investment criteria modified npv,irr
TRANSCRIPT
Evaluating ProjectsCapital Budgeting Concepts
IBS
Tanvi Gupta
Structure
Semester IIIProject Appraisal &
Finance
Sessions 3-5Project Selection- Appraising
ProjectsTime Value of Money – A recap
Investment Criteria Modified NPV, IRR , Simple, Non-
Simple , Pure and Mixed Investment
Session 26-27Multiple Projects & Constraints
Ranking, Feasible Combinations Approach. Integer programming, Goal
Programming – An overview
Session 1 -2Overview: Capital Investments
Process Key Issues in major investment
decisions
Session 15-16Structuring Projects:
Application of Portfolio Theories to Capital
Budgeting- Asset Beta from Equity Beta
Sessions 23-25Environment Appraisal of Projects – Presentations
Social Cost Benefit Analysis- Presentations & Discussions
Sessions 6 CEC 1
Sessions 28-29Project Review,
Abandonment AnalysisDetailed Project Reports –
Discussions
Sessions 12 -13Project Initiation &
Resource Allocation- Presentations & DiscussionsMarket and demand Analysis
Forecasting Technical Analysis –
Presentations
Session 17-22Cost of Project, Means of
Finance, Estimation of Working Capital, Profitability Estimations,
Balance Sheet Projections etc.CEC -3
Sessions 14 Mid Sem
Sessions 7-12Selection Contd…
Project Risk AnalysisSensitivity, Hiller Model & Decision Tree
Project Rate of Return, Real Options
Sessions 30Revision & Quiz
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Session Plan
1. Capital Budgeting Concepts2. Features of Capital Budgeting Decision3. Techniques of evaluation 4. Criteria for viability testing5. NPV V IRR6. Indifference Point 7. Modified NPV8. Modified IRR9. Annual Capital Charge
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Capital BudgetingCapital budgeting decisions relate to
acquisition of assets that generally have long-term strategic implications for the firm.
Capital budgeting decisions become fairly intricate as it impacts other areas of corporate finance like capital structure, dividends and cost of capital.
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Features Of Capital Budgeting Decision
Non-reversible, Large initial outflow followed by small
periodic inflows,Information gap and inexperience, Strategic and risky in nature, No scope of learning and correcting
from past experienceLittle flexibility.
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Types Of Projects Small vs Large Projects New vs Expansion Projects Independent and Mutually
Exclusive projectsMutually exclusive projects are those
where acceptance of one implies automatic rejection of the other.
Research & Development and Mandatory Projects
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Financial AppraisalFinancial appraisal of any project looks at return and risk characterising that particular project and examines whether return exceeds the cost of financing the project.
The first step is appropriate compilation of data on cost of the project, means of financing and projected revenues and costs.
The next step is to appraise the viability of the project using different criteria of merit.
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Techniques Of Evaluation
The methods of financial evaluation of the projects are categorized into two:Non DCF techniques. Discounted Cash Flow (DCF)
techniques
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Appraisal Criteria
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Payback Period Accounting R ate of R eturn
N on-D iscounting C riteria
N et P resent V alue Benefit C ost R atio In ternal R ate of R eturn
D iscounting C rite ria
Evaluation C rite ria
Payback Period Method
Payback period of the project is the amount of time required to recover the original investment.
• Simple in both concept and application.• Weeds out risky project ensuring acceptance of
those with substantial earlier inflows.
When done on discounted cash flow basis it is called discounted payback period.
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Payback period contd…
An illustration:A project with an initial outflow of Rs 10 lakhs is
expected to generate a constant inflow of Rs 2,50,000 for a period of 10 years.
Pay back period = 10 / 2.5 = 4 yearsThe project is paying you back the amount invested
in four years. Shorter the PB period, the better.
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Payback Period-Illustration -1
• Find the payback period
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Initial cash outflow 10,00,000Cash inflows 1st Year 3,00,000
2nd Year 5,00,0003rd Year 4,00,0004th Year 5,00,000
Payback period for the project is 2½ years.
Pay Back Period- Illustration 2
For Projects with uneven inflows :
The inflows are cumulated to find the payback period. An illustration:Initial outflow of the project is 10 lakhs. The inflows are as under:
Inflows Cumulative Inflows1. 150000 1500002. 300000 4500003. 320000 7700004. 230000 1000000 The payback period is 4 years5. 3500006. 3200007. 3500008. 2700009. 28000010. 400000
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Decision Rule
If the project’s PB period is less than a cut-off period earmarked for similar projects, accept it.
