Economics in IS/IT decision-making

961763 蔡昀芷 961744 張耀元961725 徐耀宗 961707 牛大維961714 徐詩婷 941617 黃若靜961750 涂書維 941621 江秉憲961618 陳聖祥 941725 劉得準 961755 吳偉豪 941746 陳建翔

Decision Tree

961763 蔡昀芷

What is Decision Tree

• A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility.

• Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal.

• Another use of decision trees is as a descriptive means for calculating conditional probabilities.

SAMPLE

• Wang is a manager of one famous golf club. He wants to know whether the weather is about the reasons for people to play golf. So that he could adjust the employee .

Analysis

• According to the graph we can easily to understand when the weather become worse , the customers would like stay at home or find another thing to do . Seldom of customers would play golf in bad weather .

Advantage

• Easy to understand and implement

• Are simple to understand and interpret.

• Have value even with little hard data.

• Can be combined with other decision techniques.

Disadvantage

• When there is a lot of event will effect the result , then we need to draw a big graph

• And users is difficult to find reasons why the data change in complex graph .

Scoring Model

961725 徐耀宗

What is Scoring Model

1. determine the importance of each criterion to enterprises ： This method is initially related to the team based on the organization's goals and strategies to decide to consider the Criterion, then by mutual discussions to determine the importance of each criterion to enterprises, and individual giving different weight

2. Different organization in a different environment, the criteria that are different weights ： for the different investment options, calculate the points from each of the criteria and get the weight multiplied by the total score for each program in order to score to determine the level of priority investment projects

Why Business use Scoring Model

1. many types of business value: As the business value of IT has brought many species, each different IT investment program for Key Performance Index contribution to different degrees.

2. determine the order of investment ： in this multi-objective , Multiple Criterion decision-making situation, how to determine the order of investment?

3. provide a mathematical model: This multi-criteria analysis can be used to weigh project alternatives and provide a mathematical model for selection of projects or products. 

4. keep the decision factors narrowed： The number of requirements and constraints is not important, but it is important to keep the decision factors narrowed to those the organization views as most important. 

Scoring Model RulesRule 1 ：The total weight for requirements and constraints should equal 100

Requirements+Constraints=Total=100

Scoring Model RulesRule 2 ：Total Requirements weight = 50

Total Constraints weight = 50

Scoring Model RulesRule 3 ： use 1,3,9 scoring model because it forces tough decisions and creat

es separation in the model.

Scoring Model RulesRule 4 ：The individual weights assigned to individual requirements and constraints are

a matter of negotiation among the project selection team.  In  this model, larger numbers indicate the  project is better along that line item.

Scoring = Weight × Rating

Scoring Model RulesRule 5 ：The scoring and summary columns are calculated fields and should not be mo

dified

Example

The organization has determined that X system is needed.  We have been asked to evaluate three platforms using the organization’s multi-criteria analysis. 

Step 1 ： requirements and constraints have been set based on negotiation and review of the organization’s needs.

Step 2, weights for the criteria are applied based on negotiated values.

Step 3, alternatives are selected from a “consideration set” and ratings are applied, giving us a final total.  The larger number is the best

pros and cons

pros ： • Implement a scoring scheme that is easy t

o understand and manage.

cons ：• should have quarterly meetings to review t

he scoring model and tune it based on results from the previous quarter.

Analytical Hierarchy Process (AHP)

961714 徐詩婷

What is AHP?

• A structured technique for dealing with complex decisions.

• Rather than prescribing a "correct" decision, the AHP helps the decision makers find the one that best suits their needs and their understanding of the problem.

• The AHP provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, for relating those elements to overall goals, and for evaluating

alternative solutions.

A simple AHP hierarchy

The procedure for using the AHP

1. Model the problem as a hierarchy containing the decision goal, the alternatives for reaching it, and the criteria for evaluating the alternatives.

2. Establish priorities among the elements of the hierarchy by making a series of judgments based on pairwise comparisons of the elements.

3. Synthesize these judgments to yield a set of overall priorities for the hierarchy.

4. Check the consistency of the judgments.

5. Come to a final decision based on the results of this process.

Example

• In the highly competition market, the organization can attract consumers attention by establishing good brand image. Now, we have to evaluate three alternatives and some criteria which will affect the brand image by AHP.

