Capital Budgeting

Detailed Notes on Capital Budgeting, Techniques used in Capital Budgeting and Risk Analysis in Capital Budgteing

Investment Analysis


There are some limitations in Accounting Basis:
Here cash flows in Accounting are based on Accrual Concept. I.e. accounting is based on earning irrespective of receipt. We can see here that in accounting basis Benefits are Profits after tax which includes Depreciation amount also. Depreciation expenses are those which are not yet occurred, but accounting is done to compensate the reduction in the value of asset over its useful life. Nonetheless we deduct tax on that amount. So in order calculate the Actual Cash Flows after Tax, we should take as per cash basis.

Accounting Basis Cash Basis (Alternate Methods)
Particulars Amount Particulars Amount Particulars Amount
Profit Before Depreciation and Tax XXX Profit Before Depreciation and Tax                                 XXX Profit Before Depreciation and Tax XXX
Less: Depreciation (XXX) Less: Depreciation (XXX) Less: Tax (XXX)
Profit Before Tax XXX Profit Before Tax XXX Profit After Tax XXX
Less: Tax (XXX) Less: Tax (XXX) Add: Tax Savings on Depreciation XXX
Profit After Tax XXX Profit After Tax XXX Cash Flows After Tax XXX
    Add: Depreciation XXX    
    Cash Flows After Tax XXX  
  • PROFITS AFTER TAX – These are the benefits from the Investment. It also includes non-cash items such as Depreciation. Generally this is used in accounting rate of return. Any evaluation done based on PAT may not give accurate results.
  • CASH FLOWS AFTER TAX – these are the benefits from Investment. It does not include any non-cash items. This is used in Payback Period method, Net Present Value Method, Internal Rate of Return method, Profitability Index, Discounting Payback Period method.

Capital Budgeting

  1. Capital Budgeting is Decision Making such as Investment, Dividend or Financing Decisions.
  2. Capital Budgeting is Evaluation of Expenditure Decisions, which involves current outflow of cash and the benefits are incurred in future.
  3. Capital Budgeting is forecasting of expected returns which are likely to be occurred on New Investment Project.
  4. Risk and Uncertainty both refers to a situation with more than one outcomes.
  5. Risk refers to set of Unique Outcomes for a given event, to which we can assign Probabilities.
  6. Uncertainty refers to Outcomes of a given event which are too unsure to be assigned Probabilities.
  7. Standard Deviation as a measure of Risk becomes a difficult proposition in complex situations.

Factors used in Evaluation of Project

  1. Initial Investment: It includes Cost of New Assets Purchased, Investment in Working Capital. It is the cost of New Project. It is Net Cash Outflow at the initial stage of the project.
  2. Life of the Project: The time period during the project generates positive cash flows after tax. It is decided based on Technological Obsolescence, Physical Deterioration and fall in market demand for the product.
  3. Cash Flows after Tax: It includes Sum of Profit after Tax and Depreciation and other amortizations. They are the periodical cash flows generated over the life of the Project.
  4. Terminal Inflows: it includes – Salvage Value of Fixed Assets and Recovery of Working Capital.
  5. Time Value of Money: the Value of Money differs at different points of time. So all the inflows (Periodical and Terminal) are converted into Present value by multiplying with discounting factor.
  6. Discounting Factor: It represents the cut-off rate for capital investment evaluation. Generally we use weighted average cost of capital. (We will discuss this in next few pages). If the cash flows after tax after discounted with the discounting factor is less than the initial investment, the said project should not be selected. It is the present value factor. Generally we take discounting factor as risk free rate of Interest.

Investment Evaluation Process

  1. Identification of Costs and Benefits
  2. Identification of Minimum Rate of Return
  3. Application of Capital Budgeting Techniques to arrive at Decision regarding selection of Project

Capital Budgeting Techniques


Capital Budgeting Techniques

Traditional Techniques – Non-Discounting Techniques

Accounting Rate of Return – ARR

ARR is Average Yield on Investment. ARR is a relative measure used for Investment Evaluation. The selection process is done by comparing ARR with its Cost of Capital. In this method Profit after Taxes (PAT) as calculated in Accounting Method is used for evaluation.

