It is about the risk analysis of project in terms of economic way.

1. ENGINEERING ECONOMICS
Chapter 8
Project Risk Analysis
8.1 Sensitivity Analysis
8.2 Breakeven Analysis
8.3 Probability Concepts
8.4 Probability Distribution on Excel
Er. Rajesh Bhattarai
Paschimanchal Campus
Ashad 18, 2078
Class No. 20

2. Project Risk
Cash flows are the outcome of several variables
such as prices, exchange rates, costs, wages etc.
Hence, forecasts of cash flows are subject to a
degree of uncertainty.
We can use the term risk in describing an
investment whose cash flows are not known in
advance with absolute certainty, but for which an
array of alternative outcomes and their
probabilities are known.
If there is greater variability, then the risk is higher
and if there is lower variability, then risk is lower.
We use the term project risk to refer to the
variability in a project's NPV.

3. 1. Sensitivity Analysis
It shows how an output variable changes with changes
in the input variable when other input variables are
taken as constant.
It is a means of identifying the project variables, which
when varied, have the greatest effect on project
acceptability.
One of the best ways to show the results of sensitivity
analysis is to plot sensitivity graphs and find out which
input variables affect the output variable most and
monitor the most sensitive input variable.
PW=-I+ A(P/A , I, N)+ S(P/F,I,N)+………
Only One variables changes with in diff. range

5. Example
A proposal is described by the following estimates. I= Rs. 20,000 , SV=0, N=5 Years and
net annual receipt = Rs. 7000. A return of 10% is desired on such proposals. Construct
a sensitivity graph of the life, annual receipts and rate of return for deviations over a
range of ± 20%. To which elements is the decision most sensitive.
Solution: We have given
Initial Investment I = Rs. 20000
Salvage Value S=0
Useful life=n=5 Years
Net annual receipt=Rs.7000

6. 6
2. Breakeven Analysis
Breakeven analysis are useful when one
must make a decision between alternatives
that are highly sensitive to a parameter
which is difficult to estimate. Through
breakeven analysis , one can solve for the
value of that parameter at which the
conclusion is a standoff. That value is
known as breakeven point.

7. Ex. Breakeven Analysis
Suppose that there are two alternative electric motor that provide
100 HP output. An alpha motor can be purchased for NRs. 125,000
and has an efficiency of 74%, an estimated life of 10 Years, and
estimated maintenance cost of Rs. 5000 per year. A beta motor will
cost NRs. 160000 and has an efficiency of 92%, a life of 10 Years
and annual maintenance costs of NRs. 2500. Annual taxes and
insurance costs either motor will be 1.5% of the investment. If the
minimum attractive rate of return is 12% , how many hours per
year would the motors have to be operated at full load for the
annual cost to be equal? Assume that salvage values for both are
negligible and that electricity cost of NRs. 5 Per Kilowatt hour.
Recommend the motor which is more economical for higher hour
operation.

8. Given Data
Description Motor A Motor B
Investment (125,000) (160,000)
Efficiency 74% 92%
Life 10 Yrs. 10 Yrs.
Maintenance
Cost/Yr.
5,000 2,500
Annual Tax and
insurance
1.5% of
Investment=1,875
1.5% of
Investment=2,400
Electricity Rate 5 Per Kilowatt hour 5 Per Kilowatt hour
Power 100 HP 100 HP
Use MARR 12% 12%

9. Solution: Let us consider the number of hours operation per
year= x
For Motor A For Motor B
Operating Expenses for Power
=Input * Rate * Hour
=(Output/Efficiency) * Rate * Hour
=((100/0.74)*0.746))*5*x =((100/0.92)*0.746))*5*x
=504.05 x =405.43 x
Annual Equivalent Cost (AW)
AWA=125,000 (A/P,12%,10) + 5,000 + 1,875
+504.05x
=29000+504.05x ---------------(1)
AWB=160,000 (A/P,12%,10) + 2,500 +
2,400 +405.43x
=33,220+405.43x---------------(2)
At Breakeven Point , AWA= AWB
29000+504.05x=33,220+405.43x
X=42.80 Hours/Year
Therefore 42.8 Hours/year would the motors have to be operated at fulload for anuual
costs to be equal.
If x= 50 Hours
AWA=29000+504.05*50=54,202.50
AWB=33,220+405.43*50=53,491.50
Conclusion : Cost of AWA ‹AWB
Therefore Motor B is selected