There are three alternatives have been considered:

1. Advertisement 2. Brand representative 3. Placement marketing

Step1: Model the problem as a hierarchy

• It consists of an overall goal, a group of options or alternatives for reaching the goal, and a group of factors or criteria that relate the alternatives to the goal.

Goal

Criteria

Alternatives

Step 2: Establish priorities among the elements of

the hierarchyPairwise comparisons• Once the hierarchy is built, the decision makers systema

tically evaluate its various elements by comparing them to one another two at a time.

• In making the comparisons, the decision makers can use concrete data about the elements, or they can use their judgments about the elements' relative meaning and importance.

• It is the essence of the AHP that human judgments, and not just the underlying information, can be used in performing the evaluations.

The Fundamental Scale of AHP

The Fundamental Scale of AHP

• The AHP converts these evaluations to numerical values that can be processed and compared over the entire range of the problem.

• A numerical weight or priority is derived for each element of the hierarchy, allowing diverse and often incommensurable elements to be compared to one another in a rational and consistent way.

Step 2

Pairwise comparisons of hierarchy 1

Step 3: Synthesize these judgments to yield a set of overall priorities for the hierarchy.

1. Sum up all of entry in the same matrix column;

2. Normalized matrix: divide each entry by the sum the same matrix column; and

3. Relative importance of attribute (Wi1): average of each normalized matrix row means attribute’s weight and W is a n*1 matrix

Eqn (1)

1. Sum up all of entry in the same matrix column

2. Normalized matrix: divide each entry by the sum the same matrix column

3. Relative importance of attribute (Wi1)

(a): 0.546+0.6+0.471+0.445 = 2.062(b): 0.181+0.2+0.235+0.222 = 0.838(c): 0.136+0.1+0.235+0.222 = 0.693(d): 0.136+0.1+0.059+0.111 = 0.406

Eqn (1)

n=4

Step 4:Check the consistency of the judgments

• Verification on consistency is to inspect the match between subjective decision-making results and the logical transitivity.

• Consistency index (C.I.) is the measurement indictor for pairwise consistency and the formula is as follow

Eqn (2)

1. Calculate weighted supermatrix( )

2. The result divided by the average

Table2.1 Wi1 from Table2.4

：

Eqn (3)Maximal Eigenvalue ：

3. Calculate the maximal or principal eigenvalue

4. Calculate Consistency Index (C.I.)

C.I. ≤ 0.1, this pairwise comparison matrix is acceptable.

Do step 2 to 4 over the hierarchy 2

0.54

Step 5: Come to a final decision based on the results of this process.

• Numerical priorities are calculated for each of the decision alternatives.

• These numbers represent the alternatives' relative ability to achieve the decision goal, so they allow a straightforward consideration of the various courses of action.

↓Table 5.1 The weighted value of each alternatives.

↓Table 5.2 The weighted value of each criteria (from Table 2.4).

Table 4.1 AverageTable 4.2 Average

Table 4.3 AverageTable 4.4 Average

• Value for Advertisement: 0.24*0.515+0.33*0.210+0.16*0.173+0.30*0.102 = 0.251

• Value for Brand representative: 0.14*0.515+0.57*0.210+0.54*0.173+0.16*0.102 = 0.302

• Value for Placement marketing: 0.64*0.515+0.10*0.210+0.32*0.173+0.54*0.102 = 0.460

0.30

• In the evaluation of expenditure :

So, the decision-maker can choose the placement marketing as the alternative to establishing brand image.

Result

Placement marketing > Brand representative > Advertisement

Application - Decision Making Problems

• Planning• Generating a Set of Alternatives• Setting Priorities• Choosing a Best Alternatives• Allocating Resources• Determining Requirements• Predicting Outcomes/Risk Assessment• Designing Systems• Measuring Performance• Insuring the Stability of a System• Optimization• Resolving Conflict

Advantages of AHP

• Systematized the complex problems from different perspectives.

• Improve the communication between team members.

• Provide decision-makers choose the appropriate program by the comprehensive assessment.

Disadvantages of AHP

• As the simplification of the hierarchy structure, some important dependencies may be hided and the decision-making might be over-simplification.

• It's hard to compare the attributes between tangible and Intangible.

Regression Analysis

961750 涂書維

About Regression Analysis

• In statistics, regression analysis helps us understand the relationship between a dependent variable and one or more independent variables.

• In economics, regression analysis is widely used for understanding the relationship between factors, or prediction and forecasting.

