Dr. M. Fouzul Kabir Khan
Professor of Economics and Finance
North South University
● Management
use of sensitivity and
breakeven analysis
● Steps in sensitivity analysis
● Developing optimistic and pessimistic
forecasts
● Steps in breakeven analysis
● The role of simulation
●
People are generally risk-averse
◦ Simply looking at the expected value of the net present
value may not be enough
Consider a choice between two prizes, you can have Tk.
100,000 for certain or a lottery ticket which will pay Tk.
200,000 with a probability of 0.5 and Tk. 0 with a probability
of 0.5, which one will you choose?
Please note that the two choices have the same expected value
●
Certainty equivalent
An amount that would be accepted in lieu of a chance to receive
a possibly higher, but uncertain, amount.
●
A graphical illustration
◦ Risk aversion: decreasing marginal utility of wealth concave
function relating wealth and utility
◦ Risk neutral: constant marginal utility of wealth
◦ Risk lover: increasing marginal utility of wealth
Utility function
Consider two projects, A and B which have the following
Payoffs
●
According to expected value criteria project A is preferred
E[UA] = 0.6*(100,0001/2)=189.7
E[UB] = 0.6*(50,0001/2)+0.4*(50,0001/2) =223.6
We can calculate the certainty equivalent of the two
projects
For project A,
For Project B,
U(CE) = 189.7 U(CE) = 223.6
CE1/2= 189.7
CE1/2= 223.6
CE = 36,000
CE = 50,000
Because project B has the greater certainty equivalent, it is
the preferable project
If people are risk neutral, then expected net present value will
give the right answer
●
●
●
●
Analyzing project risks by making mechanical trial
and error changes to forecast values of selected
variables.
Analyzing the risks of investment projects, by
changing the values of forecasted variables.
Finding the values of particular variables which give
the project a Breakeven NPV of zero.
Identification of those variables which will have
significant impacts on the NPV, if their future
values vary around the forecast values.
● The variables having significant impacts on the NPV
are known as ‘sensitive variables’.
● The variables are ranked in the order of their
monetary impact on the NPV.
● The most sensitive variables are further
investigated by management.
●
Using Sensitivity:
Sensitive variables are investigated and managed
in two ways:
●
•
(1) Ex ante; in the planning phase; more effort is used
to create better forecasts of future values. If
management decides the project is too risky, it is
abandoned at this stage.
(2) Ex post; in the project execution phase;
management monitors the forecasted values. If the
project is performing poorly, it is abandoned or sold off
prior to its planned termination.
Using Breakeven:
•
Forecasted calculated Breakeven values of variables
are continuously compared against actual
outcomes during the execution phase.
Sensitivity and Breakeven analyses are also known
as: ‘scenario analysis’, and ‘what-if analysis’.
● Point values of forecasts are known as: ‘optimistic’,
‘most likely’, and ‘pessimistic’.
● Respective calculated NPVs are known as: ‘best
case’, ‘base case’ and ‘worst case’.
● Variables giving a ‘breakeven’ value, return an NPV
of zero for the project.
●
●
Calculate the project’s NPV using the most likely value
estimated for each variable.
●
Select from the set of uncertain variables those which
the management feels may have an important bearing
on predicted project performance.
●
Forecast pessimistic, most likely, and optimistic values
for each of these variables over the life of the project.
●
Recalculate the project’s NPV for each of these three
levels of each variable. While each particular variable is
stepped through each of its three values, all other
variables are held at their most likely values.
●
Calculate the change in NPV for the pessimistic to
optimistic range of each variable.
●
Identify sensitive variables.
Important: Selection of appropriate variables, and
establishing valid upper and lower forecast values.
●
Degree of management control.
●
Management's confidence in the forecasts.
●
Amount of management experience in assessing
projects.
●
Extrinsic variables more problematic than intrinsic
variables.
●
Time and cost of analysis.
●
Large blowouts in initial construction costs for
Sydney Opera House, Montreal Olympic Stadium.
●
Big budget films are shunned by critics and public
alike; e.g ‘Waterworld’: whilst cheap films become
classics; eg.‘Easy Rider’.
●
High failure rate of rockets used to launch
commercial satellites.
a)
Use forecasting –error information from the
forecasting methods: e.g. - upper and lower
bounds; prediction interval; expert opinion;
physical constraints, are applied to the
variables.
This method is formalized, but arguable,
slow and expensive.
b)
Use ad hoc percentage changes: a fixed
percentage, such as 20%,or 30%, is added to and
subtracted from the most likely forecast value.
This method is vague and informal, but fast,
popular, and cheap.
+20%
?
-20%
●
●
Sensitivity analysis
◦ Partial sensitivity analysis
◦ Worst and best-case analysis
◦ Monte-carlo analysis
According to bridge supporters, the salvage value after 30
years will be $50 million. According to ferry supporters, the
bridge will have zero salvage value after 30 years
●
Carry out sensitivity analysis changing
◦ salvage value,e.g. plugging the bridge supporters
salvage value in ferry supporters profile
◦ the discount rate
◦ the construction costs
◦ annual benefit