ARR = (Average PAT pa)/ (Net Initial Investment) X 100

Average PAT pa = (Total PAT during Project Life)/ (Number of Years)

Net Initial Investment = Initial Investment less Salvage Value

Pay Back Period

It is the time duration required for complete recovery of Initial Investment. It the period during which the total cash inflows from the project will become equals to Total cash outflows.

The Project/Investment is said to be Viable if it has the Lower Payback Period, as Initial Investment can be recovered at the earliest.


  1. Determine the Initial Investment.
  2. Determine Cash Flows after Tax during the life of the project.
  3. Calculate Payback Period based on CFAT.

Cash Flows after Tax

In case of UNIFORM CFAT per annum In case of DIFFERENTIAL CFAT for various years
Payback Period = (Initial Investment)/(CFAT per annum)

This can also be done in Cumulative Approach, but it is simpler if we use the above formula.

Cumulative Approach

1.       Compute Cumulative CFAT at the end of every year.

2.       Determine the year in which Cumulative CFAT > Initial Investment.

3.       Payback Period = Time at which Cumulative CFAT = Initial Investment.

Accept the project if Payback period is less than the maximum period, else reject the project.

Discounting Techniques

Discounted Payback Period

This is done same as Payback Period, but here we are discounting the Cash Flows after Tax and are considering the change in the value of money over the period of time. (Implies we are considering TIME VALUE OF MONEY).

Step by Step Procedure of COMPUTATION OF Payback Period after discounting CFAT at a predetermined rate:

  1. Determine Cash Outflows – Initial Investment.
  2. Determine Cash Inflows – CFAT
  3. Determine Discounting Factor. And Calculate Present Value Factors for each year over the life of the Project.
  4. Calculate Discounting CFAT = CFAT*Present Value Factors for each year separately.
  5. Calculate Cumulative CFAT at the end of each year over the life of the Project.
  6. Determine the year in which Cumulative Discounted Cash flows exceeds Initial Investment.
  7. Discounted Payback Period is the period in which Cumulative Discounted CFAT = Initial Investment.
  8. Decision – if the Discounted Payback Period is less than the Maximum or Benchmark period – Accept, else reject the said project.

The Process for calculating Discounted Payback Period is same for uniform as well as differential CFAT.

Net Present Value – NPV

It is an Absolute Measure used for Investment Evaluation.

It is Sum of the Present Values of all Future Cash Inflows less Sum of Present Values of Cash Outflows associated with the project.

Here we have to consider CFAT instead of PAT and Terminal Inflows as Cash Inflows.

Cash Outflows include – Initial Investment (Cost of the Project) and Working Capital Investment.

NPV = Discounted Cash Inflows less Discounted Cash Outflows


  1. Computation of Cost of Investment – Initial Investment and additional Investment made over the life of the project (after discounting)
  2. Identification of Relevant Cash flows –
    1. Operating Cash flows
    2. Terminal Cash flows
  3. Identification of Cost of Capital – Discounting Rate.
  4. Compute NPV = Discounted Cash Inflows – Discounted Cash Outflows.
  5. Decision – the Project is selected if NPV is positive, else rejected.



  1. Operating Cash Inflows: these are the inflows that are regularly incurred during the life of the project.
  2. Terminal Cash Inflows: it generally includes salvage value and Residual Working Capital.

Why Discounting is done in NPV? Which is better ARR or PBP or NPV?

Rupee today has more value than the rupee tomorrow. In Payback period and ARR we do not consider this change in the value of Money. This is major limitation of ARR and PBP.

Present Value is not equal to Future Value.

In order to overcome this limitation, we follow NPV method. In this method we take into consideration the change in the value of money. The conversion of Future Values into Present Values is done by discounting. So NPV is more accurate than ARR and PBP.



Profitability Index/Desirability Index/Benefit Cost Ratio – PI

It is a variant of NPV. PI as same parameters as NPV.


It is the ratio of Present Value of Operating Cash Inflows to Present Value of Net Investment Cost.

