Transcript The Time Value of Money - Vocational Training Council

B280F Introduction to Financial Management
Lecture 6
Capital-Budgeting Decision
Criteria
By Charles Chiu, PhD, CFA
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What is Capital Budgeting?

Capital Budget


The list of planned investment projects.
Capital budgeting is the process of
analyzing alternative long term
investments and making long-term
investment decisions.
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About Capital Budgeting Decisions
Outcome
is uncertain.
Investment involves a
long-term commitment.
Capital budgeting:
Analyzing alternative longterm investments and deciding
which assets to acquire or sell.
Decision may be
difficult or impossible
to reverse.
Large amounts of
money are usually
involved.
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Types of Investment Decisions

Selection decisions


concerning proposed projects such as
investments in long-term assets. i.e.,
property, plant, and equipment, or
resource commitments in the form of new
product development, market research, refunding of long-term debt, and introduction
of a computer.
Replacement decisions

such as replacement of existing facilities
with new facilities.
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I will choose the
project with the most
profitable return on
available funds.
Plant
Expansion
?
Limited
Investment
Funds
?
New
Equipment
?
Office
Renovation
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Decision Process
1.
2.
Develop and rank all investment
projects
Authorize projects based on:




Government regulation
Production efficiency
Capacity requirements
NPV
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Nonfinancial Considerations
Employee working conditions
Environmental concerns
Employee morale
Corporate image
Product quality
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How do we
decide if a
capital
investment
project
should be
accepted or
rejected?
Decision-making Criteria in
Capital Budgeting

The ideal evaluation method
should:
1.
2.
3.
include all cash flows that occur
during the life of the project,
consider the time value of money,
and
incorporate the required rate of
return on the project.
Decision-making Criteria in
Capital Budgeting






Payback Period
Discounted Payback Period
Net Present Value (NPV)
Profitability Index (PI)
Internal Rate of Return (IRR)
Modified Internal Rate of Return
(MIRR)
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Decision Rule


All of these techniques attempt to
compare the costs and benefits of a
project
The over-riding rule of capital
budgeting is to accept all projects for
which the cost is less than, or equal
to, the benefit:


Accept if:
Reject if:
Cost Benefit
Cost > Benefit
Payback Period


How long will it take for the project to
generate enough cash to pay for
itself?
The payback period measures the
length of time to recover the amount
of initial investment. It is computed
by dividing the initial investment by
the cash inflows through increased
revenues or cost savings.
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Example
Assume: Cost of investment
Annual free cash flows
$18,000
$ 3,000
Payback period =
initial investment cost
$18,000
=
= 6 years
increased revenues or cost savings $ 3,000
Decision rule: Choose the project with the shorter
payback period, because the shorter the payback
period, the less risky the project, and the greater the
liquidity.
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Consider two projects whose free cash inflows are not
even. Assume each project costs $1,000.
Year A ($) B ($)
1
100
500
2
200
400
3
300
300
4
400
100
5
500
6
600
When cash inflows are not even, the payback period has
to be found by trial and error.
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The payback period of project A is 4 years.
($1,000 = $100 + $200 + $300 + $400 )
The payback period of project B is:
($1000 = $500 + $400 + $100)
or
$100
= 0.33 years.
$300
The payback period of project B is 2.33 years.
Project B is the project of choice in this case, since it
has the shorter payback period.
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
Advantages




It deals with cash flows rather than accounting
profits and therefore focuses on the true timing of
the project’s benefits and costs.
It is simple to compute and easy to understand.
It can be used as a rough screening device,
eliminating projects whose returns do not
materialize until later years.
Shortcomings



It ignores the time value of money.
It does not consider any required rate of return
It ignores the impact of cash inflows received after
the payback period
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Discounted Payback Period


Discounts the cash flows at the
firm’s required rate of return.
Payback period is calculated using
these discounted net cash flows.
Discounted Payback Period
(500)
250
250
250
0
1
2
3
250 250
4
5
Discounted
Year
Cash Flow
0
1
-500
250
2
250
3
250
CF (14%)
-500.00
219.30
280.70
192.37
88.33
168.74
1 year
2 years
2.52 years
Net Present Value

Net present value (NPV) is the excess of
the present value (PV) of cash inflows
generated by the project over the amount
of the initial outlay (IO):
n
NPV 
FCF t
 1  k 
t
 IO
t 1

