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A Project Is Not a Black Box
Principles of Corporate FinanceBrealey and Myers Sixth Edition
Slides by
Matthew Will Chapter 10
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 2
Topics Covered
Sensitivity Analysis Break Even Analysis Monte Carlo Simulation Decision Trees
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 3
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.
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 4
Sensitivity Analysis
Example
Given the expected cash flow forecasts for Otoban 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.
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 5
Sensitivity Analysis
315- FlowCashNet
3.0flow cash Operating
1.5after taxProfit
1.550% @ .Taxes
3profitPretax
1.5onDepreciati
3Costs Fixed
30Costs Variable
37.5Sales
15-Investment
10-1 Years0Year
Example - continued
NPV= 3.43 billion Yen
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 6
Sensitivity AnalysisExample - continued
Possible Outcomes
bil 2bil 3bil 4Cost Fixed
275,000300,000360,000CostVar Unit
380,000375,000350,000priceUnit
.16.1.04ShareMarket
mil 1.1mil 51mil .9SizeMarket
OptimisticExpectedcPessimistiVariable
Range
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 7
Sensitivity AnalysisExample - continuedNPV Calculations for Pessimistic Market Size Scenario
NPV= +5.7 bil yen3.3815- FlowCashNet
3.38flow cash Operating
1.88after taxProfit
1.8850% @ .Taxes
3.75profitPretax
1.5onDepreciati
3Costs Fixed
33Costs Variable
41.25Sales
15-Investment
10-1 Years0Year
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 8
Sensitivity AnalysisExample - continued
NPV Possibilities (Billions Yen)
6.53.40.4Cost Fixed
11.13.415.0-CostVar Unit
5.03.44.2-priceUnit
17.33.410.4-ShareMarket
5.73.41.1SizeMarket
OptimisticExpectedcPessimistiVariable
Range
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 9
Break Even Analysis
Point at which the NPV=0 is the break even point. Otoban Motors has a breakeven point of 8,000 units
sold.
Sales, 000’s
PV (Yen)
Billions
400
200
19.6
85 200
Break even
NPV=9
PV Inflows
PV Outflows
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 10
Monte Carlo Simulation
Step 1: Modeling the Project Step 2: Specifying Probabilities Step 3: Simulate the Cash Flows
Modeling Process
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 11
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
+150(.6)
+30(.4)
+100(.6)
+50(.4)
-550
NPV= ?
-250
NPV= ?
-150
0
or
Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 12
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
+150(.6)
+30(.4)
+100(.6)
+50(.4)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148
Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 13
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
+150(.6)
+30(.4)
+100(.6)
+50(.4)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148 81220.22080.960
Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 14
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148
+150(.6)
+30(.4)
+100(.6)
+50(.4)
*450
331
45015010.1
660 450150
10.1
660Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 15
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148
+150(.6)
+30(.4)
+100(.6)
+50(.4)
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
*450
331
18.88815010.1
812 18.888150
10.1
812
Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 16
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
812
456
660
364
148
+150(.6)
710.73
+30(.4)
+100(.6)
403.82
+50(.4)
-150
0
*450
331
or
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
-550
NPV= ?
-250
NPV= ?
40.55.44460.18.888 40.55.44460.18.888
Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 17
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
812
456
660
364
148
+150(.6)
710.73
+30(.4)
+100(.6)
403.82
+50(.4)
-550
NPV=96.12
-250
NPV=117.00
-150
0
*450
331
or
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
12.9655010.1
73.710 12.96550
10.1
73.710
Turboprop
Piston
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
10- 18
Decision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
812
456
660
364
148
+150(.6)
710.73
+30(.4)
+100(.6)
403.82
+50(.4)
-550
NPV=96.12
-250
NPV=117.00
-150
0
*450
331
or
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
Turboprop
Piston