Analysis of Risk and Uncertainity

Chap-12

• Description ,measurement and types of risk• Methods for Incorporating risk factor in the

analysis of capital budgeting

Sources of Risk

• Project Specific Risk• Competitive Risk• Industry Specific Risk• Market Risk• International Risk

Different Perspectives of Risk

• Stand-alone Risk: The risk of a firm in investing in one and only one project.

• Firm Risk : Project’s risk to the company.• Market Risk: Systematic Risk

Measures of Risk

• Standard Deviation• Coefficient of Variation

Measures to quantify Risk

• Sensitivity Analysis• Scenario Analysis• Simulation• Decision-tree Approach

Incorporation of Risk into Capital Budgeting

• RADR(Risk-adjusted Discount Rate Approach)• Certainty-Equivalent Approach• Probability Distribution Approach

DECISION TREE ANALYSIS

STEPS• DELINEATE THE DECISION TREE

• EVALUATE THE ALTERNATIVESC21 : 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

Techniques to handle risk in Capital Budgeting

Sensitivity Analysis : One variable is changed at a time.(“What if “ analysis)

Scenario Analysis: Several variables are changed at a time.(“What if “ analysis)

Simulation analysis : For developing the probability profile of a criterion of merit by randomly combining values of variables that bear on the chosen criterion.

Sensitivity Analysis

Evaluation:• Shows how vulnerable a project is to changes

in values of the underlying variables.• Indicates where further work to be done.Limitations:• Only one variable is changed at a time.• Subjective Analysis

Sensitivity Analysis

Assume that you are the financial manager of Gopal Flour Mills. Gopal is considering setting up a new flour mill near Bangalore. Based on Gopal’s previous experience, the project staff of Gopal has developed the figures

Note : Salvage value has been assumed to be nil and the straight line method of depreciation is used .

Cash Flow forecast for Gopal’s Flour Mill ProjectYear 0 Year 1-10

INVESTMENT (20,000)

• SALES 18,000

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

• FIXED COSTS 1,000

DEPRECIATION 2,000

• PBT(PRE-TAX PROFIT) 3,000

• TAXES 1,000

• PROFIT AFTER TAXES 2,000

• CASH FLOW FROM OPERATION 4,000

• NET CASH FLOW 4,000

NPV = -20,000,000 + 4,000,000 (5.650) = 2,600,000

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 4,000NPV = -20,000,000 + 4,000,000 (5.650) = 2,600,000

RS. IN MILLION

RANGE NPV 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

Scenario Analysis

Three Scenarios are considered.• Expected(normal)Scenario• Pessimistic Scenario• Optimistic Scenario

The NPV of the Project of Gopal Flour Mills will be calculated in the three scenarios.

SCENARIO ANALYSISPROCEDURE1. SELECT THE FACTOR AROUND WHICH SCENARIOS WILL BE BUILT2. ESTIMATE VALUES OF EACH OF THE VARIABLES FOR EACH SCENARIO3. CALCULATE NPV / IRR UNDER EACH SCENARIO

NET PRESENT VALUE FOR THREE SCENARIOS(RS. IN MILLION)

SCENARIO 1 SCENARIO 2 SCENARIO 3INITIAL INVESTMENT 200 200 200UNIT SELLING PRICE (IN RUPEES) 25 15 40DEMAND (IN UNITS) 20 40 10 REVENUES 500 600 400VARIABLE COSTS 240 480 120FIXED COSTS 50 50 50DEPRECIATION 20 20 20PRE-TAX PROFIT 190 50 210TAX @ 50% 95 25 105PROFIT AFTER TAX 95 25 105ANNUAL CASH FLOW 115 45 125PROJECT LIFE 10 YEARS 10 YEARS 10 YEARSSALVAGE VALUE 0 0 0NET PRESENT VALUE (AT A DISCOUNT 377.2 25.9 427.4RATE OF 15 PERCENT)

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

PROJECT SELECTION UNDER RISK

• Judgmental Evaluation

• Payback Period Requirement

• Risk Adjusted Discount Rate

• Certainty Equivalent Method

Relative Importance of Various Methods of Assessing Project Risk

Technique % of companies rating it as very important or important

Sensitivity Analysis 90.10

Scenario Analysis 61.60

RADR 31.70

Decision tree Analysis 12.20

Monte Carlo Simulation 8.20

Break-Even Analysis

Accounting BEP:Fixed costs +DepreciationContribution margin ratioFinancial BEPNPV=0i.e. PV of Cash inflows=PV of cash outflows

Real Options

• Real Options: Opportunities to respond to changing market

conditions and influence the outcomes of a project.

Types of Options:• Growth Option• Abandonment Option• Timing Option

Value

• Project worth = NPV(traditional) + Option valueOr

• Value of the option=NPV(traditional)-NPV of the Option

• The option value will depend on the number of options available, the greater the number of options the greater is the option value and the greater is the project’s worth.

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

Mini Case

• Airways ltd Case -to be discussed in class( Financial Management(Prasanna Chandra)

• (Page no.342)• Southern Air ways Case-Assignment(Page No.359)