CHAPTER 13 The Basics of Capital Budgeting: Evaluating Cash Flows. Should we build this plant?. What is capital budgeting?. Analysis of potential additions to fixed assets. Longterm decisions; involve large expenditures. Very important to firm’s future. Steps.
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1. Estimate CFs (inflows & outflows).
2. Assess riskiness of CFs.
3. Determine k = WACC for project.
4. Find NPV and/or IRR.
5. Accept if NPV > 0 and/or IRR > WACC.
Projects are:
independent, if the cash flows of one are unaffected by the acceptance of the other.
mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.
BRIDGE vs. BOAT to get
products across a river.
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.
Inflow (+) or Outflow () in Year exclusive projects?
0
1
2
3
4
5
N
NN

+
+
+
+
+
N

+
+
+
+

NN



+
+
+
N
+
+
+



N

+
+

+

NN
The number of years required to recover a project’s cost,
or how long does it take to get the business’s money back?
2.4
0
1
2
3
CFt
100
10
60
100
80
Cumulative
100
90
30
0
50
PaybackL
=
2 + 30/80 = 2.375 years
1.6
0
1
2
3
CFt
100
70
100
50
20
Cumulative
100
30
0
20
40
PaybackS
=
1 + 30/50 = 1.6 years
Strengths of Payback: exclusive projects?
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.
Discounted Payback: Uses discounted exclusive projects?
rather than raw CFs.
0
1
2
3
10%
CFt
100
10
60
80
PVCFt
100
9.09
49.59
60.11
Cumulative
100
90.91
41.32
18.79
Discounted
payback
2 + 41.32/60.11 = 2.7 yrs
=
Recover invest. + cap. costs in 2.7 yrs.
NPV: Sum of the PVs of inflows and outflows. exclusive projects?
Cost often is CF0 and is negative.
Project L:
0
1
2
3
10%
100.00
10
60
80
9.09
49.59
60.11
18.79 = NPVL
NPVS = $19.98.
Enter in CFLO for L:
100
10
60
80
10
CF0
CF1
CF2
CF3
I
NPV
= 18.78 = NPVL
NPV = PV inflows  Cost
= Net gain in wealth.
Accept project if NPV > 0.
Choose between mutually
exclusive projects on basis of
higher NPV. Adds most value.
0
1
2
3
CF0
CF1
CF2
CF3
Cost
Inflows
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
NPV: Enter k, solve for NPV. exclusive projects?
IRR: Enter NPV = 0, solve for IRR.
0
1
2
3
IRR = ?
100.00
10
60
80
PV1
PV2
PV3
0 = NPV
Enter CFs in CFLO, then press IRR:
IRRL = 18.13%.
IRRS = 23.56%.
N exclusive projects?
I/YR
PV
PMT
FV
Find IRR if CFs are constant:
0
1
2
3
IRR = ?
100
40
40
40
INPUTS
3 100 40 0
9.70%
OUTPUT
Or, with CFLO, enter CFs and press
IRR = 9.70%.
Q. How is a project’s IRR exclusive projects?
related to a bond’s YTM?
A. They are the same thing.
A bond’s YTM is the IRR
if you invest in the bond.
0
1
2
10
IRR = ?
...
1,134.2
90
90
1,090
IRR = 7.08% (use TVM or CFLO).
If IRR > WACC, then the project’s rate of return is greater than its cost some return is left over to boost stockholders’ returns.
Example: WACC = 10%, IRR = 15%.
Profitable.
Enter CFs in CFLO and find NPVL and
NPVS at different discount rates:
NPVL
50
33
19
7
NPVS
40
29
20
12
5
k
0
5
10
15
20
(4)
NPV ($) exclusive projects?
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
Crossover
Point = 8.7%
S
IRRS = 23.6%
L
Discount Rate (%)
IRRL = 18.1%
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
Mutually Exclusive Projects for independent projects:
k < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
NPV
L
k > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
IRRS
S
%
k 8.7 k
IRRL
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.
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.
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.
$158.1 give them a better IRR?
(1+MIRRL)3
$100 =
MIRR for Project L (k = 10%)
0
1
2
3
10%
100.0
10.0
60.0
80.0
10%
66.0
12.1
10%
MIRR = 16.5%
158.1
100.0
TV inflows
PV outflows
MIRRL = 16.5%
To find TV with 10B, enter in CFLO: give them a better IRR?
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.
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.
0
1
2
k = 10%
800
5,000
5,000
Enter CFs in CFLO, enter I = 10.
NPV = 386.78
IRR = ERROR. Why?
We got IRR = ERROR because there give them a better IRR?
are 2 IRRs. Nonnormal CFstwo sign
changes. Here’s a picture:
NPV Profile
NPV
IRR2 = 400%
450
0
k
100
400
IRR1 = 25%
800
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.
Could find IRR with calculator: give them a better IRR?
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
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%
NO. Reject because MIRR = 5.6% < k = 10%.
Also, if MIRR < k, NPV will be negative: NPV = $386,777.
S and L are mutually exclusive and will be repeated. k = 10%. Which is better? (000s)
0
1
2
3
4
Project S:
(100)
Project L:
(100)
60
33.5
60
33.5
33.5
33.5
S 10%. Which is better? (000s) L
CF0 100,000 100,000
CF1 60,000 33,500
Nj 2 4
I 10 10
NPV 4,132 6,190
NPVL > NPVS. But is L better?
Can’t say yet. Need to perform common life analysis.
Replacement Chain Approach (000s)
0
1
2
3
4
Project S:
(100)
(100)
60
60
60
(100)
(40)
60
60
60
60
NPV = $7,547.
Or, use NPVs: generate additional profits.
0
1
2
3
4
4,132
3,415
7,547
4,132
10%
Compare to Project L NPV = $6,190.
If the cost to repeat S in two years rises to $105,000, which is best? (000s)
0
1
2
3
4
Project S:
(100)
60
60
(105)
(45)
60
60
NPVS = $3,415 < NPVL = $6,190.
Now choose L.
Consider another project with a 3year life. If terminated prior to Year 3, the machinery will have positive salvage value.
Year
0
1
2
3
CF
($5,000)
2,100
2,000
1,750
Salvage Value
$5,000
3,100
2,000
0
CFs Under Each Alternative (000s) prior to Year 3, the machinery will have positive salvage value.
0
1
2
3
1. No termination
2. Terminate 2 years
3. Terminate 1 year
(5)
(5)
(5)
2.1
2.1
5.2
2
4
1.75
Assuming a 10% cost of capital, what is the project’s optimal, or economic life?
NPV(no) = $123.
NPV(2) = $215.
NPV(1) = $273.
Conclusions optimal, or economic life?
(More...)
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Reason projects should be estimated using this higher marginal cost of capital.: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital.
Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital.
(More...)
Reason projects should be estimated using this higher marginal cost of capital.: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects.
Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing.
(More...)
Reason projects should be estimated using this higher marginal cost of capital.: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted.
Solution: Implement a postaudit process and tie the managers’ compensation to the subsequent performance of the project.