PI = (Present value of operational Cash Inflows)/(Present Value of Net Investment)

PI represents amount obtained at the end of the project life, for every rupee invested in the project. The higher the PI the better the project, since greater return for every rupee invested.

NPV is amount of surplus obtained. PI is what the benefit is for every rupee invested in the project.

NPV does not consider the size disparity and Investment changes in the Project. These Limitations are compensated by PI.


  1. Computation of Cost of Investment – Initial Investment and additional Investment made over the life of the project (after discounting)
  2. Identification of Relevant Cash flows –
    1. Operating Cash flows
    2. Terminal Cash flows
  3. Identification of Cost of Capital – Discounting Rate.
  4. Compute PI = Discounted Cash Inflows ÷ Discounted Cash Outflows.
  5. Decision – the Project is selected if PI is greater than 1, else rejected.



Here discounting factor is Weighted Average Cost of Capital.

When NPV > 0, PI will always be greater than 1, as both NPV and PI use same factors.

NPV = A-B and PI = A/B

Where A = Discounted Cash flows after Tax and B = Discounted Cash Outflows.

Which should be preferred – NPV or PI:

NPV gives ranking in absolute terms. PI gives ranking for every rupee invested.

Generally NPV should be preferred since NPV indicates the economic contribution or surplus of the project in absolute terms.

In capital rationing situations, for deciding between mutually exclusive projects, PI is a better evaluation technique.

Internal Rate of Return – IRR

IRR is the rate at which Sum of Discounted Cash inflows is equal to Total Investment. It is the maximum return on Investment.

At IRR, Sum of Discounted Cash Inflows less Sum of Discounted Cash Outflows = 0

As we know, when Sum of Discounted Cash Inflows = Sum of Discounted Cash Outflows, NPV = 0.

And at IRR, Sum of Discounted Cash Inflows = Sum of Discounted Cash Outflows.

So we can conclude that, at IRR, NPV = 0.

IRR is different from Cost of Capital. Differences –

Cost of Capital – Ke[1] Internal Rate of Return – IRR
1.       It is the minimum required on any investment made.

2.       It is related to Financing Aspect – Procurement of Funds.

1.       It is the Maximum Return earned on any Investment.

2.       It is related to Investment Aspect – Utilization or Application of Funds.

The Discount rate i.e. Cost of Capital is assumed to be known in the determination of NPV, while in IRR calculation NPV = 0 and the discount rate which satisfies the condition is determined.

Decision is made by comparing IRR and Cost of Capital.

[1] It is the cost incurred to obtain required capital. It includes Equity Dividend, Preference Dividend, and Interest on debentures and any other cost involved.  Whereas IRR is the maximum return on Investment.


  1. Identify all Cash outflows of the project and the periods in which they are occurred.
  2. Identify all Cash Inflows of the Project and their periods.
  3. Compute NPV at any arbitrary discount rate, say 10%.
  4. Choose another Discount rate in such a way that the desired NPV is Negative, if the other is positive and positive if the other is Negative.
  5. Compute the change in NPV over the two selected discount rates.
  6. On Proportionate basis, compute discount rate at which NPV = 0.

There are several alternatives regarding calculation of IRR, we can discuss them with the help of an example.

Decision Making


Here Ke = Cost of Capital

Methods for Calculation of IRR under different circumstances:CB7.PNG


At IRR, NPV = 0.

Higher the NPV, higher will be the IRR. However NPV and IRR may give conflicting results in evaluation of different projects.

In that case NPV prevails. NPV is superior to IRR because of the following reasons.