Predictions by Regression

• Three goals– Modeling :

Making assumptions since the true form of the data-generating process is not known.

– Predicting :Models for prediction are often useful even when the assumptions are moderately violated. It gives us a acceptable and reasonable result.

– Characterization : How one task leads to and justifies the other tasks.

Do Forecasting by Regression Analysis

• Data:– Usually a subset of entire data.– Identify the effective predictors of the variable of inter

est.

• Scatter Diagram:– Variables like x-value and y-value are selected from d

ata.– It gives us an overall view of the problem.– Use it to determine relationship between variables: Dir

ect, Inverse, Linear or Curvilinear, etc..

• The Model:– If we have determined the relationship betwee

n variables, we can make the function.Example: function y = a + bx + e if there is a linear relationship.

– The predictive line is a "best fit" to the sample data. Notice that there is a error term accounting for variables.

• Measuring Error in Estimation: – variability about the mean value can be meas

ured by calculating the variance

• Confidence Interval:– Interval estimates can be calculated to obtain

a measure of the confidence we have in our estimates that a relationship exists

Example

• What is the relationship between advertisement costs and sells?

• We have the function y = 377.2 + 1.404x + e after calculating the data. We can draw the predictive line:

Advantages

• Regression Analysis Prediction Method help IS/IT managers do forecasting, and get a probably result.

• It helps managers understand the relationship between one factor and another.

• It gives managers an overall view of the problem.

Cases: invoice, inventory control.

Disadvantages

• It may conclude to a wrong result if there is a non-linear relationship between two variables.

• The sample data may not represent to the whole data.

• It only works best with binary variables.

Decision tree analysis

961618 陳聖祥

What is decision tree

• A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility.

• Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal.

Expected Monetary Value

• A specific analytical technique in which a calculation is made to determine the average of all potential outcomes when the future includes a number of particular scenarios that may or may not ultimately happen.

Formula

Example

• The decision is whether to build a factory to take advantage of a product and the resultant EMV from each choice. If demand is high, then there will be ten years of £ 1m sales, if low £ 0.5m. There is an 0.6 probability of high demand and 0.4 for low demand. The cost of a small unit is £ 2.0m, with a capacity of £ 0.5m; a large unit £ 3.5m; for £ 1m and a medium unit at £ 2.75m with a capacity of £ 0.75m. If a small unit is built, then a further small unit can be brought on stream after two years (i.e. to last eight years).

Example

• Using IT1, the probability of earning 8m is 0.6,and the probability of earning 4m is 0.4.It costs 4.2m.

• Using IT2, the probability of earning 7.5m is 0.6,and the probability of earning 5m is 0.4.It costs 3.75m.

• Using IT3, the probability of earning 10m is 0.6,and the probability of earning 5m is 0.4.It costs 4.5m.

Decision tree

Solution

• EMV1(IT1):7*0.6+5*0.4=6.26.2-4.2=2

• EMV2(IT2):7.5*0.6+5*0.4=6.56.5-3.75=2.75

• EMV3(IT3):10*0.6+5*0.4=88-4.5=3.5

• EMV4(Do nothing):0• Due to the expected income, we choose “IT

3”.

Advantages

• Easy to understand

• Map nicely to a set of business rules

• Applied to real problems

• Make no prior assumptions about the data

• Able to process both numerical and categorical data

Disadvantages

• Output attribute must be categorical

• Limited to one output attribute

• Decision tree algorithms are unstable

• Trees created from numeric datasets can be complex

Total Cost of Ownership

961755 吳偉豪

What is TCO?

• Total Cost of Ownership (TCO) is defined as all of the possible costs incurred in the life cycle of a workstation, from acquisition to disposal.

• Traditionally, calculate IT costs often only calculate acquisition cost. But acquisition cost has only 20% of TCO, the enterprise often ignore the other 80%.

TCO

• The IS/IT cost can divide into three categories:

1.Acquisition Cost( 獲取成本 ): Include hardware, software, system, database, network…., the purchase cost at first.

TCO

2.Operational Cost( 操作成本 ): Operational costs are the recurring expenses which are related to the operation of a business. Include update, support, training cost.

3.Control Cost( 控制成本 ): The cost for planning the whole IS/IT (Centralization Cost), and the cost for making the enterprise standardized (Standardization Cost).

