Discusses various risks involved in capital budgeting - useful to the students of under graduate, post graduate and professional course students in finance and management
Discuss the concept of risk in investment decisions.
Understand some commonly used techniques, i.e., payback, certainty equivalent and risk-adjusted discount rate, of risk analysis in capital budgeting.
Focus on the need and mechanics of sensitivity analysis and scenario analysis.
Highlight the utility and methodology simulation analysis.
Explain the decision tree approach in sequential investment decisions.
Focus on the relationship between utility theory and capital budgeting decisions.
Capital Budgeting is about how one should evaluate the financing options based on the superior financial performance through mathematical techniques. These techniques have been discussed in the presentation in detail.
This presentation is prepared by Toran Lal Verma. The presentation deals with the calculation of cost of debt, equity, preference share and retained earnings.
Investment Decision — Capital Budgeting Techniques — Pay Back Method — Accounting Rate Of Return — NPV — IRR — Discounted Pay Back Method — Capital Rationing — Risk Adjusted Techniques Of Capital Budgeting. — Capital Budgeting Practices
Discuss the concept of risk in investment decisions.
Understand some commonly used techniques, i.e., payback, certainty equivalent and risk-adjusted discount rate, of risk analysis in capital budgeting.
Focus on the need and mechanics of sensitivity analysis and scenario analysis.
Highlight the utility and methodology simulation analysis.
Explain the decision tree approach in sequential investment decisions.
Focus on the relationship between utility theory and capital budgeting decisions.
Capital Budgeting is about how one should evaluate the financing options based on the superior financial performance through mathematical techniques. These techniques have been discussed in the presentation in detail.
This presentation is prepared by Toran Lal Verma. The presentation deals with the calculation of cost of debt, equity, preference share and retained earnings.
Investment Decision — Capital Budgeting Techniques — Pay Back Method — Accounting Rate Of Return — NPV — IRR — Discounted Pay Back Method — Capital Rationing — Risk Adjusted Techniques Of Capital Budgeting. — Capital Budgeting Practices
Cost of Capital- features of capital-meaning of cost of capital-factors affecting cost of capital-Computation of cost of capital-cost of equity capital-cost of preference capital-cost of debenture-weighted average cost of capital
Capital structure- Factors affecting capital structure- Problems on EPS- Capital structure theories
Describes in detail the steps involved in the calculation of Internal Rate of Return. Useful to students of Under graduate, post graduate and professional course students pursuing course in finance
Many investors mistakenly base the success of their portfolios on returns alone. Few consider the risk that they took to achieve those returns. Since the 1960s, investors have known how to quantify and measure risk with the variability of returns, but no single measure actually looked at both risk and return together. Today, we have three sets of performance measurement tools to assist us with our portfolio evaluations. The Treynor, Sharpe and Jensen ratios combine risk and return performance into a single value, but each is slightly different. Which one is best for you? Why should you care? Let's find out.
Portfolio performance measures should be a key aspect of the investment decision process. These tools provide the necessary information for investors to assess how effectively their money has been invested (or may be invested). Remember, portfolio returns are only part of the story. Without evaluating risk-adjusted returns, an investor cannot possibly see the whole investment picture, which may inadvertently lead to clouded investment decisions.
Cost of Capital- features of capital-meaning of cost of capital-factors affecting cost of capital-Computation of cost of capital-cost of equity capital-cost of preference capital-cost of debenture-weighted average cost of capital
Capital structure- Factors affecting capital structure- Problems on EPS- Capital structure theories
Describes in detail the steps involved in the calculation of Internal Rate of Return. Useful to students of Under graduate, post graduate and professional course students pursuing course in finance
Many investors mistakenly base the success of their portfolios on returns alone. Few consider the risk that they took to achieve those returns. Since the 1960s, investors have known how to quantify and measure risk with the variability of returns, but no single measure actually looked at both risk and return together. Today, we have three sets of performance measurement tools to assist us with our portfolio evaluations. The Treynor, Sharpe and Jensen ratios combine risk and return performance into a single value, but each is slightly different. Which one is best for you? Why should you care? Let's find out.