Advantages
 It recognizes the time value of money.
 It is easy to compute whether the cash
flows form an annuity or vary from
period to period
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Computation
Choose a discount rate – the
minimum required rate of return.
Calculate the present
value of cash inflows.
Calculate the present
value of cash outflows.
NPV =  - 
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Decision Rule
If the Net Present General decision rule . . .
Value is . . .
Then the Project is . . .
Positive . . .
Acceptable, since it promises a
return greater than the required
rate of return.
Zero . . .
Acceptable, since it promises a
return equal to the required rate
of return.
Negative . . .
Not acceptable, since it
promises a return less than the
required rate of return.
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Foundation of the NPV Approach




The market value of the firm is based on the
present value of the cash flows it is
expected to generate.
Additional investments are “good” if the
present value of the incremental expected
cash inflows exceeds their cost.
Thus, “good” projects are those which
increase firm value - or, good projects are
those projects that have positive NPVs!
Conclusion - Invest only in projects with
non-negative NPV.
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Sources of NPV
o
o
o
o
o
Economies of Scale
Cost Advantages
Product differentiation
Distribution Advantage
Regulatory Protection
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Profitability Index (Benefit/Cost Ratio)

The profitability index is the ratio of the total
PV of future cash inflows to the initial
investment
n
PI 


FCF t
 1  k 
t
t 1
IO
This index is used as a means of ranking
projects in descending order of attractiveness.
Decision rule: If the profitability index is
greater than or equal to 1.00, then accept the
project.
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Internal Rate of Return

Internal rate of return (IRR) is defined as
the rate of interest that equates I with the
PV of future cash inflows.
n
FCF t
 1  IRR 
t
 IO
t 1


At IRR: NPV = 0
Decision rule: Accept the project if the
IRR is greater than or equal to the
required rate of return or hurdle rate.
Otherwise, reject it.
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
Advantage


IRR is a good decision-making tool as long
as cash flows are conventional. (- + + +
+ +)
Shortcoming

If there are multiple sign changes in the
cash flow stream, we could get multiple
IRRs. (- + + - + +)
1
2
3
(500)
200
100
(200)
400
300
0
1
2
3
4
5
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Mutually Exclusive Investments


A project is said to be mutually
exclusive if the acceptance of one
project automatically excludes the
acceptance of one or more other
projects.
In the case where one must choose
between mutually exclusive
investments, the NPV and IRR
methods may result in contradictory
indications.
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Contradictions May Occur When



Projects that have different life
expectancies.
Projects that have different sizes of
investment.
Projects whose cash flows differ over
time. For example, the cash flows of one
project increase over time, while those of
another decrease.
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Causes for Contradiction




The contradictions result from different
assumptions with respect to the reinvestment
rate on cash flows from the projects.
The NPV method discounts all cash flows at the
cost of capital, thus implicitly assuming that
these cash flows can be reinvested at this rate.
The IRR method implies a reinvestment rate
at IRR. Thus, the implied reinvestment rate
will differ from project to project.
The NPV method generally gives correct
ranking, since the cost of capital is a more
realistic reinvestment rate.
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Modified Internal Rate of Return
(MIRR)


IRR assumes that all cash flows
are reinvested at the IRR.
MIRR provides a rate of return
measure that assumes cash
flows are reinvested at the
required rate of return.
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MIRR Steps
1.
Calculate the PV of the cash outflows.

2.
Calculate the FV of the cash inflows at
the last year of the project’s time line.
This is called the terminal value (TV).

3.
Using the required rate of return.
Using the required rate of return.
MIRR: the discount rate that equates the
PV of the cash outflows with the PV of
the terminal value, ie, that makes:
PVoutflows = PVinflows
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Example

Suppose we are considering investing in an
asset that yields $1000 in year one, $1100
in year two, $1500 in year three and $3200
in year four. If your required rate of return is
12%, and the asset costs $5000, determine
the IRR and MIRR.
$4000 = $1000/(1+IRR) + $1100/(1+IRR)2
+ $1500/(1+IRR)3 + $3200/(1+IRR)4
IRR
= 20.09%
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To find the Modified IRR
$4000 = [$1000(1.12)3 + $1100(1.12)2 +
$1500(1.12) + $3200]/(1 + MIRR)4
$4000 = [$1405 + $1380 + $1680 +$3200]
/(1 + MIRR)4
$4000(1 + MIRR)4 = $7665
(1 + MIRR) = 1.1766
MIRR = 17.66%
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Importance of Capital Budgeting
 Capital
budgeting is probably the most
important issues in corporate finance


Identifying investment opportunities
which offer more value to the firm than
their cost - the value of the future cash
flows need to be greater than the
investment required
estimating the size, timing and risk of
future cash flows is the most
challenging aspect of capital budgeting
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