If there are multiple projects, accept the one with lowest PB period.
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Shortcomings of PB Period Criteria
The time value of money is not considered. This can be overcome by introducing discounting factor in the inflows of the project.
Ignores post PB period cash inflows. It is more a measure of capital recovery.
Inability to handle Multiple Cash Out Flows
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Accounting Rate Of Return
Accounting Rate of Return is defined as average profit as % of average investment over the life of the project
To enable the firm make a conscious decision whether to accept or reject a proposal, it needs to be compared with some acceptance/ rejection criteria.
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Investment AverageProfit Average=Return of Rate Accounting
Accounting Rate Of Return- Illustration Accounting rate of return = Average PAT/ Average book value of investmentAn illustration:Year Sales Revenue Opex Depreciation Annual Income
0 (90000)1 120000 60000 30000 300002 100000 50000 30000 200003 80000 40000 30000 10000Average annual income = (30000+20000+10000)/3 = 20000Average book value of investment = (90000 + 0) /2 = 45000ARR = 20000/45000 = 44%
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Decision Rule
If ARR is greater than the external yardstick of similar projects or of industry, accept the project.
For Multiple projects project with highest ARR should be accepted.
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Merits & Shortcomings of ARR criteria
Merits:Return on investment unlike return of investment as in
PB periodConsiders returns over entire life of project Shortcomings:Time Value of money is ignoredAccounting income and not cash flows are
considered.
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Net Present Value (NPV)
NPV is the difference between present value of inflows and present value of outflows.
Money has time value. Firstly, money can be employed productively to generate real returnsSecondly, due to uncertainties in future , individuals prefer current consumption to future consumptionThirdly, due to inflation a rupee today has a higher purchasing power than a rupee in the future.
The three components of nominal or market interest rate = Real rate of interest or return + expected rate of inflation + risk premium to compensate for uncertainty.
To calculate present value of future flows, an appropriate discounting rate is used.
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NPV - Illustration 1 That discounting rate can be comprehended as cost of capital An illustration:
Initial outflow of the project is 10 lakhs. The inflows are as under:Yr Inflows PVIF(10%) PV inflows1. 150000 .909 1363502. 300000 .826 2478003. 320000 .751 2403204. 230000 .683 1570905. 350000 .621 2173506. 320000 .564 1804807. 350000 .513 1795508. 270000 .467 1260909. 280000 .424 11872010. 400000 .386 154400
------------PV of inflows 18,08,150=======
NPV = PV of inflows – PV of outflows= 18,08,150 – 10,00,000= 8,08,150 ₹
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Decision RuleIf NPV is positive, accept the project as after taking
into consideration the uncertainties and riskiness the project is generating positive returns.
If NPV is negative , reject the proposed project.If NPV is zero , theoretically one should be indifferent
but in practice marginally viable projects should be rejected.
In case of multiple projects, project with highest NPV should be accepted.
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Computing NPV Illustration 2Project ‘A’
Year Cash flow Present Value at 10%Year 0 -10,00,000 -10,00,000Year 1 5,00,000 5,00,000/1.1 = 4,54,545 Year 2 5,00,000 5,00,000/1.12 = 4,13,223 Year 3 5,00,000 5,00,000/1.13 = 3,75,657
NET PRESENT VALUE 12,43,425 – 10,00,000= 2,43,425
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Computing NPV – Illustration 2 contdProject ‘B’
Year Cash flow Present Value at 10%Year 0 -10,00,000 -10,00,000Year 1 8,00,000 8,00,000/1.1 = 7,27,273 Year 2 2,00,000 2,00,000/1.12 = 1,65,289 Year 3 8,00,000 8,00,000/1.13 = 6,01,052
NET PRESENT VALUE 14,93,614 – 10,00,000= 4,93,614
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Additive Property Of NPV
NPVs of different projects can be added to arrive at total NPV.
NPV (A+B) = NPV (A) + NPV (B) Additive property of NPVs helps in isolating the
impact that each project makes on the value of the firm.