Portfolio performance measures should be a key aspect of the investment decision process. These tools provide the necessary information for investors to assess how effectively their money has been invested (or may be invested). Remember, portfolio returns are only part of the story. Without evaluating risk-adjusted returns, an investor cannot possibly see the whole investment picture, which may inadvertently lead to clouded investment decisions.
Portfolio Management and it's objectives
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
K.M.Nafiz
Risul Islam Tonu
Saiful Islam
Md Ismail Hossain
Rajib Hossain
Md Mamun Islam
Sadrul amin
Khairul Basar
Md. Faysal Alam
Md. Nazrul Islam
Sadia Afrin
Zannatul Ferdous Labonno
Farhana Akter
Fears in business operations are known as risks. They mainly affect external and international
relations and other business relations. In the event where operational risks are prominent, the
viability of a business in the future deteriorates and is a complete failure or crippling of the entire
business system. Risk aversion also takes into consideration proper analysis of future prospect of
a specific business before even making an ideal analysis of future prospect of a specific business
before engaging in capital investment
- See more at: http://www.customwritingservice.org/blog/risks-and-returns/
This is a presentation of Chapter 13 Risk Analysis based on the textbook Managerial Economics written by W.Bruce Allen, Keith Weigelt, Neil A. Doherty and Edwin Mansfield 8th Edition
PLEASE HIT LIKE IF IT'S HELPFUL! :D
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
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The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
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The U.S. economy is continuing its impressive recovery from the COVID-19 pandemic and not slowing down despite re-occurring bumps. The U.S. savings rate reached its highest ever recorded level at 34% in April 2020 and Americans seem ready to spend. The sectors that had been hurt the most by the pandemic specifically reduced consumer spending, like retail, leisure, hospitality, and travel, are now experiencing massive growth in revenue and job openings.
Could this growth lead to a “Roaring Twenties”? As quickly as the U.S. economy contracted, experiencing a 9.1% drop in economic output relative to the business cycle in Q2 2020, the largest in recorded history, it has rebounded beyond expectations. This surprising growth seems to be fueled by the U.S. government’s aggressive fiscal and monetary policies, and an increase in consumer spending as mobility restrictions are lifted. Unemployment rates between June 2020 and June 2021 decreased by 5.2%, while the demand for labor is increasing, coupled with increasing wages to incentivize Americans to rejoin the labor force. Schools and businesses are expected to fully reopen soon. In parallel, vaccination rates across the country and the world continue to rise, with full vaccination rates of 50% and 14.8% respectively.
However, it is not completely smooth sailing from here. According to M Capital Group, the main risks that threaten the continued growth of the U.S. economy are inflation, unsettled trade relations, and another wave of Covid-19 mutations that could shut down the world again. Have we learned from the past year of COVID-19 and adapted our economy accordingly?
“In order for the U.S. economy to continue growing, whether there is another wave or not, the U.S. needs to focus on diversifying supply chains, supporting business investment, and maintaining consumer spending,” says Grace Feeley, a research analyst at M Capital Group.
While the economic indicators are positive, the risks are coming closer to manifesting and threatening such growth. The new variants spreading throughout the world, Delta, Lambda, and Gamma, are vaccine-resistant and muddy the predictions made about the economy and health of the country. These variants bring back the feeling of uncertainty that has wreaked havoc not only on the stock market but the mindset of people around the world. MCG provides unique insight on how to mitigate these risks to possibly ensure a bright economic future.
Resume
• Real GDP growth slowed down due to problems with access to electricity caused by the destruction of manoeuvrable electricity generation by Russian drones and missiles.
• Exports and imports continued growing due to better logistics through the Ukrainian sea corridor and road. Polish farmers and drivers stopped blocking borders at the end of April.
• In April, both the Tax and Customs Services over-executed the revenue plan. Moreover, the NBU transferred twice the planned profit to the budget.
• The European side approved the Ukraine Plan, which the government adopted to determine indicators for the Ukraine Facility. That approval will allow Ukraine to receive a EUR 1.9 bn loan from the EU in May. At the same time, the EU provided Ukraine with a EUR 1.5 bn loan in April, as the government fulfilled five indicators under the Ukraine Plan.
