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CHAPTER 11The Basics of Capital Budgeting
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Copyright © 2001 by Harcourt, Inc. All rights reserved.
What is capital budgeting?
Menganalsis tamban potensi fixed asset.
Keputusan jangka panjang; menyangkut dana dalam jumlah besar.
Sangat penting dan berpengaruh pada perusahaan di masa depan.
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Steps
1. Estimasi Cash Flows (inflows & outflows).
2.Menilai risiko arus kas.
3. Menentukan k = WACC (adj.).
4. Menghitungd NPV and IRR.
5. Menerima jika NPV > 0 dan IRR > WACC.
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independent dan mutually exclusive projects
Projects are:
independent, jika cash flows yang satu tidak dipengaruhi oleh penerimaan yang lain.
mutually exclusive, jika cashflow yang satu dipengaruhi secara negatif dengan penerimaan yang lain
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An Example of Mutually Exclusive Projects
BRIDGE vs. BOAT to get products across a river.
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Normal Cash Flow Project:Cost (negative CF) followed by aseries of positive cash inflows. One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.Most common: Cost (negativeCF), then string of positive CFs,then cost to close project.Nuclear power plant, strip mine.
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Inflow (+) or Outflow (-) in Year
0 1 2 3 4 5 N NN
- + + + + + N
- + + + + - NN
- - - + + + N
+ + + - - - N
- + + - + - NN
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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?
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Payback for Project L(Long: Large CFs in later years)
10 60
0 1 2 3
-100
=
CFt
Cumulative -100 -90 -30 50
PaybackL 2 + 30/80 = 2.375 years
0100
2.4
80
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Project S (Short: CFs come quickly)
70 2050
0 1 2 3
-100CFt
Cumulative -100 -30 20 40
PaybackL 1 + 30/50 = 1.6 years
100
0
1.6
=
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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.
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Discounted Payback: Uses discountedrather than raw CFs.
10 8060
0 1 2 3
CFt
Cumulative -100 -90.91 -41.32 18.79
Discountedpayback 2 + 41.32/60.11 = 2.7 years
PVCFt -100
-100
10%
9.09 49.59 60.11
=
Recover invest. + cap. costs in 2.7 years.
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.
k1CF
NPV tt
n
0t
NPV: Sum of the PVs of inflows and outflows.
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What’s Project L’s NPV?
10 8060
0 1 2 310%
Project L:
-100.00
9.09
49.59
60.1118.79 = NPVL NPVS = $19.98.
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Calculator Solution
Enter in CFLO for L:
-100
10
60
80
10
CF0
CF1
NPV
CF2
CF3
I = 18.78 = NPVL
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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 ofhigher NPV. Adds most value.
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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.
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Internal Rate of Return: IRR
0 1 2 3
CF0 CF1 CF2 CF3
Cost Inflows
IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.
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.NPV
k1CF
tt
n
0t
.0
IRR1CF
tt
n
0t
NPV: Enter k, solve for NPV.
IRR: Enter NPV = 0, solve for IRR.
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IRR Solution (Try 10%)IRR Solution (Try 10%)
$40,000$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $ 7,000(PVIF10%,5)
$40,000$40,000 = $10,000(.909) + $12,000(.826) + $15,000(.751) + $10,000(.683) + $ 7,000(.621)
$40,000$40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347
= $41,444 [Discount Rate terlalu $41,444 [Discount Rate terlalu rendahrendah!!]]
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IRR Solution (Try 15%)IRR Solution (Try 15%)
$40,000$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $ 7,000(PVIF15%,5)
$40,000$40,000 = $10,000(.870) + $12,000(.756) + $15,000(.658) + $10,000(.572) + $ 7,000(.497)
$40,000$40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479
= $36,841$36,841 [Discount [Discount Rate is too Rate is too high!!high!!]]
