Project Appraisal – Capital Budgeting Methods
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Transcript of Project Appraisal – Capital Budgeting Methods
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Project Appraisal CapitalBudgeting Methods
Dr. Janardhan G NaikM.com, LL.B, AICWA,Ph.D
Cost Accountant and
Professor, Head Dept of Accountancy
Gogte College of Commerce,Belgaum 590 006 Karnataka State, INDIA
Cell : (0091) 9448578089 Email:[email protected]
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Project Appraisal
Based on the Techno-Economic Analysis,
and other factors of detailed project report
a Project Appraisal or capital budgeting orcapital expenditure or investment
decisions are arrived.
The decision is to select a particular
project or not or which alternate project is
the best to be selected
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Types of Investment Decisions
Public SectorInvestment Decisions
Private SectorInvestment Decisions
Expansion of existing business
Expansion of new business
Replacement and modernisation
Research & Development project
Independent (accept or reject) investments Contingent investments
Mutually exclusive investments
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Public Sector Investment Decisions
1. By Administrative Ministry:
1. If the project is within the ceiling of approvedbudget and plan provisions
2. For Railway, Defense, Dept. of AtomicEnergy, Dept of Space, & Dept. ofElectronics, no budget ceiling.
2. By Committee for Public InvestmentBoard (CPIB) if the project is above theceiling of approve budget and planprovisions
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Procedure
Pre-Feasibility Report (PFR) evaluation (clearance orobjection) by Project Appraisal Division of the PlanningCommission, Dept. of Public Enterprises, Dept. ofEnvironment & Forest, Dept. of Plan Finance from
different angles Techno-Economic Feasibility Report (TEFR) preparation
if PFR is cleared, and submitted to Public InvestmentBoard through secretary of the Administrative Ministry forsecond stage clearance
Detailed Project Report (DPR) prepared, if TEFR iscleared and submitted for clearance for PIB and also byCabinet Committee on Economic Affairs (CCEA)
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Private Sector Investment
Evaluation Criteria In private Sector Board of
Directors or Top management
takes project decisions. Procedure ofInvestment Decisions:
1. Estimation of cash flows
2. Estimation of the required rate ofreturn (the opportunity cost of capital)
3. Evaluation Criteria i.e. Application ofdecision rules to choose
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Investment Decision Rule
Consider all cash flows to determine the true profitabilityof the project.
Maximise the shareholders wealth.
Choose among mutually exclusive projects whichmaximises the shareholders wealth.
Rank projects according to their true profitability.
Bigger cash flows are preferable to smaller ones andearly cash flows are preferable to later ones.
Provide for an objective and unambiguous way ofseparating good projects from bad projects.
Decision rules must be capable of application to anyinvestment project.
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Components of Cash Flows
Initial Investment
Net Cash Flows
Revenues and Expenses Depreciation and Taxes
Change in Net Working Capital Change in accounts receivable
Change in inventory Change in accounts payable
Change in Capital Expenditure
Free Cash Flows
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Components of Cash Flows
Terminal Cash Flows
Salvage Value Salvage value of the new asset
Salvage value of the existing asset now
Salvage value of the existing asset at the end of its
normal
Tax effect of salvage value
Release of Net Working Capital
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Cash Flows - Types
Conventional Cash flow has initial cash outlay
followed by cash inflows. Conventional projects
produce initial negative and subsequent positive
cash flows, i.e. the initial outflow followed byinflows, i.e., + + + + +.
Non-conventional cash flow has cash outlays
mingled with cash inflows throughout the life ofthe project. Non-conventional investments
produce cash flows of the pattern like,
+ + + + + + + + .
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Estimation of the Required Rate
of Return (RRR) RRR may be cost of capital (after tax) or
the opportunity cost of capital (after tax)
After Tax because cash flows are takenpost tax.
RRR would be used as the Discounting
rate for cash flow.
