decision If the conservative approach is selected: STATES OF NATURE WORST Maximin Alternatives Low High PROFIT decision Maximin demand demand payoff Small 8 8 8 Medium 5 15 5 Large -11 22 -11 The decision with the best profit from the column of worst profits is selected. 47  Minimax Regret Approach 1. The minimax regret approach requires the construction of a regret table or an opportunity loss table. This is done by calculating for each state of nature the difference between each payoff and the best payoff for that state of nature. 2. Then, using this regret table, the maximum regret for each possible decision is listed. 3. The decision chosen is the one corresponding to the minimum of the maximum regrets. 48 CAL Heights: Minimax Regret Decision If the mini-max regret approach is selected: Step 1: Determine the best payoff for each state of nature and create a regret table. STATES OF NATURE Alternatives Low High Small 8 8 Medium 5 15 Large -11 22 Best Profit Best Profit for Low demand for High demand 8 22 49 CAL Heights: Minimax Regret Decision If the minimax regret approach is selected: Step 1: Create a regret table (continued). STATES OF NATURE For a profit payoff table, entries in Alternatives Low High the regret table represent profits Small 0 14 that could have been earned. Medium 3 7 Large 19 0 If they knew in advanced that the demand would be low, they would have built a small complex. Without this “psychic insight”, if they decided to build a medium facility and the demand turned out to be low, they would regret building a medium complex because they only made 5 million dollars instead of 8 million had they built a small facility instead. They regret their decision by 3 million dollars. 50  Solving CAL Heights Problem Interpretation of decisions Suppose that information regarding the probability (or likelihood) that there will be a high or low demand is unavailable. – A conservative or pessimistic decision maker would select the decision alternative is determined by the conservative approach. – An optimistic decision maker would select the decision alternative rendered by the optimistic approach. – The mini-max regret approach is generally selected by a decision maker who reflects on decisions “after the fact”, and “regrets” their decisions based upon the profits that they could have made (or cheaper costs that they could have spent) had a different decision been selected. 51  Decision Making with Probabilities Expected Value Approach – If probabilistic information regarding the states of nature is available, one may use the expected value (EV) approach. – Here the expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring. – The decision yielding the best expected return is chosen. 52  CAL Heights Revisited Suppose market research was conducted in the community where the complex will be built. This research allowed the company to estimate that the probability of low demand will be 0.35, and the probability of high demand will be 0.65. Which decision alternative should they select? 53  CAL Heights Revisited STATES OF NATURE Alternatives Low (0.35) High (0.65) Small 8 8 Medium 5 15 Large -11 22 54  CAL Heights Revisited STATES OF NATURE Alternatives Low High (0.35) (0.65) Expected value (EV) Small 8 8 8(0.35) + 8(0.65) = 8 Medium 5 15 5(0.35) + 15(0.65) = 11.5 Large -11 22 -11(0.35) + 22(0.65) = 10.45 Recall that this is a profit payoff table. Thus since the decision to build a medium complex has the highest expected profit, this is our best decision. 55 Uncertainty In Future Events Decision Under Risk & Uncertainty  Uncertainty in Future Events Decisions taken under specific assumptions concerning applicable revenues, costs and other quantities important to an engineering economy analysis are sometimes called “Decision under Certainty”. But more realistic situations are those when estimated future quantities are uncertain and project outcomes are risky. Decisions under risks – are decisions in which the analyst models the decision problem in terms of assumed future outcomes or scenarios, whose probabilities of occurrence can be estimated. Decision under uncertainty, by contrast, is a decision problem characterized by several unknown futures for which probabilities of occurrence cannot be estimated. The probabilistic estimates of an event value to occur are called random variables.  Decision Tree Decision Tree, also called Decision Flow Networks and Decision Diagrams, are powerful means of depicting and facilitating the analysis of important problems, especially those that involve sequential decisions and variable outcomes over time. Decision Trees are used in practice because – they make it possible to breakdown a large, complicated problem into a series of smaller simple problems, and – they enable objective analysis and decision making that includes explicit consideration of the risk and effect of the future. The name Decision Tree is appropriate, because it shows branches for each possible alternative for a given decision and for each possible outcome that can result from each alternative. It helps to reduce abstract thinking to a logical visual pattern of cause and effect.  Definition of Decision Tree A decision tree is a flowchart-like structure made of nodes and branches. – At each node, a split on the data is performed based on one of the input features, generating two or more branches as output. More and more splits are made in the upcoming nodes and increasing numbers of branches are generated to partition the original data. This continues until a node is generated where all or almost all of the data belong to the same class and further splits — or branches — are no longer possible.  Decision Trees Three types of “nodes” – Decision nodes - represented by squares (□), where decisions have to be made – Chance nodes - represented by circles (Ο), where circles denote different possible outcomes – Terminal nodes - represented by triangles ( this is optional) Solving the tree involves pruning all but the best decisions at decision nodes, and finding expected values of all possible states of nature at chance nodes. Pruning is represented by Pruned Branch Process followed – Create the tree from left to right – Solve the tree from right to left  Using Decision Trees Can be used as visual aids to structure and solve sequential decision problems Especially beneficial when the complexity of the problem grows  Example Decision Tree Chance Event 1 node Decision Event 2 node Event 3  Mary’s Factory Mary is a manager of a mobile factory. Her factory has been quite successful the past three years. She is wondering whether or not it is a good idea to expand her factory this year. The cost to expand her factory is $1.5M. If she does nothing and the economy stays good and people continue to buy lots of gadgets she expects $3M in revenue; while only $1M if the economy is bad. If she expands the factory, she expects to receive $6M if economy is good and $2M if economy is bad. She also assumes that there is a 40% chance of a good economy and a 60% chance of a bad economy. (a) Draw a Decision Tree showing these choices.  