10 - 1
Lecture Twelve
Capital Budgeting
The Basics
Should we
build this
plant?
10 - 2
What is capital budgeting?
A process for planning and
evaluating opportunities
(projects/assets) that have an
unexpected cash flow or will yield
returns (have repercussions) for
periods longer than one year
10 - 3
Steps
1.A: Identify Projects
a. Types
b. Categories
i. Environmental
i. Independent
ii. New machine
ii. Mutually exclusive
iii. Replacement
iii. Compliments
1.B: Estimates CFs (inflows & outflows)
a. Normal
b. Non-normal
2. Assess riskiness of CFs
a. High
b. Average
c. Low
10 - 4
Steps (cont.)
3. Determine k = WACC (adj.).
4. Evaluate Cash Flows or Project
a. Payback
d. IRR
b. Discounted Payback
e. MIRR
c. NPV
5. Criteria for Accepting/Rejecting Projects
a. Example: accept if NPV > 0 and/or IRR > WACC.
6. Review Process after 1 or More years of Operation
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An Example of Mutually Exclusive
Projects
BRIDGE vs. BOAT to get
products across a river.
10 - 6
Normal Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.
Most common: Cost (negative
CF), then string of positive CFs,
then cost to close project.
Nuclear power plant, strip mine.
10 - 7
Inflow (+) or Outflow (-) in Year
0
1
2
3
4
5
N
-
+
+
+
+
+
N
-
+
+
+
+
-
-
-
-
+
+
+
N
+
+
+
-
-
-
N
-
+
+
-
+
-
NN
NN
NN
10 - 8
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?
10 - 9
Payback for Project L
(Long: Most CFs in out years)
0
1
CFt
-100
Cumulative -100
PaybackL
= 2
2
10
-90
+
30/80
2.4
60 100
-30
0
3
80
50
= 2.375 years
10 - 10
Project S (Short: CFs come quickly)
0
CFt
-100
Cumulative -100
PaybackL
1.6 2
3
70 100 50
20
-30
40
1
0 20
= 1 + 30/50 = 1.6 years
10 - 11
Strengths of Payback:
1. Provides an indication of a
project’s risk and liquidity.
2. Easy to calculate and understand.
Weaknesses of Payback:
1. Ignores the TVM.
2. Ignores CFs occurring after the
payback period.
10 - 12
Discounted Payback: Uses discounted
rather than raw CFs.
0
10%
1
2
3
10
60
80
CFt
-100
PVCFt
-100
9.09
49.59
60.11
Cumulative -100
-90.91
-41.32
18.79
Discounted
= 2
payback
+ 41.32/60.11 = 2.7 yrs
Recover invest. + cap. costs in 2.7 yrs.
10 - 13
NPV: Sum of the PVs of inflows and
outflows.
n
CFt
NPV  
.
t
t  0 1  k 
Cost often is CF0 and is negative.
n
NPV  
t 0
CFt
1  k
t
 CF0 .
10 - 14
What’s Project L’s NPV?
Project L:
0
-100.00
10%
1
2
3
10
60
80
9.09
49.59
60.11
18.79 = NPVL
NPVS = $19.98.
10 - 15
Calculator Solution
Enter in CFLO for L:
-100
CF0
10
CF1
60
CF2
80
CF3
10
I
NPV
= 18.78 = NPVL
10 - 16
Rationale for the NPV Method
NPV = PV inflows - Cost
= Net gain in wealth.
Accept project if NPV > 0.
Choose between mutually
exclusive projects on basis of
higher NPV. Adds most value.
10 - 17
Using NPV method, which project(s)
should be accepted?
If Projects S and L are mutually
exclusive, accept S because
NPVs > NPVL .
If S & L are independent,
accept both; NPV > 0.
10 - 18
Internal Rate of Return: IRR
0
1
2
3
CF0
Cost
CF1
CF2
Inflows
CF3
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
10 - 19
NPV: Enter k, solve for NPV.
n
CFt
 NPV.

t
t  0 1  k 
IRR: Enter NPV = 0, solve for IRR.
n
CFt
 0.

t
t  0 1  IRR
10 - 20
What’s Project L’s IRR?
0
IRR = ?
-100.00
PV1
1
2
3
10
60
80
PV2
PV3
0 = NPV
Enter CFs in CFLO, then press IRR:
IRRL = 18.13%. IRRS = 23.56%.
10 - 21
Find IRR if CFs are constant:
0
IRR = ?
-100
INPUTS
2
3
40
40
40
3
N
OUTPUT
1
I/YR
-100
40
0
PV
PMT
FV
9.70%
Or, with CFLO, enter CFs and press
IRR = 9.70%.
10 - 22
Q.
A.
How is a project’s IRR
related to a bond’s YTM?
They are the same thing.
A bond’s YTM is the IRR
if you invest in the bond.
0
1
2
IRR = ?
-1134.2
10
...
90
90
1090
IRR = 7.08% (use TVM or CFLO).