• The USA has finally approved an aid package for Ukraine, which includes USD 7.8 bn of budget support; however, the conditions and timing of the assistance are still unknown.
• As in March, annual consumer inflation amounted to 3.2% yoy in April.
• At the April monetary policy meeting, the NBU again reduced the key policy rate from 14.5% to 13.5% per annum.
• Over the past four weeks, the hryvnia exchange rate has stabilized in the UAH 39-40 per USD range.
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
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how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
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1. Dr. Mohamed Kutty Kakkakunnan
Associated Professor
P.G. Dept. of Commerce
NAM College Kallikkandy
Kannur – Kerala – India
2. Risk Analysis in Capital Budgeting
• Decision making the most important function
• Survival and growth of the firm depends upon the
decisions made by management
• Capital expenditure is a decision to invest funds in
assets with the anticipation of an expected series
of earnings in future
• Future is uncertain and thus, risky
OK. Now what is decision making?
Decision making refers to the process of selecting
the preferred course of action from a range of
possibilities
3. Decision making is the process of selecting one course of
action out of possible courses of actions
When select, a rational man will select?
To select , it is assumed that, he
1. Has complete knowledge of all possible courses
2. Has complete knowledge on the consequences
selecting or rejecting alternatives
3. Can attach definite payoffs (returns) or utilities to each
possibilities
4. Can order the payoffs of each course of actions in
unique sequence from highest to the lowest payoffs
4. However, the assumptions do not hold
good due to :-
• Lack of knowledge about all the possibilities and
• Lack of knowledge about the consequences or
outcomes of each individual actions
Thus, decision making becomes a complex affair
and the decision maker takes his decisions under
risk and uncertainty
Further,
– Risk and profitability are related
– Higher risk creates loath among the investors
• Thus, proper balance must be struck between risk
and profitability
5. What is risk?
Capital expenditure?
Invests with the anticipation of future expected
earnings
Estimates future cash inflows and earnings form
the project
Uncertain future – future conditions may change-
cannot estimate with 100% accuracy
Chances for variations in the actual
Technically this variation is called ‘risk’
Thus, risk is the variability in the actual returns in
relation to the estimated returns
6. What is risk?
Is the variability that is likely to occur in the
future returns from the investment
“the variability in the actual returns emanating
from a project over its working life, in relation to
the estimated returns as forecasted at the time of
initial capital budgeting decision”
Decision making situations
A decision maker has to face three situations while
taking the decision
1. Certainty
2. Risk
3. uncertainty
7. Under certainty, the decision maker knows all the
possible courses of actions and the effects of accepting
or rejecting each course of action
When the decision maker knows the effects, but does not
know the probability of occurring the events or
effects. Such situation is known as risky situation.
In such condition, on the basis of past experience,
decision maker may assign proximities for the events or
outcomes (objective probability)
When both the effects and probabilities are not known, it
is known as uncertainty
No past data or experience – rely on guess – (subjective
probability)
8. Thus the major difference between risk and
uncertainty is that risk can be quantified or risk is
concerned with quantification of the likelihood of
the future outcomes
No such quantification is possible in uncertainty
Risk can be measured by volatility (instability /
unpredictability) of returns, a certain outcome
has (stability), no variance and volatility
Risk means possibility of a future loss, which can
be foreseen
Business risk (resulting from investment
decisions) Financial risk (from financial decisions)
9. Risk Analysis in Project Selection
The evaluation criterion of projects are based on cash
flows (operational cash flows)
Capital investment refer to the current outlay of funds
with the anticipation of a series of future expected
cash inflows
Estimates future cash inflows or earnings
Chances for variation – known as risk
It is the volatility (instability) of returns, the dispersion or
spread of likely returns around the expected returns
Thus, while capital budgeting, the risk should be
considered
10. Techniques for Incorporating Risk in Capital Budgeting
1. Probability and Expected Values
2. Risk Adjusted Rate of Returns
3. Sensitivity Analysis
4. Simulation
5. Certainty Equivalent
6. Standard Deviation
7. Decision Tree And
8. Game Theory
9. Payback Period
11. Probability and Expected Values
The concept of probability is fundamental to the use of risk
analysis techniques
What is probability?
