Topic 7:
The Standard Capital
Investment Tool Kit
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Learning Objectives Satisfied
7. Cash Flow Estimations and Capital Budgeting
Techniques
Objectives: Understand the following concepts
3Why it is so hard for firms to find profitable investment
opportunities
3Role of taxes and depreciation in determining initial
outlay, operating cash flows and terminal cash flow
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Learning Objectives Satisfied
3The process of evaluating capital budgeting projects
3Net Present Value
3Internal Rate of Return
3Profitability Index
3Pay Back Period
3Conflicts between NPV and IRR and how to resolve
these conflicts
3How to tie the capital budgeting decision to the overall
goal of shareholder wealth maximization
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The Standard Capital Investment
Tool Kit
Purpose:
This lecture provides an overview of the
discounted cash flow (DCF) tools used to help
management make decisions about capital
utilization
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Efficient Use of Invested Capital
• The process by which firms make their
investment decisions is often referred to as
“capital budgeting”
• This is misleading because it implies that
there is not enough capital available to fund
all of the positive NPV projects that are
ready for action
-5-
Efficient Use of Invested Capital
• Capital is rationed by interest rates
– When there are many valuable opportunities,
interest rates are bid higher
– Only those opportunities with competitive
prospects are able to obtain funding
• Capital “rationing” within a firm is arbitrary
and inconsistent with financial theory
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Efficient Use of Invested Capital
• Decision-makers are concerned whether a
potential investment will provide a positive
NPV
– Requires analysis of potential profitability and
risk
– as well as “fit” with the firm’s other activities
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Efficient Use of Invested Capital
• Also concerned with efficient use of
existing resources
– Should existing resources be transferred to
other uses within the firm?
– Should existing resources be sold?
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Efficient Use of Invested Capital
• In this lecture we will examine the basic
tool kit for applying the DCF security
valuation model to the problem of
measuring NPV
• Later we’ll look at more direct approaches
to testing for potential economic rents
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Lessons from the Theory of
Finance
• Always bear in mind that the market is the
best reference for determining value
• The tools we are about to discuss are
second-best, and need to be used cautiously
• The primary purpose is to discover the
presence of economic rents.
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Milestones in Development of NPV Analysis
• 1899: Irving Fischer first articulates concept
NPV = Mkt value of securities minus cost of resources
• 1929: Irving Fischer, Theory of Interest
NPV is part of theory of optimal resource allocation
• 1951: Joel Dean, Capital Budgeting
Implementation of DCF methodology in current form
• 1973: Black & Scholes develop 1st Option Pricing
Model
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Discounted cash flow net present
value (DCF-NPV):
General model:
n m
NPV = C 0 + Â Â
p jC jt
t=1 j=1(1 + R )
n
NPV = Â
t
Ct
t
t=0 (1 + R )
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NPV Example
•
•
•
•
C(0) = -$250
C(1) = $110
C(2) = $121
C(3) = $133.10
• Required Return = 10%
• NPV = $50
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Discounted cash flow NPV
Advantages:
• Accounts for time value of money
• Considers all cash flows over the project’s life
• Grounded in the NPV Rule by a model of the
security valuation process
• Attempts to measure total wealth created by the
project
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Discounted cash flow NPV
Advantages:
• NPVs are additive
– Measures project’s contribution to the value of the firm
– The NPV of the whole firm is the sum of the
incremental NPVs of its parts
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Discounted cash flow NPV:
Disadvantages:
•
•
•
Measures economic rent indirectly
– Looks for symptom (positive NPV)
– Doesn’t look directly for the competitive advantages that create
economic rents
Cash flow estimates must capture all nuances of project’s contribution
to firm
