Upon completion of this chapter you should understand: Approach to solving time value of money applications; uncertainty, risk and decision trees; determining operating costs; calculating annual costs. Inviting you refer.
Chapter 6 – Unit 1 Time Value of Money Application IET 350 Engineering Economics Learning Objectives – Chapter 6 Upon completion of this chapter you should understand: Approach to solving time value of money applications Uncertainty, risk and decision trees Determining operating costs Calculating annual costs Learning Objectives – Unit 1 Upon completion of this unit you should understand: Approach to solving time value of money applications Uncertainty, risk and decision trees Determining operating costs Calculating annual costs Applications Annual cost calculation is a frequent application for time value of money techniques Annual cost determination includes: Product unit costs Product unit costs Purchase versus lease comparison Equipment economic justification Loan calculations Additionally, annual cost calculations are used for a wide variety of investment decision analysis Solving TVM Relationships Steps for solving time value of money applications: Describe situation using cash flow diagram Summarize known and unknown factors using the diagram Determine the unknown factors using equivalence and time g q value of money calculations Consider the affect of uncertainty and risk using decision trees, what‐if analysis and sensitivity analysis Review how the problem will impact other projects and sources of funds Consider noneconomic effects on the solution Combine economic and noneconomic factors to make a recommendation or decision Solving TVM Relationships Problem solving forms part of thinking. Considered the most complex of all intellectual functions, problem solving has been defined as higher‐order cognitive process that requires the modulation and control of more routine or fundamental skills (Goldstein & Levin 1987) It occurs if an organism or an artificial (Goldstein & Levin, 1987). It occurs if an organism or an artificial intelligence system does not know how to proceed from a given state to a desired goal state. It is part of the larger problem process that includes problem finding and problem shaping. http://en.wikipedia.org/wiki/Problem_solving The first step to solving a problem is defining it Selecting ROI Value Determination of the ROI value (interest rate) to be used in time value of money calculations is critical since it directly affects the analysis ROI determination uses one of the following methods: g Management sets a target or minimum ROI ROI is set equal to alternative investments such as Treasury bills, mutual funds or other investments ROI is set equal to the interest rate for corporate loans Minimum or target ROI set based on recent projects ROI Combination of above methods Selecting ROI Value Minimum or target ROI values change over time due to factors such as: Economic environment factors such as the inflation rate Investment opportunities in financial instruments at high Investment opportunities in financial instruments at high ROI rates Federal discount loan rate – prime interest rate Organization’s cash flow situation – high cash flow may result in lower ROI projects being funded. End Unit 1 Material Additional Reading Ö How to Think About Time Value of Money Problems: http://www.tvmcalcs.com/tvm/how_to_think_about_time_value_problems Go to Unit 2 Uncertainty and Risk Chapter 6 – Unit 2 Uncertainty and Risk IET 350 Engineering Economics Learning Objectives – Unit 2 Upon completion of this unit you should understand: Approach to solving time value of money applications Uncertainty, risk and decision trees Determining operating costs Calculating annual costs 11 Definitions Uncertainty is the state of having limited knowledge Uncertainty makes it impossible to exactly describe existing state or future outcome Uncertainty means there may be more than one possible y y p outcome Risk is the degree or state of uncertainty where some possible outcomes have an undesired effect. Probability is the likelihood or chance that some state or result will happen Probability of a future event occurring can be estimated 12 Uncertainty and Economics We have assumed certainty to this point regarding costs, returns, life, salvage value, ROI, etc Reality is that all factors associated with financial and y y economic analysis are variable and can only be estimated. This is especially true of future values and analysis over extended periods of time Since economic analysis and decision making necessitates determining future states, we need to consider the effects of uncertainty 13 Tools for Uncertainty Tools that can assist in estimating future values: Historical, theoretical and subjective probabilities Estimating expected values and variation Best case/worst case (scenario) estimating What‐if analysis Sensitivity analysis Decision trees 14 Probability Probability can be estimated using: Historical data – reviewing the actual (historical) results for similar factors such as machine life, ROI and annual costs Mathematical functions Mathematical functions – certain types of events have