CAPITAL BUDGETING AND RISK- Risk Analysis NOTES

Risk is inherent in almost every business decision. More so in capital
budgeting decision as they involve costs
and benefits extending over a long period of time during which many
things can change in unanticipated ways. A research and development
project may be more risky than an expansion project and the latter tends
to be more risky than a replacement project. In view of such
differences, variations in risk need to be considered explicitly in
capital investment appraisal. Risk analysis is one of the most complex
and slippery aspects of capital budgeting.

3.2 Perspectives on Risk

You can view a project from at least three different perspectives:
Stand alone risk- This represents the risk of a project when it is
viewed in isolation.
Firm risk- Also called corporate risk; this represents the contribution
of a project to risk: the firm.
Market risk- This represents the risk of a project from the point of
view of a diversified investor. It is also called systematic risk.
Since the primary goal of the firm is to maximize shareholder value,
what matters finally is the risk that a project imposes on shareholders.
If shareholders are well diversified market risk is the most appropriate
measure of risk.

In practice, however, the project’s stand-alone risk as well as its
corporate risk are considered important. Why? The project’s stand-alone
risk is considered important-for the following reasons:

Measuring a project’s stand-alone risk is easier than measuring its
corporate risk a, far easier than measuring its market risk.
In most of the cases, stand-alone risk, corporate risk, and market
risk are correlated. If the overall economy does well, the firm too
would do well.
The proponent of a capital investment is likely to be judged on the
performance of that investment.
In most firms, the capital budgeting committee considers investment proposals one at a time.

Corporate risk is considered important for the following reasons:

Undiversified shareholders are more concerned about corporate risk
than market risk.
Empirical studies suggest that both market risk and corporate risk
have a bearing on required returns. Perhaps even diversified
investors consider corporate risk in addition to market risk when
they specify required returns.
The stability of over-all corporate cash flows and earnings is
valued by managers, workers, suppliers, creditors, customers, and
the community in which the firm operates. If the cash flows and
earnings of the firm are perceived to be highly volatile and risky,
the firm will have difficulty in attracting talented employees,
loyal customers, reliable suppliers, and dependable lenders. This
will impair its performance and destroy shareholder wealth.
Recognizing the importance of stand-alone risk, firm risk, and
market risk, we will discuss risk from all the three perspectives.

3.3 Causes of Risk

Insufficient number of similar investments – Thus opportunity for
outcomes to average out
Bias in data and its assessment
Changing external economic environment invalidating past experiences
Misinterpreting data
Errors of analysis
Managerial talent availability and emphasis
Salvageability of investment
Obsolescence

*3.4 Methods of Dealing with Risk in Capital Budgeting

Different techniques have been suggested and no single technique can be
deemed as best in all situations. The variety of techniques suggested to
handle risk in capital budgeting fall into two broad categories:

Approaches that consider the standalone risk of a project
Approaches that consider the risk of a project in the context of the
firm or in the context at the market.

This chapter discusses different techniques of risk analysis explores
various approaches to project selection under risk, and describes risk
analysis in practice. The techniques are discussed in the following order

Risk adjusted discount rate approach
Certainly equipments approach
Sensitivity analysis
Scenario analysis
Breakeven analysis
Hillier model
Simulation analysis
Decision tree analysis
Corporate risk analysis

Risk Adjusted Discount Rate Approach

The approach is based on the premise that the riskiness of a project may
be accounted for by adjusting the discount rate (cost of capital). Relatively risky projects have relatively high discount rates while relatively safe projects have relatively low discount rates.
Remember CAPM which was expressed as: f m −+= RRRR f )( β , where the
expected return was said to be function of the risk free rate plus a
risk premium. This expression can be re expressed as follows: = RK +α afa
Where: Ka = the risk adjusted cost of capital for project a
Rf = the risk free rate
α a = the risk adjustment premium
As the risk increase so does α a and Ka such that, α a can be expressed
as a function of the proportional relations between the standard
deviation of the total firms cash flows i.e

3.4.2 Certainly Equivalent Approach
Proponents of this approach object to the use of a discount rate that
lumps together the risk free rate and risk premium. They conclude that
two important things account for the valuation process: time value of
money and risk attitudes, which should be separated.
The decision rule associated with certainty equivalent approach is to
undertake a project if its certainty equivalent NPV is greater than
zero. Certainty equivalent of the cash flows Ct can be calculated in
several ways some of these are:

Reducing the cash flow estimate by a sufficient number of standard
deviations to ensure that the occurrence will be certain under the
normal distribution. This is done by reducing the cash flow
estimates by 3 standard deviations (i.e. to be 99.72% certain that
the occurrence will be at least equal to the certainty equivalent)
Reducing the cash flow estimate by a factor “B” that reflects the
financial manager’s willingness to trade the estimate for the
certainty equivalent
A time adjusted method where if the manager feels less certain of
estimated cash flow over time, then B is reduced as the uncertainty
of the future increases

3.4.3 Sensitivity Analysis
Since the future is uncertain, one may like to know what will happen to
the viability of the project when some variable like sales or investment
deviates from its expected value. In other words, you may want to do
“what if” analysis or sensitivity analysis.
To understand the nature of sensitivity analysis, let us consider an
example. Suppose you are the financial manager of Pembe Flour Mills.
Pembe is considering setting up a new flour mill near Kitale. Based on
Pembe previous experience, the project staff of Pembe
has developed the figures shown in Exhibit 13.2 (Note that the salvage
value has assumed to be nil and the cost of capital to be 12 percent.)

NPV based on the expected values of the underlying variables looks
positive. You however, aware that the underlying variable can vary
widely and hence you would like to explore the effect of such variations
on the NPV. So you define the optimist and pessimistic estimates for the
underlying variables. These are shown in the left hand co1umns of
Exhibit the figure below. With this information, you can calculate the
NPV for optimistic and pessimistic values of each of the underlying
variables.

To do this, vary one variable at a time. For example, to study the
effect of an adverse variation in sales (from the expected $18 million
to the pessimistic $15 million), you maintain the values of the other
underlying variables it their expected levels (This means the investment
is held at $20 million, variable costs as a proportion of sales are held
at 66.67 percent, fixed costs are held at $I million, so an and so forth.)

The NPV when the sales are at their pessimistic level and other
variables at their expected level is shown on the right side of the
above table. Likewise you can calculate the effect of variations in the
values of the underlying variables. The NPVs for the pessimistic
expected and optimistic forecasts are shown on the right side of the
table Evaluation very popular method for assessing risk, sensitivity
analysis has certain merits:

It shows how robust or vulnerable a project is to changes in values
of the underlying variables.
It indicates where further work may be done. If the NPV is highly
sensitive changes in some factor, it may be worthwhile to explore
how the variability of the critical factor may he contained.
It is intuitively very appealing as it articulates the concerns that
project eva1uating normally have.

Notwithstanding its appeal and popularity, sensitivity analysis suffers
from several 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 decision maker to accept the project while another
may reject it. .

3.4.4 Scenario Analysis
Insensitivity analysis, typically one variable is varied at a time. In
scenario analysis several variables are varied simultaneously. Most
commonly three scenarios are considered: expected (or normal) scenario,
pessimistic scenario and optimistic scenario and optimistic scenario. In
the normal scenario all variables assume their normal values in the
pessimistic scenario all the variables assume their pessimistic values
and in the optimistic scenario all variables assume their optimistic values

Scenario analysis may be regarded as an improvement over sensitivity
analysis because it considers variations in several variables together.

However, scenario analysis has its own 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, viz., recession,
stability, and boom. It can in fact 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 va1ues (3 ×10) to do the scenario analysis.

3.4.4 Break-even Analysis

In sensitivity analysis we ask what will happen to the project if sales
decline or costs increase or something else happens. As a financial
manager, you will also be interested in knowing how much should be
produced and sold at a minimum to ensure that the project does not ‘lose
money’. Such an exercise is called break even analysis and the minimum
quantity at which loss is avoided is called the break-even point. The
break -even point may be defined in accounting terms or financial terms.
Accounting Break-even Analysis Suppose you are the financial manager of
Pembe Mills is considering setting up a new flour mill near Kitale.
Based on Pembe previous
experience, the project staff of Pembe has developed the figures shown
in the previous example. Note that the ratio of variable costs to sales
is 0.667 (12/18). This means that every dollar of sales makes a
contribution of $ 0.333. Put differently, the contribution margin ratio
is 0.333.

