stand alone risk and portfolio risk
• A project’s stand-alone risk reflects uncertainty
about its cash flows.
• all the inputs are expected values, and actual
values can vary from expected values.
• techniques are used to assess stand-alone risk: (1)
sensitivity analysis,(2) scenario analysis, and (3)
Monte Carlo simulation, (4) Hillier model (5) RADR
(6) CEC, (7) Decision tree analysis
•
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI




estimated initial cash outflows and future cash
inflows are bound to deviate
The deviation could be due to PEST
The variables may change
 Initial capital investment, sales volume, sales
price, variable cost, fixed cost, tax rate etc can
change
Sensitivity analysis is a technique for
determining what would happen to NPV
estimate if the predicted value of one variable
proves to be wrong.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI




The sensitivity analysis is to freeze all the variables
except one and then see how sensitive our
estimate of NPV is to change in that one variable.
The sensitivity analysis helps to identify which
variable needs or deserves more attention.
When senior managers review capital budgeting
studies, they are interested in the base-case NPV,
but they always go on to ask the financial analyst a
series of “what if” questions: What if unit sales
turn out to be 25% below the base-case level?
The sensitivity analysis is called “What – if”
analysis.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI




if sensitivity ratio of NPV to sales revenue is 2.50,
then one rupee increase in sales revenue makes
Rs.2.50 increase in NPV.
Decrease in sales revenue by one rupee makes
decrease in NPV by Rs.2.50
NPV to sales revenue change is more sensible
(more levered). Small change in sales revenue
makes more change in NPV.
The relationship of sales volume and sale price
with NPV are positive. Unlike that the
relationships of initial investment, variable costs,
fixed costs and tax rate with NPV are inverse.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


Sensitivity analysis measures the percentage
change in NPV that results from a given
Percentage change in an input, other variables
held at their expected values.
It begins with a base-case situation, where the
project’s NPV is found using the base-case
value for each input variable.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Nepal Bulb Factory observes high potentiality in
introducing a new bulb in the market.
The factory identified the different variables that
have bearing on the NPV of the investment in the
new product. The initial investment estimated in a
new plant that runs for 5 years is Rs.500,000.
The bulbs to be produced and sold each year are
10,000. The expected sales price per bulb is Rs.50.
The variable cost per bulb is Rs.20. The estimated
annual fixed cash cost is Rs.120,000. The corporate
tax rate of the government is 40 %.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
The required return on capital is 10 %. The
factory made optimistic sales price estimation
of Rs.55 per bulb and pessimistic sales price
estimation of Rs.48 per bulb.
Required:(a)Base-case NPV(b)NPV of optimistic
sales price estimation and percentage increase
in NPV(c)The sensitivity of sales price
deviation to NPV(d)
NPV of pessimistic
sales price estimation
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI



Scenario analysis is a technique for
determining what would happen to base-case
NPV estimate if the predicted value of more
than one variable proves to be wrong.
the financial analysis of change in the value of
more than one variable is called scenario
analysis.
The upper and lower limits of values of
different variables are taken as the highest and
lowest ranges beyond which the values would
not cross.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Pinky Company made estimations for its new
product needed to be launched in the market.
Selling price per unit is Rs.600
Variable costsper unit is Rs.400
Yearly fixed cash cost is Rs.500,000
Net working capital requirement is Rs.400,000
Sales quantity for a year is 50,000 units
The company feels that its estimates would
range within 5 percent.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Required:
(a) The lower bound and upper bound statement
(b) The worst case, the base-case and the best case
estimates statement
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

A 4-year project will costs Rs.1,600,000 for
commissioning of plant. The depreciation
applicable is straight-line to zero.
The sales will be 20,000 units per year, price per
unit will be Rs.200, variable costs will be Rs.140
and cash fixed costs will be Rs.200.000.
The required rate of return on the project is 16
percent and the relevant tax rate is 30 percent.
The project’s cost, units sales, sales price,
variable costs and fixed costs projections made
are probably be accurate to within 5 percent.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Required:
(a) The lower and upper bounds of the projections
(b) The worst-case and best-case scenarios
(c) The base-case NPV, the worst-case NPV
and the best-case NPV
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


