FMANAGEMENT
INANCIAL
ESSENTIALS OF
CHAPTER 12
Lecture 8
The Basics of Capital Budgeting
Lecture Outline
Net Present Value (NPV)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)
Regular Payback
Discounted Payback
2
What is capital budgeting?
Analysis of potential additions to fixed
assets for expanded operation.
Capital budgeting decisions involve large
expenditures and are key determinants of
long-run performance
Very important to firm’s future.
3
Steps to Capital Budgeting
1.
Estimate CFs (inflows & outflows).
2. Assess riskiness of CFs.
3. Determine the appropriate cost of capital.
4. Find NPV and/or IRR.
5. Accept if NPV > 0 and/or IRR > WACC.
4
Independent vs. Mutually Exclusive
Projects?
The decision on one project may or may be
related to that on other projects
Independent projects: if the cash flows of
one are unaffected by the acceptance of the
other.
Mutually exclusive projects: if the cash
flows of one can be adversely impacted by
the acceptance of the other.
5
Normal vs. Non-normal Cash
Flow Streams?
This refers to the pattern of cash flows of a
project during life of the project.
Normal cash flow stream: Cost (negative
CF) followed by a series of positive cash
inflows.
Nonnormal cash flow stream: the signs of
cash flows change more than once.
Most common: Cost (negative CF), then string
of positive CFs, then cost to close project.
Examples include nuclear power plant, strip
mine, etc.
6
Net Present Value (NPV)
Sum of the PVs of all cash inflows and outflows
of a project:
N
CFt
NPV = ∑
t
+
(
1
r
)
t =0
where r is the cost of capital.
Positive NPV means that the project adds value
to the firm, why?
For two alternative projects, either compare
their NPV’s, or use “incremental cash flows” to
see if NPV positive.
7
Example
Compare two projects: Short (S) and Long (L):
Year
0
1
2
3
Cash Flow
L
S
-100
-100
10
70
60
50
80
20
∆CF
0
-60
10
60
∆CF is the difference between CFL and CFS.
8
What is Project L’s NPV?
Suppose the cost of capital is WACC = 10%
Year
0
1
2
3
CFt
- 100
10
60
80
PV of CFt
- $100.00
9.09
49.59
60.11
NPVL= $ 18.79
Excel: =NPV(rate,CF1:CFn) + CF0
Here, CF0 is negative.
9
What is Project S’ NPV?
The same cost of capital: WACC = 10%
Year
0
1
2
3
CFt
- 100
70
50
20
PV of CFt
- $100.00
63.64
41.32
15.02
NPVS = $ 19.98
Excel: =NPV(rate,CF1:CFn) + CF0
Here, CF0 is negative.
10
NPV by Financial Calculator
Enter CFs into the calculator’s CFLO register.
CF0 = -100
CF1 = 10
CF2 = 60
CF3 = 80
Enter I/YR = 10, press NPV button to get NPVL
= $18.78.
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Rationale for the NPV Method
NPV = PV of inflows – Cost
= Net gain in wealth
If projects are independent, accept if the
project NPV > 0.
If projects are mutually exclusive, accept
projects with the highest positive NPV,
those that add the most value.
In this example, accept S if mutually
exclusive (NPVS > NPVL), and accept both
if independent.
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Internal Rate of Return (IRR)
IRR is the discount rate that forces PV of
inflows equal to cost, and the NPV = 0:
N
CFt
0 = ∑
t
t = 0 (1 + IRR )
Solving for IRR with a financial calculator:
Enter CFs in CFLO register.
Press IRR; IRRL = 18.13% and
IRRS = 23.56%.
Solving for IRR with Excel:
=IRR(CF0:CFn,guess for rate)
13
Similarity of a Project’s IRR to a
bond’s YTM
Think of a bond as a project. The YTM on
the bond would be the IRR of the “bond”
project.
Both are the rate of return expected to be
earned on investment.
EXAMPLE: Suppose a 10-year bond with a
9% annual coupon and $1,000 par value sells
for $1,134.20.
Solve for IRR = YTM = 7.08%, the annual return
for this project/bond.
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Rationale for the IRR Method
If IRR > WACC, the project’s return exceeds
its costs and there is some return left over to
boost stockholders’ returns.
If IRR > WACC, accept project.
If IRR < WACC, reject project.
If projects are independent, accept both
projects, as both IRR > WACC = 10%.
If projects are mutually exclusive, a possible
decision rule is to accept the one with higher
IRR, provided IRR>WACC.
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NPV Profiles
A graphical representation of project NPVs
at different costs of capital. For example
WACC
0
5
10
15
20
NPVL
$50
33
19
7
(4)
NPVS
$40
29
20
12
5
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NPV vs. IRR Decisions Rules for
Independent Projects
For independent project, the two decision rules
always lead to the same accept/reject decision.
NPV ($)
IRR > r
and NPV > 0
Accept.
r > IRR
and NPV < 0.
