economic analysis of project planning & managment

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Project


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From Wikipedia, the free encyclopedia

For the urban low-income housing buildings called projects, seepublic housing. For other uses, see Project

(disambiguation).

For Wikipedian Projects, seeWikipedia:WikiProject

A project inbusiness and scienceis typically defined as a collaborative enterprise, frequently involving research or

design, that is carefullyplanned to achieve a particular aim.[1]Projects can be further defined as temporary rather than

permanent social systems that are constituted by teams within or across organizations to accomplish

particulartasksunder time constraints.[2]

Overview[edit]

The wordprojectcomes from theLatinwordprojectum from the Latin verbproicere, "before an action" which in turn

comes frompro-, which denotes precedence, something that comes before something else in time (paralleling

the Greek ) and iacere, "to do". The word "project" thus actually originally meant "before an action".

When the English language initially adopted the word, it referred to a plan of something, not to the act of actually

carrying this plan out. Something performed in accordance with a project became known as an "object".

Specific uses[edit]

School and university[edit]

At school, educational institute and independent work project is involved in a normal essay assignment. It requires

students to undertake their own fact-finding and analysis, either from library/internet research or from gathering data

empirically. The written report that comes from the project is usually in the form of a dissertation, which will contain

sections on the project's inception, analysis, findings and conclusions....[3]

Engineering project[edit]

Engineering projects are, in many countries, specifically defined by legislation, which requires that such projects should

be carried out by registeredengineers and/or registered engineering companies. That is, companies with license to

carry out such works as design and construction ofbuildings,power plants, industrial facilities, installation and erection

ofelectrical grid networks, transportation infrastructure and the like.

The scope of the project is specified in acontract between the owner and the engineering and construction parties. As a

rule, an engineering project is broken down intodesignandconstruction phases. The outputs of the design process

aredrawings, calculations, and all other design documentation necessary to carry out the next phase. The next phase

would normally be sending the project plans to a developer who will then help construct the plans (construction phase).
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Project management[edit]

Inproject managementa project consists of a temporary endeavor undertaken to create a unique product, service or

result.[4] Another definition is a management environment that is created for the purpose of delivering one or more

business products according to a specified business case.

Projectobjectivesdefine target status at the end of the project, reaching of which is considered necessary for the

achievement of planned benefits. They can be formulated asSMART criteria:[5] Specific, Measurable (or at least

evaluable) achievement, Achievable (recently Agreed-to or Acceptable are used regularly as well), Realistic (given the

current state of organizational resources) and Time terminated (bounded). The evaluation (measurement) occurs at the

project closure. However a continuous guard on the project progress should be kept by monitoring and evaluating. It is

also worth noting that SMART is best applied for incremental type innovation projects. [citation needed] For radical type

projects it does not apply as well. Goals for such projects tend to be broad, qualitative, stretch/unrealistic and success

driven.

Project Cycle ManagementFrom Wikipedia, the free encyclopedia

This article has multiple issues. Please help improve it or discuss these

issues on the talk page.

This article relies on references to primary

sources. (June 2013)

This article includes a list of references, related reading or external links,

but its sources remain unclear because it lacksinline citations.(June2013)

Project Cycle Management (PCM) is used inEuropeAid terminology describe decision-making procedures used

during the life-cycle of a project(including key tasks, roles and responsibilities, key documents and decision options).

Projects go through definite and describable phases. Each phase can be brought to some sense of closure as the next

phase begins. Phases can be made to result in deliverables or accomplishments to provide the starting point for the

next phase. Phase transitions are ideal times to update planning baselines, to conduct high level management reviews,

and to evaluate project costs and prospects.

Definition of 'Compounding'The ability of an asset to generate earnings, which are then reinvested in order to generate their

own earnings. In other words, compounding refers to generating earnings from previous earnings.

Also known as "compound interest".
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Compound Interest Formula

P = principal amount (the initial amount you borrow or deposit)r = annual rate of interest (as a decimal)t = number of years the amount is deposited or borrowed for.A = amount of money accumulated after n years, including interest.n = number of times the interest is compounded per year

Example:

An amount of $1,500.00 is deposited in a bank paying an annual interest

rate of 4.3%, compounded quarterly. What is the balance after 6 years?

