fInvestment Appraisal
underRisk & Uncertainty
1 Risk and Uncertainty
- As in investment appraisal all decision are based on forecast
and the forecast are subject to uncertainty so, while
performing calculation we should consider uncertainty.
1.1 Risk
- Variability of potential returns
- Quantifiable: that is possible outcomes have associated
probabilities.
1.2 Uncertainty
- Unquantifiable: outcomes cannot be mathematically modelled
2 Incorporating risk and uncertainty
-
Sensitivity Analysis
Probability Analysis (EV)
Simulation
Discounted payback
Risk-adjusted discount rates
2.1 Sensitivity Analysis
- “What if ?” analysis question
- How much cash inflow is allowed to decrease or cash outflow
is allowed to increase before our decision change (i.e. NPV
equal to zero)
- The lower the percentage, the more sensitive the NPV is to
that project variable, as the variable would need to change by
a smaller amount to make the project non-viable.
Formula:
Sensitivity Margin=
NPV
PV of cash flow under consideration
2.1.1 Advantage and Disadvantages of Sensitivity
Analysis
2.1.2 Advantage
- Simple
- Allows manager to take subjective judgment
- Identifies critical
estimates.
Disadvantage
- Assumes other thing remain constant when one
variablechanges
- Does not take likelihood of a variable changing.
Question 1
An investment of $40,000 today is expected to give rise to annual
contribution of $25,000. This is based on selling one product, with
a sales volume of 10,000 units, selling price of $12.50 and variable
costs per unit of $10. Annual fixed cost of $10,000 will be incurred
for the next four years. The discount rate is 10%.
Required:
(a) Calculate the NPV of this investment.
(b) Calculate the sensitivity of your calculation to the following:
(i) Initial investment
(ii) Selling price per unit
(iii) Variable cost per unit
(iv) Sales volume
(v) Fixed costs
(vi) Discount rate
3 Expected Value
-
It is the weighted average of all the possible outcomes.
Where weightings based on probability estimates
3.1 Calculating an EV
EV=∑P.X
Where,
P= Probability of an outcome
X=Value of outcome
3.1.1 Points to remember when using Expected Value
- It finds the long run average outcome if project is
done multiple times
- It is not most likely result (i.e. value obtain is not
corresponding to the data)
- Not useful for one off project. (Managers should only use EV
method is these kinds of projects have been carried out in past)
3.1.2 Strengths and Weaknesses of EVs
Strengths
Deals with multiple outcomes
Quantifies probabilities
Relatively simple calculation
Weaknesses
Subjective probabilities
Only gives long run average
Risk neutral decision(ignore risk
attitude)
Assists decision making
To use EV for decision making three condition should be fulfilled:
- Reasonable basis for making forecasts and estimating the
probability of different outcomes.
- Decision is relatively small in relation to business, so risk is
small in magnitude.
- Reoccurring decision, i.e. not one off.
Question 2
Dralin Co is considering an investment of $460,000 in a noncurrent asset expected to generate substantial cash inflows over
the next five years. Unfortunately the annual cash flows from this
investment are uncertain, but the following probability distribution
has been established:
Annual cash flow
($)
50,000
20,000
150,000
Probability
0.3
0.5
0.2
At the end of its five year life, the asset is expected to sell for
$40,000. The cost of capital is 5%.
Should the investment be undertaken?
3.2 Joint Probabilities
The probability of one thing AND another thing happening
Formula:
P(X, Y) =P(X)*P(Y)
Where,
P(X) = Probability of Event X
P(Y) = Probability of Event Y
Example 1
Probability of a business’s bank account having a positive cash flow
in month 1 is 20% AND the probability of it having a positive cash
flow in month 2 is 40%, then the joint probability of it having a
positive cash flow in both (month 1 AND month 2) can be found by
multiplying the individual probabilities together.
The probability of one thing OR another thing happening
Formula:
P(X OR Y) =P(X) + P(Y)
Where,
P(X) = Probability of Event X
P(Y) = Probability of Event Y
Example 2
The probability if a positive cash flow in either month (month one
OR month 2) for the bank account. (Probability same as example
1) calculate the probability.
Question 3- Joint Probability
A company has estimated cash flows for a project, incorporating
the probability of each present cash flow value into its estimates
as follows:
Present cash flow
$100,000
$200,000
Year 1
Probability
20%
80%
Present cash flow
$200,000
$300,000
Year 2
Probability
30%
70%
The proposed investment will cost $400,000 payable in full at the
start of the project.
Calculate the following figures:
a. The mean(Expected) present cash flow in year 1
b. The mean(Expected) present cash flow in year 2
c. The mean(Expected) NPV of the investment
d. The probability of the investment having a negative NPV
e. The probability of the investment having a $0 NPV
4 Further techniques for adjusting for risk and uncertainty
4.1 Simulation
- It is computer-based method of evaluating an investment
project whereby the probability distribution associated with
individual project variables and interdependencies between
project variables are incorporated (multiple variable at a time)
- Radom numbers are assigned to a range of different values of
project variable to reflect its probability distribution
- Each simulation run randomly selects values of project
variables using random numbers and calculates a mean
(expected) NPV
- A picture of the probability distribution of the mean
(expected) NPV is built up from the results of repeated
simulation runs.
- The project risk can be assessed from the probability
distribution as the standard deviation of the expected returns,
together with the most likely outcome and the probability of
a negative NPV
Advantage of simulation
- It includes probabilities and incorporate multiply variable at
a time
- Wide variety of applications (Inventory control, component
replacement, corporate models etc.)
Disadvantage of simulation
- Complex to calculate, does not take account of likelihood of
variable changing.
- Probability distributions may be difficult to formulate.
4.2 Adjusted Payback
- If risk and uncertainty are considered to be same, payback
can be used to adjust for risk and uncertainty in investment
appraisal
- As uncertainty (risk) increases, the payback period can be
shortened to increase the emphasis on cash flows that are
nearer to the present time and hence less uncertain and vice
versa
4.2.1 Discounted Payback
- Discounted payback adjusts for risk in investments appraisal
in that risk is reflected by the discount rate employed
- Discounted payback can therefore be seen as an adjusted
payback method
Question 4
A project with the following cash flows is under consideration:
To
(20,000)
T1
8,000
T2
12,000
T3
4,000
Cost of Capital 8%
Required:
Calculate the Discounted Payback Period.
T4
2,000
4.3 Risk-adjusted discount rates
- The risk associated with an investment project can be
incorporated into the discount rate as a risk premium over the
risk free rate of return
- The risk premium can be determined on a subjective basis,
for example launching a new project is risker than expansion
of existing operations
- Risk premium can be determined theoretically by using capital
asset pricing model in an investment appraisal context, by
ungearing proxy equity beta and re-gearing it