Advanced Capital
Budgeting
Contents  Re-visit the basics
 Compare various project evaluation methods
 Unequal project lives
 Capital Rationing
 Capital budgeting during Inflationary conditions
 Evaluation techniques under Risk & Uncertainty
Capital Budgeting ??
• Capital Budgeting refers long term planning of capital expenditure.
• Heavy funds outlay, hence very risky decisions.
• Benefits of project are spread over several time periods in the future.
• Cost-benefit analysis for profit maximization, (↑ risk, ↑ return)
• Decisions involve extensive estimations and future predictions.
• Long term commitment of funds under uncertain future conditions.
Critical Evaluation – Why ??

Very high initial investments

Effect of decisions are known only in the future

Decisions are irreversible, so acceptance of project very critical

Quantification of future events and cash flows complicated.
There are too many known / unknown factors which influence
the project. Hence, every cash flow is only a probable figure.
Consideration of risk and uncertainty is highly necessary.
Evaluation Methods
 Payback
Period
 Discounted Payback
 Accounting Rate
 Net
of Return (ARR)
Present Value (NPV)
 Profitability Index
 Internal Rate
(PI)
of Return (IRR)
Comparison of Appraisal Methods

NPV vs. PI –

Both methods use the concept of time value of money.

For given project, NPV and PI would give the same result,
i.e. Accept or Reject.

However, in case of mutually exclusive projects NPV
method should be preferred.

NPV indicates the economic contribution or surplus of the
project in absolute terms. Higher the NPV, better the
project.
Comparison of Appraisal Methods

NPV vs. IRR –

Both methods use the concept of time value of money.

However, for certain situations both methods may give
conflicting results (w.r.t. accept / reject)

Conflict arises in projects where cash outflows arise at different
pts. of time and huge differences between initial CFAT and later
years CFAT.

Under situations of variance, NPV method should be adopted
since it is directly linked to the wealth maximization principle.

Also, it is presumed that cash inflows are re-invested at the rate
of IRR, while NPV method, re-investment is at the cut-off rate.
Re-investment at the cut-off rate is more realistic / practical than
re-investment at IRR rate.
Unequal Projects Lives
 In case of mutually exclusive projects, NPV is a correct method.
 But, for projects with unequal lives, NPV may give incorrect results.
 Hence, for comparison purposes, it is important to bring the projects
at a same footing.
 Therefore, Annual Equivalent Value (AEV) is computed by dividing
the NPV by the PV Annuity factor over the project life.
 The AEVs are compared and decision taken for selection of project.
 AEV =
NPV
PV Annuity Factor (r, n)
Capital Rationing
 Firms normally have fix annual budget for Capex. (max amt.)
 Firms select a combination of projects within the budget to
maximize the profitability.
 Such type of selection process is known as Capital Rationing.

Capital Rationing may be due to external and/ or internal constraints.

External factors include imperfections in capital market, such as lack
of market information, non-availability of easy funds etc.