Decision Tree Example 40 % Chance of a Good Economy Profit = $6M Expand Factory Cost = $1.5 M 60% Chance Bad Economy Profit = $2M Good Economy (40%) Profit = $3M Don’t Expand Factory Cost = $0 Bad Economy (60%) Profit = $1M NPVExpand = (.4(6) +.6(2)) – 1.5 = $2.1M NPVNo Expand =.4(3) +.6(1) = $1.8M $2.1 > 1.8, therefore you should expand the factory  Mary’s Factory – Discounting Before Mary takes this to her boss, she wants to account for the time value of money. The gadget company uses a 10% discount rate. The cost of expanding the factory is borne in year zero but the revenue streams are in year one. (c) Compute the NPV in part (a) again, this time account the time value of money in your analysis. Should she expand the factory? Time Value of Money 40 % Chance of a Good Economy Profit = $6M Expand Factory Cost = $1.5 M 60% Chance Bad Economy Profit = $2M Good Economy (40%) Profit = $3M Don’t Expand Factory Cost = $0 Bad Economy (60%) Profit = $1M Year 0 Year 1  Time Value of Money Recall that the formula for discounting money as a function of time is: PV = S (1+i)-n [where i = interest / discount rate; n = number of years / S = nominal value] So, in each scenario, we get the Present Value (PV) of the estimated net revenues: a) PV = 6(1.1)-1 = $5,454,454 b) PV = 2(1.1)-1 = $1,818,181 c) PV = 3(1.1)-1 = $2,727,272 d) PV = 1(1.1)-1 = $0.909,091  Time Value of Money Therefore, the PV of the revenue streams (once you account for the time value of money) are: PVExpand =.4(5.5M) +.6(1.82M) = $3.29M PVDon’t Ex. = 0.4(2.73) + 0.6(.910) = 1.638 So, should you expand the factory? Yes, because the cost of the expansion is $1.5M, and that means the NPV = 3.29 – 1.5 = $1.79 > $1.64 Note that since the cost of expansion is borne in year 0, you don’t discount it.  Decision Tree Problem Mr. X has got an offer from Company A for a salary Rs 80K per month. If he does not accept, he can try Company B with a probability of cracking 60%. If he accepts Company B he will get a salary of 90K per month. If he does not get the offer from Company B, he can sit for Company C, who has 3 types of vacancies where he is eligible. The offer packages are 120K, 100K and 60K and the probability of cracking the jobs are 10%, 40% and 50% respectively. Should he accept A ? Suggest the best alternative.  Solution Reject A  CVP Analysis Cost-Volume-Profit Analysis  Fixed, Variable, Marginal & Average Costs Fixed costs are constant or unchanging regardless of the level of output or activity. Telephone monthly rentals are fixed costs In contrast, variable costs depend on the level of output or activity. Telephone charges per unit is the variable cost A marginal cost is the variable cost for one more unit, Marginal cost is used to decide whether the additional unit should be made, purchased, or sold. The average cost is the total cost divided by the number of units. Average cost is thus calculated by dividing the total cost for all units by the total number of units. Decision makers use average cost to attain an overall cost picture of the investment on a per unit basis.  Classification of costs Variable costs can be further classified into Direct Material costs Direct Labor costs Direct expenses The overhead costs can be classified into Factory overhead Administration overhead Selling overhead Distribution overhead – Direct material costs are those costs of materials that are used for the product – Direct labor cost is the amount labor wages paid to the workers who are directly engaged in the production of the goods. – Direct expenses (electricity, consumables etc.) are those expenses that vary with the production volume. – Overhead cost is the aggregate of indirect material, indirect labor and indirect other expenses (Factory overhead). Administration, selling and distribution overheads are the expenses on such heads, not directly variable with the change in volume.  Selling price of a product Selling Price of a product is derived as follows: – Direct Material costs + Direct Labor costs + Direct Expenses = Prime costs – Prime costs + Factory overhead = Factory costs – Factory cost + Works Office and administrative overhead= Costs of production – Cost of production + Opening finished stock – Closing finished stock = Costs of Goods sold – Costs of goods sold + Selling and Distribution overhead = Cost of sales – Costs of sales + profit = Sales Turn over – Sales/ Quantity sold= Selling price per unit  Cost-Volume-Profit (CVP) Assumptions and Terminology The sales volume which equates total revenue with related costs and results in neither profit nor loss is called the Break-Even Volume or Point (BEP) Total costs can be divided into a fixed component and a component that is variable with respect to the level of output. In CVP analysis following assumptions are made: – Constant Sales Price – Constant Variable cost per unit – Constant total fixed cost – Constant sales mix – Units sold equals units produced CVP analysis is used to determine both in units and in sales (Rs.) – The volume required to break even – The volume required to achieve target profit levels – The effects of discretionary expenditures – The selling price or costs required to achieve target volume levels. CVP analysis helps analyze the sensitivity of profits to change in selling prices, costs, volume and Sales mix.  Breakeven Analysis Total Variable Cost = Unit Variable Cost x Quantity Total Cost = Fixed Cost + Total Variable Cost Total Revenue = Unit Selling Price x Quantity Breakeven point: The output level at which total Total Revenue Rs revenue is equal to total cost. Profit Total Costs Variable Costs Fixed Costs Loss Break-even Point Production Quantity  BEP-Example Units produced/sold- X units. Fixed cost = Rs. 225; Variable cost/unit = Rs.20 Sales price /unit= Rs. 35; Rs. Total Revenue 1000 At BEP: Total Cost= Total Revenue = 35X i.e., 35X = 225 + 20X Profit Total Costs Or, X= 15 units 800 = Rs. 225 + 20X Variable Costs 600 = 20X BEP 400 Fixed Costs 200 Loss = Rs. 225 0 X 10 20 25 5 15 (X)# of Units  CVP Computations Sales (V) = Variable Cost (v) + Fixed Cost (FC) + Profit (p) Contribution (P)= Fixed cost (FC) + Profit (p) Sales = Variable Cost + Contribution V= v+P 𝑣 𝑃 or, + =1 𝑉 𝑉 𝑃 𝑣 𝑉−𝑣 Or, 𝑉 = 1- 𝑉 = 𝑉 At BEP (Profit (p) = 0), V= v+FC+0; or, FC= (V-v) 𝑃 𝐹𝐶 𝑉 = 𝑉 Or, Sales value (V) at BEP 𝑃 𝑣 V = FC/ 𝑉 = FC/ (1- 𝑉) Or, BEP (in units) X (at BEP)= FC / (Vx− vx) = FC/ (Sales price/unit- Variable cost/unit)  CVP Problem From the following data, calculate the required sales to achieve a targeted profit of Rs. 6000. Period Sales Profit 1 12,000 5000 2 18,000 8000  CVP-Problem Solution V1 = v1 + FC+ P1 V2 = v2 + FC + P2 V = v + (P2- P1) 6000= v + 3000 Or, v = 3000 v / V = 0.5 FC= 12000-6000-5000 = 1000. So for 6000 profit, V= 0.5V+ 1000 + 6000 or, V = 14,000  CVP Problem Sums Sales 4,000 units @ Rs 25 = 1,00,000 Total Costs = Material Consumed = 40,000 Labor charges = 20,000 Variable overhead = 10,000 Fixed overhead = 18,000 Total cost = 88,000 Calculate 1. Number of units to be sold to break even 2. Sales needed to earn a profit of 20% on sales 3. Extra units which should be sold to obtain the present profit, if it propose to reduce the sales price by 20% 4. Selling price to be fixed to bring down its BEP to 600 units under present condition.  