Workbook8.1.xls
Project NPV
Thousands
Project NPV Versus Unit Selling Price
3500
3000
2500
2000
1500
1000
500
0
-5000.00
0.50
1.00
-1000
-1500
Unit Selling Price
1.50
Unit Price
Project NPV
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
-1,089,246
-760,522
-431,798
-152,699
78,041
308,148
538,254
768,361
1,228,575
1,458,682
1,688,789
1,918,895
2,149,002
2,379,109
2,609,216
2,839,323
Reqd Rate % Project NPV
Project NPV Versus Required Rate of
Return
Thousands
$1,166,326
$1,049,852
$941,407
$840,352
$746,103
$658,130
$575,947
$499,112
$427,220
$359,900
$296,814
$237,652
$182,127
$129,978
$80,964
$34,865
-$8,523
-$49,388
-$87,902
NPV in Dollars
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1,500
1,000
500
0
10
20
30
-500
Required Rate of Return
40
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
1,100,281
1,054,273
1,008,264
962,256
916,248
870,240
824,231
778,223
732,215
686,207
640,198
594,190
548,182
Project NPV Versus Unit Production Cost
Thousands
Project NPV
Project NPV
Unit Cost
1,200
1,000
800
600
400
200
0
0.00
0.05
0.10
0.15
0.20
Unit Production Cost: Dollars
0.25
Each forecast value is entered into the model, and
one solution is given.
● Solutions can be summarized automatically, or
individually by hand.
● Variables are ranked in order of the monetary
range of calculated NPVs.
● Management investigates the sensitive variables.
● More forecasting is done, or the project is accepted
or rejected as is.
●
Strengths:
◦ Easy to understand.
◦ Forces planning discipline.
◦ Helps to highlight risky variables.
◦ Relatively cheap.
● Weaknesses
◦ Relatively unsophisticated.
◦ May not capture all information.
◦ Limited to one variable at a time.
◦ Ignores interdependencies.
●
●
Project risk analysis by simultaneous adjustment of
forecast values.
●
Simulation allows the repeated solution of an evaluation
model.
●
Each solution randomly selects values from
predetermined probability distributions.
●
All solutions are summarized into an overall distribution
of NPV values.
●
This distribution shows management how risky the
project is.
●
The treatment of risk by using simulation is known as
‘stochastic’ modeling.
●
Other names for our term ‘Simulation’, are - ‘Risk
Analysis’, ‘Venture Analysis’,’Risk Simulation’, ‘Monte
Carlo Simulation’.
●
The name ‘Monte Carlo Simulation’ helps visualization
of repeated spins of the roulette wheel, creating the
selected values.
●
Each execution of the model is known as a ‘replication’
or ‘iteration’.
●
●
●
●
●
Follows the initial creation and basic testing of the
representative model.
Is sometimes used as a test of the model.
Emphasizes the need for formal forecasting, and
requires close specification of the forecast variables.
Draws managements attention to the inherent risk in
any project.
Focuses attention on accurate model building.
 Uniform: upper and lower bounds
required.
 Triangular: pessimistic, most likely,
and optimistic values required
 Normal: mean and variance required.
 Exponential: initial value and growth
factor required.