Is a measure of someone’s opinion about the likelihood that an
event will occur
Varies from 0 to 1 (non-occurrence to occurrence)
A probability distribution consists of more than one estimates,
varying from certainty to uncertainty – from pessimism to
optimism
Thus, probability distribution shows the range of associated
probability and consist of a number of estimated
Generally, the number of estimates will be smaller and may
make, best guess, high guess and low guess or
Can be optimistic, most likely and pessimistic
12. Making a series of guesses (three in our example) is an
improvement over a single figure
The forecaster says the range of variation in cash inflows from
a minimum of Rs. 100000 to a maximum of Rs. 200000
Still there are chances for improvement by incorporating more
information
He can add his degree of confidence to the above guess, by
attaching probabilities of the likelihood of occurrence of the
above figures
Optimistic /
Best Guess
Rs. 200,000
High Guess
Rs. 150000
Pessimistic /
Low guess
Rs. 100,000
Best Guess
Rs. 200,000
Probability 0.2
High Guess
Rs. 150,000
Probability 0.6
Low guess
Rs. 100,000
Probability 0.2
13. With the help of probability one can say the chance
of cash earnings or inflows
Thus, there are chances for varying cash flow from
Rs. 20,000 to Rs. 90,000
The probability can be assigned on the basis of past
experience or past data (objective probability).
Lack of past data or experience compels one to rely
on guess (subjective probability)
Low guess 100,000 x 0.2 = 20000
High guess 150,000 x 0.6 = 90,000
Best guess 200,000 x 0.2 = 40000
14. Calculation of Expected Net Present Values (ENPV)
After assigning probabilities, the next step is to calculate
Expected Net Present Values
Expected Net Present Value is equal to the difference between
expected values of cash inflows minus expected value of cash
outflow
Or it is the sum of the present values of expected net cash flows
Expected values are calculated by multiplying the cash flows by
their respective probabilities
Since cash outflow takes place immediately (current / present) it
is certain and not related with future there is no need for
calculating expected values of cash outflows
Expected values of cash inflows need be calculated
Expected value of cash inflows = Cash Inflows X Probability
To calculate present value the product so obtained above will be
multiplied by the appropriate PV Factor at the prescribed
interest rate
15. Expected Net Cash Flow – Single Period
Two projects X and Y with initial investment of
Rs. 5000 and discount rate 10%
Possible
Events
PROJECT -X PROJECT - Y
Cash
Inflow
Probability Cash
Inflow
Probability
A 4000 0.1 12000 0.10
B 5000 0.2 10000 0.15
C 6000 0.4 8000 0.50
D 7000 0.2 6000 0.15
E 8000 0.1 4000 0.10
16. Calculation of Expected Values of Projects X & Y
Possible
events
1
PROJECT - X PROJECT - Y
Cash
inflow
2
Probabi
lity
3
Expecte
d values
4 (2x3)
Cash
inflow
5
Probab
ility
6
Expecte
d values
7 (5x6)
A 4000 0.1 400 2000 0.10 200
B 5000 0.2 1000 10000 0.15 1500
C 6000 0.4 2400 8000 0.50 4000
D 7000 0.2 1400 6000 0.15 900
E 8000 0.1 800 4000 0.10 400
EXPECTED CASH INFLOW 6000 8000
It shows that Project Y has higher Expected cash inflow than that
of X. thus, it is preferable
17. Now, we can calculate the expected net present
value of these projects
ENPV = EPVCIF – EPVCOF
Project X
EPVCIF @ 10% = 6000 X 0.909 = 5454
EPVCOF = 5000
ENPV = 5454 – 5000 = 454
Project Y
EPVCIF @ 10% = 8000 X 0.909 = 7272
EPVCOF = 5000
ENPV = 7272 – 5000 = 2272
Conclusion
18. Calculation of ENPV – Multi-period
Find the sum of Expected Present Values of Cash inflows of
different years and deduct the total from cash outlays
Project X; initial investment Rs. 5000; Discount rate 10 %
Year 1 Year 2 Year 3
Cash
inflow
Probability
Cash
inflow
Probability
Cash
inflow
Probability
1000 0.1 1000 0.2 1000 0.3
2000 0.2 2000 0.3 2000 0.4
3000 0.3 3000 0.4 3000 0.2
4000 0.4 4000 0.1 4000 0.1
20. ENPV help us to incorporate risk in capital projects
decisions
To get better insight into the risk we calculate dispersion of
cash flows
Dispersion is the difference between possible cash flows
that can occur and their expected values
It indicates the degree of risk
Commonly used measures of dispersion are standard
deviation and variance
Standard deviation is the square root of the mean of
squared deviations
Deviation is the difference between an outcome and the
expected mean value of all outcomes
21. Variance measures the deviation about expected
cash flows of each of the possible cash flows
It is the square of standard deviation
The greater the standard deviation and variance the
greater the dispersion and thus, risk and
uncertainty also
Variance of NCF = (NCF1-ENCF)2 Probability 1 +
(NCF2-ENCF)2 Probability 2 + ….