CVP Calculations for a Single Product Sales in Units required to achieve target 𝐹+𝑃𝑟𝑜𝑓𝑖𝑡 pretax profit, Q = 𝑉𝑥−𝑣𝑥 where F = total fixed costs Vx = selling price per unit vx = variable cost per unit Vx-vx = contribution margin per unit To find the breakeven point in units, set Profit = 0. July 2013  CVP Calculations for a Single Product Sales in Rs. required to achieve target F + Profit = pretax profit CMR where F = total fixed costs CMR = contribution margin ratio = (Vx- vx)/Vx Note that CMR Total Revenue − Total Variable Costs can also be CMR = computed as Total Revenue 𝑉−𝑣 𝑣 𝑃 = 𝑉 = 1- 𝑉 = 𝑉 To find the breakeven point in sales Rs, set Profit = 0.  Breakeven Point Calculations Bill’s Briefcases makes high quality cases for laptops that sell for $200. The variable costs per briefcase are $ 80, and the total fixed costs are $ 360,000. Find the BEP in units and in sales $ for this company. 𝐹𝐶+𝑝 (=0) $360,000 BEP in units = = 𝑉𝑥−𝑣𝑥 $200 / unit − $80 / unit $360,000 = = 3,000 units $120 / unit F +0 $360,000 BEP in sales $ = = 𝐹𝐶+𝑝 (=0) = ($200 − $80) / $200 𝑉𝑥−𝑣𝑥 CMR 𝑉𝑥 $360,000 = = $600,000 60%  Using CVP to Determine Target Cost Levels Suppose that Bill’s marketing department says that he can sell 6,000 briefcases if the selling price is reduced to $170. Bill’s target pretax profit is $210,000. Determine the highest level that his variable costs can so that he can make his target. Recall that F = $360,000. Use the CVP formula for units, but solve for vx: 360,000+210,000 Q = 6,000 units = 170−𝑣𝑥 $360,000 + $210,000 $170/unit − Vx = = $95/unit 6,000 units Variable Cost, vx= 170-95 i.e V x= $75/unit If Bill can reduce his variable costs to $75/unit, he can meet his goal.  Using CVP to Compare Alternatives Currently Bill’s salespersons have salaries totaling Rs.80,000 (included in F of Rs. 360,000) and earn a 5% commission on each unit (Rs.10 per briefcase). He is considering an alternative compensation arrangement where the salaries are decreased to Rs.35,000 and the commission is increased to 20% (Rs.40 per briefcase). Compute the BEP in units under the proposed alternative. Recall that Sales Price = Rs.200/unit and Variable cost/unit = Rs.80 currently. First compute F and V x under the proposed plan: F = Rs.360,000 – Rs.45,000 decrease in = Rs.315,000 Salaries, v x = Rs.80 + Rs.30 (increase in commission) = Rs.110 Then compute Q under the proposed plan: Units needed 𝑅𝑠 315,000 = = 3,500 𝑢𝑛𝑖𝑡𝑠 to breakeven 𝑅𝑠 200 − 𝑅𝑠 110  Determining the Indifference Point Compute the volume of sales, in units, for which Bill is indifferent between the two alternatives. The indifference point in units is the Q for which the profit equations of the two alternatives are equal. Current Plan Proposed Plan Contribution margin per unit Rs120 Rs.90 Total fixed costs Rs.360,000 Rs.315,000 Profit (current plan) = Rs.120Q – Rs.360,000 Profit (proposed plan) = Rs.90Q - Rs.315,000 Rs.120Q – Rs.360,000 = Rs.90Q – Rs.315,000 Rs.30Q = Rs.45,000 Q = 1,500 units  Life Cycle Costs Life-cycle cost analysis (LCCA) is a tool to determine the most cost-effective option among different competing alternatives to do a project, when each is equally appropriate to be implemented on technical grounds.  Life Cycle Costing- Definition Life cycle costing is defined as the total cost throughout its life including planning, design, acquisition & support costs & any other costs directly attributable to owning / using the asset. Category of LCC Capital assets : Initial costs Operating costs Disposal costs LIFE CYCLE COMPUTATION Simple Formula: Capital (Initial Investment cost) + lifetime operating costs + lifetime maintenance costs + disposal costs – residual value  Cash Cost versus Book Cost A cost that involves payment of cash is called a cash cost (and results in a cash flow) – to distinguish it from one that does not involve a cash transaction and is reflected in the accounting system as a noncash cost. The noncash cost is often referred to as a book cost. – Book costs are costs that do not involve cash payments but rather represent the recovery of past expenditures over a fixed period of time. The most common example of book cost is the depreciation charged for the use of assets such as plant and equipment. – In engineering economic analysis, only those costs that are cash flows or potential cash flows from the defined perspective for the analysis need to be considered. Costs reflected only in the accounting system (in the accounting books) are called book costs.  Sunk Costs Sunk Costs: Cost that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative Example Paid Rs.15 for a concert ticket. The show is great, but after 45 minutes you are tired and are thinking about your long day tomorrow. Should you stay and “get your money’s worth”? – Question: when is the optimal time to leave? At the end of the night, no matter what, your Rs.15 is sunk. – Each moment your stay: MB = additional enjoyment of concert MC = lost sleep time – For each moment you are home early: MB = sleep time and more productive day tomorrow MC = missed remaining part of the concert The Rs.15 price that you paid should not enter into this decision making process, either way you look at it.  Opportunity Costs Opportunity cost or an economic opportunity loss is the value of a product forgone to produce or obtain another product. – Opportunity cost analysis is an important part of a company’s decision-making process, but is not treated as an actual cost in any financial statement. This may be referred to as the opportunity cost of doing the best thing and ignoring the next best thing to be done. – The notion of opportunity costs plays a crucial part in ensuring that scarce resources are used efficiently. Thus, opportunity costs are not restricted to monetary or financial costs; the real cost of output foregone, lost time, pleasure or any other benefit.  