Expands the meaning for MIS

• TCO emphasize that it has not only hardware and software cost, but also has other costs(Operational cost, Control cost). But enterprise often ignores to compute, leading the costs higher than the benefits and the investment fails.

Example

• There are two similar functions software, Blackberry Enterprise Server and Microsoft Exchange Server. A company use TCO to decide which one to purchase.

TCO = Acquisition Cost + Operational Cost

And the cheaper one is better.

Blackberry Server

TCO ($166182)

Microsoft Server

TCO ($108034)

Because Microsoft

Server is cheaper.

So buy Microsoft

Server.

Advantage

• Obviously it is sensible to consider ALL costs when an asset is acquired.

• TCO is a long-term measure, and reduces the total costs over time.

Disadvantage

• The effort that is needed to do a TCO analysis.

• Performing a TCO analysis has itself a cost.

• No general formula exists.

• Sometimes it can be difficult to determine whether, and to what extent, certain costs must be allocated to an asset.

Disadvantage

• TCO does not offer help for the valuation of intangible assets.

• Because TCO is a long-term measure, it reduces costs over time. If you have to cut cost immediately, TCO is not very useful.

• Generally, TCO does not assess the risks that are involved with a purchase of an asset.

Data Envelopment Analysis(DEA)

(資料包絡分析 )

961744 張耀元

What is DEA?

• A non-parametric technique for effectiveness evaluation with several variables.

• A powerful method widely used in the evaluation of performance of Decision Making Units (DMUs).

Basic DEA mode

• The efficiency of each DMU is the ratio (sum of weighted outputs)/(sum of weighted inputs), adjusted to be a number between 0 and 1.

• If a DMU’s efficiency = 1 ,called a benchmark.

Data Envelopment Analysis

• Those DMUs which do attain an efficiency of 1 form a mathematical space which "envelops" all the other DMU points, hence the name “Data Envelopment Analysis”.

Efficient Frontier• Units A,B,C and D define the Efficient Fro

ntier, while units E,F and G are inefficient.

• E could become efficient and move to the efficient frontier at point E', by increasing its outputs or decreasing its input.

ExampleMake decision of selecting the most benefit I

S

for a company.

1) Calculate DMU’s efficiency score of the three IS.

Inputs Outputs

Human Resource Cost benefit

IS A 50 60 150

IS B 90 60 180

IS C 100 120 240

Example(cont.)In order to calculate the three DMUs’ efficiency which

are between 0 and 1, we shall consider three unknown

variables u1, v1, v2 with the following conditions…

For IS A ：MAX[(u1*150) / (v1*50+v2*60)]

(u1*150) / (v1*50+v2*60) ≤ 1

(u1*180) / (v1*90+v2*60) ≤ 1

(u1*240) / (v1*100+v2*120) ≤ 1

u1, v1, v2 ≥ 0

(Using SOLVER.XLAM in Excel)

After find out variables (u1,v1,v2)

A’s efficiency = (u1*150) / (v1*50+v2*60)

un Unknown variables which are the coefficients of the output units.

vn Unknown variables which are the coefficients of the input units.

Example(cont.)Use the same method to find B and C’s efficiency.

For IS B ：MAX[(u1*180) / (v1*90+v2*60)]

(u1*150) / (v1*50+v2*60) ≤ 1

(u1*180) / (v1*90+v2*60) ≤ 1

(u1*240) / (v1*100+v2*120) ≤ 1

u1, v1, v2 ≥ 0

After find out variables (u1,v1,v2)

B’s efficiency = (u1*180) / (v1*90+v2*60)

Example(cont.)

For IS C ：MAX[(u1*240) / (v1*100+v2*120)]

(u1*150) / (v1*50+v2*60) ≤ 1

(u1*180) / (v1*90+v2*60) ≤ 1

(u1*240) / (v1*100+v2*120) ≤ 1

u1, v1, v2 ≥ 0

After find out variables (u1,v1,v2)

C’s efficiency = (u1*240) / (v1*100+v2*120)

Example(cont.)2) Put the DMUs’ on the axis and connect the DMUs

which have efficiency = 1 to find out the efficiency frontier.

In this way, we can find the most benefit IS.

The real achievable targets can also be defined for C

in the decisions.

Advantages

• Can handle multiple inputs and outputs

• Understand the relative allocation efficiency of resources, to provide decision-makers to improve the situation and direction

• The effect is better while the unit of measure of the homogeneity is higher.