Solution:Using the compound interest formula, we have thatP = 1500, r= 4.3/100 = 0.043, n = 4, t= 6. Therefore,

So, the balance after 6 years is approximately $1,938.84.

Measurement of Cash Flow

Mathematics of Money:

Compound Interest Analysis With ApplicationsThis site is a part of the JavaScript E-labs learning objects for decision making.

Other JavaScript in this series are categorized under different areas of applications

in the MENU section on this page.
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Compound Interest: The future value (FV) of an investment ofpresent value (PV) dollars earning interest at an annual rate of rcompounded m times per year for a period of t years is:

FV = PV(1 + r/m)mt

or

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt isthe number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning8.5% per year, with interest re-invested each month, the futurevalue is

FV = PV(1 + r/m)mt = 20,000(1 + 0.085/12)(12)(4) = $28,065.30

Notice that the interest earned is $28,065.30 - $20,000 =

$8,065.30 -- considerably more than the corresponding simpleinterest.

Effective Interest Rate: If money is invested at an annual rate r,compounded m times per year, theeffective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield ifcompounded only once per year. In this context r is also called

the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly hasa nominal rate of rnom = 0.098, and an effective rate of:

r eff=(1 + rnom /m)m = (1 + 0.098/12)12 - 1 = 0.1025.


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Thus, we get an effective interest rate of 10.25%, since thecompounding makes the CD paying 9.8% compounded monthlyreally pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r =interest rate per period, n = number of periods, k = number ofpayments, R = monthly payment, and D = debt balance after Kpayments, then

R = P r / [1 - (1 + r)-n]

and

D = P (1 + r)k - R [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose onedecides to pay more than the monthly payment, the question is howmany months will it take until the mortgage is paid off? The answeris, the rounded-up, where:

n = log[x / (x P r)] / log (1 + r)

where Log is the logarithm in any base, say 10, or e.

Future Value (FV) of an Annuity Components: Ler where R =payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasingannuity is an investment that is earning interest, and into whichregular payments of a fixed amount are made. Suppose one makesa payment of R at the end of each compounding period into an

investment with a present value of PV, paying interest at an annualrate of r compounded m times per year, then the future value aftert years will be

FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i


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where i = r/m is the interest paid each period and n = m t is the

total number of periods.

Numerical Example: You deposit $100 per month into an account

that now contains $5,000 and earns 5% interest per yearcompounded monthly. After 10 years, the amount of money in theaccount is:

FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i =

5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12) =

$23,763.28

Value of a Bond: Let N = number of year to maturity, I = the

interest rate, D = the dividend, and F = the face-value at the end ofN years, then the value of the bond is V, where

V = (D/i) + (F - D/i)/(1 + i)N

V is the sum of the value of the dividends and the final payment.

You may like to perform some sensitivity analysis for the "what-if"scenarios by entering different numerical value(s), to make your"good" strategic decision.

discounting present participle of discount(Verb)

Verb

Deduct an amount from (the usual priceof something).

Reduce (a product or service) in price.

Definition of 'Discounting'

The process of determining the present value of a payment or a stream of payments that is to bereceived in the future. Given the time value of money, a dollar is worth more today than it would

be worth tomorrow given its capacity to earn interest. Discounting is the method used to figure out

how much these future payments are worth today.

Discount FormulaDiscount is defined as the deduction in the price of something as a gift to the customers. It is the product of the

original price and the discount rate. The discount rate is given in percentage.


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The Discount Formula is given as,

DiscountingFrom Wikipedia, the free encyclopedia

For discounting in the sense of downplaying or dismissing, see Minimisation (psychology). For the band of the same

name, seeDiscount (band).