Opportunity Cost- Explained Opportunity cost is not the sum of the available alternatives when those alternatives are, in turn, mutually exclusive to each other. It is the highest value of the options forgone. Use for any precludes all the others. If someone chooses to spend money, that money could be used to purchase other goods and services so the spent money is part of the opportunity cost as well. Add the value of the next best alternative and you have the total opportunity cost. – If you miss work to go to a concert, your opportunity cost is the money you would have earned if you had gone to work plus the cost of the concert  Opportunity cost-Example Scarcity of resources is the basic concept of economics. Scarcity necessitates Trade-offs and Trade-offs result in an opportunity cost. – While the cost of goods and services is often thought in monetary terms, the opportunity cost of a decision is based on what must be given up (the next best alternative) as a result of the decision. Any decision that involves a choice between two or more options has an opportunity costs. Opportunity costs contrasts to accounting cost in that accounting costs do not consider foregone opportunities. – Consider the cost of an MBA education is Rs 10 Lakhs for two years. This is the monetary cost of education. However, when making the decision to go back to college, one should consider the opportunity cost, which includes the income the student would have earned if he would have continued in his service. If the salary he would forego in the two years is Rs 12 lakhs, the opportunity costs would be RS 22 lakhs in two years for obtaining the degree. – Again consider a small business, which owns the building in which it operates, and thus pays no rent for office space. But this does not mean that the company's cost for office space is zero. Instead, the business owner must consider the opportunity cost associated with reserving the building for its current use. Perhaps the building could have been rented out to another company, with the business itself relocated to a location with a higher level of customer traffic. The foregone money from these alternative uses of the property is an opportunity cost of using the office space, and thus should be considered in calculations of the small business's expenses. The opportunity cost is useful when evaluating the cost and the benefit of the choice. Recurring Costs and Non-recurring Costs Recurring Costs: Repetitive and occur when a firm produces similar goods and services on a continuing basis – Office space rental Non-recurring Costs: Not repetitive, even though the total expenditure may be cumulative over a period of time – Typically involve developing or establishing a capability or capacity to operate – Examples are purchase cost for real estate and the construction costs of the plant  Incremental Costs Incremental Costs: Difference in costs between two alternatives. – Suppose that A and B are mutually exclusive alternatives. If A has an initial cost of $10,000 while B has an initial cost of $14,000, the incremental initial cost of B over A is (B - A), which is $4,000.  Example Choosing between Model A & B Incremental Cost Items Model A Model B Cost Purchase Price $10,000 $17,500 $7,500 Installation Costs 3,500 5,000 1,500 Annual Maintenance 2,500 750 -1,750 Annual Utility 1,200 2,000 800 Disposal Cost 700 500 -200  Incremental Cost- Problem In the design of a 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 1.2 Kg as compared with 1.35 Kg for steel casting. The aluminium can be cast for Rs 80 per Kg. and the steel one for Rs 35 per Kg. The cost of machining per unit is Rs 150 for aluminium and Rs 170 for steel. Every Kg of excess weight is associated with a penalty of Rs 1300 due to increased fuel consumption. Which material should be specified and what is the economic advantage of the selection per unit.  Incremental Problem- Solution Item Aluminium Steel Differential cost Weight of the Casting 1.2 Kg 1.35 Kg - Cost of making casting 1.2X Rs 80 1.35 X Rs. 35 -48.75 = Rs. 96 = Rs. 47.25 Cost of machining the Rs. 150 Rs. 170 + 20.00 Casting Penalty for excess weight - (1.35-1.20) X +195 in fuel consumption Rs. 1300 Total Additional Cost for Rs. 166.25 Steel Casting Decision: The total cost/unit of a jet engine part made of aluminium is less than that of an engine made by steel by Rs. 166.25. Hence it is recommended.  Short Definitions of Different Costs CLASSIFICATION OF COSTS – A key objective in engineering applications is the satisfaction of human needs, which will nearly always imply a cost. – Economic analyses may be based on a number of cost classifications: First (or Initial) Cost : Cost to get activity started such as property improvement, transportation, installation, and initial expenditures. Operation and Maintenance Cost : They are experienced continually over the useful life of the activity. Fixed Cost : Fixed costs arise from making preparations for the future, and includes costs associated with ongoing activities throughout the operational life-time of that concern. Fixed costs are relatively constant; they are decoupled from the system input/output, for example. Variable Cost : Variable costs are related to the level of operational activity (e.g. the cost of fuel for construction equipment will be a function of the number of days of use). Incremental or Marginal Cost : Incremental (or marginal) cost is the additional expense that will be incurred from increased output in one or more system units (i.e. production increase). It is determined from the variable cost. Sunk Cost : It cannot be recovered or altered by future actions. Usually this cost is not a part of engineering economic analysis. Life-Cycle Cost : This is cost for the entire life-cycle of a product, and includes feasibility, design, construction, operation and disposal costs.  Learning Curve A learning curve reflects increased efficiency and performance with repetitive production of a good or service. The concept is that some input resources decrease, on a per-output- unit basis, as the number of units produced increases.  Learning Curve- A Management tool Learning is a property of all living organisms. They can trace improvement patterns characteristic of themselves. Since organized groups can be looked upon as living entities, they can be expected to exhibit learning and to trace such patterns. Improvement does not just happen. It is the result of continued seeking and resourceful striving. The most important ingredients in learning curve performance are vision and leadership. Continued improvement is a chain of influences which starts with the conviction that progress is possible, continues with the creation of an environment and support of work which promote it. Consequently, the learning curve can be regarded as a primary tool of management.  