RRR is considered as cut off rate for
project selection
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Evaluation Criteria
1. Traditional or Non-discounted Cash Flow
Criteria
1. Payback Period (PB)a. Post pay back Cash flow / Profitability
b. Bailout payback periodc. Discounted Payback Period (DPB)
2. Payback reciprocal3. Accounting Rate of Return (ARR)
2. Discounted Cash Flow (DCF) Criteria1. Net Present Value (NPV)2. Internal Rate of Return (IRR)
3. Profitability Index (PI)
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Payback Period (PBP)
Payback is the number of years
required to recover the original cash
outlay invested in a project. Calculation of payback is different
for:
Annual cash inflows are uniform or constant Annual cash inflows are unequal or varying
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Payback Period- constant annual
cash inflows i.e. annuity The payback period canbe computed by dividing
cash outlay by the
constant annual cash
inflow ie (annuity).
E.g. A project requires
an outlay of Rs 50,000
and yields annual cash
inflow of Rs 12,500 for 7years. What is the
payback period ?
0Initial InvestmentPayback = =Annual Cash Inflow
C
C
Rs 50000PBP = -----------------
Rs 12500PBP = 4 years
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Payback Period- Varying annual
cash inflows Payback period can be foundout by adding up (cumulate)the cash inflows until the totalis equal to initial cash outlay.
I) Project X requires a cashoutflow of Rs 20,000, &generates cash inflows of Rs8,000; 7,000; 5,000; and 4,000during the next 4 years. What isthe payback?
Answer: At 3 yrs Rs 20000 = 20000
II) If in 2nd year cash flow is6000, What is the new payback?
Answer: At 3 yrs Rs 1900020000,
3 years + 12 (1,000/4,000)months
= 3 years + 3 months
(I) Years Cash flow Cum Flow
Cash out 0 -20000
Cash inflow 1 8000 8000
2 7000 150003 5000 20000
4 4000 24000
(II) Years Cash flow Cum Flow
Cash out 0 -20000
Cash inflow 1 8000 8000
2 6000 14000
3 5000 19000
4 4000 23000
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Payback - Acceptance Rule
Accept project if its payback period is
less than the maximum orstandard
payback period set by management. While in ranking alternate projects,
highest rank for shortest payback period
and lowest rank for highest payback
period.
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Payback Period Evaluation
Merits:
1. Simplicity
2. Cost effective
3. Short-term effects4. Risk shield
5. Liquidity
Demerits:
1. Post payback Cash flows
ignored
2. Cash flow patterns (timing)irrelevant
3. Terminal or scrap value
ignored
4. Inconsistent with shareholder
value creation5. Aggregation of payback periods of
all projects of the firm not possible
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Post Payback Cash flow/Profitability
Project X has payback of 3 years when cash out =cash in, But postcash flow is just 4000 extra. Select on payback basis, but reject on
post pay back cash flow. Project Y has payback of 3years + 12 x (2000/8000)months
PBP = 3Yrs + 3 months. But post cash flow is Rs 6000 extra. Selecton post payback basis, although rejected on payback baisi