Internal capital rationing consists of self-imposed restrictions by the
management, e.g. no borrowing policy, min. expected rate of return.
Capital Rationing (contd.)
 Projects with positive NPV be selected to max. shareholders’ wealth.
 Under capital rationing, there are two major decisions faced by the
management – maximize returns and / or full utilization of funds.
 Thus, less profitable projects may be selected to utilize total funds or
major funds be remain unutilized in order to maintain high profits.
 For capital rationing, PI should also be used along with NPV. Also,
capital rationing can be solved using linear programming (simplex).
Nature of project
Indivisible
Divisible
Meaning
Investment made in full, no
partial/ proportionate invt.
Partial invt. is possible
and NPV calculated
Steps involved in
decision making
Combination of projects to
utilize max funds. Select max
NPV projects.
Compute PI of projects
and rank them. Select
projects with max PI.
Inflation & Capital
Budgeting
$ Inflation results in erosion of value of money over a period of time.
$ Since cash inflows of an investment occur over long future periods,
the impact of inflation must be considered during project evaluation.
$ Generally, managers think that inflation can be offset by increasing
the selling prices of its commodities.
$ The same is not always true, since input costs (being sensitive) rise
at a fast rate, and selling prices are ruled by Competition & Govt.
$ Financial performance are based on financial statements that are
prepared conventionally, based on historical costs.
$ Hence, under inflation financial analysis may be vitiated, and may
result in exaggerating the profit figure. Replacement of depreciated
assets is affected due to historical costs and current funds required.
Inflation (contd.)
$ A project is subjected to inflationary pressures from time to time,
ranging from 6 months to more than one or two years.
$ Following guidelines should be used for such project appraisals –
# Make provision for cost escalation, w.r.t. expected inflation rate
# Various sources of finance should be verified for probable revisions in
interest rates by lenders.
# Adjustments should be made in cash flows and profitability projection
# Assess the financial viability of the project at the revised rate and
justify the same for its economic feasibility. The rate of return should
also include the rate of inflation per annum
# Projects with early payback period should be preferred being less
risky i.e. less prone to inflation.
Risk & Uncertainty (contd.)
∞ ↑ Risk ≈ ↑ Returns
∞ Techniques to manage risk –
a) Payback
b) Risk-adjusted discount rate
c) Certainty Equivalent
d) Sensitivity analysis
e) Scenario analysis
f) Decision Tree analysis
g) Cash flow Probability
h) Standard Deviation
i)
Simulation model
Techniques of Risk Mgt.
A. Payback
• Oldest and commonly used method for recognizing risk associated
with investment projects.
• Payback criteria is primarily used for mitigating risk rather than
measure profitability. Suitable for capital deficiency, cautious mgt. etc
• Firms prefer shorter payback
• Payback ensures liquidity by quick recovery of capital.
• Reduction of risk element by eliminating longer projects.
• Payback only considers risks related to time, but ignores the time
value of money.
Techniques of Risk Mgt.
B. Risk-Adjusted Discount Rate
• Expected rate of return consists of a risk-free rate (+) premium for
business risk (+) financial risk.
• Based on the above reasoning, risks related to time preference may
also be added to the risk-free rate.
• Such a composite rate is known as Risk-adjusted Discount Rate,
reflecting the management’s attitude towards risk involved in projects.
• Under this approach, a higher rate of discount is adopted for more
risky projects & lower discount rate for projects considered less risky.
• The approach is simple to understand, recognizes risk and uncertainty.
• However, no concrete way of deriving risk premium, i.e. computation
of the higher rate of discount. No risk adjustment made for cash flows
Techniques of Risk Mgt.
C. Certainty Equivalent Approach
• According to Certainty Equivalent approach, adjustments for risk are
made to the cash flows itself, arising in the future.
• Cash flows are reduced to conservative level by applying a correction
factor termed as Certainty Equivalent Co-efficient (CEC).
• This correction factor is the ratio of risk-less (certain) cash flows to
risky cash flows, i.e. CEC = Risk-less cash flows / Risky cash flow
• CEC assumes a value between 0 and 1, and varies inversely with risk.
• CEC are subjectively / objectively established by the decision maker
and multiplied by the cash flows to arrive at adjusted cash flows.
• These adjusted cash flows are further used for project evaluation
through payback, NPV, IRR or any other method.
Techniques of Risk Mgt.
C. Certainty Equivalent Approach (contd.)
• The Certainty Equivalent approach explicitly recognizes risk involved
in investment projects.
• However, process of reducing the cash flows is more subjective /
person dependent and can be inconsistent for different projects.
• This approach also suffers from the drawback of prior floating of the
cash flows, before adjusting the same for risk element. Such practices
defeat the whole purpose of certainty equivalent co-efficient.
• Certainty equivalent is a superior approach than risk-adjusted discount
rate method, because it can measure risk more accurately.
• Under risk-adjusted method, more the time - higher risk is associated,
that may not be true. Gestation time is riskier than future stability. In
such situations, CEC is better option than risk-adjusted discount rate.
Techniques of Risk Mgt.
D. Sensitivity Analysis
• Sensitivity analysis measures how sensitive / responsive are the
estimated parameters (cash flows, discount rate, project life etc.) of a
project against the estimation errors / market forces / uncertainty.
• Hence, Sensitivity Analysis is a way of analysing the changes in
project’s NPV (or IRR) for a given change in one of the variables.
Higher sensitive the NPV, more critical is the variable.
• Three important steps in sensitivity analysis are –
i. Identification of variables having influence on project’s NPV.
ii. Definition of the underlying (mathematical) relationship
between the variables.
iii. Analysis of the impact of the change in each of the variable on
the project’s NPV. (‘management by exception’)
Techniques of Risk Mgt.
D.Sensitivity Analysis
• During sensitivity analysis, the decision maker computes
the project’s NPV (or IRR) under three assumptions –