Learning Rate Varies While the learning curve is a universal phenomenon, it has many variations in form. In airframe manufacture three-fourths of the direct labor input is assembly; the balance is represented by men engaged in machine work. In such a largely man-paced operation, an 80% curve is commonly found. But when the proportion of assembly work is lower, the downward slope of the curve is not so steep. If the ratio of assembly to machine work is 50/50, the slope is about 85%. If the ratio is one-fourth assembly and three-fourths machine work, the operation is largely machine-paced, and the slope is around 90%.  Learning Curve The learning curve is an analytical tool that can be used to estimate the rate at which cumulative experience allows workers to do tasks faster and with less cost. Learning curve theory is based on three assumptions: The amount of time required to complete a given task or unit of a product will be less each time the task is undertaken. The unit time will decrease at a decreasing rate. The reduction in time will follow a predictable pattern. The concept of a Learning Curve is motivated by the observation (in many diverse production environments) that, each time the cumulative production doubles, the hours required to produce the most recent unit decreases by approximately the same percentage.  Learning Curve-Example For example, for an 80% learning curve, ▪ If cumulative production doubles from 50 to 100, then the hours required to produce the 100-th unit is 80% of that for the 50-th unit. ▪ If cumulative production doubles from 100 to 200, then the hours required to produce the 200-th unit is 80% of that for the 100-th unit.  An 80% learning curve 1st unit Unit 80% Learning Curve Man 1000 hours 2nd Man-hours per unit 800 1ST 1000 2ND 1000 X.80 800 4TH 800 X.80 640 4th 600 8TH 640 X.80 512 8th 16TH 512 X.80 410 16th 32ND 410 X.80 328 400 32nd 200 0 10 20 30 40 50 Cumulative units produced Learning Curves 107  The log - linear method Power Law: Exponential Decay function in time & cost. In Log-Log scale it is straight line. yx log yx Cum. units Cum. units (x) (log x) The learning curve is a strategic, not a tactical concept – cannot be used as a short-range operating control. A learning curve strategy can reduce the ability to innovate At some point, the learning curve will “plateau” 108  Manufacturing strategy and the learning curve Capacity expands automatically Break-even points reduced automatically Worker compensation plans should account for learning effects The learning curve is a strategic, not a tactical concept – cannot be used as a short-range operating control A learning curve strategy can reduce the ability to innovate At some point, the learning curve will “plateau” 109  Strategic Applications of a Learning Curve Frequent Decreases in Selling Price. As the hours required to produce the most recent unit continually decreases, the cost to produce the unit continually decreases. Therefore, you can frequently decrease the selling price without decreasing total profit. Each decrease in selling price increases your market share, which in turn leads to a “faster ride” down the learning curve, which in turn makes it tougher for your competitors. Reinvest Increased Profits As the hours required to produce the most recent unit continually decreases, the cost to produce the unit continually decreases. Therefore, your profits increase. You can reinvest the incremental profit to improve the product or the production process, or you can reinvest the incremental profit in another area of the firm. 110  Learning Curve- contd. Most learning curves assume a constant percentage reduction occurs as the number of units produced is doubled. Essentially, the learning curve is a mathematical function that can be used to chart the progress of workers as they learn to do their work faster. This can be expressed by the relationship between the amount of time it takes an organization with a learning rate percentage of r to produce the nth item in an equation Tn = T1 (nb) and in Logarithmic scale, it is Log Tn = Log T1 + b Log n In the equation: – Tn = time required to complete the nth task & T1 is the 1st task – b = ln(r)/ln(2), where r = learning rate percentage (say 80%) = ln(.8)/ln(2)= (-) 0.322 – (index “b” is a measure of learning rate and here it is -- 0.322 for 80% learning curve)  Learning Curve -Problem Example: in airplane industry, it is observed that, as output doubled, there is a 20 percent reduction in direct production worker-hours per unit between doubled units. Thus, if it took 100,000 hours for Plane 1, it would take 80,000 hours for Plane 2, 64,000 hours for Plane 4, and so forth. Because the 20 percent reduction meant Unit 4 took only 80 percent of the production time required for Unit 2, which is referred to as an “80 percent learning curve.” In the above example what would be the time required to produce the eighth aircraft, if the first unit takes 100000hours, second one takes 80,000hours, and the 4 th unit takes 64,000 hours? If the company wishes to quote the price for 8 aircrafts where the cost is calculated as a multiple Rs 20 per hour and the profit is expected to be 25 – Answer – Tn = T1 (n ᵇ) i.e. T8 = (100)(8-0.322) = 51.2 minutes – Since, b= ln(0.80)/ln(2) = -0.322  Problem continued T Tn ᵇ Hours per unit Cum Hours per unit T1 (100,000)(1-0.322) 100,000 100,000 T2 (100,000)(2-0.322) T3 (100,000)(3-0.322) T4 (100,000)(4-0.322) T5 (100,000)(5-0.322) T6 (100,000)(6-0.322) T7 (100,000)(7-0.322) T8 (100,000)(8-0.322) Total =  Learning Curve Problem-2 Learning Curve –Addl. Problem : A firm must make a bid on a contract to make 12 units of a new product. Engineering analysis indicates that the nature of this product and its manufacturing processes resemble those for the firm’s current Model 206, so the firm decides to base its bid on the 85 percent learning rate it experienced on that model. If engineers estimate that the first unit will require 10 hours of labor, how many hours will the 12 unit require? How many hours will the firm take to make all 12 units? If the cost of the item is calculated based on labor hours engaged and is Rs. 1000 per labor hour and the firm wants a profit of 20% on the cost, what should it quote per piece for the 12 pce order?  Problem solution Solution: Find the unit times for an 85 percent learning rate Unit Produced Unit Time change Hours per Unit Cumulative Hours Required 1 1.0000 10.0 hrs. 10.00 hrs. 2 0.8500 8.50 18.50 3 0.7729 7.73 26.23 4 0.7225 7.23 33.45 5 0.6857 6.86 40.31 6 0.6570 6.57 46.88 7 0.6337 6.34 53.22 8 0.6141 6.14 59.36 9 0.5974 5.97 65.33 10 0.5828 5.83 71.16 11 0.5699 5.70 76.86 12 0.5584 5.58 82.44 Tn = T1 (nb) T2 = T1 (2 (-0.234)) = 10x 0.85= 8.50 When b= ln (r) /ln (2) = ln (0.85)/ln (2) = (-) 0.234 T12 = 10 (12) -0.234 = 5.58 hours This table indicates that the 12 th unit will require 5.58 hours, and the total number of hours needed to make all 12 units to 82.44 hours.  