Very difficult to capture the value of real options
– such as growth options, abandonment options, and other operating
options
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Discounted cash flow NPV:
Guidelines for Application:
•
•
•
Ignore sunk costs (Problem 5)
Focus on incremental benefits and costs (Problem 6)
Discount using opportunity cost of capital
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Example: Opportunity Cost of Capital
• Given:
– T-Bill rate is 5%
– Expected return on market portfolio is 12%
– Project is twice as risky as average investment
• Therefore
OCC = 5% + 2(12% - 5%) = 19%
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Discounted cash flow NPV:
Guidelines for Application:
•
•
•
•
Ignore sunk costs (Problem 5)
Focus on incremental benefits and costs (Problem 6)
Discount using opportunity cost of capital
Discount nominal cash flows at the nominal rate and real cash
flows at the real rate
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Basic techniques for inflation
adjustment:
• Make cash flow estimates in terms of
tomorrow’s dollars and evaluate using the
nominal discount rate
• Or, make cash flow estimates in terms of
today’s dollars and evaluate using the real
discount rate
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Inflation Example
Inflation = 10%
Nominal cash flows
• C(0) = -$250
• C(1) = $110
• C(2) = $121
• C(3) = $133.10
• Nominal Required
Return = 13.3%
• NPV = $32.86
Real cash flows
• C(0) = -$250
• C(1) = $100
• C(2) = $100
• C(3) = $100
• Real Required
Return = 3%
• NPV = $32.86
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Discounted cash flow NPV:
Guidelines for Application:
•
•
•
•
Ignore sunk costs (Problem 5)
Focus on incremental benefits and costs (Problem 6)
Discount using opportunity cost of capital
Discount nominal cash flows at the nominal rate and real cash
flows at the real rate
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Discounted cash flow internal
rate of return (DCF-IRR):
• Definition: The yield implied by the cash
flow estimates
– Found by a trial-and-error search for the
discount rate that makes NPV=0
– Also known as ROR
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Discounted cash flow IRR
Advantages:
• Grounded in the Rate of Return Corollary of
the NPV Rule, by a model of the security
valuation process
• Relating to it seems easy
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IRR Example
•
•
•
•
C(0) = -$300
C(1) = $110
C(2) = $121
C(3) = $133.10
• IRR = 10%
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NPV Profile
$80.00
$60.00
$40.00
$20.00
$0.00
($20.00)
($40.00)
($60.00)
($80.00)
0%
5%
10%
15%
20%
25%
Rate
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What is IRR really saying in this case?
• If cost of capital is below IRR, NPV is
positive
• If cost of capital is above IRR, NPV is
negative
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Discounted cash flow IRR
Disadvantages:
The IRR may be difficult to interpret
• Prefer higher IRR for lending cash flow
stream
• But, prefer lower IRR for borrowing cash
flow stream
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IRR Example
•
•
•
•
C(0) = $300
C(1) = -$110
C(2) = -$121
C(3) = -$133.10
• IRR = 10%
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NPV Profile
$80.00
$60.00
$40.00
$20.00
$0.00
($20.00)
($40.00)
($60.00)
($80.00)
0%
5%
10%
15%
20%
25%
Rate
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What is IRR really saying in this case?
• If cost of capital is above IRR, NPV is
positive
• If cost of capital is below IRR, NPV is
negative
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Discounted cash flow IRR
Disadvantages:
• Complex cash flow streams may have
multiple solutions or even no solution
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IRR Example
• C(0) = -$4,000
• C(1) = $25,000
• C(2) = -$25,000
• IRR = 25% or 400%
– There may be as many
solutions as there are
sign changes
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NPV Profile
$3,000.00
$2,000.00
$1,000.00
$0.00
($1,000.00)
($2,000.00)
($3,000.00)
($4,000.00)
($5,000.00)
Rate
- 34 -
IRR Example
• C(0) = $7,000
• C(1) = -$25,000
• C(2) = $25,000
• IRR doesn’t exist
– There may be no
solution
– NPV always positive
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NPV Profile
$8,000.00
$7,000.00
$6,000.00
$5,000.00
$4,000.00
$3,000.00
$2,000.00
$1,000.00
$0.00
Rate
- 36 -
IRR Example
• C(0) = -$7,000
• C(1) = $25,000
• C(2) = -$25,000
• IRR doesn’t exist
– There may be no
solution
– NPV always negative