(NCFn-ENCF)2 Probability n
Standard deviation = square root of variance
22. 1. Calculate the mean value of possible cash inflows
(CF) = Expected cash flow, as calculated in ENPV
2. Calculate the deviation between the mean value and
the possible cash flows (DCF)
3. Square the deviations (DCF)2
4. Multiply the squared deviations by the assigned
probabilities, to calculate the weighted squared
deviations (PDCF)2
5. Find the sum of the weighted squared deviations
(ΣPDCF)2
6. The resultant figure will be the Variance and
7. Find out the square root to get standard deviation.
Higher the value more will be the risk
23. When different projects having – (not homogenous)
a. Same standard deviation but different expected
values
b. Different standard deviations but same expected
values or
c. Different standard deviations and different
expected values, we use co-efficient of variation –
the relative measure of risk
24. Risk Adjusted Discount Rate
• Based on the assumption that risky project should get more
returns when compared to risky-free investments
• Risk premium for undertaking business risk over risk-free
investments
• Greater the risk, greater the premium
• Thus, while using discount rate for evaluation of capital
projects this risk premium is added with the usual discount rate
• Such a rate is known as risk adjusted rate of discount rate
• Such rate considers both time preference (time value and risk
preference
• Risk adjusted discount rate = risk free rate+ risk premium
• Acceptance rule:-
NPV (Positive) and IRR (IRR> Risk Adjusted Discount Rate)
25. If cost of capital and risk index is given the
following formula can be used for calculating
RADR
RADR = Rf + [Ri x (K0 – Rf)
Where Rf = risk free rate
Ri = risk index
K0 = cost of capital
26. • More or less similar to the risk adjusted
discount rate
• Here, the forecaster tries to forecast cash-
flows to some conservative level and adjusts
the “best estimate” with “intuitive correction
factor” known as “certainty-equivalent
coefficient” to be more safe
• This leads to estimate “certainty-equivalent
cash flow”
Different steps involved in this approach are:-
27. Step1
Under this method, risk is incorporated by modifying the expected
cash flows by using a correction factor known as certainty
equivalent coefficient
It expresses the relationship between certain (riskless) cash flows
and uncertain (risky) cash flows
Its value lies in between 0-1 and is indicated by “ἀ”
“ἀ0” represents cash outflow in the initial period; “ἀ1” cash flow
in the first year; “ἀ2” represents second year and so on.
There is an inverse relationship between this value and the risk
(higher the value lower the risk and vice versa)
28. Convert the expected cash flows into certainty
equivalent cash flows by using the CEC
Calculate the present value by using the
appropriate discount rate, which reflects the time
value of money (the same discount rate used for
evaluation capital projects)
Acceptance rule (both NPV and IRR can be used)
NPV (Positive)
IRR (IRR> risk-free discount rate)
29. • For evaluation of projects cash flows are estimated
• The forecasted cash flow depends upon several factors,
like volume of sales, selling price, variable costs, fixed
costs etc., which are subject to change
• Thus, NPV and IRR calculated on the basis of estimates
depends upon several factors and it is very difficult to
estimate or arrive at an accurate and unbiased forecast
of these variables
• Accuracy and reliability of NPV and IRR is questioned
and depends upon correct estimate of these variables
and reliability
• To ensure reliability and accuracy, impact of these
variables are ascertained –This method consider
30. Steps involved in Sensitivity Analysis
1. Identify the variables which influence NPV/IRR
2. Define the underlying relationship with the
help of mathematical equations
3. Analyze the impact of changes in each of these
variables
In sensitivity analyze, the decision maker makes
three assumptions – pessimistic, expected and
optimistic
On the basis of these assumptions, he can conduct
“what …. if” analysis. WHAT will be the NPV/IRR
IF the selling price is reduced by 10%?”
