Contemporary Engineering Economics, 4 th edition, © 2007 Methods of Describing Project Risk Lecture No. 46 Chapter 12 Contemporary Engineering Economics Copyright © 2006

Contemporary Engineering Economics, 4 th edition, © 2007 Chapter Opening Story – Oil Forecasts Are a Roll of the Dice Suppose that your proposed project depends on the price of oil (common to airline industry, UPS, FedEx, and any petroleum- based manufacturing industry). How would you factor the fluctuation and uncertainty into the analysis?

Contemporary Engineering Economics, 4 th edition, © 2007 Origins of Project Risk Risk: the potential for loss Project Risk: variability in a project’s NPW Risk Analysis: The assignment of probabilities to the various outcomes of an investment project

Contemporary Engineering Economics, 4 th edition, © 2007 Methods of Describing Project Risk Sensitivity Analysis: a procedure of identifying the project variables which, when varied, have the greatest effect on project acceptability. Break-Even Analysis: a procedure of identifying the value of a particular project variable that causes the project to exactly break even. Scenario Analysis: a procedure of comparing a “base case” to one or more additional scenarios, such as best and worst cases, to identify the extreme and most likely project outcomes.

Contemporary Engineering Economics, 4 th edition, © 2007 Sensitivity Analysis – Example 12.1 Transmission- Housing Project by Boston Metal Company Financial Facts:  Known with Great Confidence Required investment = $125,000 Project Life = 5 years Income tax rate = 40% MARR = 15%  Unknown but Predictable (Most Likely Values) Unit variable cost = $15 per unit Number of units = 2,000 units Unit Price = $50 per unit Salvage value = $40,000 Fixed cost = $10,000/Yr Required: Determine the acceptability of the investment

Contemporary Engineering Economics, 4 th edition, © 2007 Develop a Project Cash Flow Statement Using Most- Likely Estimates – “Base Case” Revenues: Unit Price50 Demand (units)2,000 Sales revenue$100,000 Expenses: Unit variable cost$15 Variable cost30,000 Fixed cost10,000 Depreciation17,86330,61321,86315,6135,575 Taxable Income$42,137$29,387$38,137$44,387$54,425 Income taxes (40%)16,85511,75515,25517,75521,770 Net Income$25,282$17,632$22,882$26,632$32,655

Contemporary Engineering Economics, 4 th edition, © 2007 Cash Flow Statement Operating activities Net income 25,28217,63222,88226,63232,655 Depreciation 17,86330,61321,86315,6135,575 Investment activities Investment (125,000) Salvage 40,000 Gains tax (2,611) Net cash flow ($125,500)$43,145$48,245$44,745$42,245$75,619

Contemporary Engineering Economics, 4 th edition, © 2007 Developing an Excel Worksheet to Conduct Sensitivity Analysis % deviation from the base

Contemporary Engineering Economics, 4 th edition, © 2007 Sensitivity Analysis for Five Key Input Variables Deviation-20%-15%-10%-5%0%5%10%15%20% Unit price$57$9,999$20,055$30,111$40,169$50,225$60,281$70,337$80,393 Demand12,01019,04926,08833,13040,16947,20854,24761,28668,325 Variable cost52,23649,21946,20243,18640,16937,15234,13531,11828,101 Fixed cost44,19143,18542,17941,17540,16939,16338,15737,15136,145 Salvage value37,78238,37838,97439,57340,16940,76541,36141,95742,553 Base

Contemporary Engineering Economics, 4 th edition, © % -15%-10%-5% 0%5%10%15%20% $100,000 90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10, ,000 Base Unit Price Demand Salvage value Fixed cost Variable cost Sensitivity Graph (Spider Graph)

Contemporary Engineering Economics, 4 th edition, © 2007 Break-Even Analysis Breakeven analysis is a tool used to determine when a business will be able to cover all its expenses and begin to make a profit from a project.  Excel using a Goal Seek function  Analytical Approach

Contemporary Engineering Economics, 4 th edition, © 2007 Using a Goal Seek Function in Excel NPW Breakeven Value Demand

Contemporary Engineering Economics, 4 th edition, © 2007 Break-Even Analysis (Example 12.2) Goal Seek Function Parameters 12.2

Contemporary Engineering Economics, 4 th edition, © 2007 Analytical Approach Unknown Sales Units (X) Cash Inflows: Net salvage37,389 X(1-0.4)($50)30X 0.4 (dep)7,14512,2458,7456,2452,230 Cash outflows: Investment-125,000 -X(1-0.4)($15)-9X -(0.6)($10,000)-6,000 Net Cash Flow-125,00021X + 1,145 21X + 6,245 21X + 2,745 21X X + 33,617

Contemporary Engineering Economics, 4 th edition, © 2007 PW of cash inflows PW(15%) Inflow = (PW of after-tax net revenue) + (PW of net salvage value) + (PW of tax savings from depreciation = 30X(P/A, 15%, 5) + $37,389(P/F, 15%, 5) + $7,145(P/F, 15%,1) + $12,245(P/F, 15%, 2) + $8,745(P/F, 15%, 3) + $6,245(P/F, 15%, 4) + $2,230(P/F, 15%,5) = 30X(P/A, 15%, 5) + $44,490 = X + $44,490 o PW of cash outflows: PW(15%) Outflow = (PW of capital expenditure_ + (PW) of after-tax expenses = $125,000 + (9X+$6,000)(P/A, 15%, 5) = X + $145,113 PW of Cash Flows

Contemporary Engineering Economics, 4 th edition, © 2007 The NPW: PW (15%) = X + $44,490 - ( X + $145,113) = X - $100,623. Breakeven volume: PW (15%)= X - $100,623 = 0 X b =1,430 units. NPW and Breakeven Volume

Contemporary Engineering Economics, 4 th edition, © 2007 NPW as a Function of Demand (X) Demand PW of inflow PW of OutflowNPW X X - $44, X + $145, X -$100,623 0$44,490$145, , ,773160,198-65, ,055175,282-30, ,197188, ,298188, ,338190,3674, ,620205,45240, ,903220,53775,366

Contemporary Engineering Economics, 4 th edition, © 2007 Outflow $350, , , , , ,000 50, , ,000 Profit Loss Break-even Volume X b = 1430 Annual Sales Units (X) PW (15%) Inflow Break-Even Chart – Break-Even Sales Volume at 1,430 Units

Contemporary Engineering Economics, 4 th edition, © 2007 Scenario Analysis Scenario analysis is a process of analyzing possible future events by considering alternative possible outcomes (scenarios). The analysis is designed to allow improved decision-making by allowing more complete consideration of outcomes and their implications. Source: Wikipedia

Contemporary Engineering Economics, 4 th edition, © 2007 Example 12.3 Scenario Analysis Variable Considered Worst- Case Scenario Most-Likely- Case Scenario Best-Case Scenario Unit demand1,6002,0002,400 Unit price ($) Variable cost ($) Fixed Cost ($)11,00010,0008,000 Salvage value ($)30,00040,00050,000 PW (15%)-$5,856$40,169$104,295