It represents Surplus from the Project IRR represents a point of No Surplus – No Deficit
Here Cost of Capital is Constant Here NPV is Constant as NPV is taken as Zero. It is a case of Reverse working.
Decision making is easy as a project is selected if NPV > 0 and is rejected if NPV < 0 Here decision making does not depend upon IRR itself. We have to compare IRR with Cost of Capital (Ke) and then decide whether the project is to be selected or not.

i.e. if IRR > Ke – Project is Selected

and if IRR < Ke – Project is rejected

It considers timing difference in cash flows at appropriate discount rate. IRR is greatly affected by volatility in cash flow patterns.
It is presumed that cash flows are reinvested at cut-off rate. It is presumed that cash flows are reinvested at IRR (Maximum return) which is not realistic
It does not have Interpretation problems. That is if cash outflows are at different point of times, then they are just discounted at present value factor. Here there are interpretation problems. Like there may be negative IRRs or multiple IRRs if cash outflows are at different points of time

So all these points helps us understand why NPV is more reliable than IRR.


  1. Determine Cash Inflows and Cash Outflows during the life of the project.
  2. Calculate Terminal cash flows other than the Initial Investment.
    1. Terminal Cash flows = Amount of Cash flow × Re-Investment Factor
    2. Re – Investment Factor = (1+k)n, n = number of years balance remaining
  3. Inflow = Total Terminal Values

Outflow = Initial Investment

  1. We can calculate MIRR as such that, Inflows × PVAF(MIRR%, n years) = Outflows (same as IRR).

Ranking Conflicts

The difference of opinion among NPV, PI, IRR with respect to project selection is called Disparity.

This disparity arises in Mutually Exclusive Investment proposals.

Reasons for Conflict:CB8


Equivalent Annual Flows LCM Method Terminal Value
1.       Cash flows are converted into Equivalent Annual Annuity called EAB or EAC

2.       The amounts are then compared and decisions are taken suitably.

3.       In cost comparison – the project with lower cost is selected

4.       In case of benefit comparison – the project with higher benefits are selected.

1.       This involves evaluation of alternatives over an interval equals to Lowest Common Multiple of the lives of alternatives under consideration.

2.       This is similar to Equivalent Annual Cost/ Benefit Method.

Example – if a proposal A has 3 years of life and Proposal B has 5 years of life, LCM period is 15 years. During which period machine A will be replaced 5 times and machine B will be replaced 3 times. Cash flows are extended to this period and computations are made.  The final results would then be on equal platform – equal years.

It involves estimation of Terminal Values for all the alternatives available at the end of certain period

Example – if the project life is 3 years, then the salvage value at the end of the 3rd year should be considered in the evaluation process.


  1. Calculate Initial Investment of each alternative
  2. Determine project lives
  3. Identify Annuity factor relating to each project
  4. Equivalent Annual Investment (EAI)= (Initial Investment)/(Relevant Annuity Factor)
  5. Calculate CFAT pa or Cash Outflows pa
  6. Equated Annual Benefit = CFAT pa less EAI
  7. Equated Annual Cost = Cash outflows add EAI
  8. Select the project that gives Maximum EAB or Minimum EAC as the case may be.

Application of EAC/EAB:


Evaluation of Projects

Any project can be evaluated based on Long Term Point of view or Equity funds point of view.

Particulars Long term Funds Point of View Equity Funds point of View
Investment Funds procured from ESH, PSH, Lenders shall be taken as Initial Investment Funds procured from ESH shall be taken as Investment
Discounting Rate Overall Cost of Capital being used Cost of Equity being the discounting factor
Interest on Debt and Debt Repayment Not considered Considered.

Interest on Debt should be deducted from Cash Flows and repayment of Debt shall be considered as Cash Outflow in the year of repayment

Cash Flows Particulars Amount Particulars Amount
Less: Interest NIL Less: Interest XXX
Less: Tax XXX Less: Tax XXX
Add: Depreciation XXX Less: Preference Dividend XXX
CFAT XXX Less: Debt Repayment XXX
  Add: Depreciation XXX
CFAT (earnings available to ESH) XXX

In equity funds approach Principal repayment is deducted from Post Tax profit, whereas Interest is deducted from Before Tax Profit.

Project IRR and Equity IRR

Internal Rate Return is defined as the rate of return at which Present Value of Cash flows are equal to present value of outflows, i.e. NPV = 0.

A project can be funded by Equity and/or Debt.

Calculation of the internal rate of return considering only the project cash flows (excluding the financing cash flows) gives us the project IRR. A project IRR is calculated on Free Cash Flows from the Project.

