Chapter 2
Capital Budgeting Principles and
Techniques
Capital budgeting and investment
Analysis by Alan Shapiro
Net Present Value (NPV)
• NPV is the present value of the project’s cash
flows minus the cost of the project
• The value placed on an investment project
must satisfy three criteria:
– Focus on cash
– Account for TVM
– Account for Risk
NPV Decision Rule
•
•
•
•
Invest in positive NPV projects
Reject negative NPV projects
Use the appropriate discount rate
If two projects are mutually exclusive, accept
the one with higher NPV
• Cost of capital is the minimum acceptable rate
of return on projects with similar risk.
NPV cont.
• NPV=-Initial cash investment+ PV of future CFs
• Initial investment includes any working capital
requirements
• Net CF is after tax profit plus depreciation and
other non-cash charges such as deferred taxes
less any additions to working capital during
the period
• It is cash, and only cash that matters to
shareholders
Example 1
•
•
•
•
•
Plant and equipment of $6 million
5 year contract
Sale of $10 per pound
800,000 pounds of dye in the 1st year
1,600,000 pounds per year in each of the next
4 years
• Plant is expected to be sold at its book value
in end of year 5 for $1 million
Example 1 cont.
•
•
•
•
•
Variable cost = $6.5 per pound
Fixed cost = $1,700,000 per year
Deprecation = $1,000,000 per year
Tax rate = 40%
Working capital requirement =$1,200,000 and
will be freed at end of year 5
• Required return = 10%
Example 1 cont.
• Calculate the following:
– Initial investment for this project
– Net Cash Flow for years 1-5.
– NPV
– Decide whether you would accept or reject this
project and Why?
Example 2 (Contingent projects)
• Purchase and transport mining equipment which
costs $90 million
• Cost of extracting ore = $50 per ton
• Expected to sell ore for $150 a ton
• Produce 200,00 tons a year
• 20 Years
• Construct a rail line at cost of $30 million
• Cost of transport = $10 per ton
• Required rate of return= 15%
• What are the NPVs for the mine and the railway?
Which project(s) should they take?
Strengths of NPV
• It evaluates investments in the same way that
shareholders do
• It is a theoretically correct technique
• It obeys the value additivity principle
• The NPV of a set of independent projects is
just the sum of the NPVs of the individual
projects
• It implies that the value of a firm equals the
sum of the values of its component parts
Weakness of NPV
• Many corporate executives and non technical
people have a tough time understanding the
concept
• Applying the NPV has the problem of
computing the proper discount rate.
Payback Period
• Payback period is the length of time necessary
to recoup the initial investment from net cash
flows
• Discounted payback period is the length of
time it takes to the present value of CFs to
equal the cost of the initial investment
• Find the payback period (PB) for example 1.
Payback period decision rule
• Projects with a payback less than a specified
cutoff period are accepted whereas those with
a payback beyond this figure are rejected
• The riskier the project is, the shorter the
required payback will be
Payback period Strengths and
Weaknesses
• Strength: It is simple to understand and easy
to apply
• Weaknesses:
– It ignores time value of money
– It ignores cash flows beyond the payback period:
it is biased against longer projects
Accounting rate of return
• Also known as average rate of return or
average return on book value
• It is the ratio of average after tax profit to
average book investment (the initial
investment less accumulated depreciation).
• Decision Rule
– Investments yielding a return greater than this
standard are accepted, whereas those falling
below it would be rejected.
Strengths and Weaknesses of
Accounting rate of return
• Strength: It is simple to apply
• Weakness:
– It ignores the time value of money
– It is based on accounting income rather than cash
flow. Cash flow and reported income often differ
ARR 

n
t 1
( AfterTaxprofit ) / n
( InitialOut lay  EndingBook Value) / 2
Internal Rate of Return (IRR)
• IRR is the discount rate that sets the present
value of the project cash flow to the initial
investment outlay
• It is the discount rate that equates the project
NPV to zero
• Calculate the IRR of Example 1
IRR Decision Rule
• If the IRR exceeds the cost of capital, the firm
should undertake the project; otherwise, the
project should be rejected
IRR Strengths and Weaknesses
• Strengths:
– Managers seem to visualize and understand more
easily the concept of a rate of return rather than they
do the concept of a sum discounted dollars
– It permits an investment analysis without requiring
advance specification of the discount rate
• Weaknesses:
– When cash flows change more than once (Multiple
IRR)
– When mutually exclusive projects are involved
Multiple IRRs
• IRR of 0%, 100%, and 200%
Year
0
1
2
3
Cash flow
-$200
+$1,200
-$2,200
+$1,200
Mutually exclusive projects
• In case of mutually exclusive projects choices,
NPV and IRR can favor conflicting projects
• When forced to choose between two mutually
exclusive investments, the NPV will always
provide the correct answer.