Years Project X Project Y
Cash flow Cum Flow Cash flow Cum Flow
Cash outflow 0 -20000 -20000
Cash inflow 1 8000 8000 5000 5000
2 7000 15000 6000 11000
3 5000 20000 7000 18000
4 4000 24000 8000 26000
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Bailout Payback Period
1. Consider salvage value at every years onassumption of termination of project
2. Cumulate cash inflow along with salvage
3. Payback period is that when cumulated cashinflow equal to cash outflow, Here below 3 yrs.
Years Project M
Cash flow Cum Flow Scrap Value Cum Flow +Scrap
Cash outflow 0 -20000
Cash inflow 1 6000 6000 8000 14000
2 7000 13000 5000 18000
PBP3 5000 18000 2000 20000
4 4000 22000 1000 23000
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Discounted Payback Period (DPBP)
Project N out flow Rs 4000, life 4 yr, K =10%
YearCashinflow PVF10% DistdVal
Cum DistdVal
1 3000 0.909 2727 2727
2 1000 0.827 827 3554
3 1000 0.751 751 4305
4 1000 0.683 683 4988
Total PV Cash Inflow 4988
Less Total PV Cash Outflow 4000
NPV 988
PBP (simple) = 2yrs
Distd PBP = 2yr + 12(446/751) = 2yr 7 months
Project M out flow Rs 4000, life 4 yr, K =10%
YearCashinflow PVF10% DistdVal
Cum DistdVal
1 0 0.909 0 0
2 4000 0.827 3308 3308
3 1000 0.751 751 4059
4 2000 0.683 1366 5425
Total PV Cash Inflow 5425
Less Total PV Cash Outflow 4000
NPV 1425
PBP (simple) = 2yrs
Distd PBP = 1yr + 12(692/751) = 2yr 11 months
The discounted payback period is the number of periods taken inrecovering the investment outlay on the present value basis.
The discounted payback period still fails to consider the cash flowsoccurring after the payback period.
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Reciprocal Payback (RP)
Timing of cash flow and rate of return may be
accommodated by taking reciprocal of payback
Reciprocal payback = 1/Payack x 100
= 1/3yrs x 100 = 33.3%
RP is approximation of the internal rate of return
(IRR) if the following two conditions are satisfied:
The life of the project is large or at least twice the paybackperiod.
The project generates equal annual cash inflows.
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Accounting Rate of Return Method
ARR is the ratio of theaverage after-taxprofit divided by the
investment.1) ARR on average
investment. Theaverage investment isequal to half of theoriginal investment.
2) ARR on InitialInvestment
2)
Average After Tax Profit ARR = ---------------------------------
Initial Investment
1)Average After Tax Profit
ARR = ---------------------------------Average Investment
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ARR Acceptance Rule
Accept all those projects with ARRhigherthan the minimum rateestablished by the management
Reject those projects which have ARRless than the minimum rate.
Ranking a project as number one if it
has highestARR and lowest rankwould be assigned to the project withlowest ARR.
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Evaluation of ARR Method
Merits:
1. Simplicity
2. Accounting data
3. Accounting
profitability
Limitations:
1. Cash flows ignored
2. Time value ignored
3. Arbitrary cut-off
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Net Present Value Method
Based on realistic assumptions forecastproject cash flows.
Select appropriate discount rate todiscount the forecasted cash flows.
The appropriate discount rate is theprojects opportunity cost of capital.
Present value of cash flows is found bymultiplying cash flow with PVF of theopportunity cost of capital, the discountrate.
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NPV Formula
Take sum of PV of cash inflow and cashout flow
Difference between PV of Cash inflow andPV of Cash out flow is Net Present Value(NPV)
The formula is :
31 202 3
0
1
NPV(1 ) (1 ) (1 ) (1 )
NPV(1 )
n
n
n
t
t
t
k k k k
k!
!
!
L
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Calculating Net Present Value
ProjectXcosts Rs 2,500 now and is
expected to generate year-end cash
inflows of Rs 900, 800, 700, 600
and 500 in 1 to 5 years of project
life. The opportunity cost of the
capital is 10%.
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Calculating NPV(1.Formula method & 2.Table method)
Project X out flow Rs 2500,
life 5 yrs, K =10%
Year Cash inflow PVF 10% Distd Val
1 900 0.909 818
2 800 0.827 662
3 700 0.751 526
4 600 0.683 410
5 500 0.621 311
Total PV Cash Inflow 2726
Less Total PV Cash Outflow 2500
NPV 226
2 3 4 5
1,0.10 2,0.10 3,0.10
4,0.10 5,0.
Rs 900 Rs 800 Rs 700 Rs 600 Rs500NPV Rs2,500
(1+0.10) (1+0.10) (1+0.10) (1+0.10) (1+0.10)
NPV [Rs 900(PVF )+Rs 800(PVF )+Rs 700(PVF )
+Rs 600(PVF )+Rs500(PVF
!