certain types of events have known probability distributions. Annual costs are often distributed normally. Lives of buildings and equipment tend to follow exponential and Poisson distributions Subjectivity – estimated based on knowledge, experience and all other factors Combination of the above 15 Expected Value and Variation Expected value is determined by the average of previous events. Examples for time value analysis: Expected life based on the average time to failure of several computer monitors Expected life based on the average miles of delivery trucks based on replacement Variation is typically determined by either the range or standard deviation of the historical data used to determine the expected value Little or no variation permits analysis without considering uncertainty 16 Optimistic/Pessimistic Estimates Simplified approach to uncertainty is to estimate the most likely occurrence and the extremes – best and worst case Worst case – assume everything that can go wrong, will Best case – assume everything meets ideal conditions y g The three scenarios are used to estimate the future results by providing three outcomes for what if analysis Also, a weighted average using probabilities can be found. Example, if the most likely is judged to have a 60% chance of occurring and the other two cases have a 20% change each: Texpected = 0.2TPessimistic + 0.6TMost Likely + 0.2TOptimistic 17 What‐If Calculations What‐if analysis allows a complete economic analysis incorporating uncertainty Future results are determined by analyzing all possible p outcomes of the factors in the decision process What‐if can incorporate optimistic/most likely/pessimistic estimates for each factor or other estimates and project a future result for all combinations Typically what‐if calculations are done using a spreadsheet to allow quick changes of each factor. 18 Sensitivity What‐if analysis considers how the result (output) changes with changes in the factors or variables (inputs) The degree of change is referred to as sensitivity: If the result changes slightly with changes to a variable, If the result changes slightly with changes to a variable the result has low sensitivity to that variable If the result changes significantly with changes to a variable, the result has high sensitivity to that variable Sensitivity can be measured by varying each variable a fixed amount (example 10%) and determining the percentage change in the result 19 Decision Trees Decision trees are an organized method of displaying and analyzing projects with complex uncertainties Decision trees can be combined with what‐if, sensitivity and p /p y y p y p optimistic/pessimistic analysis to clearly display the possible scenarios Decision trees incorporate: Branches for each possible state or outcome Probability of that state or outcome occurring Cost or benefit associated with each possible state or outcome 20 Decision Trees Variables with outcomes and probabilities (text pages 203‐204): Life: 8 yrs – 50% 10 yrs – y 50% Salvage: $5,000 – 50% $10,000 – 50% Annual Costs: $10,00/yr – 25% $15,00/yr – 50% $20,00/yr – 25% 21 Example Problem 6.1 Example Problem 6.1 Solution 22 End Unit 2 Material Additional Reading Ö Risk Analysis & Risk Management: http://www.mindtools.com/pages/article/newTMC_07.htm Go to Unit 3 Operating Costs 23 Chapter 6 – Unit 3 Operating Costs IET 350 Engineering Economics Learning Objectives – Unit 3 Upon completion of this unit you should understand: Approach to solving time value of money applications Uncertainty, risk and decision trees Determining operating costs Calculating annual costs 25 Operating Costs Operating costs are the annual costs related to the project or equipment. Notation → Aoperating or AO Operating costs are stated on an annual basis and do not y have time value of money associated with them Operating costs include: o o o o o Materials Labor Insurance Heat Utilities o o o o o Salaries o Marketing expenses Maintenance o Any other cost Repairs associated with Property taxes the investment Advertising 26 Salvage Value Salvage value is the revenue realized when a piece of equipment is sold at the end of its useful life Salvage value is adjusted by the cost of removing the q p equipment at the end of its life: If equipment has zero value and requires removal costs, the net salvage value may be negative Salvage value is included in the operating costs for a project or equipment purchase decisions 27 Salvage Value Salvage value and removal costs are estimated values since they occur in the future and are uncertain. Estimated salvage value and removal costs may be based on: Similar equipment previously salvaged Similar equipment previously salvaged Used equipment values on the open market Scrap value of the metal and component content Percentage of the first cost of the equipment Percentage derived from previous equipment sales Combination of above methods 28 Salvage Value Salvage value is annualized using the A/F time value of money factor Typically salvage value is included in the annual operating p j q p cost of the project or equipment: Positive salvage value is treated as a revenue Negative salvage value is treated