2. Risk and
Uncertainty
Investment decisions are based on
predictions of what will happen in
the future and therefore involve
an element of unpredictability
This unpredictability could be
described as risk or uncertainty.
3. Risk
ARISES WHERE THERE ARE SEVERAL
POSSIBLE OUTCOMES AND, BASED ON PAST
RELEVANT EXPERIENCE, PROBABILITIES CAN
BE ASSIGNED TO THE POSSIBLE OUTCOMES
RISK INCREASES AS THE VARIABILITY OF A
PROJECT’S CASH FLOW INCREASES
RISK CAN BE QUANTIFIED AND BUILT INTO A
NET PRESENT VALUE (NPV)
4. Uncertainty
Uncertainty cannot be quantified but it can be
described/analysed
The uncertainty of a project cash flows increases as
the length of a project rises, since cash flows in the
distant future are less certain than cash flows in
the short-term
Arises where there are several possible outcomes
and no information (eg experience) upon which to
create probabilities so the degree of uncertainty
cannot be quantified
5. There are a
number of
techniques
for
quantifying
the risk of a
project’s
cash flows
Risk Analysis
6. Risk Analysis Technique
PROBABILITY ANALYSIS AND EXPECTED VALUES – A
PROBABILITY ANALYSIS OF EXPECTED CASH FLOWS
CAN OFTEN BE ESTIMATED (FOR EXAMPLE USING PAST
EXPERIENCE OF SIMILAR PROJECTS) )AND USED BOTH
TO CALCULATE AN EXPECTED NPV AND TO MEASURE
RISK
EXPECTED VALUES – AN EXPECTED VALUE IS A
WEIGHTED AVERAGE THAT IS CALCULATED USING
PROBABILITIES.
7. Example – Expected NPV
Probability Forecast Project A -NPV ($m) Project B- NPV ($m)
0.25 Low Growth 1.00 -8.00
0.50 Medium Growth 2.50 4.00
0.25 High Growth 4.00 16.00
1.00 Expected Value ? ?
H Berhad is choosing between two mutually exclusive projects. The NPV of these projects in $m depends
on the rate of growth of the economy over the next five years. Forecast NPV is shown under scenarios
of low, medium and high growth.
Required: Calculate each project’s expected NPV and consider which project would be chosen.
8. Solution – Expected NPV –
Project A
Expected Value = Probability x Project NPV for each forecast
(1 x 0.25) Low growth
+ (2.50 x 0.50) Medium growth
+ (4 x 0.25) High growth
= 2.5
9. Solution – Expected NPV –
Project B
Expected Value = Probability x Project NPV for each forecast
(-8 x 0.25) Low growth
+ (4 x 0.50) Medium growth
+ (16 x 0.25) High growth
= 4.0
10. Solution – Expected NPV
PROJECT B HAS A HIGHER EXPECTED VALUE AND
WOULD THEREFORE BE CHOSEN
HOWEVER, IF THE COMPANY IS RISK AVERSE, IT
MAY BE DETERRED FROM PROJECT B DUE TO THE
NEGATIVE NPV OF -8 DURING THE FORECAST OF
LOW GROWTH
12. • A key method of analysing the
uncertainty surrounding a capital
expenditure project and enables an
assessment to be made of how
responsive the project’s NPV is to
changes in a single variable that affects
a project’s NPV
Sensitivity Analysis
(definition)
13. Sensitivity
Analysis
A project’s NPV will depend on a number of
uncertain variables (eg selling price, sales volume,
operating costs etc)
The basic approach of sensitivity analysis is to
calculate what the value of a single variable would
have to change by, to change a project’s NPV to
zero
Provides an indication of which variables a project’s
NPV is most sensitive to
Management should review critical variables to
assess whether or not there is a strong possibility of
events occurring which will lead to negative NPV
14. Sensitivity
Analysis
…..continued
Management should also pay particular attention to
controlling those variables to which the NPV is
particularly sensitive, once the decision has been
taken to accept the investment
The formulae to calculate sensitivity analysis is as
follows:
Sensitivity % = (Project NPV / Present value (PV) of
project variable) x 100
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
15. Example – Sensitivity Analysis
K Bhd is considering a project which required an initial investment of $7 m and is expected to result in
sales of 100,000 units per year at a selling price of $65 and a variable cost per unit of $20. K Bhd has a
cost of capital of 8%.
The project has a positive NPV of $1,024,000 and therefore would appear to be worthwhile
The project’s IRR has been estimated as 18.5%.
Tax can be ignored
16. Example – Sensitivity Analysis ….continued
Year DF @ 8% PV of Initial
Investment
PV of Variable
Costs
PV of Sales PV of Net Cash
Flow
$000 $000 $000 $000
0 1.000 (7,000) (7,000)
1 0.926 (1,852) 6,019 4,167
2 0.857 (1,714) 5,671 3,857
TOTAL (3,566) 11,590
Required:
Measure the sensitivity of the project to changes in:
a. Initial investment
b. Contribution Margin = Sales revenue – variable cost
c. Selling price
d. Variable cost
17. Solution –
Sensitivity
Analysis
A. Initial investment
Sensitivity = (1,024 / 7,000) x 100 =
14.6%.
An increase in the cost of
investment of 14.6% is required for
the project NPV to fall to zero
(required investment return)
18. Solution –
Sensitivity
Analysis
A. Contribution margin
Sensitivity = [1,024 / (11,590 -
3,566)] x 100 = 12.8%.
A reduction in the contribution
margin of 12.8% is required for
the project NPV to fall to zero
(required investment return)
19. Solution –
Sensitivity
Analysis
A. Selling Price
Sensitivity = (1,024 / 11,590) x
100 = 8.8%.
A reduction in the selling price
of 8.8% is required for the
project NPV to fall to zero
(required investment return)
20. Solution –
Sensitivity
Analysis
A. Variable Costs
Sensitivity = (1,024 / 3,566) x
100 = 28.8%.
An increase in the variable cost
of 28.8% is required for the
project NPV to fall to zero
(required investment return)