10. . A
If x= 50 Hours
AWA=29000+504.05*50=54,202.50
AWB=33,220+405.43*50=53,491.50
B
Total
Cost
50573.34
29000
33220
Equal Cost at= 42.8Hours

11. Exercise 2076
A plant engineer wishes to know which of two types of lightbulbs
should be used to light a warehouse. The bulbs that are currently
used cost $45.90 per bulb and last 14,600 hours before burning
out. The new bulb (at $60 per bulb) provides the same amount of
light and consumes the same amount of energy, but lasts twice as
long. The labor cost to change a bulb is $16.00. The lights are on
19 hours a day, 365 days a year. If the firm’s MARR is 15%,
what is the maximum price (per bulb) the engineer should be
willing to pay to switch to the new bulb?

12. Solution: Useful life of the old bulb:
Service hour in year =365*19=6935
Service year = 14,600/6935=2.10
For computational simplicity, let’s assume the useful life of 2
years for the old bulb. Then, the new bulb will last 4 years. Let X
denote the price for the new light bulb. With an analysis period of
4 years, we can compute the equivalent present worth cost for
each option as follows:
PW(15%)old =PW(15%)new
PW(15%)old= [45.90+45.90(P/F,15%,2)]
PW(15%)new = [X+16]
The break-even price for the new bulb will be
[45.90+45.90(P/F,15%,2)]= [X+16]
80.60=X+16
X=64.60
∴ Since the new light bulb costs only $60, so it is better to switch
to new.

13. 13
3. Scenario Analysis
Both the sensitivity and breakeven analyses have limitations, they
cannot give the right relations, when input variables are
interdependent.
A scenario analysis shows the sensitivity of NPV with regard to
changes in important variables to the range of likely values of the
input variables.
Scenario analysis is the process of estimating the expected value of
a portfolio after a given period of time, assuming specific changes in
the values of the portfolio's securities or key factors take place, such
as a change in the variable cost.
The decision-maker can have the worst case scenario, most likely
scenario, and the best case scenario.
Then these scenarios are compared to the base case value of NPV.
Best Scenario: High Demand, High S.P., Low V.C & so on
Normal Scenario: Average Demand, Average S.P., Average V..C & so
on
Worst Scenario: Low Demand, Low S.P., High V.C & so on

14. Example
14
Scenario analysis is commonly used to estimate changes to a portfolio's value in
response to an unfavorable event and may be used to examine a theoretical worst-
case scenario.
Scenario analysis is the process of estimating the expected value of a portfolio after a
given change in the values of key factors take place.
Both likely scenarios and unlikely worst-case events can be tested in this fashion—
often relying on computer simulations.
Scenario analysis can apply to investment strategy as well as corporate finance.

15. Ex. From the information given below calculate the NPV for each
scenario use MARR=20%
Description Scenario 1 Scenario 2 Scenario 3
Initial Investment (Rs.) 400 400 400
Unit selling Price Rs. 50 30 80
Demand Units 40 80 20
V.C (Rs./Unit) 24 24 24
F.C. 100 100 100
Depreciation 40 40 40
Tax% 35% 35% 35%
Project Life (N) 20 20 20

16. Solution
Description Scenario 1 Scenario 2 Scenario 3
Initial Investment (Rs.) 400 400 400
Unit selling Price Rs. 50 30 80
Demand Units
Sales (Revenue)
40
40*50=2000
80
30*80=2400
20
20*80=1600
V.C (Rs./Unit)
Total V.C.
24
24*40=960
24
24*80=1920
24
24*20=480
F.C. 100 100 100
Depreciation 40 40 40
Pre Tax Profit 2000-960-100-
40=900
2400-1920-
100-40=340
1600-480-100-
40=980
Tax% @35% 900@35%=315 119 343
Profit after tax (Net Income) 900-315=585 340-119=221 900-343=637
Net Cash flow 585+40=625 261 677
Project Life (N) 20 20 20
PW NPV=-400+
625(P/A, 20% ,20)
=2643.12
NPV=-400+
261(P/A, 20%
,20) =870.80
NPV=-400+
677(P/A, 20% ,20)
=2896.31 (Good)