Calculation of the internal rate of return considering the cash flows net of financing gives us the Equity IRR.  An Equity IRR is calculated on Free Cash Flows of Equity. It represents degree of returns of a project to the providers of Equity Capital.

Equity IRR Project IRR
Cost    =           Equity Share Capital

Cash Flows = Revenue

Less:   Cost

Less:   EAI (Instalment)

Cost =           Equity Share Capital


Cash Flows = Revenue

Less:   Cost

Interpretation of Results: – Equity IRRCB9


Replacement Analysis

When existing plants are replaced with new machinery, this analysis is made. It is done to make make or buy decisions.

Block consists of –

Several Assets in the block Only Single Asset in the block
Incremental Investment:

Opening WDV

Add: Purchase Cost

Less: Sale value of Old Asset

Incremental Investment:

Opening WDV

Add: Purchase Cost

Less: Sale value of Old Asset

Depreciation Computation:

Depreciation claimed on closing WDV of the block

Depreciation Computation:

Depreciation claimed on closing WDV of the block

Depreciation in the year of Transfer of the Old Asset

Depreciation will be claimed on the closing WDV of the block

Opening WDV = XXX

(+) Purchases = XXX

(-) Sales           = XXX

Closing WDV   = XXX (for Depreciation purpose)

Depreciation in the year of Transfer of the Old Asset

There will be no depreciation in the year of Transfer.

But Short term Capital Gains or Loss will arise.


Sale Value of Assets      XXX

(-) Book Value of Asset XXX

STCG/STCL                       XXX

Replacement analysis – NPVCB11.PNG

Optimum Replacement Cycle

Sometimes a firm may require certain assets essential for Business. It has to replace these assets on regular basis. It is not economical to continue throughout the life of the life of asset. The repairs and maintenance expenses will increase with the life of the asset.

For the purpose of Cost reduction a firm is required to replace these assets before the useful life of the asset.

The timing of replacement depends on Equated Annual Cost.

Steps involved:

  1. Find out replacement option.
  2. Calculate equated annual cost at different replacement cycles.
  3. The Optimum replacement cycle is found at a point at which the equated annual cost is minimum.

Capital Rationing

Allocation of Capital among Several investment proposals.

It is a tool used to overcome Resource Constraints situation. The basic objective of any firm is to maximize the wealth of the shareholders. Capital Rationing is a handy tool to allocate limited funds among various profitable projects.

When the capital required is more than the Capital available, and then Capital Rationing helps to generate effective returns. The reasons for shortage in money may be internal or external. External issues include Securities issued were not subscribed, as this is not in the control of the organisation.  Internal issues includes Self-imposed conditions by management for example, fixed ceilings on projects, company’s fixed debt equity ratio, where a company cannot borrow more than certain fixed amount.

Capital Rationing gives us the Optimum Combination that is best suited for the organisation.CB12


Options to Abandon

All kinds of Investment Decisions are generally irreversible in Nature. In case Traditional Investment Decisions, there is no option of Termination.

But during the implementations there may be some Strategic alternative available to conclude the project before its useful life.

The point of time at which project should be terminated is the subject matter.

All the abandoned decisions are evaluated under the following Decision Rules:

  1. Based on NPV
  2. Based on Incremental Analysis

Based on Abandonment option, we can restrict the loss.CB14

Utility Theory

The traditional Capital Budgeting techniques fail to consider the Risk Preferences of the Investor.

The Utility Theory helps the Investor by taking the Risk Preferences of each Investment and provides Reasonable Utility from each Investment Proposal.

The Term Utility refers to Satisfaction derived from different Investment Proposals.

These Utilities will vary from Investment to Investment and from Person to Person.


There is change in Price Levels as a result of Inflation.

