Capital Budgeting

Capital Budgeting 1

Capital Budgeting

Risk Analysis

02-Oct-09

Capital Budgeting 2

• Risk – The likelihood of occurrence of a known peril (Insurance)

• Risk in capital budgeting is the possibility of occurrence of a predicted variable when the certainty of occurrence of an event is not known.

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Risk & Uncertainty

Capital Budgeting 3

• Cash Flows subject to uncertainty & variations.• All projects are based on assumptions that have

certain associated risks.– Eg – Cash flow based on expected market price/volume.

What can happen if this changes?– What will happen if government legislation makes labor

cost more expensive in a labor intensive industry?– What will happen if raw material prices vary from

projected costs?

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Risks in Capital Budgeting

Capital Budgeting 4

• Specific Project Related or Stand Alone Risks– How does the variation in expected cash flow affect the

project?

• Corporate Risk– How does the variation in cash flows affect all projects?

• Market Risk– What happens to the return to stakeholders/investors?

• Not all investors are sufficiently diversified.• There are employees, suppliers, lenders who are not guided by the

portfolio theory.

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Type of Risks

Capital Budgeting 5

1. Sensitivity Analysis

2. Probability

3. Important Statistical Tools

4. Scenario Analysis

5. Simulation

6. Risk Adjusted Discount Rate

7. Certainty Equivalent approach

8. Probability Distribution Approach

9. Normal Probability Distribution

10. Decision Tree Approach02-Oct-09

Tools For Analysis

Capital Budgeting 6

• Most corporate firms use more than one tool.• Sensitivity Analysis is most popular method used by more

than 91%.• Scenario Analysis used by large corporate firms than

smaller ones.• Risk Adjusted Rate of Return (RAR) used by 33% of

corporate firms.• Simulation through Monte Carlo techniques and Decision

Tree methods – NOT USED by most corporate firms.• Most corporate firms also use Pay Back and Higher Hurdle

(Discount/WACC) rate for evaluation.02-Oct-09

Use of Risk Assessment Tools in the Industry

Capital Budgeting 7

• Simple but Very Useful Tool• Cash Flows are projected based on certain key

parameters/inputs– Selling Price– Costs– Volume of Output– Overheads

• Examine the impact on NPV with changes in one or more of the critical parameters.

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Risk Analysis – Sensitivity Analysis

Capital Budgeting 8

• Class Example & Class Work

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Sensitivity Analysis

Capital Budgeting 9

• The likelihood of the occurrence of an event in quantitative terms.

• Types of Probabilities– Objective Probability

• Based on a large number of independent and identical observations.

– Subjective Probability• Based on personal perceptions • Also known as “Expert Opinion or Expert Knowledge”

• Capital budgeting uses subjective probability in most cases.

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Probability Analysis

Capital Budgeting 10

• Estimate Expected Returns (Cash Flows) • Estimate Probabilities• Compute Expected Returns as– (Estimated Expected Returns * Estimated Probability)– NPV Prob. Expected NPV– 5686 0.60 1612– 9458 0.30 2837– 15686 0.10 1569

• The mean of the Expected NPV will be the estimated return from the project (ie 2006)

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Probability Analysis


• Mean / Expected Value • Standard Deviation of distributions• Co-efficient of Variation (Std Deviation / Mean)

• Example

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Statistical Tools


• Examines the project as a whole under different economic conditions with many variables changing at the same time instead of examining the impact of variation of one or a few variables.

• Example– What would happen in a situation of

• Economic Boom?• Economic Depression?• Stable Situation?• Stagflation?

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Scenario Analysis


• The projections under different conditions are aggregated and evaluated and

• Statistical measures applied to compute a likely scenario

• Class Exercise

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Scenario Analysis


• An attempt to replicate a real life situation by assigning values to key variables like selling price, variable costs, sales volumes etc..

• Uses random numbers.• A few thousand iterations are needed to arrive at a

meaningful distribution• Needs the aid of electronic data processing for

meaningful interpretation.• Not a very popular technique

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Simulation


1. Identify the exogenous variables– Sales – Volume, Price– Variable Costs– Fixed Costs– Tax Rate

2. Specify the probability distribution for each of the exogenous variables.

3. Compute the cumulative probability for each exogenous variable.

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Simulation – Monte Carlo


4. Compute the cumulative probability of each of he distributions.

5. Allocate RANDOM NUMBERS to all possible values of each variable in proportion to the cumulative probabilities.

6. Select corresponding random number values for each variable and their corresponding key factor values

7. Obtain the NPV

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Simulation – Monte Carlo - contd


• Perform many iterations– In real life this would be a few thousands.

• Evaluate for the distribution – Mean, – Standard Deviation and – Coefficient of Variation for the distributions

• Example• Class Work

02-Oct-09

Simulation – Monte Carlo – (contd.)


• Risk associated with projects has two dimensions– Risks may vary with projects within the same organization– The same project may experience different risks at

different time periods.

• Rationale for RAD– Shareholders have “Opportunity costs”.– These costs are directly proportionate to risk.– The RAD is therefore the premium expected over the risk

free return

02-Oct-09

Risk Adjusted Discount Rate (RADR)


• Used on the same principle as IRR & NPV using the same Accept-Reject criterion with the exception that– The hurdle rate is the RADR – not MCC.

– [CFATi / (1+Kr) ] - CO

• The RADR can also use different rates for periods with a higher risk.

02-Oct-09

Risk Adjusted Discount Rate (RADR


• Example• Cash Flows in – Year 0 Rs 1,00,000 (Outflow)– Year 1 Rs. 50,000– Year 2 Rs. 60,000– Year 3 Rs. 40,000– Riskless rate of return is 6%. RADR = 20%– Part A – Compute NPV– Part B – What would the answer be if the RADR is 25%,

26% & 28% in Years 1, 2 and 3 respectively?

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• NPV – Part A– {(50,000/(1.20)1 ) + (60,000/(1.20)2 ) + (40,000/(1.20)3 ) } – 100,000– = {41,667 + 41,667 + 23,148} – 100,000 – = 6,482

• NPV – Part B– {(50,000/(1.25)1 ) + (60,000/(1.26)2 ) + (40,000/(1.28)3 ) } – 100,000– = {40,000 + 37,793 + 19,073} – 100,000 – = - 3,134

• Class Example

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• Simple to use.• Practical as MCC at varying rates can be applied for

different projects• Disadvantages– Determination of RADR arbitrary and error prone – Adjustment of risk should be on the cash flow not the

RADR.– Compounding of risk over time implies that risk increases

over time. May not be always true. Eg. Teak Plantations

02-Oct-09

RADR - Evaluation


• An alternative to RADR.• Adjusts cash flows and NOT the hurdle rate.• The Certainty Equivalent Coefficient

– Risk Free Cash Flow / Risk Prone Cash Flow

• Use the Co-efficient to Generate Certainty Equivalent Cash Flows (CE-Cash Flow)

• Discount the CE-Cash Flows by the Risk Free rate.• Perform the standard NPV test• Example

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Certainty Equivalent Approach


• Evaluation– Simple to compute– Modifies cash flows – not the discount rate.– Issues With the Approach

• A Subjective estimate• Does not directly use the probability distribution

02-Oct-09

Certainty Equivalent Approach


• END

02-Oct-09

Capital Budgeting - Risk

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Capital Budgeting