NPV of Project ‘A’ 2,43,425NPV of Project ‘B’ 4,93,614NPV of A & B Combined 7,37,039
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Excel Formula for NPV Net Present Value: Illustration
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Merits & Shortcomings of NPV CriteriaMerits: Recognizes time value of money Considers entire stream of cash flows
Shortcomings: Change in discounting rate affects the desirability of
project As an absolute measure, acceptance of project with
higher NPV may involve acceptance of project with higher initial outflow. (16-8=8 – Project A, 12-5= 7 – Project B)
According to NPV Project A is better but a comparison at the outflow clearly entails Project A with higher outflow (BCR would have been a better proposition in such cases
Not suitable for comparison of projects with different economic lives Project with higher PV may also have a longer economic life –funds getting blocked for alonger period. (We use Equivalent Annual Charge)
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Benefit-cost ratio (BCR)criteriaPopularly known as Profitability Index BCR is the ratio of PV of inflows to OutflowsIt is a relative measureBCR = PV of Inflows/PV of outflows.Continuing with the same illustration, BCR =
18,08,150/10,00,000=1.808 > 1, the project can be accepted.
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Decision Rule
If BCR > 1 project is qualified for acceptance
If BCR < 1 the project should be rejected
If BCR = 1 then one is indifferent about the project
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Merits & Shortcomings
Merits :Recognises time value of moneyTotality of benefits are consideredRelative Measure
Shortcomings:In Multiple projects situations with limited funds , wherein more than one project can be accepted, BCR cannot be used as index cannot be aggregated
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Internal Rate of Return(IRR)
Also known as yield on investment, marginal efficiency of capital
IRR is the rate at which present values of inflows are just equal to outlays.
Under NPV criterion, discounting factor taken is as per the external factors like risk, uncertainties and cost of funding the project, While IRR is based on the facts internal to the proposal, hence it is named so.
Mathematically, IRR is the discounting rate (internal) which makes its NPV zero. But actually, It is return on investment taking time value in consideration.
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IRR….At Internal Rate of Return (IRR) of the project
the net present value (calculated at IRR) is zero.
For a project outlay of Rs. 200 and cash inflows for next 2 years at ₹ 110 and ₹ 121, the IRR may be found as follows:
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0
n
1t
t CFr)+(1
CF∑
200rr1
110
2)1(121
IRR- Illustration - 2An initial outflow of ₹ 135000Yr Cash Flow 1 30000 2 40000 3 45000 4 47500 5 50000
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IRR- Illustration - 2 contd IRR is that rate of return which equates PV of inflows to outflow
135000 = 30000/(1+r) + 40000/(1+r)2 + 45000/(1+r)3 + 47500/(1+r)4 + 50000/(1+r)5
Thus IRR is the r to be found out from the above equation Steps for finding out IRR:1. Fake Payback period to be calculated. Add up all the inflows and find
an average inflow. Based on average inflow , rate/rates from the table of PVIFA to be taken against respective life of the project.
2. Adjust it for the pattern of cash flow. (whether it is increasing or decreasing)
3. Calculate the PV using the rates and interpolation technique
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Example 2 contd….Average of inflows is 42500.(Adding up all inflows and dividing by 5)Fake PB period = 135000/42500 = 3.1764 years.Looking for the above factor in PVIFA table in the row of 5 years,
the nearest figure is 3.127 against 18% and 3.199 against 17%( or 3.2743 against 16%)
Adjusting for the pattern of flows, as the cash flows are in increasing order the discounting rates should be reduced by say 2%. (As IRR is return, due to the higher discounting at the later years , lesser return is generated)
Then substituting the values of 15% and 16% the PV of inflows are respectively 137938.05 and 134457.66. One greater than the initial outflow and one less.
Interpolating between the two we get 15 % + (137938.05-135000)/(137938.05-134457.66) X (16% - 15%)
= 15.84 %
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IRR- Illustration - 2
An initial outflow of ₹ 135000Yr Cash Flow PV(15%) PV (16%) 1 30000 30000 x.870 30000x.862 2 40000 40000x.756 40000x.743 3 45000 45000x.658 45000x.641 4 47500 47500x.572 47500x.552 5 50000 50000x.497 50000x.476 ---------------- ------------------ Total 137938.05 134457.66 ========= ==========
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Decision Criteria
If IRR > Cost of funds, accept the projectIf IRR < Cost of funds, reject the projectIf IRR = Cost of funds, One is indifferent about the
project.If there are two or more projects, project generating a
higher IRR, should be accepted.