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.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
X $1,444.05 $4,603
IRR Solution (Interpolate)IRR Solution (Interpolate)
$1,444X
=
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.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
X $1,444.05 $4,603
IRR Solution (Interpolate)IRR Solution (Interpolate)
$1,444X
=
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.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
($1,444)(0.05) $4,603
IRR Solution (Interpolate)IRR Solution (Interpolate)
$1,444X
X = X = .0157
IRR = .10 + .0157 = .1157 or 11.57%
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What’s Project L’s IRR?
10 8060
0 1 2 3IRR = ?
-100.00
PV3
PV2
PV1
0 = NPV
Enter CFs in CFLO, then press IRR:IRRL = 18.13%. IRRS = 23.56%.
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40 40 40
0 1 2 3IRR = ?
Find IRR if CFs are constant:
-100
Or, with CFLO, enter CFs and press IRR = 9.70%.
3 -100 40 0
9.70%
INPUTS
OUTPUTN I/YR PV PMT FV
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90 109090
0 1 2 10IRR = ?
Q. How is a project’s IRRrelated to a bond’s YTM?
A. They are the same thing.A bond’s YTM is the IRRif you invest in the bond.
-1134.2
IRR = 7.08% (use TVM or CFLO).
...
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Rationale for the IRR Method
If IRR > WACC, then the project’s rate of return is greater than its cost--some return is left over to boost stockholders’ returns.
Example: WACC = 10%, IRR = 15%. Profitable.
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IRR Acceptance Criteria
If IRR > k, accept project.
If IRR < k, reject project.
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Decisions on Projects S and L per IRR
If S and L are independent, accept both. IRRs > k = 10%.
If S and L are mutually exclusive, accept S because IRRS > IRRL .
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Construct NPV Profiles
Enter CFs in CFLO and find NPVL andNPVS at different discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4
NPVS
40
29
20
12
5 (4)
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Copyright © 2001 by Harcourt, Inc. All rights reserved.
-10
0
10
20
30
40
50
60
5 10 15 20 23.6
NPV ($)
Discount Rate (%)
IRRL = 18.1%
IRRS = 23.6%
Crossover Point = 8.7%
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
S
L
.
.
...
.
..
.
..
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NPV and IRR always lead to the same accept/reject decision for independent projects:
k > IRRand NPV < 0.
Reject.
NPV ($)
k (%)IRR
IRR > kand NPV > 0
Accept.
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Mutually Exclusive Projects
k 8.7 k
NPV
%
IRRS
IRRL
L
S
k < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT k > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
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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.
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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.
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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.
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Managers like rates--prefer IRR to NPV comparisons. Can we give them a
better IRR?
Yes, MIRR is the discount rate thatcauses the PV of a project’s terminalvalue (TV) to equal the PV of costs.TV is found by compounding inflowsat WACC.
Thus, MIRR assumes cash inflows are reinvested at WACC.
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MIRR = 16.5%
10.0 80.060.0
0 1 2 310%
66.0 12.1
158.1
MIRR for Project L (k = 10%)
-100.010%
10%
TV inflows-100.0
PV outflowsMIRRL = 16.5%
$100 = $158.1
(1 + MIRRL)3
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To find TV with HP 10B, enter in CFLO:
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.
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
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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.
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Pavilion Project: NPV and IRR?
5,000 -5,000
0 1 2k = 10%
-800
Enter CFs in CFLO, enter I = 10.
NPV = -386.78
IRR = ERROR. Why?
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We got IRR = ERROR because there are 2 IRRs. Nonnormal CFs--two signchanges. Here’s a picture:
NPV Profile
450
-800
0400100
IRR2 = 400%
IRR1 = 25%
k
NPV
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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.
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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
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When there are nonnormal CFs and more than one IRR, use MIRR:
0 1 2
-800,000 5,000,000 -5,000,000
PV outflows @ 10% = -4,932,231.40.
TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
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Accept Project P?
NO. Reject because MIRR = 5.6% < k = 10%.
Also, if MIRR < k, NPV will be negative: NPV = -$386,777.