Finance and Investment Capital Budgeting Techniques

Finance and Investment
Capital Budgeting
Associate Professor: Dr.Mohamed Masry
PhD, MA, Sheffield Hallam University, UK.
MBA, BA, AAST, Egypt.

Key Concepts and Skills
• The payback rule and its shortcomings
• Accounting rates of return and their problems
• The net present value rule and why it is the
best decision criteria
• The Internal rate of return
• The profitability index and its relation to NPV
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Dr. Mohamed Masry 2

Outline
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Average Accounting Return
The Payback Rule
Net Present Value
Internal Rate of Return
The Profitability Index
The Practice of Capital Budgeting

Capital budgeting techniques
Capital budgeting is the process of identifying,
analyzing, and selecting investment projects
whose returns (cash flows) are expected to
extend beyond one year.
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What Is Capital Budgeting?
• Capital budgeting is a process that businesses use to
evaluate potential major projects or investments. Building
a new plant or taking a large stake in an outside venture
are examples of initiatives that typically require capital
budgeting before they are approved or rejected by
management.
• As part of capital budgeting, a company might assess a
prospective project's lifetime cash inflows and outflows to
determine whether the potential returns it would
generate meet a sufficient target benchmark.
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Capital Budgeting
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Analysis of
potential
projects
Long-term
decisions
Large
expenditures
Difficult/impo
ssible to
reverse
Determines
firm’s
strategic
direction

Good Decision Criteria
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All cash flows
considered?
TVM considered?
Risk-adjusted?
Ability to rank
projects?
Indicates added
value to the
firm?

Independent versus Mutually Exclusive Projects
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Independent
The cash flows of one
project are unaffected
by the acceptance of
the other.
Mutually Exclusive
The acceptance of one
project precludes
accepting the other.

The capital budgeting process
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• Generate investment proposals consistent with the
firm’s strategic objectives.
• Estimate after-tax incremental operating cash flows
for the investment projects.
• Evaluate project incremental cash flows.
• Select projects based on a value-maximizing
acceptance criterion.
• Reevaluate implemented investment projects
continually and perform post-audits for completed
projects.

Classification of investment project proposals
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• New products or expansion of existing products
• Replacement of existing equipment or buildings
• Research and development
• Other (e.g., safety or pollution related)

Project evaluation: different methods
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• Payback Period (PBP)
• Average Accounting Return(AAR)
• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• Profitability Index (PI)

What Is the Average Accounting Return (AAR)?
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• The average accounting return (AAR) is a formula that
reflects the percentage rate of return expected on an
investment or asset, compared to the initial
investment's cost. The AAR formula divides an asset's
average revenue by the company's initial investment
to derive the ratio or return that one may expect over
the lifetime of an asset or project. ARR does not
consider the time value of money or cash flows, which
can be an integral part of maintaining a business.

Average Accounting Return
• Many different definitions for average accounting return (AAR)
•In this course:
• Note: Average book value is taken by the start and end of the
period divided by 2 because it assumes the book value trends
from the start value to the end value in a straight line..
• Requires a target cutoff rate
• Decision Rule: Accept the project if the AAR is greater than
target rate.
• Net cash flow(NCF)=Net income-Annual deportation cost
• The formula to calculate annual depreciation using the straight-
line method is (cost – salvage value) / useful life
Value
Book
Average
Income
Net
Average
AAR 
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Project evaluation example
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Investor is evaluating a new project for his business,
Jambura Farm (JF). He has determined that the after-tax
cash flows for the project will be 10,000; 12,000; 15,000;
10,000; and 7,000, respectively, for each of the Years 1
through 5. The initial cost (cash )outlay will be 40,000,
and salvage value=0; the company is using straight line
method of depreciation