Effects of Inflation:

1.       Cost of investment No Effect
2.       Operational Cash flows Has an effect
3.       Terminal Cash Flows Has an effect
4.       Cost of Capital Has an effect

Project Appraisal under Inflationary Conditions:

  1. Cost Escalation: Make provisions for cost escalations on all heads of cost, keeping in view the rate of inflation during likely period of delay in project implementation.
  2. Cost of Funds: Sources of Finance should be scrutinized carefully with reference to probable revision in the rate of interest.
  3. Adjustment in Projections: adjustments should be made in Cash Flow projections and profitability to take care of the Inflationary pressures affecting future projections.
  4. Re-evaluation of Financial Viability – the Financial Viability should be examined at the revised rates and should be assessed with reference to economic justification of the project.
  5. Choice of Projects: In Inflationary projects, Projects with early payback period should be selected.


Adjustment of Cash Flows Adjustment of Cut-Off Rate
Projected Cash flows should be adjusted to an Inflation Index, recognizing Selling Price increases and Cost Increases annually “Acceptance Rate” should be adjusted for Inflation, retaining cash flow projections at current price levels.
  1. Money Cash Flows:

These are the cash flows that are estimated based on Purchasing power of Respective years. These cash flows include the effect of inflation. Money cash flows are also known as Nominal Cash Flows.

Y0 Y1 (Inflation effect)
100 110
  1. Real Cash Flows:

Cash flows that are estimated based on current year purchasing power. They do not include effect of inflation.

Y0 Y1 (No Inflation effect)
100 100
  1. Money Discounted Rate:

The discounting rate adjusted after considering inflation effect.

  1. Real Discount Rate:

The discounting rate not adjusted against the effect of Inflation.

Relationship between MCF and RCF:CB16

MCF x MDR = PV of Discounted Cash Flows


MCF x Inflation Rate = RCF

RCF x RDR = Pv of Discounted Cash Flows

Inter Relation:


(MDR) = expected return with Inflation

(RDR) = Due to change in quality

(IFR)  = Due to change in Money Price

Derived Equations:

  1. (RDR) = [(1+MDR)/(1+IFR)]-1
  2. (IFR) = [(1+MDR)/(1+IFR)]-1

The rate of Inflation differs for Inflows and Outflows.

During inflation period, the revenues and expenses will increase in line with the inflation. But Depreciation on assets will be provided on Historical Cost – Not affected by Inflation.

The tax savings on Inflation will remain same, irrespective of effect of Inflation.

Risk Analysis in Capital Budgeting

Risk is generally regarded as a boundary to outcomes.

The term Risk with reference to Capital Budgeting can be defined as the difference between actual cash flows and expected cash flows from the investment.

It is a financial loss that can be sustained as a result of change in environmental conditions.



1.       Risk adjusted discount rate

2.       Certainty equivalent factor

3.       Project BEP

4.       Sensitivity analysis

5.       Scenario Analysis

1.       Probability distribution

2.       Standard deviation

3.       Decision trees

4.       Simulation

Traditional Tools

Risk Adjusted Discount Rate – RADR

Expected return changes with risk level for different Investments.

Business is all about taking the risk and earning returns. Higher the risk involved in the business, higher will be the return from the business.

The discount rate used for Investment Evaluation is the expected return from the project.

All projects do not have same risk characteristics, so same discount rate should not be used.

The discount rate should be adjusted against Risk Involved in the project. The adjusted discount rate is known as Risk adjusted discount rate.

Risk Premium Model:

It includes:

  • Risk Free Rate of Return – Minimum rate of return that is expected of any other investment alternative. If a project with risk is going to yield a return lower than risk free return, then the said project should not be undertaken.
  • Risk Premium – additional return expected from a risky investment. It consists of –
    • Firm’s Normal Risk (RN) – this is an adjustment for Firm’s Normal Risk.
    • Project’s Risk (RP) – this is adjustment for differential risk for a project.CB25


  1. It is difficult to estimate risk premium associated with a project consistently
  2. Risk Adjustment is estimated on ad hoc, unscientific and naïve basis
  3. This method assumes that risk increases with time at a constant rate, which may not be valid.

Certainty Equivalent Factor

Certainty Equivalent approach recognizes risk in Capital budgeting analysis, by adjusting estimated cash flows and employs risk free rate to discount the adjusted cash flows.