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Merits & Shortcomings
Merits:Recognizes time value of moneyCash flow considered in its entiretyHelps in assessing margin of safety of projectVariations in cost of capital does not change ranking
of projectsShortcomings:Projects with mixed stream of flows may have more
than one IRR
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NPV And IRR
Under most circumstances the priorities of the projects as given by NPV rule and IRR rule are identical.
Under cases of non-conventional cash flows and mutually exclusive projects there is a possibility of the conflict in decision-making rules of NPV and IRR.
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NPV And Discount Rate
As discount rate increases NPV falls.The discount rate at which NPV is zero is the IRR.
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Net Present Values & Discount Rate
(20.00)
-
20.00
40.00
60.00
80.00
0 10 20 28.23 35
Discount Rate (%)
NPV
NPV And IRR – Decision RulesA Comparison As per NPV rule: The project is accepted as long as the discount rate is
below 28.23% because the net present value remains positive till then.
It is rejected for discount rate beyond 28.23%.As per IRR rule: The project is accepted as long as cost of capital
remains below 28.23%, the IRR of the project. It is rejected if cost of capital exceeds 28.23%.
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Mutually Exclusive ProjectsNPVs and IRRs
NET PRESENT VALUES OF PROJECT A & B
(20.00)
-
20.00
40.00
60.00
80.00
100.00
- 5.00 10.00 15.00 20.00 25.00 30.00
Discount Rate (% )
NPV (Rs.)
NPV(A) NPV(B)
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Point Of Indifference
Due to varying sensitivities to the discount rate, the NPVs of two project would intersect at some point.
The point of indifference is that discount rate at which the NPV of two projects is equal.
NPVA = NPVB IRR of the differential cash flow gives the
discount rate at which NPVs of the two projects, is equal.
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NPV And IRRUnder most circumstance the priorities of the projects
as given by NPV rule and IRR rule are identical.Under cases of non-conventional cash flows and
mutually exclusive projects there is a possibility of the conflict in decision-making rules of NPV and IRR.
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Mutually Exclusive ProjectsNPVs and IRRs
NET PRESENT VALUES OF PROJECT A & B
(20.00)
-
20.00
40.00
60.00
80.00
100.00
- 5.00 10.00 15.00 20.00 25.00 30.00
Discount Rate (% )
NPV (Rs.)
NPV(A) NPV(B)
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NPV V IRR
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NET PRESENT VALUES OF PROJECT A & B
(20.00)
-
20.00
40.00
60.00
80.00
100.00
- 5.00 10.00 15.00 20.00 25.00 30.00
Discount Rate (% )
NPV (Rs.)
NPV(A) NPV(B)
NPV(A) > NPV(B)Project A is
preferable over Project B
NPV(B) > NPV(A)Project B is
preferable over Project A
Modified NPV
The standard net present value method is based on the assumption that the intermediate cash flows are re-invested at a rate of return equal to the cost of capital. When this assumption is not valid, the re-investment rates applicable to the intermediate cash flows need to be defined for calculating the modified net present value
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Modified NPV Calculate the terminal value of the project’s cash inflows using the
explicitly defined reinvestment rate(s) which are supposed to reflect the profitability of investment opportunities ahead of the firm.
n TV = CFt (1+r t)n-t
t=1
Step 2: Determine the modified net present value
TV
NPV* = - I
(1+ r)n
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Modified NPV – Illustration Contd.. With Two Different Reinvestment rate Project X
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Project X Cost of capitalInvestment outlay 1,10,000 1,10,000 10%
Cash inflowsYear Project X 14% 20%
1 31,000 45,928 53,5682 40,000 51,984 57,6003 50,000 57,000 60,0004 70,000 70,000 70,000
2,24,912 2,41,168Formula for Project X at 14%
Modified Net Present Value of Project X 43,618 54,721
Terminal value on reinvestment when interest rate is
Modified NPV – Illustration Contd.. With Two Different Reinvestment rate Project Y
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Cash inflowsYear Project Y 14% 20%
1 71,000 1,05,190 1,22,6882 40,000 51,984 57,6003 40,000 45,600 48,0004 20,000 20,000 20,000
2,22,774 2,48,288Formula for Project Y at 14%
Modified Net Present Value of Project Y 42,157 59,584
Terminal value on reinvestment when interest rate is
Problems with IRR• Non-Conventional Cash Flows
• Mutually Exclusive Projects
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Non-Conventional Cash Flows
C0 C1 C2
-160 +1000 -1000
TWO IRRs : 25% & 400%
NO IRR : C0 C1 C2
150 -450 375
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Mutually Exclusive Projects
C0 C1 IRR NPV(12%)
P -10,000 20,000 100% 7,857
Q -50,000 75,000 50% 16,964
Modified IRR
Modified IRR method is an attempt to reconcile with NPV method by overcoming the objection of reinvestment rate
Under the modified IRR method the cash in flows of each year are converted to terminal year by compounding them at cost of capital/any other suitable reinvestment rate.