• When projects are substantially different in
– Timing of cash flows
• Most of CFs coming in early years vs. later years
– Scale differences
• Differences in the amount of the initial investment
Differences between rankings of NPV
and IRR
Year
X
Y
0
-$100,000
-$1,000,000
1
$140,000
$1,250,000
NPV (k=15%)
$21,739
$86,957
IRR
40%
25%
Year
A
B
0
-1,000,000
-1,000,000
1
800,000
100,000
2
300,000
400,000
3
200,000
500,000
4
100,000
800,000
NPV (k=17%)
$81,154
$116,781
IRR
22.99%
21.46%
Profitability Index (PI)
• It is also called the benefit-cost ratio
• It equals the present value of future cash
flows divided by the initial cash investment
• Calculate Profitability Index (PI) for Example 1
• The project returns a present value of $X for
every $1 of the initial investment
PI Decision Rule
• As long as the profitability index exceeds 1,
the project should be accepted
• Strength:
– NPV and PI give the same accept/reject signal
• Weakness:
– NPV and PI sometimes disagree in the rank
ordering of acceptable projects
– When there are mutually exclusive projects and
when there is capital rationing
Surveys of Capital budgeting used in
practice
• Graham and Harvey (2002)
–
–
–
–
US companies
75% of CFOs always or almost always use NPV
75.7 always or almost always use IRR
Most popular secondary or supplemental method of
evaluation is the payback period due to its simplicity
along with top management’s lack of familiarity with
more sophisticated techniques
– Only about 20% of companies used accounting rate of
return
What about Kuwait? Other international surveys?
Capital Rationing
• Some firms constrain the size of their capital
budgets. Whenever such a constraint exist, we
have the situation known as capital rationing
• Capital rationing may be self-imposed or
externally imposed
– Limit CapEx to internally generated cash flows
– Limit # of attractive projects to undertake
– Current lenders may restrict the amount of future
borrowing
Heuristic approach
• Calculate the PI for each project
• Rank all projects in term of their PIs, from
highest to lowest
• Starting with the project having the highest PI,
go down the list and select all projects having
PI>1 until the capital budget is exhausted
Capital Rationing: NPV vs. PI
• The NPV method does not necessarily select
the best combination of projects under capital
rationing
• The PI approach will select the optimal
combination of projects provided that:
– The budget constraint is for 1 period only
– The entire budget can be consumed by accepting
projects in descending order of PI.
Example on Capital Rationing
Capital budget of $5 million
Project
Initial
investment
NPV
PI
Ranking
NPV
Ranking PI
A
500,000
100,000
1.20
1. D
F
B
500,000
70,000
1.14
2. C
A
C
2,000,000
300,000
1.15
3. E
E
D
3,000,000
480,000
1.16
4. F
D
E
1,000,000
170,000
1.17
5. A
C
F
500,000
125,000
1.25
6. B
B
Mutually exclusive projects with
Different Lives
• Equivalent annual cost of an asset is an
annuity that has the same life as the asset
whose present value equals the cost of the
asset
• Rule:
– Compute the equivalent annual cost of each asset.
• Select the asset with the lowest equivalent annual cost
• For a revenue generating project, this rule becomes
select the project with the highest equivalent annual
net cash flow
Example: Different Lives
Year
Dole
Daihatsu
0
$12,000
$7,500
1
$3,000
$4,000
2
$3,000
$4,000
3
$3,000
$4,000
4
$3,000
$4,000
5
$3,000
-
Present value of cost at 8%
$23,978.10
$20,740.40
Dole Truck
Daihatsu truck
Initial cost
$12,000
$7,500
Salvage Value
0
0
Life
5 years
4 years
Operating cost
$3,000/year
$4,000/year