See also:Discounts and allowances

Discounting is a financial mechanism in which adebtorobtains the right to delay payments to a creditor, for a defined

period of time, in exchange for a charge or fee.[1] Essentially, the party that owes money in the present purchases the

right to delay the payment until some future date. [2] The discount, orcharge, is simply the difference between the

original amount owed in the present and the amount that has to be paid in the future to settle the debt. [1]

The discount is usually associated with a discount rate, which is also called the discount yield.[1][1][2][3]The discount yield

is simply the proportional share of the initial amount owed (initial liability) that must be paid to delay payment for 1 year.

Discount Yield = "Charge" to Delay Payment for 1 year / Debt Liability

It is also the rate at which the amount owed must rise to delay payment for 1 year.

Since a person can earn a return on money invested over some period of time, most economic and financial models

assume the "Discount Yield" is the same as the Rate of Returnthe person could receive by investing this money

elsewhere (in assets of similarrisk) over the given period of time covered by the delay in payment. [1][2] The Concept is

associated with theOpportunity Cost of not having use of the money for the period of time covered by the delay in

payment. The relationship between the "Discount Yield" and theRate of Return on other financial assets is usually

discussed in such economic and financial theories involving the inter-relation between various Market Prices, and the

achievement ofPareto Optimality through the operations in theCapitalistic Price Mechanism,[2]as well as in the

discussion of the "Efficient (Financial) Market Hypothesis".[1][2][4]The person delaying the payment of the current Liability

is essentially compensating the person to whom he/she owes money for the lost revenue that could be earned from an

investment during the time period covered by the delay in payment. [1] Accordingly, it is the relevant "Discount Yield" that

determines the "Discount", and not the other way around.

As indicated, the Rate of Return is usually calculated in accordance to an annualreturn on investment. Since an

investor earns a return on the original principal amount of the investment as well as on any prior period Investment

income, investment earnings are "compounded" as time advances.[1][2] Therefore, considering the fact that the

"Discount" must match the benefits obtained from a similarInvestment Asset, the "Discount Yield" must be used within
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the same compounding mechanism to negotiate an increase in the size of the "Discount" whenever the time period the

payment is delayed or extended.[2][4] The Discount Rate is the rate at which the Discount must grow as the delay in

payment is extended.[5]This fact is directly tied into the "Time Value of Money" and its calculations.[1]

The "Time Value of Money" indicates there is a difference between the "Future Value" of a payment and the "Present

Value" of the same payment. TheRate of Returnon investment should be the dominant factor in evaluating the

market's assessment of the difference between the "Future Value" and the "Present Value" of a payment; and it is the

Market's assessment that counts the most.[4]Therefore, the "Discount Yield", which is predetermined by a relatedReturn

on Investment that is found in the financial markets, is what is used within the "Time Value of Money" calculations to

determine the "Discount" required to delay payment of a financial liability for a given period of time.

BASIC CALCULATION

If we consider the value of the original payment presently due to be $P, and the debtor wants to delay the payment for t

years, then an r% Market Rate of Return on a similarInvestment Assets means the "Future Value" of $P is $P * (1 + r%)t ,[2][5]and the "Discount" would be calculated as

Discount = $P * (1+r%) t - $P [2]

where r% is also the "Discount Yield".

If $F is a payment that will be made t years in the future, then the "Present Value" of this Payment, also called the

"Discounted Value" of the payment, is

$P = $F / (1+r%)t [2]

To calculate the present value of a single cash flow, it is divided by one plus the interest rate for each period of time that

will pass. This is expressed mathematically as raising the divisor to the power of the number of units of time.

Consider the task to find the present value PVof $100 that will be received in five years. Or equivalently, which amount

of money today will grow to $100 in five years when subject to a constant discount rate?

Assuming a 12% per year interest rate it follows

Discount rate[edit]

The discount rate which is used in financial calculations is usually chosen to be equal to the Cost of Capital.

TheCost of Capital, in a financial market equilibrium, will be the same as the Market Rate of Return on the financia

asset mixture the firm uses to finance capital investment. Some adjustment may be made to the discount rate to

take account of risks associated with uncertain cash flows, with other developments.