It is consistent with NPV method. It eliminates the problem of multiple IRRs if it exists
by taking a single flow at beginning and single cash flow at the end of the project.
It assumes a more realistic reinvestment rate (Usually Cost of Capital) consistent with conservatism policy.
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Modified IRR – An Illustration
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( All amounts in Rs. Million)
Year Cash flowPresent value of costs
Terminal value of the cash inflows
0 -120 1201 -80 69.572 20 34.983 60 91.254 80 105.805 100 115.006 120 120.00
189.57 467.03Cost of capital 15%
MIRR 16.22%Formula MIRR(B4:B10,0.15,0.15) 16.22%
189.57 = 467.03/(1+r)^6r = 16.2%
Modified IRR : Illustration
Annual Capital Charge- An appraisal Criteria
Annual Capital Charge is an appraisal criteria for projects:1. With unequal life spans 2. Mutually exclusive providing similar services3.Differing in Cost Patterns
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Steps for Computing ACC
Present Value of Initial Investment and Operating Costs using appropriate discount rate
Divide the sum ( as computed in the first step) by PVIFA of the life of the projects
Quotient is denoted as the ACC or Annual Capital Charge or Equivalent Annual Cost
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Criteria for ACC
Compare the two or more projects/ alternativesThe Project/alternative with minimum annual capital
charge (ACC) is to be selected.
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IllustrationHindustan Forge Ltd is evaluating two alternative systems A and
B for internal transport. While the two system serve the same purpose, system A has a life span of 7 years and system B , a life of 5 years. Assume cost of capital to be 12%.( Salvage value can be assumed to be nil) The initial outlay and operating costs associated with the system are:
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Year A B- 1,000,000 800,000
1 100,000 75,000 2 125,000 100,000 3 150,000 120,000 4 175,000 140,000 5 200,000 100,000 6 225,000 7 200,000
Solution
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Year A PV (12%) B PV(12%)
- 1,000,000 1,000,000 800,000 800,000
1 100,000 89,286 75,000 66,964
2 125,000 99,649 100,000 79,719
3 150,000 106,767 120,000 85,414
4 175,000 111,216 140,000 88,973
5 200,000 113,485 100,000 56,743
6 225,000 113,992
7 200,000 90,470
Total 1,724,865 1,177,813
PVIFA (12, 7) 4.564
PVIFA (12, 5) 3.605
ACC 377,928.32 326,716.37
As ACC for System B is lower, System B is preferred
An Illustration A project with the following inflows:
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Year Cash Flow0 -3000001 02 4170003 117000
IRR- Unrecovered Investment Balance
Year Unrecovered Investment Balance
Interest for the year Ft-1 *r
Cash Flow at the end of the year Ct
Unrecovered Investment Balance at the end Ft-1 (1+r)+Ct
1 -300000 -90000 0 -3900002 -390000 -117000 417000 -900003 -90000 -27000 117000 0
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Summary
1. Cash Flow to be used for Capital Budgeting decisions.2. For Financial appraisal of projects, non-discounting and discounting techniques
are used3. Payback period and Accounting rate of return are simple non-discounting
technique used4. PB period shows capital recovery 5. ARR takes Accounting income as the base6. NPV is the difference between cash inflows and outflow after taking time value
and discounting factor into consideration7. BCR is a relative measure – ratio of PV of inflows to outflow8. IRR is the rate of return of the project wherein its inflows just equal outflows9. NPV & IRR may differ in their viability decision for non-conventional flows. 10. Modified IRR (closer to NPV criteria )11. Annual Capital Charge for comparing projects with unequal lives.12. Unrecovered Investment Balance – An Introduction
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Any Queries?
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