A variant of the accounting break-even point is the cash break-even
point which is defined as the level of sales at which the firm neither
makes cash profit nor incurs a cash loss. The cash break even sales is
defined as:

Financial Break-even Analysis- The focus of financial break-even
analysis is on NPV and not on accounting profit, at what level of sales
will the project have a zero NPV? To illustrate how the financial
break-even level of sales is calculated, let us go back to
Pemble mill project. The annual cash flow of the project depends on
sales as follows:
Variable costs: 66.67 percent of sales
Contribution: 33.33 percent of sales
Fixed costs: $ 1 million
Depreciation: $ 2 million
Pre-tax profit: 0.333 × Sales) – $ 3 million
Tax (at 33.3%) 0.333 (0.333 Sales – $ 3 million)
Profit after tax .667 (0.333 x Sales -$ 3 million)
Cash flow (4 + 7): Es. 2 million + .667 (0.333 × Sales – $ 3 million)
= 0.222 Sales
Since the cash flow lasts for 10 years, its present value at a discount
rate of 12 percent is:
PV (cash flows) = 0.222 Sales × PVIFA (10 years, 12%)
= 0.222 Sales z 5.65(1
= 1.254 Sales
The project breaks even in NPV terms when the present value of these
cash flows equals
the initial investment of Es. 20 million. Hence, the financial
break-even occur, when
PV (cash flows) = Investment
1.254 Sales = $ 20 million
Sales = $ 15.95 million
Thus, the sales for the flour null must be $15.95 million per year for
the investment to have a zero NPV. Note that this is significantly
higher than $ 9 million which represents the accounting break-even sales

3.4.6 Simulation Analysis

Sensitivity analysis indicates the sensitivity of the criterion of merit
(NPV, IRR, or any other) to variations in basic factors and provides
information of the following type: If the quantity produced and sold
decreases by 1 percent, other things being equal, the
NPV falls by 6 percent. Such information, though useful, may not he
adequate for decision making. The decision maker would also like to know
the likelihood of such occurrences. This information can be generated by
simulation analysis which may be used for developing the probability
profile of a criterion of merit by randomly combining values of
variables which a bearing on the chosen criterion.

Procedure- The steps involved in simulation analysis are as follows:

Model the project. The model of the project shows how the net present
value is related to the parameters and the exogenous variables.
(Parameters are input variables specified by the decision maker and hold
constant over all simulation runs. Exogenous variables are input
variables which are stochastic in nature and outside the control of the
decision maker).
Specify the values of parameters and the probability distributions of
the exogenous variables.
Select a value, at random, from the probability distributions of each
of the exogenous variables.
Determine the net present value corresponding to the randomly
generated values of exogenous variables and pre-specified parameter values.
Repeat steps (3) and (4) a number of times to get a large number of
simulated net present values.
Plot the frequency distribution of the net present value.

In real life situations, simulation is done only on the computer because
of the computational tedium involved. However, to give you an idea of
what goes on in simulation, we will work with a simple example where
simulation ha been done manually. Pharma Chemicals is evaluating an
investment project whose net present value has been modelled as follows:

The firm wants to perform 10 manual simulation runs for this project. To
perform the simulation runs, we have to generate values, at random, for
the two exogenous variables: annual cash flow and project life. For this
purpose, we have to (i) set up the correspondence between the values of
exogenous variables and random numbers, and (ii) choose some random
number generating device. The table below shows the correspondence
between various variables and two digit random numbers. The table
presents a table of random digits that will be used for obtaining two
digit random numbers.

Now we are ready for simulation. In order to obtain random numbers from
the table, we may begin anywhere at random in the table and read any
pair of adjacent columns (since we are interested in a two-digit random
number) and read column-wise or row-wise.
For our example, let us use the first two columns of the table. Starting
from the top, will read down the column. For the first simulation run we
need two, two-digit random numbers, one for the annual cash flow and the
other for the project life. These
numbers are 53 and 97 and the corresponding values for annual cash flow
and project life are $3,000 and 9 years respectively. We go further in
this manner. The table shows the random numbers so obtained and the
results of simulation

Evaluation An increasingly popular tool of risk analysis, simulation
offers certain advantages:

Its principal strength lies in its versatility. It can handle
problems characterized by numerous exogenous variables following
any kind of distribution, and complex interrelationships among
parameters, exogenous variables, and endogenous variables. Such
problems often defy the capabilities of analytical methods.
It compels the decision maker to explicitly consider the
interdependencies and uncertainties characterizing the project.

Simulation, however, is a controversial tool which suffers from several
shortcomings:

It is difficult to model the project and specify the probability
distributions of exogenous variables.
Simulation is inherently imprecise. It provides a rough
approximation of the prob. ability distribution of net present value
(or any other criterion of merit). Due to imprecision, the simulated
probability distribution may be misleading when a tail the
distribution is critical.
A realistic simulation model, likely to be complex, would most
probably be constructed by a management scientist, not the decision
maker. The decision maker lacking understanding of the model, may
not use it.
To determine the net present value in a simulation run the risk-free
discount rate used. This is done to avoid prejudging risk which is
supposed to be reflected in they dispersion of the distribution of
net present value. Thus the measure of net present value takes a
meaning, very different from its usual one that is difficult to
interpret

3.4.7 Decision Tree Analysis

To analyze such situations where sequential decision making is involved
decision tree analysis is helpful.

The key steps in decision tree analysis are a follows:
Delineate the decision tree
Evaluate the alternatives
Delineate the Decision- Tree Exhibiting the anatomy of the decision
situation, the decision e shows:
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.
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 thereof, and the monetary values associated
with them.
Evaluate the Alternatives- Once the decision tree is delineated and data
about probabilities and outcomes gathered, decision alternatives may be
evaluated as follows:

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 1, 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.
Proceed backward (leftward) in the same manner, calculating the NPV
at chance points, selecting the decision alternative which has the
highest NP at various decision points, truncating inferior decision
alternatives, and assigning NPVs to decision points, till the first
decision point is reached.

Illustration
General electric have come up with an electric cycle. The firm is ready
for pilot production and test marketing. This will cost $20 million and
take few weeks. Management believes that there is a 70 percent chance
that the pilot production and test marketing will be successful. In case
of success, G.E. can build a plant costing $150 million very quickly.
The plant will generate an annual cash inflow of $30 million for 20 if
the demand is high or an annual cash inflow of $21million if the demand
is moderate. High demand has a probability of 0.6; moderate demand has a
probability 0.4. Start at the right-hand end of the tree and calculate
the NPV at chance point C, that comes first as we proceed leftward.
Advice G.E. on the best course of action

3.4.8 Corporate Risk Analysis
A project’s corporate risk is its contribution to the overall risk of
the firm. Put differently, it reflects the impact of the project on the
risk profile of the firm’s total cash flows. On a stand-alone basis a
project may be very risky hut if its returns are not highly correlated
or, even better, negatively correlated-with the returns on the other
projects its corporate risk tends to be low. Aware of the benefits of
portfolio diversification, many firms consciously pursue a strategy
diversification. Unilever Limited, for example, has a diversified
portfolio comprising, in the main, of the following businesses: soaps
and detergents, personal care products, food, and tea.

The proponents of diversification argue that it helps in reducing the
firm’s overall risk exposure. As most businesses are characterized by
cyclicality it seems desirable that there two to three different lines
of business in a firm’s portfolio. The logic of corporate
diversification for reducing risk, however, has been questioned. Why
should a firm diversify when shareholders can reduce risk through
personal diversification? All that they have to do is to hold a
diversified portfolio of securities or participate in a mutual fund
scheme. Indeed, they can do it more efficiently.

There does not seem to be an easy answer. Although shareholders can
reduce risk through personal diversification there are some other
benefits from corporate diversification. Stable earnings and cash flows
enable a firm to attract talent, to secure commitment from various
stakeholders, to exploit tax shelters fully, and to check adverse
managerial incentives.

FUNDAMENTALS OF ACCOUNTING II

DIVIDEND THEORIES AND POLICY NOTES

CAPITAL BUDGETING AND RISK- Risk Analysis NOTES

CAPITAL BUDGETING (INVESTMENT DECISIONS) NOTES

AGENCY THEORY NOTES