Limitations of Learning Curve Cannot accurately predict future curve Learning curves must be redeveloped whenever the product or production process is modified. The learning curve recognizes current skills but cannot predict the future with complete accuracy. Misleading data – The learning curve is influenced by variables such as time, previous experience, quality of training,  Non linear Break-even Analysis Cost and revenue functions do not always follow convenient linear patterns. Often realistic cost relationships develop a nonlinear pattern. This often leads to change the average cost figures to follow any regular trend. Average cost figures are defined as Average fixed cost- Since fixed costs are independent of output, their per unit amount declines as output increases. This is due to “higher sales spreading the overhead”. 𝑭 – Average Fixed cost = 𝒏 Average Variable cost – Typically this average cost declines in the beginning but takes a saucer-shaped curve, where a point is reached when more and more variable resources are required for each additional output. With increasing output, plant’s capital equipment utilization becomes more efficient. But continually increasing variable costs, which happens beyond a point eventually creates a condition in which overcrowding and over utilization of equipment impair efficiency. 𝑻𝑽 – Average Total Variable cost= 𝒏  Non-linear Break-even Average total cost- Average total cost is simply the sum of the average fixed cost and average variable cost. This makes the average cost to show the effect of both the spreading out of the fixed charges and diminishing returns of the variable costs. 𝑻𝑪 – This is given by 𝒏 ; Used as a basis for normal pricing Marginal cost- Marginal cost is calculated from either TC or TV as the extra increment of cost required to produce an additional unit of output. If the last increment of cost is smaller than the average of all previous costs, it pulls the average down. Thus, average total cost declines until it equals the Marginal cost. ∆𝑻𝑪 – Marginal cost = ∆𝒏 – This is used for Capacity Planning: excess capacity Basis for last-minute pricing  Change in Fixed Cost-its impact A change in input costs shift the cost curves. – If variable input costs are reduced then MC, AVC, and ATC will all shift downward. – If fixed costs are reduced then only ATC will shift downward. But AVC and MC will remain unaffected, when further changes take place at the reduced fixed costs.  Average Costs and Marginal Cost The marginal cost and average cost curves are related ⚫When MC exceeds ATC, average cost must be rising ⚫When MC is less than ATC, average cost must be falling This relationship explains why marginal cost curves always intersect average cost curves at the minimum of the average 120 cost curve.  MC vs. AVC & ATC $ MC will intersect the AVC at the minimum of the AVC [always] in a changing average variable cost/unit. ATC ATC* AVC R MC will intersect the ATC at the minimum of the ATC. AVC* J The vertical distance between ATC and AVC at any output is the AFC. At Q** AFC is RJ. Q* Q** Q At Q* output, the AVC is at a minimum AVC* [also max of APL]. At Q** the ATC is at a MINIMUM. TVC = AVC* x Q* TC = ATC* x Q** 121  Non linear Break even Analysis Total Fixed cost of a Company is Rs. 3000. It’s Variable cost is changing with the number of output and are given below. What is the maximum number of output that the company should produce to maximize its profit. Total Total variable Product cost 1 700 2 1300 3 1800 4 2400 5 3100 6 3900 7 4900 8 6200 What is Marginal cost? Explain.  Example- Non-linear Breakeven analysis Total Total Total Total Avg. Fixed Average Average Marginal Product Fixed variable cost cost Variable total cost cost cost cost apportioned cost n F TV TC F/n TV/n TC/n ∆𝑇𝐶 ∆𝑛 0 3000 0 3000 - - - 1 3000 700 3700 3000 700 3700 700 2 3000 1300 4300 1500 650 2150 600 3 3000 1800 4800 1000 600 1600 500 4 3000 2400 5400 750 600 1350 600 5 3000 3100 6100 600 620 1220 700 6 3000 3900 6900 500 650 1150 800 7 3000 4900 7900 429 700 1129 1000 8 3000 6200 9200 375 775 1150 1300  Price – Demand Relationship Movement along the demand curve occurs when the price of the good changes along with the quantity demanded. p= a-bD p is the price & D is the demand Where a is the intercept on the price axis and -b is the slope The amount of a good that buyers purchase at a higher price is less because as the price of a good goes up, so does the opportunity cost of buying that good. As a result, people will naturally avoid buying a product that will force them to forgo the consumption of something else they value more. Total Revenue Function Sales, S = pD =(a-bD)D To maximize Total Revenue 𝑑𝑆 𝑑 = 𝑎 − 𝑏𝐷 𝐷 𝑑𝐷 𝑑𝐷 == a-2bD=0 For Maximum S 𝑎 D= 2𝑏 Maximum S = aD-bD² a² a² a² = − = 𝟐𝒃 𝟒𝒃 𝟒𝒃 (Total Revenue i.e. Sales) 𝑎 D= 2𝑏 Break-even Point & Profitability Profit = S- TC = (aD - bD²)- (FC + vx D) = - bD² + (a- vx ) D – FC d(Profit) 𝑑𝐷 = 𝑎 − vx −2 bD = 0 To maximize Profit, the optimal value of D is Total Cost 𝑎−vx 𝑑²(𝑃𝑟𝑜𝑓𝑖𝑡) D*= , when = −2𝑏 , 2𝑏 𝑑D² i.e. negative At BEP, Total Revenue= Total Cost Max. Profit { i.e. aD-bD²= FC + vx D, which is a Quadratic function for D , with 2 values. Fixed Cost (Total Revenue i.e. Sales) D´ D* D= 𝑎 D´´ 2𝑏 BEP2 BEP 1  Engineering Economic Analysis - Seven Steps 1. Recognition and formulation of the problem. 2. Development of the feasible alternatives. 3. Development of the net cash flows (and other prospective outcomes) for each alternative. 4. Selection of a criterion (or criteria) for determining the preferred alternative. 5. Analysis and comparison of the alternatives. 6. Selection of the preferred alternative. 7. Performance monitoring and post-evaluation.  Use of cost estimates Results of cost estimating are used for a variety of purposes. – Setting selling prices for quoting, bidding, or evaluating contracts. – Feasibility study--Determining if a proposed product can be made and distributed at a profit. – Capital Budgeting-- Evaluating how much capital can be justified for changes and improvements. – Setting benchmarks for productivity improvement programs and estimating benefits thereof.  Cost estimation approaches The two fundamental approaches are “top- down” and “bottom-up.” – Top-down uses historical data from similar projects. It is best used when alternatives are still being developed and refined. Normally used at the initial screening stages, using scale up or down options. – Bottom-up is more detailed and works best when the detail concerning the desired output (product or service) has been defined and clarified. At this stage designed options are available. This method breaks down a project into small, manageable units and estimates their economic consequences. These smaller unit costs are added together to obtain an overall cost estimates.  