The discount rates typically applied to different types of companies show significant differences:
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Startups seeking money: 50 100%

Early Startups: 40 60%

Late Startups: 30 50%

Mature Companies: 10 25%

The higher discount rate for startups reflects the various disadvantages they face, compared to established

companies:

Reduced marketability of ownerships because stocks are not traded publicly.

Limited number of investors willing to invest.

Startups face high risks.

Over optimistic forecasts by enthusiastic founders.

One method that looks into a correct discount rate is thecapital asset pricing model. This model takes in account

three variables that make up the discount rate:

1. Risk Free Rate: The percentage of return generated by investing in risk free securities such as government

bonds.

2. Beta: The measurement of how a companys stock price reacts to a change in the market. A beta higher than 1

means that a change in share price is exaggerated compared to the rest of shares in the same market. A beta less

than 1 means that the share is stable and not very responsive to changes in the market. Less than 0 means that a

share is moving in the opposite of the market change.

3. Equity Market Risk Premium: The return on investment that investors require above the risk free rate.

Discount rate= risk free rate + beta*(equity market risk premium)

Discount factor[edit]

The discount factor, DF(T), is the factor by which a future cash flow must be multiplied in order to obtain the

present value. For a zero-rate (also called spot rate) , taken from a yield curve, and a time to cashflow (in

years), the discount factor is:

In the case where the only discount rate you have is not a zero-rate (neither taken from azero-coupon

bond nor converted from aswap rate to a zero-rate throughbootstrapping) but an annually-compounded rate
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(for example if your benchmark is a US Treasury bond with annual coupons and you only have itsyield to

maturity, you would use an annually-compounded discount factor:

However, when operating in a bank, where the amount the bank can lend (and therefore get interest) is

linked to the value of itsassets(includingaccrued interest), traders usually use daily compounding to

discount cashflows. Indeed, even if the interest of the bonds it holds (for example) is paid semi-annually,

the value of its book of bond will increase daily, thanks toaccrued interest being accounted for, and

therefore the bank will be able to re-invest these daily accrued interest (by lending additional money or

buying more financial products). In that case, the discount factor is then (if the usual money marketday

count conventionfor the currency is ACT/360, in case of currencies such as USD, EUR, JPY), with the

zero-rate and the time to cashflow in years:

or, in case the market convention for the currency being discounted is ACT/365 (AUD, CAD, GBP):

Sometimes, for manual calculation, the continuously-compounded hypothesis is a close-enough

approximation of the daily-compounding hypothesis, and makes calculation easier (even though

it does not have any real application as no financial instrument is continuously compounded). In

that case, the discount factor is:

Decision Criteria Under Certainty

Decisions Under Certainty, Risk and Uncertainty(It will be a good idea to read the previous posts on the subject for better understanding).

Knowledge of Outcomes

An outcome defines what will happen if a particular alternative or course of action is chosen. Knowledge of

outcomes is important when there are multiple alternatives. In the analysis of decision making, three types of

knowledge with respect to outcomes are usually distinguished:

1. Certainty: Complete and accurate knowledge of outcome of each alternative. There is only oneoutcome for each alternative.
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2. Risk: Multiple possible outcomes of each alternative can be identified and a probability ofoccurrence can be attached to each.

3. Uncertainty: Multiple outcomes for each alternative can be identified but there is no knowledge ofthe probability to be attached to each.

Taking Decisions Under Certainty

If the outcomes are known and the values of the outcomes are certain, the task of the decision maker isto compute the optimal alternative or outcome with some optimization criterion in mind.

As an example: if the optimization criterion is least cost and you are considering two different brands of aproduct, which appear to be equal in value to you, one costing 20% less than the other, then, all other thingsbeing equal, you will choose the less expensive brand.

However, decision making under certainty is rare because all other things are rarely equal.

Linear programming is one of the techniques for finding an optimal solution under certainty. Linearprogramming problems normally need computations with the help of a computer.

Taking Decisions Under Risk

The making of decisions under risk, when only the probabilities of various outcomes are known, is similarto certainty.