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NPV Profile
$0.00
($1,000.00)
($2,000.00)
($3,000.00)
($4,000.00)
($5,000.00)
($6,000.00)
($7,000.00)
($8,000.00)
Rate
- 38 -
Discounted cash flow IRR
Disadvantages:
• Biased toward projects with shorter life
spans
– may result in poor decisions
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Example of bias
•
•
•
•
C(0) = -$250
C(1) = $110
C(2) = $121
C(3) = $133.10
NPV @ 10% = $50
IRR = 20.67%
•
•
•
•
•
C(0) = -$250
C(1) = $55
C(2) = $60
C(3) = $145
C(4) = $150
NPV @ 10% = $60.98
IRR = 18.9%
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NPV Profile: Timing Bias
$150.00
$100.00
$50.00
$0.00
($50.00)
($100.00)
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Discounted cash flow IRR
Disadvantages:
• Biased toward small-scale projects
– so is not appropriate for resolving conflicts
between mutually exclusive projects
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Example of bias
•
•
•
•
C(0) = -$250
C(1) = $110
C(2) = $121
C(3) = $133.10
NPV @ 10% = $50
IRR = 20.67%
•
•
•
•
C(0) = -$2,700
C(1) = $1,100
C(2) = $1,210
C(3) = $1,331
NPV @ 10% = $300
IRR = 16.00%
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NPV Profile: Scale Bias
$1,000.00
$800.00
$600.00
$400.00
$200.00
$0.00
($200.00)
($400.00)
($600.00)
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Discounted cash flow IRR
Disadvantages:
• The IRR for the whole firm is not the sum
of the IRRs of the parts
– Thus, is difficult to measure project’s
contribution to the whole firm
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Present value index (or
profitability index)
• There are three alternate definitions:
n
[1] Prof Index =
1
C0
[2 ] Prof Index =
DCF NPV
C0
n
Â
[3] Prof Index =
Â
Ct
t=1 (1 + R )
Inflows t
t
t=0 (1 + R )
n Outflows
Â
t=0
t
t
(1 + R ) t
- 46 -
Present value index
• Advantages: Can be related to as a measure
of “bang for the buck”
• Disadvantages: Biased toward smaller-scale
projects
– so is not reliable in resolving conflicts between
mutually-exclusive projects
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Payback period
• Definition: time required to recoup the
original investment from project cash flows
• Advantages:
– Easy to compute
– Easy for people to comprehend
• Disadvantages:
– Ignores time value of money
– Fails to consider cash flows after the payback
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Payback reciprocal:
• Definition: The reciprocal of the payback
period.
– Sometimes used as estimate of IRR
– But, consistently overestimates IRR
• Shares the same disadvantages as the
Payback Period
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Other museum pieces
• Not firmly grounded in the NPV Rule
– Accounting Rate of Return
– Average Rate of Return.
• Anything not grounded in NPV Rule by a
model of the security valuation process
could lead to poor decisions and a loss of
shareholder wealth
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More sophisticated models
• As more sophisticated models of the
security valuation process are developed,
you can expect to see them applied to the
capital budgeting problem
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What are the Value Drivers?
• Market value of physical
assets
– Consider change in net worth when
new assets and liabilities are
included in the balance sheet
• When would impact on net
worth be neutral? …
Negative? … Positive?
– You may be able to stop here if
neutral or positive
• Added earning power
derived from new assets
• Option approaches continue
from here
– Value of new opportunities
– Enhanced value of human capital
• Stronger organizational capital
via enhanced flexibility
• New incentives offered to key
decision makers
– Enhanced technology
– Enhanced competitive advantage
– DCF methods focus on these
earnings
– You may be able to stop here, too
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More sophisticated models
• So, look for new developments in
application of Option Pricing Theory to
project evaluation
• Another potential source of new tools is the
concept of a “surrogate portfolio”
– This is a portfolio of traded securities which has
a distribution of payoffs that mimics the
project’s
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More sophisticated models
• Moreover, it is becoming increasingly
common to package a project as a separate
entity and sell it in the capital market
• When this is possible, capital budgeting is
simply a matter of profit maximizing
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