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Chapter 10
A Project Is Not a Black Box
Topics Covered
 Sensitivity Analysis
 Break Even Analysis
 Monte Carlo Simulation
 Decision Trees
How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects of
changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a
particular combination of assumptions.
Simulation Analysis - Estimation of the
probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of
sales (or other variable) at which the company
breaks even.
Sensitivity Analysis
Example
Given the expected cash flow
forecasts for Otobai Company’s
Motor Scooter project, listed on
the next slide, determine the
NPV of the project given
changes in the cash flow
components using a 10% cost of
capital. Assume that all
variables remain constant, except
the one you are changing.
Sensitivity Analysis
Example - continued
Investment
Sales
Variable Costs
Fixed Costs
Depreciation
P retaxprofit
.T [email protected] 50%
P rofitafter tax
Operatingcash flow
Net Cash Flow
Year 0
- 15
Years1 - 10
37.5
30
3
1.5
3
1.5
1.5
- 15
3.0
3
NPV= 3.43 billion Yen
Sensitivity Analysis
Example - continued
Possible Outcomes
Range
Variable Pessim istic Expected Optim istic
MarketSize
.9 mil
51 mil
1.1mil
MarketShare
.04
.1
.16
Unit price
350,000 375,000 380,000
Unit Var Cost
360,000 300,000 275,000
Fixed Cost
4 bil
3 bil
2 bil
Sensitivity Analysis
Example - continued
NPV Calculations for Optimistic Market Size Scenario
Year 0
Years1 - 10
Investment
Sales
Variable Costs
Fixed Costs
Depreciation
P retaxprofit
.T [email protected] 50%
P rofitafter tax
Operatingcash flow
Net Cash Flow
- 15
41.25
33
3
1.5
3.75
1.88
1.88
- 15
3.38
 3.38
NPV= +5.7 bil yen
Sensitivity Analysis
Example - continued
NPV Possibilities (Billions Yen)
Range
Variable Pessim istic Expected Optim istic
MarketSize
1.1
3.4
5.7
MarketShare
- 10.4
3.4
17.3
Unit price
- 4.2
3.4
5.0
Unit Var Cost
- 15.0
3.4
11.1
Fixed Cost
0.4
3.4
6.5
Break Even Analysis
 Point at which the NPV=0 is the break even point
 Otobai Motors has a breakeven point of 85,000 units
sold.
PV Inflows
Break even
400
NPV=0
PV (Yen)
Billions
PV Outflows
200
19.6
Sales, 000’s
85
200
Monte Carlo Simulation
Modeling Process
 Step 1: Modeling the Project
 Step 2: Specifying Probabilities
 Step 3: Simulate the Cash Flows
Decision Trees
960 (.8)
+150(.6)
220(.2)
-550
NPV= ?
Turboprop
930(.4)
+30(.4)
140(.6)
800(.8)
-150
+100(.6) or
410(.8)
0
-250
NPV= ?
Piston
100(.2)
180(.2)
220(.4)
+50(.4)
100(.6)
Decision Trees
960 (.8)
+150(.6)
220(.2)
-550
NPV= ?
Turboprop
930(.4)
+30(.4)
-150
+100(.6) or
100(.2)
410(.8)
0
NPV= ?
Piston
456
140(.6)
800(.8)
-250
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
Decision Trees
960 (.8)
+150(.6)
220(.2)
-550
930(.4)
NPV= ?
Turboprop
+30(.4)
800(.8)
+100(.6) or
100(.2)
410(.8)
0
NPV= ?
Piston
456
140(.6)
-150
-250
812
180(.2)
660
364
220(.4)
960 .80+50(.4)
 220 .20  812
100(.6)
148
Decision Trees
-550
NPV= ?
Turboprop
960 (.8)
660 +150(.6)
 150  450
1.10
220(.2)
930(.4)
+30(.4)
800(.8)
-150
+100(.6) or
331
100(.2)
410(.8)
0
NPV= ?
Piston
456
140(.6)
*450
-250
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
220(.2)
-550
NPV= ?
Turboprop
930(.4)
+30(.4)
NPV= ?
Piston
*450
800(.8)
-150
or
100(.2)
410(.8)
0
331
-250
456
140(.6)
NPV=444.55
812
NPV=550.00
 150
 888+100(.6)
.18
1.10
812
180(.2)
660
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
NPV= ?
Turboprop
220(.2)
710.73
-550
930(.4)
+30(.4)
NPV=550.00
800(.8)
-150
+100(.6) or
100(.2)
410(.8)
660
180(.2)
 888403.82
.18  .60
331  444.55  .40
0
NPV= ?
Piston
456
140(.6)
NPV=444.55
*450
-250
812
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
Turboprop
-550
NPV=96.12
220(.2)
710.73
930(.4)
+30(.4)
NPV=550.00
+100(.6) or
-250
NPV=117.00
800(.8)
-150
100(.2)
410(.8)
0
710 .73
180(.2)
331
 550  96.12
403.82
220(.4)
1.10
+50(.4)
NPV=184.55
456
140(.6)
NPV=444.55
*450
Piston
812
100(.6)
660
364
148
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
Turboprop
-550
NPV=96.12
220(.2)
710.73
930(.4)
+30(.4)
*450
NPV=550.00
800(.8)
-150
+100(.6) or
NPV=117.00
+50(.4)
NPV=184.55
331
100(.2)
410(.8)
0
Piston
403.82
456
140(.6)
NPV=444.55
-250
812
180(.2)
660
364
220(.4)
100(.6)
148

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