Probability distribution is made to each
variable whose value is expected to change in
future.
Monte Carlo Simulation analysis
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Alpine Company is planning to make
investment in a project that requires immediate
cash outlay of Rs.30,000. The project has an
estimated life of three years. The risk-free cost
of capital is 6 percent. The operating cash flows
and their probabilities are as follows:
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
The operating cash flows of the succeeding years
are not conditional to the operating cash flow of
the immediate earlier year.
 The company’s management feels it appropriate to
apply three simulation runs to identify the
operating cash flows of year 1, year 2 and year 3 by
reading the column random numbers given below:
Random numbers:
68, 20, 55
35, 50, 28
25, 05, 60

C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Required:
NPV for three simulation runs and comment on
the riskiness of the investment project
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


Decision tree analysis is an evaluation
technique that offers NPV result of capital
investment project having first year’s initial
cash inflows and succeeding year’s conditional
cash inflows estimates.
Probabilities distributions are made to the first
year’s cash inflows and the succeeding year’s
conditional cash inflows.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The investment proposal requiring Rs.180,000
initial cash outlay is expected to run for 2 years.
The OCF predicted for year 1 and year 2 are as
follows:
OCF1 = Rs.90,000
chance 0.40
Chances
OCF2
Rs.80,00
0
Rs.100,0
00
0.5
0.5
Rs.100,000 chance
0.60
OCF2
Chances
Rs.110,0
00
Rs.120,0
00
0.55
0.45
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The risk free rate of return is 12 %
Required:(a) Joint probability
(b)Decision tree analysis demonstration
(c)NPV
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Two way power calculators are ready for trial
production that costs Rs.15 million. The trial
production will take two months only. The
production manager predicts that the chance of
success is 80 percent. The factory will buy a
plant that costs Rs.120 million upon success of
the scheme. The plant is expected to generate
an annual cash inflow of Rs.20 million for 20
years if the demand remains high or an annual
cash inflow of Rs.18 million if the demand
remains low. High demand has probability of
0.75 and low demand has probability of 0.25.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The risk free rate of return is 10 %
Required:
(a)Expected net present value by
demonstrating decision tree analysis
(b)Comment on the desirability of the
investment scheme
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


Investments in projects are analyzed on the
hypothesis that a firm will operate assets for
their full physical lives.
However, such action may not be the best
course of action in all the situations.
Sometimes, the predicted situations may not
prevail during the project period. In such
adverse (bad) situation, it may be better to
abandon (terminate) the operating project
before the maturity of its potential life.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI



It means shut down / close the potential
project before its maturity.
The project should be terminated if the
abandonment value exceeds the present value
of the cash flows beyond the abandonment
year.
Such action may increase the project’s expected
profit and lower risk.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

A spring water treatment undertaking made
projection of conditional net after-tax cash
flows for its new unit of water treatment plant
at Shivapuri site.
The new unit has 40 % chance of generating
after-tax OCF of Rs.90,000 in year 1, Rs.100,000
in year 2 and Rs.120,000 in year 3.
Likewise, the unit expects 50 % chance of
realizing Rs.50,000 after-tax OCF in year 1,
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Rs.70,000 in year 2 and Rs.100,000 in year 3.
But, if the situation becomes unfavourable,
there is 10 % chance that the unit will suffer net
loss of Rs.20,000 in year 1, Rs.25,000 in year 2
and earn net profit of Rs.20,000 in year 3
The water treatment unit at Shivapuri can be
abandoned after 2 years of execution at a net
after-tax cash value of Rs.15,000 after
adjustment of the year’s loss if the unit suffers
loss.The prevailing rate on investment is 14 %.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Required:
Demonstrate decision tree and
ascertain NPV without abandonment option
and with abandonment option.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The cash outlay and expected net after tax cash
inflows of a proposed brand of Mike
Corporation are given below:
Cash Probabilit
outlay
y
$26,000