17. 8.3 Probability Concepts
The use of probability information can provide management with a range of
possible and the likelihood of achieving different goals under each investment
alternatives.
A probability distribution refers to a statistical function defining all the
possible values and probabilities that a random variables will take within a
given range. This range is bounded between the minimum and maximum
possible values.
Still, it depends on a variety of variables precisely where the potential value is
likely to be calculated from the probability distribution.
These variables include the mean (average) distribution, standard deviation etc.
Probability distributions can also be applied to construct cumulative
distribution functions (CDFs), taking the cumulative probability of
occurrences, always beginning at zero and ending at 100%

18. A conditional probability describes the probability of
an event A given that another event B has already
occurred.
P(A/B)= P(AՈB)/P(B)
Joint Probability
.

19. Conditional Joint
Assessments of Conditional and joint Probabilities

20. This marginal distribution tells us that 52% of the time
we can expect to have a demand of 2,000 units and 18%
and 30% of the time we can expect to have a demand of
1,600 and 2,400, respectively

21. Final Output of Probability Concept
Expected NPV & Expected Variance
Expected net present value is a project evaluation technique which adjusts for
uncertainty by calculating net present values under different scenarios and
probability-weighting them to get the most likely NPV.
For example, instead of relying on a single NPV, companies calculate NPVs
under a range of scenarios: say, base case, worst case and best case, estimate
probability of occurrence of each scenario, and weighs the NPVs calculated
according to their relative probabilities to find the expected NPV.
Expected NPV is a more reliable estimate than the traditional NPV because it
considers the uncertainty inherent in projecting future scenarios.
Expected NPV is the sum of the product of NPVs under different scenario and
their relevant probabilities. The following formula is used to calculate expected
NPV.
Expected NPV = Σ (p × Scenario NPV)
Scenario NPV is the NPV under a specific scenario while p stands for the
probability of occurrence of each scenario.

22. Ex. A corporation is trying to decide whether to buy the patent for a product designed
by another company. The decision to buy will mean an investment of $8 million,
and the demand for the product is not known. If demand is light, the company expects
a return of $1.3 million each year for three years. If demand is moderate, the
return will be $2.5 million each year for four years, and high demand means a return
of $4 million each year for four years. It is estimated the probability of a high
demand is 0.4 and the probability of a light demand is 0.2. The firm’s (risk-free)
interest rate is 12%. Calculate the expected present worth of the patent. On this basis,
should the company make the investment? (All figures represent after-tax values.)
I= -8,000,000 , i=12%
PW (12%)light =-8,000,000+$1,300,000(P/A,12%,3)=-$4,800,000
PW(12%)moderate=$8,000,000+$2,500,000(P/A,12%,4)=-$406,627
PW(12%)high=-$8,000,000+$4,000,000(P/A,12%,4)= $4,149,000
E[PW(12%)]=-$4,800,000*0.20 +(−$406,627*0.40)+ $4,149,000*(0.40) =$536,947
∴ Since E(PW) is positive, it is good to invest.
Expected Variance?

23. 23
Risk Analysis (Risk Simulation)
Risk simulation, in general, is the process of modeling
reality to observe and weigh the likelihood of possible
outcomes of a risky undertaking.
Monte Carlo simulations are used to model the probability of
different outcomes in a process that cannot easily be
predicted due to the intervention of random variables. It is a
technique used to understand the impact of risk and
uncertainty in prediction and forecasting models.
Monte Carlo Simulation is specific type of randomized
sampling method in which a random sample of outcomes is
generated for specified probability distributions of values of
random input variables.

24. Steps of Simulation
1.Establishing Probability distribution
2.Cumulative Probability
3.Setting Random number intervals
4.Generating Random numbers
5.To find the answer of question asked using the
above four steps So many Scenario

25. Simulation output analysis
Through the descriptive statistics and histogram of the values of the output
variable, we can determine and analyze the probability distribution of the
output variable such as net profit, NPV, IRR etc.
Simulation is the process of designing a model of a real system and
conducting experiments with the model for the purpose of understanding the
behavior for the operation of the system.
 A duplication of the original system
 To understand the implementation of the system
Use
As per different business situation
For inventory control
For financial decision etc
25

26. 22
A logical sequence of Monte Carlo simulation

27. Logical steps involved in simulating a risky investment
27

28. Best of Luck
Thank You