Disadvantages

• The efficiency is a relative value, not absolute values.

• The number of the DMUs cannot be too small.Max[a*b, 3*(a+b)]

• DEA only shows that the efficiency value, not to further understand the factors affecting efficiency.

Minimax Regret Approach

961707 牛大維

What is Minimax Regret Approach

Regret is often also called opportunity loss. Minimax regret is also called difference regret. Furthermore, the ratio regret is the ratio between the actual payoff and the best one.

The procedure in using the Minimax Regret Approach

1. Construct a return matrix.

2. Create an opportunity loss table. Opportunity loss is calculated by subtracting each value(return) in the column from the max value(best return) in the column.

3. Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number.

Example

Suppose an investor has to choose between investing in stocks, bonds or the money market, and the total return depends on what happens to interest rates. The following table shows some possible returns:

Step1:Construct a return matrix

The following table shows some possible returns:

Return Interest rates rise Static rates Interest rates fall

Stocks -4 4 12

Bonds -2 5 8

Money market 3 2 1

單位 : 百萬元

Step2: Create an opportunity loss table

Interest rates rise Static rates Interest rates fall

Stocks 3-(-4) 5-4 12-12

Bonds 3-(-2) 5-5 12-8

Money market 3-3 5-2 12-1

Opportunity Loss Tables

Opportunity loss is calculated by subtracting each value(return) in the column from the max value(best return) in the column.

單位 : 百萬元

Step2(cont.) Interest rates rise Static rates Interest rates fall

Stocks 3-(-4) 5-4 12-12

Bonds 3-(-2) 5-5 12-8

Money market 3-3 5-2 12-1

Interest rates rise Static rates Interest rates fall

Stocks 7 1 0

Bonds 5 0 4

Money market 0 3 11

Opportunity Loss Tables

單位 : 百萬元

單位 : 百萬元

Step3:find the answer

• Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number.

Interest rates rise

Static rates

Interest rates fall Maximum in the row

Stocks 7 1 0 7

Bonds 5 0 4 5

Money market

0 3 11 11

minimum 單位 : 百萬元

Result

• Therefore, using a minimax choice based on regret, the best course would be to invest in bonds, ensuring a regret of no worse than 5.

Advantage

• Suit for decision-makers who are pessimistic.

• Know the opportunity losses in advance, and reduce it possibly.

Disadvantage

• The decision is very Subjective, because everyone have different judgments about options.

• Low risk usually accompany low profit.

• Over-caution is not appropriate for a company that is expanding.

source

• quote from http://en.wikipedia.org/wiki/Minimax_regret#Minimax_regret

941617 　黃若靜

Return On Invaestment

• ROI is a financial weight tool.

• Consider the saving cost.

• Compares several investment choices, ROI is an easy to use method.

What is ROI?

esExpenditur IS/IT Annualized

Revenues

Formula

• To reduce Maintenance cost.

• To reduce Service cost.

• To reduce Time cost.

• Fewer trainings.

Example Of Revenues

• Initial investment.

• Training Cost.

• Switching Cost.

Example Of Expenditures

• The company wants to invest a ERP system.

• There are two system be selected.

• System A has more expenditures than B.

• But System A also make more revenues.

• Use ROI analysis, company will choice the best system.

Example

System A System BExpenditures $2,000,000 $1,600,000

Reduced Maintenance cost

$105,000 $95,000

Reduced Service cost

$130,000 $80,000

Reduced Time cost

$55,000 $30,000

Reduced trainings $110,000 $50,000

Revenues $400,000 $255,000

ROI%20

000,000,2$

000,400$ %16

000,600,1$

000,255$

Example

• Not easy to quantify Saving cost.

• Need many department’s data.

• Revenues are estimate.

Disadvantage

淨現值法Net Present Value (NPV)

941261 江秉憲

What is NPV?

• The net present value (NPV) is defined as the sum of the present values (PVs) of the individual cash flows.

• The NPV is simply the PV of future cash flows minus the purchase price.

• NPV is a standard method for using the time value of money to appraise long-term projects.

NPV formula

• Formula:

• － C0 ： represent the cost must pay now• CFi ： the cash flow of period i • k ： require rate of return• n ： the number of invest period

What NPV means?• NPV is an indicator of how much value an

investment or project adds to the firm.If... It means... Then...