as a cost However, if the annualized salvage value is small compared to other operating costs, it may be neglected without major impact on the decision‐making process 29 First Cost First cost is the negative cash flow associated with purchasing equipment or other types of assets and the associated installation costs First costs are included in the operating costs for a project or p g p j equipment purchase decisions. First cost and installation cost are annualized using the A/P time value of money factor Typically, first costs can be included in operating cost with certainty since the purchase price of the asset will be known. Some uncertainty may occur regarding the installation costs Depreciation costs are not included in operating costs since they are essentially the same cost as the annualized first cost.30 10 End Unit 3 Material Go to Unit 4 Annual Costs 31 Chapter 6 – Unit 4 Annual Costs IET 350 Engineering Economics Learning Objectives – Unit 4 Upon completion of this unit you should understand: Approach to solving time value of money applications Uncertainty, risk and decision trees Determining operating costs Calculating annual costs 33 11 Calculating Annual Costs Total annual costs (Atotal) for a project or equipment include three components: First cost → P which is annualized and becomes → AP Operating costs → p g AO Salvage cost → S which is annualized and becomes → AS Annualizing first cost and salvage cost results in the equation: A total = A P + A O − A S A total = P(A/P, n, i) + A O − S(A/F, n, i) Note: AS is a negative value since we are determining total cost and salvage is usually a revenue 34 Example Problem 6.2 Example Problem 6.2 Solution 35 Calculating Annual Costs Operating costs (AO) are not always constant over the life of equipment. Typically costs such as maintenance and repair increase yearly and can be estimated as gradient costs Adding a gradient maintenance cost (A g g ( M)) to the annual cost calculation results in the equation: A total = AP + A O + A M − A S A total = P(A/P, n, i) + A O + [A′ + G(A/G, n, i)] − S(A/F, n, i) Reminder: A′ = Initial annual cost ($) G = gradient amount ($) 36 12 Example Problem 6.3 Example Problem 6.3 Solution 37 Equipment Justification Equipment is not only an asset to an organization, equipment is also an investment. Like any investment, equipment must produce a return to the g organization. Therefore, time value of money is the appropriate method to calculate the annual cost or return related to equipment including: Comparisons between alternate equipment Make versus buy decisions (product) Lease versus purchase decisions (equipment) 38 Equipment Justification Equipment can be justified by determining: Whether the annual revenue generated by the equipment is positive – requires both operating cost and revenue estimates Comparing equipment ROI to the firm’s target ROI Total annual cost is less than existing equipment performing the same task Combination of above approaches Non‐economic factors are also considered such as the impact of training, required space, process changes and quality 39 13 Equipment Justification Second component to equipment justification is determining the source of funds necessary to acquire the equipment. Sources include: Purchase equipment with internal funds Lease equipment – lease cost and purchase cost must be compared at the same point in time Purchase using borrowed funds (loan) – cost of borrowing the funds would be included in the total annual cost Selling debt securities (bonds) to finance the purchase. Combination of above approaches 40 Equipment Justification Borrowed funds (loan) can be used when the firm does not have sufficient retained earnings to reinvest in equipment or when the firm wishes to retain is liquid assets (cash) for other purposes Various loan approaches are available: Traditional loan with repayment of interest and principle Interest‐only loans which requires payment of interest only with principle repaid within a specified time 41 Product Unit Cost Determination of unit product costs may include equipment costs along with the product costs of direct materials, direct labor and overhead Equipment and product costs are annualized then divide by q p p y annual volume to determine unit product cost A total = A M+L +O + A P + A O − A S A total = AM+L +O + P(A/P, n, i) + A O − S(A/F, n, i) A total Product CostUnit = units year 42 14 Example Problem 6.4 Example Problem 6.4 Solution 43 End Chapter 6 Material Student Study Guide Ö Chapter 6 Homework Assignment Ö Problem Set 6 44 15 ... 23 Chapter 6 – Unit 3 Operating Costs IET 350 Engineering Economics Learning Objectives – Unit 3 Upon completion of this unit you should understand: Approach to solving time value of money applications... 31 Chapter 6 – Unit 4 Annual Costs IET 350 Engineering Economics Learning Objectives – Unit 4 Upon completion of this unit you should understand: Approach to solving time value of money applications... Selecting ROI Value Determination of the ROI value (interest rate) to be used in time value of money calculations is critical since it directly affects the analysis ROI determination uses one of the following methods: