11. risk analysis and optimal capital expenditure decision

Financial Management I

11. Risk Analysis and Optimal Capital Expenditure Decision

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Course Content - Syllabus

*Book preference

Sr Title ICMR Ch. PC Ch. IMP Ch.

1 Introduction to Financial Management 1* 1 1

2 Overview of Financial Markets 2* 2 -

3 Sources of Long-Term Finance 10* 17 20, 21

4 Raising Long-term Finance - 18* 20, 21, 23

5 Introduction to Risk and Return 4* 8, 9 4, 5

6 Time Value of Money 3* 6 2

7 Valuation of Securities 5* 7 3

8 Cost of Capital 11* 14 9

9 Basics of Capital Expenditure Decisions 18* 11 8

10 Analysis of Project Cash Flows - 12* 10, 11

11 Risk Analysis and Optimal Capital Expenditure Decision - 13* 11, 12

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Books

1. Financial Management, Prasanna Chandra, 7th Edition,

Chapter 13

2. Financial Management, I. M. Pandey, 9th Edition, Chapter

12

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Syllabus – Risk Analysis and Optimal Capital Expenditure Decision

1. Introduction to Project Risk2. Stand-Alone Risk3. Sensitivity4. Scenario and Decision Tree Approach5. The Impact of Abandonment on NPV and Stand-Alone

Risk6. Risk Adjusted Discount Rate versus Certainty

Equivalents7. Incorporating Risk and Capital Structure into Capital

Expenditure Decisions8. Optimal Capital Expenditure9. Capital Rationing

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1. Introduction to Project Risk

• Risk is inherent in almost every business decision. In

capital budgeting decisions (capital expenditure decisions)

as they involve costs and benefits extending over a long

period of time during which many things can change.

Every investment proposal might have different risks

involved. R&D project might be more risky than an

expansion project. In view of such differences, variations

in risk need to be considered in capital investment

appraisal.• Risk analysis is most complex and slippery aspect of

capital budgeting. Many techniques have been suggested

for risk analysis. They fall into two broad categories.

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(i) Approaches that consider the stand-alone risk of a project(ii) Approaches that consider the risk of a project in the

context of the firm or in the context of the market.A figure classifies various techniques as below.

Techniques of Risk Analysis

Analysis of Stand-alone Risk

SensitivityAnalysis

Analysis of Contextual Risk

Break-evenAnalysis

SimulationAnalysis

ScenarioAnalysis

HillierModel

Decision Tree Analysis

Corporate RiskAnalysis

Market RiskAnalysis

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There are several sources of risk in a project. Main risks are

as follows, which affect the earnings and cash flow of the

project.

1. Project-specific risk: Estimation error or some factors

specific to the project like quality of management.

2. Competitive risk: Unanticipated actions of competitors.

3. Industry-specific risk: Unexpected technological

developments, regulatory changes specific to the industry

4. Market risk: Macroeconomic factors like GDP growth

rate, interest rate and inflation rate risk etc.

5. International risk: Exchange rate risk, political risk etc

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2. Stand-Alone Risk

• Stand-alone risk: This represents the risk of a project

when it is viewed in isolation.• It is the risk an asset would have if it were a firm’s only

risk.• It is measured by the variability of the asset’s expected

returns.

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3. Sensitivity Analysis

• Since the future is uncertain, you may like to know, what

will happen to the viability of the project when some

variables like sales or investment deviates from its

expected value. In other words, you may want to do ‘what

if’ analysis, also called the sensitivity analysis.• In sensitivity analysis, key variables are changed and the

resulting changes in the NPV and IRR are observed. • Consider an example as below. Suppose you are a financial

manager of Naveen Flour Mills. Naveen is considering

setting up a new floor mill. The project staff has developed

the data as beow. Assumed cost of capital as 12%.

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Cash Flow Forecast for Naveen’s Flour Mill Project

Rs. in

thousands Year 0 Year 1 - 10

1. Investment (20,000)

2. Sales 18,000

3. Variable costs (66⅔% 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

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Since the cash flow from operations is an annuity, the NPV of

this project is

-20,000,000 + 4,000,000 x PVIFA(12%, 10 years)

= -20,000,000 + 4,000,000 x 5.65 = 2,600,000

The NPV based on the expected values looks positive. The

underlying variables can vary widely and we would like to

see the effect of such variations on the NPV. So we define

the optimistic and pessimistic estimates of the underlying

variables. These are shown in LHS column of the table

below. The NPV is calculated for the optimistic and

pessimistic values of the underlying variables. To do this,

vary one variable at a time.

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Sensitivity of NPV to Variations in the Value of Key Variables

Rs. in

millionRange NPV

Key Variable Pessimistic Expected Optimistic Pessimistic Expected Optimistic

Investment 24 20 18 -0.65 2.6 4.22

Sales 15 18 21 -1.17 2.6 6.4

Variable cost

as a % of sales

70 66.67 65 0.34 2.6 3.73

Fixed costs 1.3 1 0.8 1.47 2.6 3.33

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-2

-1

0

1

2

3

4

5

6

7

NP

V in

Rs.

mil

lion

s

0Base

Change from Base

Sales

InvestmentVariable costsFixed costs

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Sensitivity analysis is a very popular method for assessing

risk. It has certain merits.• It shows how robust or vulnerable a project is to the

changes in values of the underlying variables.• It indicates where further work may be done. If the NPV is

highly sensitive to changes in some factor, it may be

worthwhile to explore how the variability of that critical

factor may be contained.• It is intuitively very appealing as it articulates the

concerns that project evaluators normally have.

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Sensitivity analysis also have some shortcomings.• It merely shows what happens to NPV when there is a

change in some variable, without providing any idea of

how likely that change will be.• Typically, in sensitivity analysis, only one variable is

changed at a time. In the real world, however, variables

tend to move together.• It is inherently a very subjective analysis. The same

sensitivity analysis may lead one decision maker to accept

the project while another may reject it.

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4. Scenario Analysis

• In Scenario Analysis, several variables are varied

simultaneously (whereas in sensitivity analysis, one

variable is varied at a time). Most commonly, three

scenarios are considered: expected (or normal) scenario,

pessimistic scenario and optimistic scenario.• In normal scenario, all variables assume their expected (or

normal values). In the pessimistic scenario, all variables

assume their pessimistic values and in the optimistic

scenario, all variables assume their optimistic values.

The NPVs of the project of Naveen Flour Mills under three

scenarios are calculated as below.

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Pessimistic, Normal and Optimistic Scenario Rs. in

millionPessimistic Scenario

Expected Scenario

Optimistic Scenario

1. Investment 24 20 182. Sales 15 18 213. Variable costs 105 (70%) 12 (66⅔%) 13.65 (65%)4. Fixed costs 1.3 1 0.85. Depreciation 2.4 2 1.86. Pre-tax profit 0.8 3 4.757. Taxes 0.27 1 1.588. Profit after taxes 0.53 2 3.179. Annual cash flow from operation 2.93 4 4.9710. NPV = (9) x PVIFA(12%, 10yrs) - (1)

(7.45) 2.6 10.06

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Scenario Analysis may be regarded as an improvement over sensitivity analysis, however it has some limitations.

• It is based on the assumption that there are few well-delineated scenarios. This may not be true in many cases. For example, the economy does not necessarily lie in three discrete states, namely, recession, stability and boom. In fact, it can be anywhere on the continuum between the extremes. When a continuum is converted into three discrete states some information is lost.

• Scenario analysis expands the concept of estimating the expected values. Thus in a case where there are 10 inputs, the analyst has to estimate 30 expected values to do the scenario analysis.

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4. Decision Tree Approach

Decision tree approach is based on the concept of tree and branches and to take a better decision.

Steps in Decision Tree Analysis• Delineate (draw) the Decision Tree• Evaluate the alternativesDelineate the Decision Tree• Draw the decision points (typically represented by

squares), the alternative options available for experimentation and action at these points and the investment outlays associated with these options.

• Draw the chance points (typically represented by circles) where outcomes are dependent on the chance process, the likely outcomes at these points along with the probabilities and the monetary values associated with them.

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Evaluate the Alternatives• Start at the right hand end of the tree and calculate the

NPV at various chance points that come first as you

proceed leftward.• Given the NPVs of chance points in step above, evaluate

the alternatives at the final stage decision points in terms

of their NPVs.• At each final stage decision point, select the alternative

which has the highest NPV and truncate the other

alternatives. Each decision point is assigned a value equal

to the NPV of the alternative selected at that decision

point.

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• Proceed backward (leftward) in the same manner,

calculating the NPV at chance points, selecting the

decision alternative which has the highest NPV at various

decision points, truncating inferior decision alternatives

and assigning NPVs to decision points, till the first

decision point is reached.

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Decision Tree

D1

C1

-Rs. 20 million

D2

C1

P=0.6

P=0.4

30 million

40 million

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6. Risk Adjusted Discount Rate versus Certainty Equivalents

• Most firms use Risk-Adjusted Discount Rate. • It is a discount rate that applies to particularly risky

stream of income.• It is equal to the risk-free rate of interest plus a risk

premium.

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9. Capital Rationing

• A situation in which a constraint is placed on the total size

of the firm’s capital investment.

11. risk analysis and optimal capital expenditure decision

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