Project Appraisal – Capital Budgeting Methods

8/6/2019 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



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



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



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


50/55

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

!


54/55

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.

Documents

Project Appraisal – Capital Budgeting Methods