Computing AAR for the Project
• Sample Project Data:
• Annual Depreciation installment= 40000-0/5=8000
• Year 1:NCF= 10000-8000=NI=2000
• Year 2:NCF=12000-8000=NI=4000
• Year 3:NCF=15000-8000=NI=7000
• Year 4:NCF=12000-8000=NI=4000
• Year 5:NCF=7000-8000=NI=-1000
• Average book value = 40000+0/2=$20000
• Required average accounting return = 20%
• Average Net Income:
 ($2000+4000+7000+4000+(1000) / 5 = $3200
• AAR = $3200/ 20000 = .16 = 16%
• Do we accept or reject the project?
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Example
•You are looking at a new project and have estimated
the following cash flows, net income and book value
data:
• Year 0:CF = -165,000
• Year 1:CF = 63,120
• Year 2:CF = 70,800
• Year 3:CF = 91,080
• Average book value = $82500 S.V=0
• Calculate the Average Accounting return

Computing AAR for the Project
• Sample Project Data:
• Annual Depreciation installment= 165,000-0/3=55000
• Year 1: CF = 63,120-55000= NI = 8120
• Year 2: CF = 70,800-55000= NI = 15800
• Year 3: CF = 91,080-55000= NI = 36,080
• Average book value = 165000+0/2=$82500
• Required average accounting return = 25%
• Average Net Income:
 ($8120 + 15800 + 36,080) / 3 = $20000
• AAR = $20,000/ 82,500 = .2424 = 24.2%
• Do we accept or reject the project?
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Decision Criteria Test - AAR
• Does the AAR rule account for the time value of
money?
• Does the AAR rule account for the risk of the
cash flows?
• Does the AAR rule provide an indication about
the increase in value?
• Should we consider the AAR rule for our
primary decision criteria?

The Initial cost for both projects =21000 and salvage value=0;
the company is using straight line method of depreciation,
calculate AAR for both projects
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YEARS PROJECT 1 PROJECT 2
NI CF NI CF
1 4000 11000 3000 10000
2 4000 11000 3000 10000
3 1000 8000 3000 10000
Average 3000 10000 3000 10000

Advantages and
Disadvantages of AAR
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Advantages
• Easy to calculate
• Needed information
usually available
Disadvantages
• Not a true rate of return
• Time value of money
ignored
• Uses an arbitrary
benchmark cutoff rate
• Based on accounting net
income and book values,
not cash flows and
market values

Payback Period
How long does it take to recover the initial cost of a project?
Computation
Estimate the cash flows
Subtract the future cash flows from the
initial cost until initial investment is
recovered
A “break-even” type measure
Decision Rule – Accept if the payback period is less than some
preset limit

Payback period solution
PBP is the period of time required for the
cumulative expected cash flows from an
investment project to equal the initial cash
outflow.
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
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Payback period solution
Yr Project JF
CF Cum CF
• 1 10,000 -30,000
• 2 12,000 -18,000
• 3 15,000 -3,000
• 4 10,000 7,000
• 5 7,000
0 -40,000 -40,000
• (*3rd yr Cum CF/4th yr CF)
Payback Periods: 3 + (3,000/10,000)*= 3.33 years

Example
Do we accept or reject the project?
Capital Budgeting Project
Year CF Cum. CFs
0 (165,000)
$ (165,000)
$
1 63,120
$ (101,880)
$
2 70,800
$ (31,080)
$
3 91,080
$ 60,000
$
Payback = year 2 +
+ (31080/91080)
Payback = 2.34 years

Decision Criteria Test Payback
• Does the payback rule:
• Account for the time value of
money?
• Account for the risk of the cash
flows?
• Provide an indication about the
increase in value?
• Permit project ranking?
• Should we consider the payback rule
for our primary decision rule?