Cost estimation approaches Top down approach in a nutshell refers to an estimate where the costs are based on using available design parameters (either known or assumed), and applying them to cost models Some of the estimating models are – Rough Order of Magnitude (ROM) Estimates Made without detailed engineering Accurate to within +50% or -30% of actual costs – Factor (Benchmark) Estimating Utilizes costs from similar projects Historical cost data is normalized and scaled to fit This two are used at the very beginning of the project where there is little or no design. Both might rely or a combination of historical cost, cost comparisons between similar projects, factoring, etc. Factoring or Benchmark estimating may be better classified as a technique to develop costs in that it is often used in combination with rough order of magnitude estimates and sometimes budget estimates as well. Even though the project may be at an early stage of design Benchmark estimating could be fairly detailed depending on the data being used.  Bottom up approaches Bottom up approach is also known as Detailed estimating approach. This method is typically used when design and scopes are complete. Bottom up approach (Detailed estimating) is basically a process where the cost engineer develops quantity takeoffs from scopes, plans and specs. The term “bottoms-up” refers to the process of making the estimate…determining the quantity to be used, applying labor, equipment, and material prices to each line item in the estimate, which is the lowest level of the estimate and then finally rolling all the costs elements up to the total cost of the project. – Example : Building estimator would make detailed quantity estimate for how much concrete, reinforcing, formwork, etc is required to construct the footing and foundation system based on the size. In a detailed estimate, each item would be shown and priced out separately in the estimate. This method to create this type of estimate is very labor intensive. Because of this it is not normally used in the early stages.  Component of Cost Estimation Integrated Approach Three basic components of an Integrated Approach for developing the Net Cash Flow for the feasible project alternatives are – Work breakdown structure (WBS) – Cost and revenue structure (classification) – Estimating techniques (models)  Work Breakdown Structure It is foundation of project planning. A framework for defining all project work elements and their relationships, collecting and organizing information, developing relevant cost and revenue data, and management activities. It defines tasks – that can be completed independent of other tasks, – facilitating resource allocation, – assignment of responsibilities and – measurement and control of the project It is followed by – identification of dependencies and – estimation of activity durations It can be used to identity the tasks in the CPM and PERT 133  Car Drive Electrical Chassis & Controls System Chassis Tire Engine Power frame mounting train Steel Inter Moun Fuel Engine Gear Struc ior Ting Tire Injec body Trans box ture Struc tion mission ture  Cost and Revenue Structure Used to identify and categorize the costs and revenues that need to be included in the analysis. The life-cycle concept and WBS are important aids in developing the cost and revenue structure for a project. Perhaps the most serious source of errors in developing cash flows is overlooking important categories of costs and revenues. Categories of Costs and Revenues Some of the Costs and Revenues typically needed in an engineering economy study- Costs Revenue – Capital Investment Sales Revenue – Labor costs Service and – Material costs Spares revenue – Maintenance costs Salvage Value – Overhead costs – Marketing costs – Disposal costs  Estimating Techniques The purpose of estimating cost is to develop cash-flow projections— not to produce exact data about the future, which is virtually impossible. Cost and revenue estimates can be classified according to detail, accuracy, and their intended use. Rough Order-of-magnitude estimates (±30%) – At the planning & evaluation stage Semi-detailed, or budget, estimates (±15%) – Preliminary or conceptual design stage Definitive (detailed) estimates (±5%) – Detailed engineering or at construction stage  Sources of Data Sources of estimating data – Accounting records (historical data) – Additional sources within the firm (sales, engineering, production, purchasing.) – Sources outside the firm (government data, industry surveys, trade journals, etc.) – Research and Development (pilot plant, test marketing program, surveys.) How estimates are accomplished – Conference (Delphi method) – Comparison – Using quantitative techniques  Choosing the source Choosing the source of data depends on the level of detail and accuracy of estimates and considers the followings: – time and effort available as justified by the importance of the study, – difficulty of estimating the items in question, – methods or techniques employed, – qualifications of the estimator(s), and – sensitivity of study results to particular factor estimates.  Estimating Techniques Indexes Unit Technique Factor Technique Estimating Relationships – Power-Sizing Technique – Learning Curve Analysis of product price and cost – Establishing product price as a markup to cost – Establishing price in relation to competition  Indexes An index is a dimensionless number that indicates how a cost or a price has changed with time (typically escalated) with respect to the base year. Cn = cost or selling price of an item in year n Ck = cost or price of the item at an earlier point in time (say year k) In = index value in year n Ik = index value in year k Cn = Ck (In /Ik ) Problem Sum A certain index for the cost of purchasing and installing utility boilers is keyed to 1974, where its baseline value was set at 100. Company XYZ installed a 50,000 lb/hr in 1989 for Rs.350,000 when the index had value of 312. This same company must install another boiler of the same size in 1996. The index in 1996 is 468.  Composite Index Index can be created for a single item or for multiple items. – For a single item, the Index value is simply the ratio of the cost of the item in the current year to the cost of the same item in the reference year, multiplied by the reference year factor. – A composite Index is created by averaging the ratios of selected item costs in a particular year to the cost of the same items in a reference year. The developer of an Index, can assign different weights to the items in the index according to their contribution to the total costs. A Composite Index is given by 𝑪𝒏𝟏 𝑪𝒏𝟐 𝑪𝒏𝒎 𝑾𝟏 +𝑾𝟐 + …..