31. Then values of these variables are changed (at least three
times, considering pessimistic, expected and optimistic) and
NPV / IRR are recalculated under these assumptions.
This method of recalculating NPV / IRR by changing each of the
forecast variable is called SENSITIVITY ANALYSIS
It is a behavioral approach that uses a number of possible
values for a given variable to assess the impact on a firms
return
It is a way of analyzing change in the project’s NPV /IRR for a
given change in one of the variables
It indicates how sensitive a project’s NPV/IRR is to changes in
particular variables
The more sensitive the NPV/IRR, the more critical is the
variable
32. Decision Tree
A decision taken today may have several implications on
future. May affect future, decisions, investment and
outcomes.
Then it is necessary to foresee the future effects or
implications of present decisions and the decision becomes
a complex one
Thus, decision cannot be considered an isolated or individual
activity, ending with a particular consequence. May lead to
several consequences, several decisions and implications.
Depends upon the chance of occurring an event, its
consequences, which again lead to problems - decisions
and so on-
Thus, decision involves a series of sequential decisions to be
taken in the order of necessity
33. Decision tree continues
Decision tree is an analytical technique to handle such
sequential decisions
• Also known as Decision Flow Networks and Decision
Diagrams
• Is a powerful means of depicting and facilitating important
problems, especially that involves sequential decisions and
variable outcomes over time
• A decision tree is a pictorial representation in tree form
which indicates the magnitude an probability and inter-
relationship of all possible outcomes
• It is a graphic display of the relationship between a present
decision and future events, future decisions and their
consequences
34. • The sequence of events over time is depicted in a format similar to
the branches of a tree
• In capital budgeting, a decision tree shows the sequential cash
flows and NPV of the proposed project under different
circumstances
Steps in decision tree approach
• Decision tree deals with sequential decisions i.e present decision –
its consequences requiring future decisions and their future
consequences
• The consequences of present decision are influenced by chance
events and that of future consequences is also the effect of chance
events
• However, at the time of taking the decision chance event is
unknown but probability can be assigned and a probability
distribution can be constructed.
• When the decisions and outcomes are depicted by a graph we will
get the decision tree
35. Steps continues
The steps involved in the construction of decision tree
are:-
1. Define the investment proposal (purchasing machine,
entering new market, production of a new product
etc)
2. Identify the decision alternatives
3. Draw a decision tree indicating the decision points,
chance events and other data. The relevant data
regarding the probability distribution, cash flow,
expected present value etc should be shown on the
branches. Show the decision points by squares and
chance events by circles
4. Analyze the data and select the best alternative
36. Thus, the first step is to draw a diagram which shows the
structure of the problem.
Decision trees are constructed left to right. The branches
represent the possible alternatives which could be
made and various possible outcomes which might arise
Example
A company has a proposal to conduct a research project
for developing a product. If it conducts, there are
chances for success or failure in developing the
product. If it succeeds, the company may decide to
launch the product immediately or postpone the
launching for one year. There is a competitor to the
company in the market. Whatever be the decision, the
competitor may enter the market or stay away from
the market . Draw a decision tree (structure only)
assuming that all the possibilities have equal chance
37. D1
D2
CONDUCT 0.5
SUCCESS 0.5
FAILURE 0.5
IMM
EDIA
TE
0.5
POST
PONE
0.5
NOT TO CONDUCT 0.5
ENTER 0.5
STAY OUT 0.5
ENTER 0.5
STAY OUT 0.5
ENTER 0.5
STAYOUT 0.5
ENTER 0.5
STAY OUT 0.5