!
10)] Rs2,500
NPV [Rs 900 0.909+Rs 800 0.826+Rs 700 0.751+Rs 600 0.683
+Rs500 0.620] Rs2,500
NPV Rs2,725 Rs2,500 +Rs225
! v v v v
v
!
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NPV Acceptance Rule
Accept the project when
NPV is positive NPV > 0
Reject the project when
NPV is negative NPV < 0
May accept the project when
NPV is zero NPV = 0
Suitablitiy: For selecting one amongmutually exclusive projects; the one with the
higher NPV should be selected.
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Evaluation of the NPV Method
Merits of NPV :Most acceptable investmentrule as it has below merits:
1. Time value
2. Suited for constant &even cash flows
3. Measure of trueprofitability
4. Considers flow overentire life
5. Value-additivity6. Shareholder value7. Assumed to be reinvested
at cost of capital
Limitations:1. Not easy to find
Discount rate
2. Difficulties Cash flow
estimation3. Ranking of projects
1. Projects with unevenlife decisions
2. Projects with uneven
investment3. Mutually exclusive
projects
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Internal Rate of Return (IRR)
IRR is the rate that equates the present value of investment
outlay with the present value of cash inflows over life of project.
IRR implies that the rate of return is equal to the discount rate
which makes NPV = 0. It is Discounted Rate of Return
In the following equation, r is IRR when NPV= 0
31 20 2 3
01
0
1
(1 ) (1 ) (1 ) (1 )
(1 )
0(1 )
n
n
n
t
tt
n
t
t
t
C CC CC
r r r r
CC
r
CC
r
!
!
!
!
!
L
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Calculation of IRR
a) When constant (annuity) cash flows
b) When unequal cash inflow
a) Constant (annuity) Cash Flows When annual cash inflows are constant IRR is equal to
r of present value annuity factor (PVAF) for the life ofthe project (n) of mean cash flow.
IRR = PVAF(n,r) {Cash outlay/Constant cash inflow)
By referring to PVAF table for given n life of project,find r which is IRR, that produces zero NPV
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Constant (annuity) Cash Flows
Project X outlay is Rs 18,000 and its annual cashinflow is Rs 6,000 for 5 years. What is IRR of X ?
The IRR of the investment can be found out asfollows:
NPV = Cash outflow Annuity cash inflow(PVAFn,,r)
NPV = 18000 6000(PVAF 5,r) = 0
PVAF 5,r = (18000/6000)= 3
From PVAF table we find PVAF 5,r= 3, For 5 years, at
20% from PVAF table it is 2.991, is nearer to 3. So thatis r = IRR.
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Uneven Cash Flows
IRR is found by Trial and Error Select any discount rate to compute the present value of
cash inflows.
If the present value of inflows is higher than the presentvalue of outflows, ie NPV is positive, a higher rate shouldbe tried.
If the calculated present value of the expected cash inflowis lower than the present value of cash outflows, ie NPV isnegative, a lower rate should be tried.
Repeat until net present value becomes zero or elseinterpolate between two rate causing positive and negativeNPV to find IRR when NPV = 0
C
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Uneven Cash Flows(IRR is found by Trial and Error)
Project Z needs Rs 60000 outlay and produces cashflow of Rs15000, 20000,30000 & 20000 in 4 years of life.Find IRR?
IRR determination by Trial & Error (trial started with 14%, then 15% )
Years Cash Inflow PVF 14% PV Cash flow PVF 15% PV Cash flow
1 15000 0.877 13155 0.870 13050
2 20000 0.769 15380 0.756 15120
3 30000 0.675 20250 0.658 19740
4 20000 0.592 11840 0.572 11440
85000 60625 59350
Less Cash ouflow -start of 1st year 60000 60000
NPV = PV inflow - PV outflow 625 -650
At 14% NPV is 625 and at 15% NPV is -650 So r lies between 14 - 15%
By Interpolation r = 14% + 625/(625+650) x (15% - 14%)
r = IRR = 14.50%
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Uneven Cash Flows(modified annuity method)
IRR is found by modifying annuity method
using average cash inflow
Average cash inflow =(15000+20000+30000+20000)/4 =
21250 NPV = Cash outflow Average cash inflow(PVAFn,,r) = 0
NPV = 60000 - 21250(PVAF 4,r) = 0
PVAF 4,r = (60000/21250)= 2.82
From PVAF table we find PVAF 4,r= 2.82, For 4 years, at15% from PVAF table it is 2.85, is nearer to 2.82. So try
with 15% to get IRR.