Pessimistic

Most Likely

Optimistic
• Most important question in sensitivity analysis –
“What If ?”
Techniques of Risk Mgt.
E.Scenario Analysis
• Simple sensitivity analysis assumes that the variables are
independent.
• However, in practice the variables may be inter-related
• For e.g. increase in sales quantity. reduction in selling
prices, increase in variable costs etc.
• Hence, Scenario Analysis considers impact of alternative
combinations of variables.
Techniques of Risk Mgt.
F. Decision Tree Analysis
• During capital budgeting, decision makers have to identify & evaluate
the various alternative courses of action, leading to the final decision.
• However, present investment decisions may have implications on
future decisions, and may affect future events. Hence, a series of
decisions should be judged, ranging from present to the future.
• Decision Tree is an technique to evaluate such sequential decisions.
• When a sequential series of conditional decisions are required to be
taken under uncertainty, a decision tree model facilitates visualization
and evaluation of all possible options for action.
• A decision tree is a graphic display of the relationship between a
present decision vis-à-vis future events, decisions & its consequences.
Techniques of Risk Mgt.
F. Decision Tree (contd.)
• Basic steps for decision tree–
o
Investment proposal should be defined
o
Clearly identify decision alternatives
o
Decision tree should be drawn indicating the decision points,
events and other data such as projected cash flows, probabilities.
o
Analyse the results and select the best alternative.
• Decision tree clearly brings out the implicit assumptions, calculations
for all to check and revise accordingly.
• Visualization of alternatives in graphic form is easier to comprehend.
• This approach not suited to increased variables, alternatives etc.
Techniques of Risk Mgt.
G. Probability of Cash Flows
• The most crucial information for capital budgeting decision is the
forecast of future cash flows.
• However, future is uncertain and hence we need to provide a range of
probabilities associated with the cash flow estimates.
• Probability can be described as a measure of someone’s opinion about
the likelihood of occurrence of an event. (optimist, normal, pessimist)
• Under this approach, probabilities are assigned to future cash flows
and further analysis is carried out for payback, NPV, IRR etc.
• This approach recognizes the risk associated with estimation of future
cash flows and provides for reduction in the same via probabilities.
• But, assigning probabilities is subjective and may lack consistency.
Techniques of Risk Mgt.
H.Standard Deviation & Co-efficient of Variation
• Assigning probabilities to cash flows exhibits the risk element in
capital budgeting decisions.
• However, a better approach to risk analysis is to measure the spread /
dispersion of the cash flows, through Standard Deviation or Variance.
• Standard Deviation is the deviation from the mean cash flows. Higher
the std. deviation, higher the risk and vice versa.
• Co-efficient of Variation is a relative measure of risk. It is useful for
comparing projects with same std. deviation but different values or
same values but different std. deviations etc. ↑ CV implies ↑ risk
• Co-efficient of Variation (CV) = Std. deviation
expected value (mean)
• Final selection of project depends on investors’ attitude towards risk.
Techniques of Risk Mgt.
I. Simulation Model
• Use of simulation models are an outcome of the deficiency of decision
tree method for managing large quantum of data and alternatives.
• Simulation is a quantitative procedure whereby a series of organized
experiments are conducted to predict the probable outcome of the
given alternatives.
• It implies construction of a model to represent a real-life situation,
which allows substitution of critical variables within the model.
• Simulation makes use of probabilities and random number series to
predict the uncertain events and its influence on the final outcome of
the project.