Sensitivity and Breakeven Analysis Lecture No. 25 Chapter 10 Fundamentals of Engineering Economics Copyright © 2008

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

Methods of Describing Project Risk  Sensitivity (what-if) Analysis: a means of identifying the project variables which, when varied, have the greatest effect on project acceptability.  Break-Even Analysis: a means of identifying the value of a particular project variable that causes the project to exactly break even.  Scenario Analysis: a means of comparing a “base case” to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes.

Example 10.1 Sensitivity Analysis – Know which Variable is Most Critical to Your Bottom Line Project Nature: Capstone Turbine Corporation’s MicroCHP generator

Cash Flow Statement for Capstone’s MicroCHP Project – Most-Likely Estimates

Sensitivity Analysis for Five Key Input Variables Base

Sensitivity Graph for Capstone’s MicroCHP Project

Example Sensitivity Analysis for Mutually Exclusive Alternatives

Capital (Ownership) Cost  Electrical power: CR(10%) = ($30,000 - $3,000)(A/P, 10%, 7) + (0.10)$3,000 = $5,845  LPG: CR(10%) = ($21,000- $2,000)(A/P, 10%, 7) + (0.10)$2,000 = $4,103  Gasoline: CR(10%) = ($20,000-$2,000)(A/P, 10%, 7) + (0.10) $2,000 = $3,897  Diesel fuel: CR(10%) = ($25,000 -$2,200)(A/P, 10%, 7) +(0.10) $2,200 = $4,903

Annual O&M Cost  Electrical power: $500 + (3.84 + 5)M = $500 + 8.84M  LPG: $1,000 + (25.2 + 6)M = $1,000  M  Gasoline: $800 + (31.9 + 7)M = $800  M  Diesel fuel: $1,500 + (19.95 + 9)M = $1,500 + 28.95M

Annual Equivalent Cost (AEC)  Electrical power: AEC(10%) = 6,345 + 8.84M  LPG: AEC(10%) = 5,103  M  Gasoline: AEC(10%) = 4,697  M  Diesel fuel: AEC(10%) = 6,403  M

Sensitivity Analyses for Mutually Exclusive Alternatives LPG

Break-Even Analysis Using a Goal Seek Function in Excel Breakeven Value Demand Goal Seek Set cell: To value: By changing cell: OkCancel ?X $F$7 0 $B$6 NPW Issue: How much sales can decrease below forecasts before the project begins to lose money?

Example 10.3 Break-Even Analysis with Excel

Example 10.4 Scenario Analysis Variable Considered Worst- Case Scenario Most-Likely- Case Scenario Best-Case Scenario Market size1,0001,5002,000 Market growth rate3%5%8% Unit price$72,000$80,000$86,000 Unit variable cost$65,000$60,000$56,000 Fixed cost$9,000,000$8,000,000$6,500,000 Salvage value$4,000,000$7,000,000$8,000,000

Worst-Case Scenario

Best-Case Scenario

NPW and IRR under Each Scenario Worst-Case Scenario Most-Likely Scenario Best-Case Scenario ($42,755)$11,107$87, %23%67%