Chapter 13 Risk Analysis in Capital Budgeting

Chapter 13

RISK ANALYSIS IN CAPITAL BUDGETING

Centre for Financial Management , Bangalore

OUTLINE

• Sources and Perspectives of Risk

• Sensitivity Analysis

• Scenario Analysis

• Break-even Analysis

• Hillier Model

• Simulation Analysis

• Decision Tree Analysis

• Corporate Risk Analysis

• Managing Risk

• Project Selection under Risk

• Risk Analysis in Practice


TECHNIQUES FOR RISK ANALYSIS

Techniques of riskanalysis

Analysis of stand-alone risk

Analysis of contextual risk

Sensitivityanalysis

Break-evenanalysis

Simulationanalysis

Scenarioanalysis

Corporate risk analysis

Market riskanalysis

Hilliermodel

Decision treeanalysis


SOURCES AND PERSPECTIVE OF RISK

Sources of Risk

• Project-specific risk• Competitive risk• Industry-specific risk• Market risk• International risk

Perspectives on Risk

• Standalone risk• Firm risk• Market risk


SENSITIVITY ANALYSIS(‘000)

YEAR 0 YEAR 1 - 10

1. INVESTMENT (20,000)

2. SALES 18,000

3. VARIABLE COSTS (66 2/3 % OF SALES) 12,000

4. FIXED COSTS 1,000

5. DEPRECIATION 2,000

6. PRE-TAX PROFIT 3,000

7. TAXES 1,000

8. PROFIT AFTER TAXES 2,000

9. CASH FLOW FROM OPERATION 4,000

10. NET CASH FLOW 4,000

NPV = -20,000,000 + 4,000,000 (5.650) = 2,600,000 ( discount rate = 12 % )

RS. IN MILLION

RANGE NPV

KEY VARIABLE PESSIMISTIC EXPECTED OPTIMISTIC PESSIMISTIC EXPECTED OPTIMISTIC

INVESTMENT (RS. IN MILLION) 24 20 18 -0.65 2.60 4.22

SALES (RS. IN MILLION) 15 18 21 -1.17 2.60 6.40

VARIABLE COSTS AS A 70 66.66 65 0.34 2.60 3.73

PERCENT OF SALES

FIXED COSTS 1.3 1.0 0.8 1.47 2.60 3.33

PESSIMISTIC, NORMAL AND OPTIMISTIC

SCENARIO


Pessimistic Scenario

Expected Scenario

Optimistic Scenario

1. Investment 24 20 18

2. Sales 15 18 21

3. Variable costs 10.5 (70%) 12 (66.7%) 13.65 (65%)

4. Fixed costs 1.3 1.0 0.8

5. Depreciation 2.4 2.0 1.8

6. Pre-tax profit 0.8 3.0 4.75

7. Tax 0.27 1.0 1.58

8. Profit after tax 0.53 2.0 3.17

9. Annual cash flow from operations 2.93 4.0 4.97

10. Net present value (9) x PVIFA (12%, 10 yrs) – (1)

(7.45) 2.60 10.06

BREAK-EVEN ANALYSIS

• ACCOUNTING BREAK-EVEN ANALYSISFIXED COSTS + DEPRECIATION 1 + 2

= = RS. 9 MILLION

CONTRIBUTION MARGIN RATIO 0.333

CASH FLOW FORECAST FOR NAVEEN’S FLOUR MILL PROJECT

(‘000)