+𝑾𝒎 In = 𝑪𝒌𝟏 𝑪𝒌𝟐 𝑪𝒌𝒎 x Ik 𝑾𝟏+𝑾𝟐+⋯+𝑾𝒎 Where, m = the Total number of items in the index Cnm = the Unit cost (or price) of the mth item in year n Ckm = the Unit cost (or price) of the mth item in year k Wm = weightage assigned to the mth item Ik = Composite Index value in year k  Problem of Index Develop a composite index for the price of a boiler in 2004 when 1986 is the reference year having an index value of 99.2. The weight placed on Mild steel cost is 3 times that of either Stainless steel or Boiler steel cost, because roughly three times cost is incurred in Mild steel plates compared to the other two items of cost. Type Per Kg cost 1986 1992 2004 Stainless steel 114 138 240 Boiler steel 103 127 230 Mild Steel 93 117 221 If the Index is estimated to be 253 in 2010, determine the corresponding 2010 price of the steels used in Boiler from the Index of 2004  Solution to Composite Index Problem 𝑪𝒏𝟏 𝑪𝒏𝟐 𝑪𝒏𝒎 𝑾𝟏 +𝑾𝟐 + …..+𝑾𝒎 In = 𝑪𝒌𝟏 𝑪𝒌𝟐 𝑪𝒌𝒎 x Ik 𝑾𝟏+𝑾𝟐+⋯+𝑾𝒎 Where, m = the Total number of items in the index Cnm = the Unit cost (or price) of the mth item in year n Ckm = the Unit cost (or price) of the mth item in year k Wm = weightage assigned to the mth item Ik = Composite Index value in year k In the problem, W1= 1, W2= 1, & W3= 3 And Ck1= 114, Ck2= 103, Ck3= 93 , Cn1 = 240, Cn2= 230, Cn3= 221 240 230 221 1 114 +1 103 +3 93 Then I2004= 𝑋99.2 = 2.29𝑋99.2 1+1+3 = 227.56 Steel prices estimated for 2010 in Rs., corresponding to 2004 Index are 253 253 Stainless steel: 240 x = 𝑅𝑠 267; 𝐵𝑜𝑖𝑙𝑒𝑟 𝑠𝑡𝑒𝑒𝑙: 230 𝑋 = 𝑅𝑠. 256 227.6 227.6 253 & Mild Steel : 221 X = Rs 246 227.6  Unit Technique Involves a “per unit factor” that can be estimated effectively. Examples: – Construction cost per square foot – Capital cost of a plant per kilowatt of capacity – Revenue per customer served – Operating cost per mile – Maintenance cost per hour  Problem- of Unit Technique We need a preliminary estimate of the cost of a particular house. Use the factor of, say, Rs.55 per square foot and assume that the house is approximately 2,000 square feet. Estimated cost of the house = Rs.55 x 2,000 = Rs.110,000  Factor Technique The factor technique is an extension of the unit technique C = cost being estimated Cd = cost of the selected component d that is estimated directly fm = cost per unit of component m Um = number of units of component m C =  Cd +  fm Um d m  Problem on Factor Technique We need a refined estimate of the cost of the house. Assume that the house is approximately 2,000 square feet of living space, has one lawn attached and two garages. Use the factor of, say, Rs.50 per square foot of living space, Rs.50,000 for the lawn and Rs.80,000 per garage. Estimated cost of the house = Rs.50 x 2,000 + Rs.50,000 + (Rs.80,000 x 2)= Rs.310,000  Power-Sizing Technique Power sizing technique is also sometimes referred to as the exponential model. This is often used to cost industrial plants and equipment CA = cost for plant A (To estimate) CB = cost for plant B (which we have estimated based on Cost Index) SA = size of plant A SB = size of plant B X = cost-capacity factor to reflect economies of scale CER i.e. Cost Estimating Relationship, CA /CB = (SA /SB )X or CA = CB (SA /SB )X The value of the Cost-capacity factor will depend on the type of plant or equipment being estimated. For example, X= 0.68 for nuclear generating plants and 0.79 for fossil generating plants. X< 1 indicates Economics of scale i.e. each additional unit of capacity costs less than the previous unit and vice versa. X=1 indicates linear relationship.  Problem on Power Sizing Technique Make a preliminary estimate of the cost of building a 600-MW fossil fuel power plant. It is known that a 200-MW plant cost Rs.100 million 20 years ago when the appropriate cost index was 400. That cost index is now 1,200. The power-sizing factor is 0.79. Today’s estimated cost of a 200-MW plant = – Rs.100 million x (1,200/400) = Rs.300 million Today’s estimated cost of a 600-MW plant = – Rs.300 million x (600/200)0.79 = Rs.714 million Problem on Power Sizing Technique The cost of building a wafer fabrication facility with a capacity of 500,000 units per year was Rs.2,500,000 in year 2000. Estimate the cost of a similar wafer fabrication facility with a capacity of 1,500,000 units per year for year 2008. The technological changes dictate that an additional piece of equipment must be integrated with the facility and the cost of this new equipment has been estimated to be Rs.50,000 for year 2008. Consider the cost-capacity factor (X) is 0.65 and the cost index for wafer fabrication facility has increased by an average rate of 12% per year for the past 8 years.  Solution First, estimate the cost of the old facility in year 2008 using Cost Indexes technique: C2008 = I 2008 X C2000 I 2000 I2008 = (1.12)⁸ I2000 Or, C2008 = (1.12)⁸(2, 500, 000) = Rs.61,89, 908 Next, use power sizing technique: C(1500) = C(500) X (1500,000/500,000)ᵡ , where, ᵡ = 0.65 = 6,189,908 X (2.04) = 12,641, 919 Finally, add the estimated cost of the additional equipment Rs.50,000; total cost is Rs.12,691,919.32.  Segmentation Model In Segmenting Model an estimate is decomposed into its individual components. Estimates are made at those lower levels, and then the estimates are aggregated (added) back together. It is much easier to estimate at the lower levels because they are more readily understood. This approach is common in engineering estimating in many applications and for any level of accuracy needed. A Bottom-up approach. – Objects are divided into the major sub-systems: say, chassis, drive train, controls, and cutting/ collection system for a lawn mower. Each of these is further divided as appropriate, and unit material/ labor etc. costs are estimated at the lowest levels. Then overheads are apportioned to evaluate the potential costs of the product. Example-next slide. This is also referred to as the design to price approach  lawn mower cost estimates -Material costs Decompose the design specifications for the Lawn mower into its subcomponents, estimate the material costs for each of the subcomponents, and then sum these costs up to obtain their overall estimate. http://2.bp.blogspot.com/-QUmAwRYAlAw/UGH2qma5dBI/AAAAAAAAAG8/H2zn4XOfRXU/s1600/10.jpg Ans.-The total material cost estimate of $173.45 was calculated by summing up the estimates for each of the four major subsystem levels (chassis, drive train, controls, and cutting & collection system).  Material Selection - Problem Bottom up Approach:- After machining, the finished volume of a certain metal part is 0.17 cc. Fixed cost is apportioned @ 20% of the variable cost. Which raw material to choose? Brass Aluminum Machining time/piece (min) 0.64 0.42 Cost of material (Rs/Kg) 96 52 Scrap value (Rs/Kg) 24 none Cost of operator (Rs/hr) 120.00 120.00 Density of material (Kg/cc) 5.0 3.0 Volume of raw material (cc) 0.3 0.45 156 Labor and Material Costs- Calculation Labor cost per piece = (time per piece)(labor cost per time) – Brass: (0.64 min/piece)(Rs120/hr)(1hr/60 min) = Rs1.28/pc – Aluminum: (0.42 min/piece)(Rs120/hr)(1hr/60 min) = Rs0.84/pc Material cost per piece = (volume of raw)(Kg per volume)(cost per Kg) - (left over vol.