25%
50%
25%
Project periods
1
2
3
4
$33,810 $45,629 $59,997 $95,600
$6,702 $7,149 $6,733 $23,116
($9,390) ($7,356) ($6,660) $10,501
The expected cash flows for each scenario are
discounted at 12 percent cost of capital.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
The project after 2-year of operation can be
abandoned for $18,244 net cash inflow if things
go badly into loss
 Required:
(a) Develop a decision tree and NPV
(b) Develop a decision tree and NPV if the firm
has the option to abandon the project after 2year of operation for $18,244 net cash inflow if
things go badly into loss
(c) Decision about the action to be chosen
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI





Method for incorporating risk into the capital
budgeting decision
The amount of risk inherent in the project is
incorporated in the discount rate employed in
the present value calculations
Risky projects will have higher discount rate
Safer projects will have low discount rate
Risk adjusted discount rate is that discount rate
that combines time as well as risk preference of
the investors
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI




Risk Adjusted Discount Rate (RADR) = Risk
Free rate + Risk Premium
Under CAPM, RADR = Rf + (Rm – Rf)β
Calculate the NPV using the risk adjusted rate
In case of IRR compare the IRR with risk
adjusted rate
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


Difficulties as to how to express precisely
higher risk in terms of higher discount rate
Adding risk premium to the discount rate leads
to the compounding of the risk over time
does not consider the probability distribution
of the cash flow
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The cash flows of project X are given below
Year
0
1
2
3
Cash flow
-100000
50000
60000
40000
Risk free rate of return = 6%
Risk adjusted rate of return for the project = 20%
Required:
Should the project be accepted or rejected
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

NPV = 6410
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI





Alternative to risk adjusted discount rate approach
The risk of the project is taken into consideration
by adjusting expected cash flows not the discount
rate
Eliminates the problem arising out of inclusion of
the risk premium in the discount rate
The risk adjustment factor is expressed in terms of
certainty equivalent coefficient(CEC)
CEC represents the relationship between
certain(risk less) and uncertain (risky) cash flows
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI



CEC = RISKLESS CASHFLOW / RISKY
CASHFLOW
CEC is a fractional value which can have a
value between 0 and 1
Higher the risk lower the CEC
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

A project of rs 100000 with 3 years of life is
expected to generate the following cash inflows
year
cash flow
1
50000
2
60000
3
40000
Risk adjusted rate of return is 15% where as the
risk free rate of return is 6%
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
The CEC for the cash flows are as follows
year
cash flow CEC
1 50000
0.9
2 60000
0.7
3 40000
0.6
Evaluate the desirability of the project
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


Ans -25
NOTE THAT the CE cash flows should be
discounted at the rate of risk free rate. It is
because the risk factor has already been
discounted through the CE coefficient.
Discounting by the RADR will mean
discounting the same risk twice
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Aristo Corporation is planning to launch either
Air-tight Containers or Microwave Containers.
Either of the product launch needs initial
investment of Rs.5,000.
The marketing manager has made safe (certain)
cash flow estimations and ambitious (risky)
cash flow estimations for a period of three
years.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Years
1
2
3
Air-tight Containers
Certain Risky CF Expected
CF
CF
Rs.2,000 Rs.5,000 Rs.4,000
Rs.6,000 Rs.10,00 Rs.7,000
0
Rs.8,000 Rs.16,00 Rs.10,00
0
0
Microwave Containers
Certain Risky CF Expected
CF
CF
Rs.4,000 Rs.5,000 Rs.3,400
Rs.5,000 Rs.10,00 Rs.8,000
0
Rs.9,000 Rs.18,00 Rs.12,00
0
0
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The risk-free return of the investment is 5
percent.
Required:
(a) NPV(s) of Air-tight Containers and Microwave
Containers
(b) The product to be launched
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

BBA 2013, T.U.
The following particulars of the projects M and
N are provided.
Years
0
1
2
3
Project M
Cash
Certainty
flow
equivalen
t
coefficien
(in Rs.)
t
1
10,000
4,000
0.9
4,000
0.8
2,000
0.6
Project N
Cash
Certainty
flow
equivalen
t
coefficien
(in Rs.)
t
-10,000
1
5,000
6,000
3,000
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
0.8
0.7
0.5
Riskless discount rate is 10 per cent.
Required:
The project required to be selected by using
NPV rule.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI




Under RADR the method implies increasing
risk over time since the discount rate remains
the same
The assumption of increasing risk with time
may not be valid
The RADR method would penalize the project
With CEC management is able to specify
directly the degree of risk for the particular
future
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


The CEC depends on the perception of the
investor
Doesnot assume the probability distribution of
the cash flow
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI


H. S. Hillier suggests to obtain the expected net
present value and the standard deviation of the
net present value through analytical derivation.
Two cases of such analysis are proposed.