Instead of optimizing the outcomes, the general rule is to optimize the expected outcome.

As an example: if you are faced with a choice between two actions one offering a 1% probability of a gainof $10000 and the other a 50% probability of a gain of $400, you as a rational decision maker will choose thesecond alternative because it has the higher expected value of $200 as against $100 from the first alternative.

Taking Decisions Under Uncertainty

Decisions under uncertainty (outcomes known but not the probabilities) must be handled differentlybecause, without probabilities, the optimization criteria cannot be applied.

Some estimated probabilities are assigned to the outcomes and the decision making is done as if it isdecision making under risk.

Definition of 'Net Present Value - NPV' The difference between the present value of cash inflows and the present value of cash

outflows. NPV is used in capital budgeting to analyze the profitability of an investment or

project.

NPV analysis is sensitive to the reliability of future cash inflows that an investment or

project will yield.

Formula:


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In addition to the formula, net present value can often be calculated using tables, and

spreadsheets such as Microsoft Excel.

Investopedia explains 'Net Present Value - NPV'

NPV compares the value of a dollar today to the value of that same dollar in the future,

taking inflation and returns into account. If the NPV of a prospective project is positive, it

should be accepted. However, if NPV is negative, the project should probably be rejected

because cash flows will also be negative.

For example, if a retail clothing business wants to purchase an existing store, it would first

estimate the future cash flows that store would generate, and then discount those cash

flows into one lump-sum present value amount, say $565,000. If the owner of the store was

willing to sell his business for less than $565,000, the purchasing company would likely

accept the offer as it presents a positive NPV investment. Conversely, if the owner would

not sell for less than $565,000, the purchaser would not buy the store, as the investment

would present a negative NPV at that time and would, therefore, reduce the overall value of

the clothing company.

Payback periodFrom Wikipedia, the free encyclopedia

This article needs additional citations for verification. Please

help improve this article by adding citations to reliable sources. Unsourced

material may be challenged and removed. (March 2009)

Payback period in capital budgeting refers to the period of time required for the return on an investment to "repay" the

sum of the original investment. For example, a $1000 investment which returned $500 per year would have a two year

payback period. The time value of money is not taken into account. Payback period intuitively measures how long

something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback

periods. Payback period is widely used because of its ease of use despite the recognized limitations described below.

The term is also widely used in other types of investment areas, often with respect to energy efficiencytechnologies,maintenance, upgrades, or other changes. For example, acompact fluorescent light bulb may be described as having a

payback period of a certain number of years or operating hours, assuming certain costs. Here, the return to the

investment consists of reduced operating costs. Although primarily a financial term, the concept of a payback period is

occasionally extended to other uses, such as energy payback period (the period of time over which the energy savings
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of a project equal the amount of energy expended since project inception); these other terms may not be standardized

or widely used.

Payback period as a tool of analysis is often used because it is easy to apply and easy to understand for most

individuals, regardless of academic training or field of endeavour. When used carefully or to compare similar

investments, it can be quite useful. As a stand-alone tool to compare an investment to "doing nothing," payback period

has no explicit criteria for decision-making (except, perhaps, that the payback period should be less than infinity).

The payback period is considered a method of analysis with serious limitations and qualifications for its use, because it

does not account for thetime value of money, risk, financingor other important considerations, such as theopportunity

cost. Whilst the time value of money can be rectified by applying a weighted average cost of capital discount, it is

generally agreed that this tool for investment decisions should not be used in isolation. Alternative measures of "return"

preferred by economists are net present value and internal rate of return. An implicit assumption in the use of payback

period is that returns to the investment continue after the payback period. Payback period does not specify any required

comparison to other investments or even to not making an investment.

Payback period is usually expressed in years. Start by calculating Net Cash Flow for each year: Net Cash Flow Year 1

= Cash Inflow Year 1 - Cash Outflow Year 1. Then Cumulative Cash Flow = (Net Cash Flow Year 1 + Net Cash Flow

Year 2 + Net Cash Flow Year 3 ... etc.) Accumulate by year until Cumulative Cash Flow is a positive number: that year

is the payback year.

To calculate a more exact payback period: Payback Period = Amount to be Invested/Estimated Annual Net Cash Flow

1{[1]}

It can also be calculated using the formula:

Payback Period = (p - n)p + ny

= 1 + ny - np (unit:years)

Where

ny= The number of years after the initial investment at which the last negative value of cumulative cash flow occurs.

n= The value of cash flow at which the last negative value of cumulative cash flow occurs.

p= The value of cash flow at which the first positive value of cumulative cash flow occurs.

This formula can only be used to calculate the soonest payback period; that is, the first period after which the

investment has paid for itself. If the cumulative cash flow drops to a negative value some time after it has reached a

positive value, thereby changing the payback period, this formula can't be applied. This formula ignores values that

arise after the Payback Period has been reached.

Additional complexity arises when the cash flow changes sign several times; i.e., it contains outflows in the midst or at

the end of the project lifetime. The modified payback period algorithm may be applied then. First, the sum of all of the
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cash outflows is calculated. Then the cumulative positive cash flows are determined for each period. The modified

payback is calculated as the moment in which the cumulative positive cash flow exceeds the total cash outflow.

Internal rate of return

The internal rate of return (IRR) is a rate of return used in capitalbudgeting to measure and compare the profitability ofinvestments. It isalso called the discounted cash flow rate of return (DCFROR) or simplythe rate of return (ROR).[1] In the context of savings and loans the IRR isalso called the effective interest rate. The term internal refers to the factthat its calculation does not incorporate environmental factors (e.g.,the interest rate or inflation).

Contents

1 Definition 2 Uses

3 Calculation

o 3.1 Example

3.1.1 Numerical solution

3.1.2 Numerical Solution for Single Outflow and MultipleInflows

4 Problems with using internal rate of return

5 Mathematics

6 See also

7 References

8 Further reading

9 External links

Definition

The internal rate of return on an investment or project is the "annualizedeffective compounded return rate" or discount rate that makes the netpresent value of all cash flows (both positive and negative) from aparticular investment equal to zero.
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In more specific terms, the IRR of an investment is the interest rate atwhich the net present value of costs (negative cash flows) of theinvestment equals the net present value of the benefits (positive cashflows) of the investment.

Internal rates of return are commonly used to evaluate the desirability ofinvestments or projects. The higher a project's internal rate of return, themore desirable it is to undertake the project. Assuming all other factorsare equal among the various projects, the project with the highest IRRwould probably be considered the best and undertaken first.

A firm (or individual) should, in theory, undertake all projects orinvestments available with IRRs that exceed the cost of capital.Investment may be limited by availability of funds to the firm and/or bythe firm's capacity or ability to manage numerous projects.

Uses

Important: Because the internal rate of return is a rate quantity, it is anindicator of the efficiency, quality, or yield of an investment. This is incontrast with the net present value, which is an indicator of the valueormagnitude of an investment.

An investment is considered acceptable if its internal rate of return isgreater than an established minimum acceptable rate of return or cost ofcapital. In a scenario where an investment is considered by a firm thathasequity holders, this minimum rate is the cost of capital of theinvestment (which may be determined by the risk-adjusted cost of capitalof alternative investments). This ensures that the investment issupported by equity holders since, in general, an investment whose IRRexceeds its cost of capital adds value for the company (i.e., it iseconomically profitable).

Benefitcost ratioFrom Wikipedia, the free encyclopedia

This article does not cite any references or sources. Please

help improve this article by adding citations to reliable sources. Unsourced

material may be challenged and removed. (March 2007)
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A benefit-cost ratio (BCR) is an indicator, used in the formal discipline ofcost-benefit analysis, that attempts to

summarize the overallvalue for moneyof a project or proposal. A BCR is the ratio of the benefits of a project or

proposal, expressed in monetary terms, relative to its costs, also expressed in monetary terms. All benefits and costs

should be expressed in discounted present values.

Benefit cost ratio (BCR) takes into account the amount of monetary gain realized by performing a project versus the

amount it costs to execute the project. The higher the BCR the better the investment. General rule of thumb is that if the

benefit is higher than the cost the project is a good investment.

Rationale[edit]

In the absence of funding constraints, the best value for money projects are those with the highest net present

value. Where there is a budget constraint, the ratio ofNPVto the expenditure falling within the constraint should

be used. In practice, the ratio of PV of future net benefits to expenditure is expressed as a BCR. (NPV-to-investment is net BCR.) BCRs have been used most extensively in the field of transport cost-benefit appraisals.

The NPV should be evaluated over the service life of the project.

Problems[edit]

Long-term BCRs, such as those involved inclimate change, are very sensitive to the discount rate used in the

calculation of net present value, and there is often no consensus on the appropriate rate to use.

The handling of non-monetary impacts also present problems. They are usually incorporated by estimating them

in monetary terms, using measures such as WTP (willingness to pay), though these are often difficult to assess.

Alternative approaches include the UK's New Approach to Appraisal framework.

A further complication with BCRs concerns the precise definitions of benefits and costs. These can vary

depending on the funding agency.

What are Decision Trees?

A flow chart or diagram representing a classification system or a predictive model.

The tree is structured as a sequence of simple questions. The answers to these questions

trace a path down the tree.

The end product is a collection of hierarchical rules that segment the data

into groups, where a decision (classification or prediction) is made for each group.

The hierarchy is called a tree, and each segment is called a node.

The original segment contains the entire data set, referred to as the root node of

the tree.

A node with all of its successors forms a branch of the node that created it.

The final nodes (terminal nodes) are called leaves. For each leaf, a decision is
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made and applied to all observations in the leaf.

Classification Tree: Categorical Response / Target

Regression Tree: Continuous Response / Target

Predictor variables => Inputs

What are Decision Trees?Moore, Jesse, & Kittler ASA Q&P Research Conference

Decision treeFrom Wikipedia, the free encyclopedia

This article is about decision trees in decision analysis. For the use of the term in machine learning, seeDecision tree

learning.

Traditionally, decision trees have been created manually.

A decision tree is a decision support tool that uses a tree-like graphormodel of decisions and their possible

consequences, includingchance event outcomes, resource costs, andutility. It is one way to display an algorithm.

Decision trees are commonly used inoperations research, specifically indecision analysis, to help identify a strategy

most likely to reach a goal.

Overview[edit]

Decision Tree is a flow-chart like structure in which internal node represents test on an attribute, each branch

represents outcome of test and each leaf node represents class label (decision taken after computing all attributes). A

path from root to leaf represents classification rules.
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Indecision analysisa decision tree and the closely relatedinfluence diagramis used as a visual and analytical decision

support tool, where theexpected values (orexpected utility) of competing alternatives are calculated.

A decision tree consists of 3 types of nodes:

1. Decision nodes - commonly represented by squares

2. Chance nodes - represented by circles

3. End nodes - represented by triangles

Decision trees are commonly used inoperations research, specifically indecision analysis, to help identify a strategy

most likely to reach a goal. If in practice decisions have to be taken online with no recall under incomplete knowledge, a

decision tree should be paralleled by a probability model as a best choice model or online selection model algorithm.

Another use of decision trees is as a descriptive means for calculatingconditional probabilities.

Decision trees,influence diagrams,utility functions, and otherdecision analysis tools and methods are taught to

undergraduate students in schools of business, health economics, and public health, and are examples ofoperations

research ormanagement science methods.

Decision tree building blocks[edit]

Decision tree elements[edit]

Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths).

Therefore, used manually, they can grow very big and are then often hard to draw fully by hand. Traditionally, decision

trees have been created manually - as the aside example shows - although increasingly, specialized software is

employed.

Decision tree using flow chart symbols[edit]

Commonly a decision tree is drawn using flow chartsymbols as it is easier for many to read and understand.
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Analysis example[edit]

Analysis can take into account the decision maker's (e.g., the company's)preference orutility function, for example:
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The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference

coefficients (greater than $400Kin that range of risk aversion, the company would need to model a third strategy,

"Neither A nor B").