NPV > 0 the investment would add value to the firm

the project may be accepted

NPV < 0 the investment would subtract value from the firm

the project should be rejected

NPV = 0 the investment would neither gain nor lose value for the firm

We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation.

The advantage of NPV

• NPV gives an absolute value.

• NPV allows for the time value of the cash flows.

The disadvantage of NPV

• It is very difficult to identify the correct discount rate.

• NPV as method of investment appraisal requires the decision criteria to be specified before the appraisal can be undertaken. 

Example of YunLin Station of Taiwan High Speed Rail Corporation

Example of YunLin Station of Taiwan High Speed Rail Corporation(co

nt.)• For investor:

– When the sale rate increase and the actual sale amount is higher than the predict amount, the investor would get a higher rate of return.

• For government– First, government translate the interest to inve

stors who eventually will raise the land’s value in order to gain a higher return.

– Second, the NPV is bigger than 0, so this plan is working.

Conslusion

• NPV is a central and standard method to help companies making decisions, but it still needs other methods to do an exact prediction.

Reference

• 論文 - 從財務面探討以不動產證券化推動區段徵收之研究─以高鐵雲林車站特定區為例。

• http://wiki.mbalib.com/zh-tw/净现值• http://en.wikipedia.org/wiki/Net_present_v

alue

Payback period method

941725 劉得準

introduction

• Payback period method is a favorite method for company to estimate the invested.

• Assessing the payback period.

• The manager has to decide the payback period before chose the investing plan.

introduction

• The standard of assessment ：

1. The cost’s payback period in

specific time.

2. The payback period shorten will

be better.

Formula

• Cost of capital investment / annual cash inflow = Payback period.

• Depreciation expense must be added back to annual/net cash inflow.

• Assume the company will invest 5 million dollars in current project, according payback period this plan will make 3 million dollars at first year,2 million dollars at second year and 1 million dollars at third year.

Income revenue: 3 million 2 million 1 million dollars

0 1 2 3

expense: -5 million dollars

Advantage

• Easy to count : The formula is very simple.

• Easy to understand: The theory is not complexity.

• Easy to operate

Disadvantage

• Managers will easy to ignore the different period have different time value of money.

• The payback period method can not evaluate the cash flow completely in each operating time.

• It’s hard to decide the payback period for managers first.

The case of fail

• The initial cost of System A,B,C are 10,000,000.

• System A : 200+300+500=1,000

• System B : 500+300+200=1,000

• System C : 500+300+200=1,000

• The payback period of System A,B,C are three years.

• The total return of System A & B are 6,000,000, but System C is 60,000,000.

• Conclusion: The payback period can not predict each cash flow exactly.

• Investing plan : A,B and C ‘s total return• unit ： 10 thousand

YEAR A B C

0 -1000 -1000 -1000

1 200 500 500

2 300 300 300

3 500 200 200

4 600 600 6000

Payback period 3 3 3

Case• Sierra company intend to invest the EWT s

ystem to save the cost of testing employee.– System A

• Initial cost ： $20,000• Saving cost of each year ： $4,000• Fixed number ： 5 years

– System B• Initial cost ： $28,000• Saving cost of each year ： $8,000• Fixed number ： 5 years

• Cost saving + salvage value = total return• The initial cost of System A is 20,000,the secon

d year’s total return is 21,000.• The initial cost of System B is 28,000,the secon

d year’s total return is 28,000.• Conclusion : system A is better than system B.

Internal Rate of Return (IRR)

941746 陳建翔

Introduction

• The internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the profitability of investments.

• It is also called the discounted cash flow rate of return (DCFROR) or simply the rate of return (ROR).

Definition

• Using a discount rate to calculate the net present value of a product, make the net present value discount rate of zero is the internal rate of return.

Formula

0)1( 0

1

Cr

CFNPV

n

tt

t

NPV : net present valueCF : cash flow of each periodC0 : initial costr : Internal Rate of Return

Decision-making

• IRR > Expected return on investment

– This case can be invested .

• IRR > Expected return on investment

– This case can not be invested.

Advantage

• List all of the cash flow.

• List all the time of the cash flow in or out.

• Easy comparison with the cost of capital.

Disadvantage

• Without taking into consideration the amount of investment

• It may have multiple solutions.

• When different cases have different risk it can not make decisions .

Example

Period Case A Case B

0 -1000 -1500

1 300 400

2 350 350

3 450 450

4 400 800

Solution

tt IRRCFPV )1/(