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NPV Profile Graph to find IRR
Cash inflow
Annuity
PVAF(6,r) NPV
5430 1% 11472
5430 5% 75615430 10% 3649
5430 15% 550
5430 16%IRR 0
5430 20% (1942)
5430 25% (3974)
Initial outlay Rs 20000, life 6 Yrs
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Acceptance Rule of IRR
Accept the project when r> k.
Reject the project when r< k.
May accept the project when r= k.
Kis cost of capital (WACC)
Ranking based on highest IRR first, and last
for lower IRR
In case of independent projects, IRR and NPVrules will give the same results if the firm has
no shortage of funds.
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Evaluation of IRR Method
Merits: Time value of money
Profitability measure forentire life
Determination ofopportunity cost ofcapital not prerequisite
Uniform ranking as IRRis in %
Acceptance rule
Shareholder valuemaximised
Limitations:
1. Multiple rates
2. Mutually exclusiveprojects
3. Different projects IRRcant be added
4. Assumed to be reinvestedat IRR which may notmatch cost of capital
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NPV Versus IRR
1. Reinvestment Assumption
2. Varying Opportunity Cost of Capital
3. Conventional Independent Projects Ranking
4. Lending and borrowing-type projects
5. Problem of Multiple IRRs (non-conventional)
6. Ranking of Mutually Exclusive Projects
7. Timing of Cash Flows8. Scale of Investment
9. Project Life Span
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Reinvestment Assumption
The IRR method assumes that the cash
flows generated by the project can be
reinvested at its internal rate of return,
The NPV method assumes that the cash
flows are reinvested at the opportunity
cost of capital.
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Varying Opportunity Cost of
Capital There is no problem in using NPVmethod when the opportunity cost of
capital varies over time.
If the opportunity cost of capital varies
over time, the use of the IRR rule
creates problems, as there is not a
unique benchmark opportunity cost ofcapital to compare with IRR.
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Conventional Independent Projects
Conventional Independent Projects which
are economically independentof each
other, NPV and IRR methods result in
same accept-or-reject decision if the firm
is not constrained for funds in accepting
allprofitable projects.
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Lending or borrowing-type projects
(Both are conventional projects)
Project R is a lending type, which involves initial outflow Rs 1000,followed by inflow of Rs 1200 over one year life.
This has NPV 91 positive, Accepted. But IRR = 20%
Project Q is a borrowing type, where there is initial inflow of Rs 1000,followed by outflow of Rs 1200 at first year end of life.
This has NPV -91, Rejected.
But IRR = 20% for both Q and R. Choose any project on IRR basis.
Borrowing type Project Q yr end outflow Rs 1200, life 1 yr, K =10%
Year Cash outflow PVF 10% Distd Val
1 1200 0.909 1091
Total PV Cash outflow 1091
Total PV Cash inflow yr0 1000
NPV -91
IRR comes to 20%
Lending type Project R out flow Rs 1000, life 1 yr, K =10%
Year Cash inflow PVF 10% Distd Val
1 1200 0.909 1091
Total PV Cash Inflow 1091
Less Total PV Cash Outflow 1000
NPV 91
IRR comes to 20%
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Problem of Multiple IRRs
(non-conventional)
A project may have
both lending and
borrowing features
together (non-conventional).
IRR method can yield
multiple internal rates
of return because of more than one change
of signs in cash flows is
possible here.
