Монте карло_Break even

1.

Principles of
Corporate
Finance
Chapter 10
A Project Is Not a Black Box
Seventh Edition
Richard A. Brealey
Stewart C. Myers
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

2. Topics Covered

10- 2
Topics Covered
Sensitivity Analysis
Break Even Analysis
Monte Carlo Simulation
Decision Trees
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

3. How To Handle Uncertainty

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.
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

4. Sensitivity Analysis

10- 4
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.
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

5. Sensitivity Analysis

10- 5
Sensitivity Analysis
Example - continued
Investment
Sales
Variable Costs
Fixed Costs
Depreciati on
Pretax profit
.Taxes @ 50%
Profit after tax
Operating cash flow
Net Cash Flow
Year 0
- 15
- 15
Years 1 - 10
37.5
30
3
1.5
3
1.5
1.5
3.0
3
NPV= 3.43 billion Yen
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

6. Sensitivity Analysis

10- 6
Sensitivity Analysis
Example - continued
Possible Outcomes
Range
Variable
Pessimistic Expected Optimistic
Market Size
Market Share
.9 mil
.04
51 mil
.1
1.1 mil
.16
Unit price
350,000
375,000
380,000
Unit Var Cost
Fixed Cost
360,000
4 bil
300,000
3 bil
275,000
2 bil
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7. Sensitivity Analysis

10- 7
Sensitivity Analysis
Example - continued
NPV Calculations for Optimistic Market Size Scenario
Year 0
Years 1 - 10
Investment
Sales
Variable Costs
Fixed Costs
Depreciati on
Pretax profit
.Taxes @ 50%
Profit after tax
Operating cash flow
Net Cash Flow
McGraw Hill/Irwin
- 15
- 15
41.25
33
3
1.5
3.75
1.88
1.88
NPV= +5.7 bil yen
3.38
3.38
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

8. Sensitivity Analysis

10- 8
Sensitivity Analysis
Example - continued
NPV Possibilities (Billions Yen)
Range
Variable
Pessimistic Expected Optimistic
Market Size
Market Share
1.1
- 10.4
3.4
3.4
5.7
17.3
Unit price
- 4.2
3.4
5.0
Unit Var Cost
Fixed Cost
- 15.0
0.4
3.4
3.4
11.1
6.5
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

9. Break Even Analysis

10- 9
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
McGraw Hill/Irwin
200
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

10. Monte Carlo Simulation

10- 10
Monte Carlo Simulation
Modeling Process
Step 1: Modeling the Project
Step 2: Specifying Probabilities
Step 3: Simulate the Cash Flows
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

11. Decision Trees

10- 11
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
McGraw Hill/Irwin
100(.2)
180(.2)
220(.4)
+50(.4)
100(.6)
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

12. Decision Trees

10- 12
Decision Trees
960 (.8)
+150(.6)
220(.2)
-550
NPV= ?
Turboprop
930(.4)
+30(.4)
-150
+100(.6) or
McGraw Hill/Irwin
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
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

13. Decision Trees

10- 13
Decision Trees
960 (.8)
+150(.6)
220(.2)
-550
930(.4)
NPV= ?
Turboprop
+30(.4)
800(.8)
+100(.6) or
McGraw Hill/Irwin
100(.2)
410(.8)
0
NPV= ?
Piston
456
140(.6)
-150
-250
812
180(.2)
660
364
220(.4)
148
960 .80 +50(.4)
220 .20 812
100(.6)
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

14. Decision Trees

10- 14
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
McGraw Hill/Irwin
100(.2)
410(.8)
0
NPV= ?
Piston
456
140(.6)
*450
-250
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

15. Decision Trees

10- 15
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
220(.2)
-550
NPV= ?
Turboprop
930(.4)
+30(.4)
*450
812 NPV=550.00
150 888+100(.6)
.18 or
1.10
NPV= ?
Piston
McGraw Hill/Irwin
456
140(.6)
NPV=444.55
331
-250
812
800(.8)
-150
100(.2)
410(.8)
0
180(.2)
660
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

16. Decision Trees

10- 16
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)
McGraw Hill/Irwin
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
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

17. Decision Trees

10- 17
Decision Trees
960 (.8)
NPV=888.18
Turboprop
-550
+150(.6)
NPV=96.12
+30(.4)
220(.2)
710.73
930(.4)
NPV=550.00
+100(.6) or
NPV=117.00
McGraw Hill/Irwin
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
-250
812
100(.6)
660
364
148
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

18. Decision Trees

10- 18
Decision Trees
960 (.8)
NPV=888.18
Turboprop
-550
+150(.6)
NPV=96.12
+30(.4)
220(.2)
710.73
930(.4)
*450
NPV=550.00
800(.8)
-150
+100(.6) or
NPV=117.00
+50(.4)
McGraw Hill/Irwin
NPV=184.55
331
100(.2)
410(.8)
0
403.82
456
140(.6)
NPV=444.55
Piston
-250
812
180(.2)
660
364
220(.4)
100(.6)
148
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved