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Financial Management and Analysis of Projects :
7. Knowledge Management :
7.11. Undertaking Sensitivity and Risk Analyses
7.11.2. Steps 2 and 3: Calculate Effects of Changing Variables
7.11.2.1.
The values of the basic indicators of project viability (FIRR and
FNPV) should be recalculated for different values of key variables.
This is preferably done by calculating sensitivity indicators (SIs)
and switching values (SVs).
7.11.2.2. Switching Values (SVs) are
sometimes used for conducting sensitivity analysis, but their application
is not mandatory. It is the financial analyst's responsibility to
determine whether a demonstration of the impacts of switching values
would support any decisions used in their selections. The SV of
a variable is that value at which a project's FNPV becomes zero
(or the FIRR equals the discount rate). The SVs are normally given
in terms of the percentage change in the value of the variable needed
to turn a project's FNPV equal to zero. SVs are useful to determine
those variables that are most likely to affect project outcomes.
SVs of the more important (or potent) variables should be presented
in order of declining sensitivity
7.11.2.3. The meaning of these concepts
is presented in the following Box and a sample calculation immediately
follows. Sensitivity indicators and switching values can be calculated
for the FIRR and FNPV as shown below.
Using Sensitivity Indicators and Switching Values
| |
Sensitivity
Indicator |
Switching
Value |
| Definition |
1.
Towards the Net Present Value
Compares percentage change in FNPV with percentage change
in a variable or combination of variables.
2.
Towards the Internal Rate of Return
Compares percentage change in FIRR above the cut-off rate
with percentage change in a variable or combination of variables.
|
1.
Towards the Net Present Value
The percentage change in a variable or combination of variables
to reduce the FNPV to zero (0).
2.
Towards the Internal Rate of Return
The percentage change in a variable or combination of variables
to reduce the FIRR to the cut-off rate (=discount rate).
|
| Expression |
1.
Towards the Net Present Value
| SI
= |
(FNPVb-
FNPV1) / FNPVb |
|
|
|
(Xb
- X1 ) / Xb |
where:
Xb - value of variable in the base case
X1 - value of the variable in the sensitivity test
FNPVb - value of FNPV in the base case
FNPV1 - value of the variable in the sensitivity
test
2.
Towards the Internal Rate of Return
| SI
= |
(
FIRRb - FIRR1 ) / ( FIRRb
- d ) |
|
|
|
(
Xb - X1 ) / Xb |
where:
Xb - value of variable in the base case
X1 - value of the variable in the sensitivity test
FIRRb - value of IRR in the base case
FIRR1 - value of the variable in the sensitivity
test
d - discount rate |
1.
Towards the Net Present Value
|
SV
=
|
(
100 x FNPVb ) |
X
|
(
Xb - X1 ) |
|
|
|
|
(
FNPVb - NPV1 ) |
Xb |
where:
Xb- value of variable in the base case
X1 - value of the variable in the sensitivity test
FNPVb - value of FNPV in the base case
FNPV1 - value of the variable in the sensitivity
test
2.
Towards the Internal Rate of Return
|
SV
= |
(100
x ( FIRRb - d )) |
X |
(
Xb - X1 ) |
|
|
|
|
(
FIRRb - FIRR1 ) |
Xb |
where:
Xb - value of variable in the base case
X1 - value of the variable in the sensitivity test
FIRRb - value of FIRR in the base case
FIRR1 - value of the variable in the sensitivity
test
d - discount rate |
| Calculation
example |
1.
Towards the Net Present Value
- Base
Case:
- Price
= Pb = 300
FNPVb = 20,912
- Scenario
1:
- P1
= 270 (10% change)
FNPV1 = 6,895
|
SI
= |
(
20,912 - 6,895 ) / 20,912 |
=
6.70 |
|
|
|
(
300 - 270 ) / 300 |
2.
Towards the Internal Rate of Return
- Base
Case:
- Price
= Pb = 300
FIRRb = 15.87%
- Scenario
1:
- P1
= 270 ( 10% change )
FIRR1 = 13.31%
d = 12%
|
SI
= |
(
0.1587 - 0.1331 ) / ( 0.1587 - 0.12 ) |
|
|
|
(
300 - 270 ) / 300 |
= 6.61 |
1.
Towards the Net Present Value
- Base
Case:
- Price
= Pb = 300
FNPVb = 20,912
- Scenario
1:
- P1
= 270 (10% change)
FNPV1 = 6,895
|
SV
= |
(
100 x 20,912 ) |
X |
(
300 - 270 ) |
=
14.9% |
|
|
|
|
(
20,912 - 6,895 ) |
300 |
2.
Towards the Internal Rate of Return
- Base
Case:
- Price
= Pb = 300
FIRRb = 15.87%
- Scenario
1:
- P1
= 270 (10% change)
FIRR1 = 13.31%
d = 12%
|
SV
= |
(
100 x ( 0.1587 - 0.12 )) |
x |
(
300 - 270 ) |
|
|
|
|
(
0.1587 - 0.1331 ) |
300 |
=
15.1% |
| Interpretation |
(i)
percentage change in FNPV respectively
(ii) percentage change in FIRR above the cut-off rate (12%)is
larger than percentage change in variable: price is a key variable
for the project.
|
A
change of approximately 15 % in the price variable is necessary
before the FNPV becomes zero or before the FIRR equals the cut-off
rate. |
| Characteristic |
Indicates
to which variables the project result is or is not sensitive.
Suggests further examination of change in variable. |
Measures
extent of change for a variable that will leave the project
decision unchanged. |
7.11.2.4. The switching value is, by definition, the reciprocal of the sensitivity
indicator. Sensitivity indicators and switching values calculated
towards the FIRR yield slightly different results if compared to
SIs and SVs calculated towards the FNPV. This is because the FIRR
approach discounts all future net benefits at the FIRR value and
the FNPV approach at the discount rate d.
Example of the Base Case for a Project
| |
PV
@12% |
1996 |
1997 |
1998 |
1999 |
2000 |
2001 |
2002 |
2003 |
2004 |
2005 |
| Benefits |
2,104 |
0 |
283 |
339 |
396 |
453 |
509 |
566 |
566 |
566 |
566 |
| Costs: |
| Investment |
1,687 |
1,889 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| Operations
and maintenance |
291 |
0 |
61 |
61 |
61 |
61 |
61 |
61 |
61 |
61 |
61 |
| Total
Costs |
1,978 |
1,889 |
61 |
61 |
61 |
61 |
61 |
61 |
61 |
61 |
61 |
| Net
Cash Flow |
126 |
-1,889 |
222 |
278 |
335 |
391 |
448 |
505 |
505 |
505 |
505 |
7.11.2.5.
In the base case, the FNPV is 126 and the FIRR is 13.7%. The sensitivity
of the base case FNPV has been analyzed for (adverse) changes in
several key variables, as follows:
- An
increase in investment cost by 10%,
- A
decrease in economic benefits by 10%,
- An
increase in costs of operation and maintenance by 10%,
- An
adverse foreign-exchange movement of 20%, and
- A
delay in the period of construction, causing a delay in revenue
generation by one year.
7.11.2.6.
Proposed changes in key variables should be well explained. The
sensitivity analysis should be based on the most likely changes.
The effects of the above changes are summarized in the following
table.
Sensitivity Analysis: A Numerical Example
| Item |
Change |
FNPV |
FIRR
% |
SI (FNPV) |
SV
(FNPV) |
| Base
Case |
|
126 |
13.7 |
|
|
| Investment |
+
10% |
-
211 |
9.6 |
13.3 |
7.5% |
| Benefits |
-
10% |
-
294 |
7.8 |
16.6 |
6.0% |
| Operating
and Maintenance Costs |
+
10% |
68 |
12.9 |
2.3 |
43.4% |
| Foreign
Exchange Movements |
-
20% |
-
294 |
7.8 |
16.6 |
6.0% |
| Construction
delays |
One
year |
-
99 |
10.8 |
NPV
178% lower |
|
| SI
= Sensitivity Indicator, SV = Switching Value |
7.11.2.7. Combinations of variables can also be considered. For example, the
effect on the FNPV or FIRR of a simultaneous decline in economic
benefits and an increase in investment cost can be computed. In
specifying the combinations to be included, the project analyst
should state the rationale for any particular combination to ensure
it is plausible.
 Back
7.11.1. Step 1: Identify the Key Variables | Next
7.11.3. Step 4: Analyze Key Variable Changes |
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