Future cash flows are Uncertain Cash flows.

Under this approach all the future expected cash flows are converted into risk less amounts by applying CE factor.CB26

Difference between Certainty Equivalent Approach and Risk Adjusted Discount Rate:

Point Certainty Equivalent Approach Risk Adjusted Discount Rate
Factor Used Here Cash Flows are adjusted Here Discount Rate is adjusted
Time effect Cash flows are adjusted for risk overtime under this method This method assumes that risk increases with time and at Constant Rate
Ease It is difficult to specify series of CEFs It is comparatively easier to adjust Discount Rate
Accuracy This is superior to Risk Adjusted Discount Rate approach, as it can measure risk more accurately Cash flows are more uncertain than the cost of capital. Risk is adjusted only in the Discount Rates, and is not recognised in the Cash Flows

Sensitivity Analysis

NPV is computed based on set of critical factors such as Initial Investment, Selling Price per unit, Volume, Operating Expenses, Discounting Rate, etc.

If any one of these factors changes, NPV will also be affected. Sensitivity Analysis measures this change.

SA is a tool to forecast the impact of various factors on the original computed NPV and this approach the Behavioural Change of each Variable will be computed in Advance.

Steps involved:

  1. Compute NPV based on Original Data
  2. Identify Critical Factors that would affect NPV
  3. Compute % change in each variable that leads to NPV as Zero
  4. Identify the most Sensitivity Variable.


Scenario Analysis

Meaning –

  1. It is the Analysis of the NPV or IRR of a Project under a Series of Specific Scenarios, based on Macro-Economics, Industry and Firm Specific factors
  2. This Analysis seeks to establish “Worst Case” and “Best Case” scenarios, so that the whole range of possible outcomes can be considered

Steps involved in Scenario Analysis are –

  1. Identify various sources of Uncertainty for the future success of the Project. These are the basic factors around which scenarios will be built
  2. Determine the Scenarios for each factor à Best Case, Average or Most Likely or Worst Case
  3. Estimate the values for each of the variables in the Investment Analysis (Revenue, Growth, Operating Margin, etc) under each scenario
  4. Assign probability of occurrence for each of the scenarios, based on Macro and Micro Factors
  5. Compute NPV and IRR under each Scenario
  6. Arrive at the appropriate decision on the project, based on the NPV under all scenarios, rather just Base Case NPV or Mean NPV

Advantages –

  1. This Analysis brings in the probabilities of changes in key variables
  2. This Analysis helps the Analyst to change more than one variable at a time

Limitations –

  1. There are No clearly delineated scenario in many cases
  2. If there are many important variables to consider, there may give rise to huge number of Scenarios for analysis
  3. There is no clear guiding principle to indicate how the decision maker will use results of Scenario Analysis

Modern Tools

Probability Distribution

  • Probability – the chance of occurrence or non-occurrence of an event is denoted by Probability. If an event is certain to be happen its probability is “1”. In such a case the chance for Non-occurrence is “Zero”. The probability for given event lies between “0-1”.
  • Probability Distribution – An estimate leads to Several Outcomes, the chance of occurrence of each outcome being assigned with probabilities. The series of outcomes and their probabilities is known as Probability Distribution.
  • Expected Value or Mean Value – It is simply Weighted Average of all the Outcomes multiplied by their respective probabilities.

Standard Deviation

The project cash flows are mere estimates. There would be difference between actual Cash flows and expected cash flows. Such difference or variability is known as Risk of the Project.

The Risk of the project can be studied with a statistical tool known as Standard Deviation.

SD is a standardized unit of measure to find out difference in cash flows from the mean value. It is denoted by σ.

Steps involved:


Higher the Standard Deviation, Higher will be Risk involved in the Project.

Coefficient of Variance or Risk Reward Ratio:

It is used to overcome limitation of Standard Deviation.  It is a relative measure for measuring risk. It is also known as Risk Reward Ratio.

Hiller Model:

Project Cash flows are estimated based on Information available at the time of evaluation.

The cash flows of the project may have some inter relationship.