The Initial cost for both projects =18000 and salvage
value=0; the company is using straight line method of
depreciation, calculate payback period for both projects
Years Project 1CF Project 2CF
1 7000 5000
2 6000 6000
3 5000 7000
4 3000 3000

Advantages and Disadvantages of Payback
• Advantages
• Easy to understand
• Adjusts for uncertainty of
later cash flows
• Biased towards liquidity
• Disadvantages
• Ignores the time value of
money
• Requires an arbitrary cutoff
point
• Ignores cash flows beyond the
cutoff date
• Biased against long-term
projects, such as research and
development, and new projects

Payback Summary
Payback period =
• Length of time until initial
investment is recovered
• Accept if payback < some specified
target
• Doesn’t account for time value of
money
• Ignores cash flows after payback
• Arbitrary cutoff period
• Asks the wrong question
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AAR Summary
Average Accounting Return=
• Average net income/Average book
value
• Accept if AAR > Some specified target
• Needed data usually readily available
• Not a true rate of return
• Time value of money ignored
• Arbitrary benchmark
• Based on accounting data not cash
flows
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What Is an Annuity?
An annuity is a financial investment that generates
regular payments for a set time. In modern times,
an annuity is most often purchased through an
insurance company or a financial services
company.
• Present value and future value are terms that are
frequently used in annuity contracts. The present
value of an annuity is the sum that must be
invested now to guarantee a desired payment in
the future,
• The future value is the total that will be achieved
over time.
Present Value Vs. Future Value in Annuities

Present Value Vs. Future Value in Annuities
• Present value is the sum
of money that must be
invested to achieve a
specific future goal.
• Future value is the dollar
amount that will accrue
over time when that sum
is invested.
• The present value is the
amount you must invest
to realize the future
value.
The present value of an annuity
is the current value of all the
income that will be generated
by that investment in the
future. In more practical terms,
it is the amount of money that
would need to be invested
today to generate a specific
income down the road.
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Investor is evaluating a new project for his business,
Jambura Farm (JF). He has determined that the after-tax
cash flows for the project will be 10,000; 12,000; 15,000;
10,000; and 7,000, respectively, for each of the Years 1
through 5. The initial cash outlay will be $40,000.
Jambura Farm has determined that the appropriate
discount rate (k) for this project is 13%.
Project evaluation example

Net Present Value
NPV is the present value of an investment project’s
net cash flows minus the project’s initial cash
outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n
+ . . . +
+ - ICO
NPV =

 

n
0
t
t
t
)
R
1
(
CF
NPV

NPV Solution
10,000 7,000
10,000 12,000 15,000
(1.13)1 (1.13)2 (1.13)3
+ +
+ - $ 40,000
(1.13)4 (1.13)5
NPV = +

NPV = 10,000(PVIF13%,1) + 12,000(PVIF13%,2) +
15,000(PVIF13%,3) + 10,000(PVIF13%,4) +
7,000(PVIF13%,5) - 40,000
NPV = 10,000(.885) + 12,000(.783) +
15,000(.693) + 10,000(.613) +
7,000(.543) - 40,000
NPV = 8,850 + 9,396 + 10,395 + 6,130 + 3,801 - 40,000
= - 1,428
NPV Solution

Example
• You are looking at a new project and have
estimated the following cash flows, net income
and book value data:
• Year 0: CF = -165,000
• Year 1: CF = 63,120 NI = 13,620
• Year 2: CF = 70,800 NI = 3,300
• Year 3: CF = 91,080 NI = 29,100
• Average book value = $72,000
• Your required return for assets of this risk is 12%.

Computing NPV for the Project
• Using the formula:
NPV = -165,000+ 63,120/(1.12)1 + 70,800/(1.12)2 +
91,080/(1.12)3 = 12,627.41
Capital Budgeting Project NPV
Required Return = 12%
Year CF Formula Disc CFs
0 (165,000.00) =(-165000)/(1.12)^0 = (165,000.00)
1 63,120.00 =(63120)/(1.12)^1 = 56,357.14
2 70,800.00 =(70800)/(1.12)^2 = 56,441.33
3 91,080.00 =(91080)/(1.12)^3 = 64,828.94
12,627.41
Dr. Mohamed Masry

No! The NPV is negative. This means that the
project is reducing shareholder wealth. [Reject as
NPV < 0 ]
The management of Jambura Farm has determined
that the required rate is 13% for projects of this
type.
Should this project be accepted?
NPV Acceptance Criterion

NPV
Strengths &
Weaknesses
Strengths:
– Cash flows
assumed to be
reinvested at
the hurdle rate.
– Accounts for
TVM.
– Considers all
cash flows.
Weaknesses:
– A bit complicated
than PBP
–May not include
managerial
options embedded
in the project.