Another example[edit]

Decision trees can be used to optimize an investment portfolio. The following example shows a portfolio of 7 investment

options (projects). The organization has $10,000,000 available for the total investment. Bold lines mark the best

selection 1, 3, 5, 6, and 7, which will cost $9,750,000 and create a payoff of 16,175,000. All other combinations would

either exceed the budget or yield a lower payoff.[1]
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Influence diagram[edit]

A decision tree can be represented more compactly as an influence diagram, focusing attention on the issues and

relationships between events.

The squares represent decisions, the ovals represent action, and the diamond represents results.

Advantages and disadvantages[edit]

Amongst decision support tools, decision trees (andinfluence diagrams) have several advantages. Decision trees:

Are simple to understand and interpret. People are able to understand decision tree models after a briefexplanation.

Have value even with little hard data. Important insights can be generated based on experts describing a

situation (its alternatives, probabilities, and costs) and their preferences for outcomes.

Possible scenarios can be added

Worst, best and expected values can be determined for different scenarios

Use awhite box model. If a given result is provided by a model.

Can be combined with other decision techniques. The following example uses Net Present Value calculations,

PERT 3-point estimations (decision #1) and a linear distribution of expected outcomes (decision #2):

Disadvantages of decision trees:
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For data including categorical variables with different number of levels, information gain in decision trees are

biased in favor of those attributes with more levels.[2]

Calculations can get very complex particularly if many values are uncertain and/or if many outcomes are linked

How to Evaluate a Decision Tree Modelby Anna Assad, Demand Media

A decision tree can help you make tough choices between different paths and outcomes, but only if you evaluate the model

correctly. Decision trees are graphic models of possible decisions and all related possible outcomes in a tree form, with the

outcomes shown as "branches" off each choice. You can use a decision tree to help you make all kinds of business decisions,

including new product development, new marketing strategies and workforce changes.

Forecast.it

Estimate. Execute. Deliver. IT project cost estimation

FeaturesStep 1

Assign a numerical value to each possible outcome on the tree. Use dollar amounts for outcomes. For example, if one

outcome would gain the company $100,000, mark "$100,000" next to it. Estimate company value for outcomes without a

specific price tag.

Step 2

Label the likelihood of each outcome. Use whole percentages for each outcome on the same branch. The outcome

percentages must total 100 for each set of possible outcomes for the same branch. For example, for a decision branch with

four possible outcomes, the percentages of all four outcomes must equal 100. Use past experience and data to estimate thepossibility of each outcome.

Step 3

Make a separate list for each decision and its possible outcomes. Calculate an adjusted outcome value by multiplying the

likelihood percentage by the value. For example, label an outcome worth $300,000 that has a 30-percent chance of

succeeding as $90,000 on your list.

Step 4

Review each branch on the tree for costs. You must factor in the costs of the decisions when looking at outcome values.

Subtract the cost for each decision from your adjusted outcome values. Label the results "Final Outcomes."

EvaluationStep 1

Look at the possible decisions on the tree for all "Final Outcomes." Mark the decisions that carry a lot of risk and the

decisions that have a low probability of a successful outcome.
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Step 2

Look at the risky decisions. Consider whether your business can tolerate the amount of risk. For example, a decision with an

outcome of $150,000 that costs $20,000 to attempt is dangerous if your business can't afford to lose $20,000. Eliminate

outcomes with unaffordable attached risks.

Step 3

Look at the decisions for the outcomes with the lowest chance of success. Consider whether possible outcomes justify the

implementation expenses for each decision. Eliminate choices that carry a high cost or a lot of risk without a significant

outcome.

Step 4

Consider the remaining decisions. Refer to the "Final Outcomes" list for reference. Select the path leading to a significant

final outcome that has a high chance of succeeding.

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Consider a more certain outcome, even if the value is less than the other outcomes, if you

cannot take any risks with your decision.
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