YEAR 0 YEAR 1 - 10

1. INVESTMENT (20,000)

2. SALES 18,000

3. VARIABLE COSTS (66 2/3% OF SALES) 12,000

4. FIXED COSTS 1,000

5. DEPRECIATION 2,000

6. PRE-TAX PROFIT 3,000

7. TAXES 1,000

8. PROFIT AFTER TAXES 2,000

9. CASH FLOW FROM OPERATION 4,000

10. NET CASH FLOW (20,000) 4,000

• CASH BREAK-EVEN ANALYSIS

HILLIER MODEL

Uncorrelated Cash Flows

n Ct

NPV = – I t = 1 (1 + i)t

n t2 ½

(NPV) = t = 1 (1 + i)2t

Perfectly Correlated Cash Flows

n Ct

NPV = – I t = 1 (1 + i) t

n t

(NPV) = t = 1 (1 + i)t


SIMULATION ANALYSIS

PROCEDURE

1. CHOOSE VARIABLES WHOSE EXPECTED VALUES

WILL BE REPLACED WITH DISTRIBUTIONS

2. SPECIFY THE PROBABILITY DISTRIBUTIONS OF

THESE VARIABLES

3. DRAW VALUES AT RANDOM AND CALCULATE NPV

4. REPEAT 3 MANY TIMES AND PLOT DISTRIBUTION

5. EVALUATE THE RESULTS


DECISION TREE ANALYSIS

STEPS

• DELINEATE THE DECISION TREE

• EVALUATE THE ALTERNATIVES

C21 : HD ANNUAL CASH FLOW

0.6 30 MILLION

D21 : INV

C2 EMV (C2) = RS.194.2 m

150 m

C11 : S

D2 EMV (D2) = RS.44. 2 m C22 : LD ANNUAL CASH FLOW

p : 0.7 0.4 20 MILLION

D11 : PILOT PROD

C1 EMV (C1) = RS.30. 9 m D22 : STOP

& TEST MKTG

- RS.20 m C12 : F

D1 EMV (D1) = RS.10. 9 m D3 D31 : STOP

p : 0.3

D12 : DO NOTHING


LIMITATIONS

SENSITIVITY ANALYSIS • NO IDEA OF LIKELIHOOD

• ONE FACTOR IS VARIED AT A TIME

SCENARIO ANALYSIS • SCENARIOS MAY NOT BE CLEARLY DELINEATED

SIMULATION ANALYSIS • DEFINING THE DISTRIBUTIONS IS DIFFICULT

• TRADITIONAL SIMULATION ANALYSIS DOESN’T PERMIT

INTERACTIONS AMONG VARIABLE

• BUSINESS AS USUAL ASSUMPTIONS

DECISION TREE ANALYSIS • STAGES MAY NOT BE CLEARLY DEFINED

• OUTCOMES MAY NOT BE CLASSIFIED INTO BROAD CLASSES

• PROBABILITIES & CASH FLOWS ARE DIFFICULT TO DEFINE


CORPORATE RISK ANALYSIS

• A project’s corporate risk is its contribution to the

overall risk of the firm

• On a stand-alone basis a project may be very risky but

if its returns are not highly correlated – or, even better,

negatively correlated — with the returns on the other

projects of the firm, its corporate risk tends to be low


MANAGING RISK

• FIXED AND VARIABLE COST

• PRICING STRATEGY

• SEQUENTIAL INVESTMENT

• FINANCIAL LEVERAGE

• INSURANCE

• LONG-TERM ARRANGEMENTS

• STRATEGIC ALLIANCE

• DERIVATIVES


PROJECT SELECTION UNDER RISK

• Judgmental Evaluation

• Payback Period Requirement

• Risk Adjusted Discount Rate

• Certainty Equivalent Method


RISK ANALYSIS IN PRACTICE

• Conservative Estimation of Revenues

• Safety Margin in Cost Figures

• Flexible Investment Yardsticks

• Acceptable Overall Certainty Index

• Judgment on Three Point Estimates


SUMMING UP A variety of techniques have been developed to handle risk in capital budgeting.

Sensitivity analysis or “what if” analysis answers questions like “what happens to NPV if sales decline by 5 percent?”

Scenario analysis is an extension of sensitivity analysis

Break-even analysis establishes the minimum quantity at which loss is avoided. The break-even point may be defined in accounting terms or financial terms.

Simulation analysis is a technique for developing the profitability profile of a criterion of merit by combining values of variables that have a bearing on the chosen criterion.

Decision tree analysis is a useful tool for analysing sequential decisions in the face of risk.

A project’s corporate risk is its contribution to the overall risk of the firm.

There are several ways of incorporating risk in the decision process : judgmental evaluation, payback period requirement, risk-adjusted discount rate method, and certainty equivalent method


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Chapter 13 Risk Analysis in Capital Budgeting

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