P Rs
-
-
-
iscount Rate ( )
P (Rs)
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Ranking of Mutually Exclusive Projects
The NPV and IRR rules give conflicting rankingto the projects under the following conditions: The cash flow pattern of the projects may differ. That is,
the cash flows of one project may increase over time,while those of others may decrease orvice-versa.
The cash outlays of the projects may differ.
The projects may have different expected lives.
Investment projects are said to be mutually exclusive
when only one investment could be accepted andothers would have to be excluded.
Two independent projects may also be mutuallyexclusive if a financial constraint is imposed.
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Timing of Cash Flows
Cash Flows (Rs) NPV
Project C0 C1 C2 C3 at 9% IRR
M 1,680 1,400 700 140 301 23%
N 1,680 140 840 1,510 321 17%
Both projects are lending type, with initial outlay
of Rs 1680, with life of 3 yrs, and K at 9%.
But their NPV at 9% are different, Select N
But their too IRR differ. On IRR basis accept M
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Scale of Investment
Ca sh Flo w (Rs) NPV
Projec t C0 C1 at 10% IRR
A -1,000 1,500 364 50%
B -100,000 120,000 9,080 20%
Both projects are lending type. But initial outlayof A is Rs 1000, while B is Rs 100000. But life of
both is 1 yr, and K at 10%. But their NPV at 10% are different, Select B
But their IRR too differ. On IRR basis accept A
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Project Life Span
Cas lo s( s)
Project C0 C1 C2 C3 C4 C5 PV at 10% I
X
10,000 12,000 908 20Y 10,000 0 0 0 0 20,120 2,495 15%
Both projects are lending type with same initialoutlay of Rs 10000. But life of X is 1 yr and of Y
is 5yrs. K at 10%. But their NPV at 10% are different, Select Y
But their IRR too differ. On IRR basis accept X
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Modified Internal Rate of
Return (MIRR) The modified internal rate of return (MIRR)
is the compound average annual rate that is
calculated with a reinvestment rate different
than the projects IRR.
Modified internal rate of return is the
compound average annual rate that is
calculated with a reinvestment rate different
than the projects IRR.
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Profitability Index
Profitability index is the ratio of the
present value of cash inflows, at the
required rate of return, to the initial cash
outflow of the investment.
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Profitability Index
It is time adjusted method, also known asbenefit-cost ratio
Sum ofPresentValue ofCash inflows
PI = ----------------------------------------------------Sum ofPresentValue ofCash outflows
Net Present Value PI (Net) = ----------------------------------------------------
Sum of Present Value of Cash outflows
PI (Net) = (PI - 1)
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Profitability Index
The initial cash outlay of M project is Rs 1,00,000 and itcan generate cash inflow of Rs 40000, 30000, 50000and 20000 in year 1 through 4. Opportunity cost ofcapital is10%. Calculate PI.
.1235.11,00,000Rs
1,12,350RsPI
12,350Rs100,000Rs112,350RsNPV
0.6820,000Rs+0.75150,000Rs+0.82630,000Rs+0.90940,000Rs
)20,000(PVFRs+)50,000(PVFRs+)30,000(PVFRs+)40,000(PVFRsPV 0.104,0.103,0.102,0.101,
!!
!
vvvv
!
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Acceptance Rule
The following are the PI acceptancerules: Accept when PI > 1 or PI (net) is +Ve
Reject when PI < 1 or PI (net) is -Ve May accept PI = 1 or PI (net) is 0
The project with positive NPV will havePI greater than one. PI less than meansthat the projects NPV is negative.
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Evaluation of PI Method
Merits
Time value of money.
Shareholder valuemaximisation.. A project
with PI > 1 will havepositive NPV and ifaccepted, it will increaseshareholders wealth.
Relative measure of aprojects profitability - as
the present value of cashinflows is divided by theinitial cash outflow
Limitations:
PI criterion requirescalculation of cash flowsand
Estimate of the discountrate.
In practice both are poseproblems in estimation.