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

Sensitivity and Breakeven Analysis

Lecture No. 25Chapter 10Fundamentals of Engineering EconomicsCopyright © 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 10.2 - 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 + 31.20M

Gasoline: $800 + (31.9 + 7)M = $800 + 38.90M

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 + 31.20M Gasoline:

AEC(10%) = 4,697 + 38.90M Diesel fuel:

AEC(10%) = 6,403 + 28.95M

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:

Ok Cancel

? 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 AnalysisVariable

Considered

Worst-

Case

Scenario

Most-Likely-Case

Scenario

Best-Case

Scenario

Market size 1,000 1,500 2,000

Market growth rate 3% 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 $87,231

-24% 23% 67%