The Interrelationship of project cash flows will be studied in the following manner:

  • Dependent Cash flows
  • Independent Cash flows

Dependent Cash Flows:

Cash flows of a particular year will have an effect on cash flows from following years. In such a case cash flows will have Perfectly Dependent Correlation.

The raise of NPV is calculated as follows:

  1. Compute Standard Deviation for each year Cash Flows.
  2. Discount the Standard Deviation of Cash Flows with Risk Free Rate of Return (as risk already eliminated)
  3. Standard Deviation of NPV is sum of Discounted Standard Deviation of each year Cash flows
  4. CB29

Independent Cash Flows:

Cash flows are said to be Independent if the Cash Flow of a particular year does not affect cash flows of the following years.

Independent Cash flows are also known as Uncorrected Cash Flows (No Relation)

The risk of NPV with respect to Independent Cash Flows is computed as under: Variance Model

  1. Compute Variance of Cash Flows for all the years.
  2. Double Discount CB30Variance of Cash flows with Risk Free Rate
  3. The sum of Discounted Variance of Cash flows for all the years.
  4. Variance of NPV (Risk of NPV) CB31


In the absence of information CF are assumed to be Independent in nature.

Normal Distribution Curve and Application of Probability:

  1. Compute the value of Z using the following formula CB33

Where, X = Desired NPV/Desired Value

CB32 = Originally estimated NPV

  1. If in Step 1 value is negative it means that the value of ‘Z’ falls in the left tail of Normal Distribution Curve.
  2. If it (Z) is positive, it means that Z falls on the right tail of the Normal Distribution Curve.
  3. Compute Table Value Corresponding to Z Value
  4. Find out probability for the event
    1. Tail – Right or Left
    2. Requirement </>
    3. Action – Add/Less 0.5 from Z value
      Tail Requirement Action
      Right Tail > Deduct value Z from 0.5
      Right Tail < Add Value of Z to 0.5
      Left Tail > Add 0.5 to value of Z
      Right Tail < Less 0.5 from Value of Z

Joint Probability and Expected NPV:

If the probability distribution of a particular project is not perfectly depended on cash flows of earlier years, the risk of NPV and expected NPV will be computed in the following manner:

Expected NPV:

  1. Identify Investment Alternatives(project outcome)
  2. Compute Joint Probability for each alternative P(XUY)
  3. Compute NPV for each alternative
  4. Expected NPV = the sum of [bxc]

Risk of NPV:

  1. Compute Deviation of NPV (Exp NPV at each alternative – NPV) = CB34
  2. Square the deviation of NPV for each alternative CB35
  3. Multiply Squared Deviations with Joint Probability with each alternative – CB36
  4. The sum of “c” will be variance of NPV for all alternatives – CB37
  5. CB38

Decision Trees

The decision maker has to identify various investment alternatives before making a decision. Sometimes an investment leads to further investment in future periods.

The interconnection between various investments should be carefully studied for better Investment Evaluation.

A decision Tree is a graphical tool used to present complex investment Decisions. It provides complete picture about the future investment in each stage of investment and its consequences and impact in an effective manner

Construction of Decision Tree:

Decision Nodes are denoted by Squares – Rect

Chance Nodes are denoted by Circles – circle

  1. All the Investment alternatives starting from Decision Points. These are represented by Chance Nodes.
  2. Assign Probabilities to each Chance Node
  3. All the Decision Nodes and Chance Nodes should be Serially Numbered.

Evaluation of Decision Tree:

All decision Trees are drawn from Left to Right. But its evaluation starts from right to left.

  1. Expected Monetary Value at Chance Node – EMV:

It is aggregate value of all branches starting from the chance node

  1. Expected Monetary Value at Decision Node:

It is Highest Expected Value of various Chance Nodes starting from Decision Point.




It is a Mathematical Model that represents Decision Making under the conditions of Uncertainty. It involves a series of Prediction over the number of Variables involved in the Decision. It is also based on the concept of Probability.

Simulation is a tool used for Decision Making and it provides Trial and Error approach for Optimum Solution.