No correlation among cash flows
Perfect correlation among cash flows
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Un-correlation cash flows illustration
An investment project of a corporate entity has
setup to launch a new product for which
Rs.15,000 was set-aside. The investment’s riskfree return is 6.5 percent.
The entity realizes that the estimated cash
flows of three years are uncorrelated. The
uncorrelated cash flows with their likelihoodness to occur were already finalized.
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Year 1
Estimate Probabilit
d CF
y
Rs.5,000 0.25
Rs.6,000 0.5
Rs.7,000 0.25
Year 2
Estimate Probabilit
d CF
y
Rs.6,000 0.3
Rs.7,000 0.4
Rs.8,000 0.3
Year 3
Estimate Probabilit
d CF
y
Rs.7,000 0.15
Rs.8,000 0.7
Rs.9,000 0.15
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Required:
(a) Expected cash flow for each year
(b) Expected NPV
(c) Standard deviation from the expected NPV
(d) The likeliness of the expected NPV going to
the limit of Rs.3,000
(e) The likeliness of the expected NPV going to
the limit of less than Rs.3,000
(f) The likeliness of the expected NPV going to the
limit of more than Rs.3,000

C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

Correlation among cash flows illustration
The probability and correlated ATC of two
consecutive years of a Trading House for
Rs.15,000 initial investment are as follows:
Year I
ATC
Probabilit
y
Rs.10,00
0.25
0
Rs.11,00
0.5
0
Rs.12,00
0.25
0
Year II
ATC
Probabilit
y
Rs.15,00
0.2
0
Rs.17,00
0.6
0
Rs.19,00
0.2
0
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
The risk-free rate of return is 7 percent.
Required:
(a) Expected NPV
(b) Standard deviation
 Expected NPV moving to Rs.12,000
(d) Expected NPV falling between Rs.12,000 to
Rs.15,000
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Rank Zerox is exploring an investment scheme
that requires initial cost of Rs.20,000. The
estimated uncorrelated cash inflows of three
years along with chance of occurrence are as
follows:
Year 1
Year 2
Year 3
Probabilit Net cash Probabilit Net cash Probabilit Net cash
y
flows
y
flows
y
flows
0.35
Rs.4,000
0.25
Rs.6,000
0.3
Rs.8,000
0.3
Rs.6,000
0.5
Rs.8,000
0.4
Rs.10,00
0
0.35
Rs.8,000
0.25
Rs.10,00
0.3
Rs.12,00
0
0
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
The risk free rate of return expected is 6 %.
Required:
(a) Expected cash inflows
(b) Expected Net Present Value
(c) Standard deviation
(d) Chance of the expected NPV going up to
Rs.2,500

C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

The correlated cash flows estimated for a
project requiring investment of Rs.6,000 with 8
percent risk free return are provided below:
Year I
Net cash Probabilit
flows
y
Rs.4,000
0.25
Rs.5,000
0.5
Rs.6,000
0.25
Year II
Net cash Probabilit
flows
y
Rs.5,000
0.4
Rs.6,000
0.2
Rs.7,000
0.4
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI
Required:
(a) Expected NPV
(b) Standard deviation
(c) The chance of the expected NPV going upto
Rs.5,000
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

There are several ways of incorporating risk in the
project decision process
Judgemental evaluation
 Payback period requirement
 Certainty equivalent method
 Risk adjusted discounted rate method



Judgemental evaluation: informal, based on the
judgement
Payback period requirement: if an investment is
considered risky a shorter payback period is
required. This assumes that risk is the function of
time
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI

CEC method is superior to RADR
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI



BREAK EVEN POINT CAPACITY
UTILIZATION (BEPCU)
DEBT SERVICE COVERAGE RATIO(DSCR)
SENSITIVITY ANALYSIS
C.I.D - PROJECT RISK ANALYSIS BIMESH MAN PATI