Discount Rate (%)
0 3 6 9 12 15
IRR
NPV@13%
Sum of CF’s Plot NPV for each
discount rate.
Net
Present
Value
$000s
15
10
5
0
-4
NPV Profile

IRR is the discount rate that equates the present value of
the future net cash flows from an investment project with
the project’s initial cash outflow.
CF1 CF2 CFn
(1+IRR)1 (1+IRR)2 (1+IRR)n
+ . . . +
+
ICO =
Internal rate of return

15,000 10,000 7,000
10,000 12,000
(1+IRR)1 (1+IRR)2
Find the interest rate (IRR) that causes the
discounted cash flows to equal 40,000.
+ +
+
+
$40,000 =
(1+IRR)3 (1+IRR)4 (1+IRR)5
IRR Solution

$ 40,000 = 10,000(PVIF10%,1) + 12,000(PVIF10%,2) +
15,000(PVIF10%,3) + 10,000(PVIF10%,4) +
7,000(PVIF10%,5)
$ 40,000 = 10,000(.909) + 12,000(.826) + 15,000(.751)
+ 10,000(.683) + 7,000(.621)
$ 40,000 = 9,090 + 9,912 + 11,265 +6,830 + 4,347
= 41,444 [Rate is too low!!]
IRR Solution (10%)

Tk 40,000 = 10,000(PVIF15%,1) + 12,000(PVIF15%,2) +
15,000(PVIF15%,3) + 10,000(PVIF15%,4) +
7,000(PVIF15%,5)
Tk 40,000 = 10,000(.870) + 12,000(.756) + 15,000(.658)
+ 10,000(.572) + 7,000(.497)
Tk 40,000 = 8,700 + 9,072 + 9,870 + 5,720 + 3,479
= 36,841 [Rate is too high!!]
IRR Solution (15%)

.10 41,444
.05 IRR 40,000 4,603
.15 36,841
X 1,444
.05 4,603
1,444
X
=
Interpolate

.10 41,444
.05 IRR 40,000 4,603
.15 36,841
(1,444)(0.05)
4,603
1,444
X = X = .0157
IRR = .10 + .0157 = .1157 or 11.57%
X
Interpolate

No! JF will receive 11.57% for each dollar invested in
this project at a cost of 13%. [ IRR < Hurdle Rate ]
The management of Jambura Farm has determined that
the hurdle rate is 13% for projects of this type.
IRR Acceptance Criterion

Strengths:
– Accounts for TVM
– Considers all cash flows
– Less subjectivity
Weaknesses:
– Assumes all cash flows
reinvested at the IRR
– Difficulties with project
rankings and multiple IRRs
IRR Strengths & Weaknesses

PI is the ratio of the present value of a project’s future net
cash flows to the project’s initial cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n
+ . . . +
+ ICO
PI =
PI = 1 + [ NPV / ICO ]
<< OR >>
Profitability Index (PI)

No! The PI is less than 1.00. This means that the
project is not profitable. [Reject as PI < 1.00 ]
PI =1+(-1428 / 40,000)
= .9643
PI Acceptance Criterion

Strengths:
– Same as NPV
– Allows comparison of
different scale projects
Weaknesses:
– Same as NPV
– Provides only relative
profitability
– Potential ranking problems
PI Strengths & Weaknesses

Method Project Comparison Decision
PBP 3.3 3.5 Accept
IRR 11.47% 13% Reject
NPV -1,424 0 Reject
PI .96 1.00 Reject
Jambura Farm’s Independent Project
Evaluation Summary

Assignment
• Consider an investment that costs $100,000
and has a cash inflow of $25,000 every year
for 5 years. The required return is 9% and
required payback is 4 years.
• What is the payback period?
• What is the NPV?
• Should we accept the project?
• What decision rule should be the primary
decision method?

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