10 - 23
Rationale for the IRR Method
If IRR > WACC, then the project’s
rate of return is greater than its
cost-- some return is left over to
boost stockholders’ returns.
Example: WACC = 10%, IRR =
15%. Profitable.
10 - 24
IRR Acceptance Criteria
If IRR > k, accept project.
If IRR < k, reject project.
10 - 25
Decisions on Projects S and L per IRR
If S and L are independent, accept
both. IRRs > k = 10%.
If S and L are mutually exclusive,
accept S because IRRS > IRRL .
10 - 26
Construct NPV Profiles
Enter CFs in CFLO and find NPVL and
NPVS at different discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
10 - 27
NPV ($)
k
0
5
10
50
40
Crossover
Point = 8.7%
30
15
20
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
S
IRRS = 23.6%
10
L
Discount Rate (%)
0
0
-10
5
10
15
20
23.6
IRRL = 18.1%
10 - 28
NPV and IRR always lead to the same
accept/reject decision for independent
projects:
NPV ($)
IRR > k
and NPV > 0
Accept.
k > IRR
and NPV < 0.
Reject.
k (%)
IRR
10 - 29
Mutually Exclusive Projects
k < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
k > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
NPV
L
S
k
8.7
k
IRRS
%
IRRL
10 - 30
To Find the Crossover Rate
1. Find cash flow differences between the
projects. See data at beginning of the
case.
2. Enter these differences in CFLO register,
then press IRR. Crossover rate = 8.68%,
rounded to 8.7%.
3. Can subtract S from L or vice versa, but
better to have first CF negative.
4. If profiles don’t cross, one project
dominates the other.
10 - 31
Two Reasons NPV Profiles Cross
1. Size (scale) differences. Smaller
project frees up funds at t = 0 for
investment. The higher the opportunity
cost, the more valuable these funds, so
high k favors small projects.
2. Timing differences. Project with faster
payback provides more CF in early
years for reinvestment. If k is high,
early CF especially good, NPVS > NPVL.
10 - 32
Reinvestment Rate Assumptions
NPV assumes reinvest at k
(opportunity cost of capital).
IRR assumes reinvest at IRR.
Reinvest at opportunity cost, k, is
more realistic, so NPV method is
best. NPV should be used to choose
between mutually exclusive projects.
10 - 33
Managers like rates--prefer IRR to NPV
comparisons. Can we give them a
better IRR?
Yes, MIRR is the discount rate which
causes the PV of a project’s terminal
value (TV) to equal the PV of costs.
TV is found by compounding inflows
at WACC.
Thus, MIRR assumes cash inflows are
reinvested at WACC.
10 - 34
MIRR for Project L (k = 10%)
0
1
2
3
10.0
60.0
80.0
10%
-100.0
10%
10%
MIRR = 16.5%
-100.0
PV outflows
$158.1
$100 =
(1+MIRRL)3
MIRRL = 16.5%
66.0
12.1
158.1
TV inflows
10 - 35
To find TV with 10B, enter in CFLO:
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
I = 10
NPV = 118.78 = PV of inflows.
Enter PV = -118.78, N = 3, I = 10, PMT = 0.
Press FV = 158.10 = FV of inflows.
Enter FV = 158.10, PV = -100, PMT = 0,
N = 3.
Press I = 16.50% = MIRR.
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Why use MIRR versus IRR?
MIRR correctly assumes reinvestment
at opportunity cost = WACC. MIRR
also avoids the problem of multiple
IRRS.
Managers like rate of return
comparisons, and MIRR is better for
this than IRR.
10 - 37
Pavilion Project: NPV and IRR?
0
-800
k = 10%
1
2
5,000
-5,000
Enter CFs in CFLO, enter I = 10.
NPV = -386.78
IRR = ERROR. Why?
10 - 38
We got IRR = ERROR because there
are 2 IRRs. Nonnormal CFs--two sign
changes. Here’s a picture:
NPV Profile
NPV
IRR2 = 400%
450
0
-800
100
IRR1 = 25%
400
k
10 - 39
Logic of Multiple IRRs
1. At very low discount rates, the PV of
CF2 is large & negative, so NPV < 0.
2. At very high discount rates, the PV of
both CF1 and CF2 are low, so CF0
dominates and again NPV < 0.
3. In between, the discount rate hits CF2
harder than CF1, so NPV > 0.
4. Result: 2 IRRs.
10 - 40
Could find IRR with calculator:
1. Enter CFs as before.
2. Enter a “guess” as to IRR by
storing the guess. Try 10%:
10
STO
IRR = 25% = lower IRR
Now guess large IRR, say, 200:
200
STO
IRR = 400% = upper IRR
10 - 41
When there are nonnormal CFs and
more than one IRR, use MIRR:
0
-800,000
1
5,000,000
2
-5,000,000
PV outflows @ 10% = -4,932,231.40.
TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
10 - 42
Accept Project P?
NO. Reject because MIRR =
5.6% < k = 10%.
Also, if MIRR < k, NPV will be
negative: NPV = -$386,777.