Reject.
r = 18.1%
IRRL = 18.1%
r (%)
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NPV vs. IRR Decision Rules for
Mutually Exclusive Projects
If r < 8.7%: NPVL > NPVS
IRRS > IRRL
CONFLICT
NPV
L
If r > 8.7%: NPVS > NPVL ,
IRRS > IRRL
NO CONFLICT
S
r
8.7
%
r
IRRL
IRRs
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Finding the Crossover Rate
Find cash flow differences between the
projects. See Slide 8.
Enter the ∆CFs in CFj register, then press
IRR. Crossover rate = 8.68%, rounded to
8.7%.
If the NPV profiles don’t cross, one project
dominates the other.
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Reasons Why NPV Profiles Cross
Size (scale) differences: the smaller project
frees up funds at t = 0 for investment. The
higher the opportunity cost, the more
valuable these funds, so a high WACC
favors small projects.
Timing differences: the project with faster
payback provides more CF in early years
for reinvestment. If WACC is high, early
CF especially good, NPVS > NPVL.
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Find Project P’s NPV and IRR
Project P has cash flows (in 000s): CF0 = -$800,
CF1 = $5,000, and CF2 = -$5,000.
0
1
2
5,000
-5,000
WACC = 10%
-800
Enter CFs into calculator CFLO register.
Enter I/YR = 10.
NPV = -$386.78.
IRR = ERROR
Why?
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The Problem of Multiple IRRs
For non-normal cash flow stream, there can be
multiple IRR, as is the case with Project P:
NPV
IRR2 = 400%
450
0
-800
100
400
WACC
IRR1 = 25%
22
How Can There Be Multiple IRRs?
At very low discount rates, the PV of CF2 is
large and negative, so NPV < 0.
At very high discount rates, the PV of both
CF1 and CF2 are low, so CF0 dominates and
again NPV < 0.
In between, the discount rate hits CF2
harder than CF1, so NPV > 0.
Result: 2 IRRs.
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Is There a Better IRR Measure?
There are advantages in using IRR: easily
understood, and easy to communicate.
That is why many manager prefer IRR to NPV.
An alternative, more versatile IRR measure is
the Modified Internal Rate of Return (MIRR).
The following example illustrates how to
calculate MIRR.
But IRR has the problem of not being applicable
to non-normal cash flow streams.
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Calculating MIRR: An Example
0
10%
-100.0
1
2
3
10.0
60.0
80.0
10%
10%
PV100.0
outflows
MIRR = 16.5%
$158.1
$10 =
(1 + MIRRL)3
0
MIRRL = 16.5%
66.0
12.1
158.
TV1inflows
Excel: MIRR(CF0:CFn,Finance_rate,Reinvest_rate)
We assume that both rates = WACC.
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What MIRR Specifically Is
Separate all cash inflows from cash outflows
Each cash outflow is discounted back to the
present at the WACC to be added to the PV of
costs.
MIRR is the discount rate at which the PV of
the terminal value (TV) equals the PV of costs.
Each cash inflow is compounded at the WACC
to the end of the project to be added to the
“terminal value” (TV)
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The Advantage of MIRR over IRR
An implicit assumption in calculating PV/FV is
that cash flow can be reinvested at the rate used
for discounting/compounding.
The theoretical advantage of MIRR: reinvestment
at the opportunity cost, i.e. WACC, this is more
realistic than IRR.
The practical advantage: the problem of multiple
IRR with non-normal cash streams is avoided.
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NPV, or IRR, or MIRR?
For independent project, the decision rules
based NPV, IRR, and MIRR would lead to
the same decision (provided that IRR is
applicable).
The mutually exclusive projects, since the
goal is to maximize firm value, the one
project with the highest NPV should be
chosen.
If the projects differ in size, the decision rule
based on NPV may conflict with that based on
IRR or MIRR
What is the Payback Period?
The number of years required to recover a
project’s cost, or “How long does it take to
get our money back?”
Calculated by adding project’s cash inflows
to its cost until the cumulative cash flow for
the project turns positive.
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Calculating Payback Period
Project L’s Payback Calculation
0
1
2
3
CFt
-100
10
60
80
Cumulative
-100
-90
30
50
PaybackL = 2 + 30 / 80
= 2.375 years
PaybackS = 1.600 years, (Please Verify)
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Advantages / Disadvantages of Payback
Advantages
Provides an indication of a project’s risk and
liquidity.
Easy to calculate and understand.
Disadvantages
Ignores the time value of money.
Ignores CFs occurring after the payback
period.
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Discounted Payback Period
Uses discounted cash flows rather than raw CFs.
0
10%
1
2
3
10
60
80
CFt
-100
PV of CFt
-100
9.09
49.59
60.11
Cumulative
-100
-90.91
-41.32
18.79
Disc PaybackL = 2 + 41.32 / 60.11 = 2.7 years
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Practice Questions:
Chapter 12
• Questions 5, 6, 8
• Problems 6, 7, 13, 16, 19.
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