A value of a variable is selected from its
distribution using a random number
generator.
For example: Sales 90 units; selling price per
unit $2,350; component cost per unit
$1,100; labor cost per unit $280.
These values are incorporated into the
model, and an NPV is calculated for this
replication.
The NPV for this replication is stored, and
later reported as one of many in an overall
NPV distribution.
●
Each replication is unique.
●
Selection of values from the distribution is made
according to the particular distributions
●
The automated process is driven by a random number
generator.
●
Excel add-ons such as ‘@Risk’ and ‘Insight’ can be used
to streamline the process.
●
About 500 replications should give a good picture of
the project’s risk.
●
●
●
Management can view the risk of the project.
Probability of generating an NPV between two given
values can be calculated.
Probability of loss is the area to the left of a zero
NPV.
●
Benefits
◦ Focuses on a detailed definition and analysis of risk.
◦ Sophisticated analysis clearly portrays the risk of a project
◦ Gives the probability of a loss making project
◦ Allows simultaneous analysis of variables
●
Costs
◦ Requires a significant forecasting effort.
◦ Can be difficult to set up for computation.
◦ Output can be difficult to interpret.

Base case


NPV 10.26mn kina, EIRR 16.14%
Scenario analysis, with 10 percent import tariff and
zero percent export tax
NPV 13.85mn kina, EIRR 17.2% (with private sector
jobs, new business, and tourism benefits)
 NPV 1.4mn kina, EIRR 12.6% (without private sector
jobs, new business, and tourism benefits)

Trade transaction cost rate
Reduction in TTC benefits (%)
0
-10
-15
-20
-25
-30
-35
-40
ENPV
10.26
7.06
5.46
3.86
2.26
0.66
(0.94)
(2.53)
EIRR
16.14%
14.89%
14.25%
13.60%
12.93%
12.25%
11.55%
10.83%
Capital costs
Increase in capital costs (%)
0
10
15
20
25
30
35
40
ENPV
10.26
7.06
5.46
3.86
2.26
0.66
(0.94)
(2.53)
EIRR
16.14%
14.63%
13.96%
13.34%
12.76%
12.22%
11.71%
11.22%
Sensitivity Test
Base case
Reduce benefits by 15%
Increase costs by 15%
Increase costs by 15% and reduce benefits by 15%
EIRR (%) NPV (k mn) Switching value
16.14%
13.31%
13.69%
11.13%
10.26
3.17
4.71
(2.37)
21.72%
27.75%

Monte Carlo simulation conducted using four
variables, which are:
◦
◦
◦
◦
Reduction in trade transaction costs
Capital costs
Import tariff
Benefits from social development program
Reduction in trade transaction cost
Type of Distribution
Import tariff
Type of Distribution
BetaPERT*
BetaPERT*
Lowest Value
0%
Lowest Value
0%
Highest Value
40%
Highest Value
32%
Most Likely Value
12%
Most Likely Value
20%
Capital cost
Type of Distribution
Mean (k mn)
Standard Deviation
Interpretation
Normal
81.96
4.01
69% probability of cost within K77.95mn – K85.97mn
95% probability of cost within K69.94mn – K89.98mn
99% probability of cost within K65.95mn – K103.99mn
Benefits from social development program
Type of Distribution
Normal
Mean in year 1(k mn)
0.27
Standard Deviation
0.07
Interpretation
69% probability of benefit within K0.20mn – K0.34mn
95% probability of benefit within K0.13mn – K0.41mn
99% probability of benefit within K0.06mn – K0.48mn
* The betaPERT distribution is derived from the beta distribution and is commonly used in project risk analysis.
It is also sometimes used as a "smoother" alternative to the triangular distribution. It is a continuous probability
distribution. The parameters for the betaPERT distribution are minimum, likeliest, and maximum. When the
sample size is high, the difference between the normal distribution and BetaPERT distribution is the kurtosis.






NPV varies from –K29.78mn to K83.69mn.
Probability of NPV being positive is 72.02% and
negative is 17.98%.
Mean NPV is K12.57mn and median NPV is
K10.58mn. Both are higher than the base case.
It shows that, the base was rather conservative.
The probability of a ‘conservative’ base case
delivering positive NPV is very high, meaning
that the project is fundamentally sound.
The project is highly influenced by the changes
in reduction in trade transaction cost.