Methods

1
CHAPTER 11 Capital Budgeting Decision Methods

• Methods
• Payback Period
• Discounted Payback Period
• Accounting Rate of Return (ARR)
• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• Profitability Index (PI)
• Modified Internal Rate of Return (MIRR)
• Unequal Lives
• Economic Life
• Capital Rationing

2
What is capital budgeting?

• Analysis of potential additions to fixed assets
• Can consider investment in people also
• Long-term decisions involve large expenditures
• Very important to firms future

3
Investment Proposals

• Replacement Maintenance of the business
• Replacement Cost Reduction
• Expansion of existing products or markets
• Expansion into new products or markets
• Safety and/or environmental projects
• Other such as parking lots

4
Similarities between capital budgeting and
individual investment decisions?

• YES, conceptually, but stocks and bonds exist and
  capital budgeting projects are created.

5
Steps

• 1. Generate ideas. Search for investment
  opportunities.
• 2. Estimate the CFs (inflows and outflows).
• 3. Assess the riskiness of the CFs.
• 4. Determine WACC project cost of capital.
• 5. Find NPV, IRR, and/or MIRR.
• 6. Accept if NPV gt 0 and/or IRR gt cost of
  capital.
• 7. Post Audit already committed investments and
  evaluate cash flows

6
What is the difference between independent and
mutually exclusive projects?

• Projects are independent if the cash flows of one
  are not affected by the acceptance of the other
• Projects are mutually exclusive if acceptance of
  one impacts adversely on the cash flows of the
  other
• Projects can also be inter-dependent, if one
  project depends on another.

Finance 402
7
Example of mutually exclusive projects
Bridge vs. boat to get products across a river.
8
What is the payback period?

• The expected number of years required to recover
  a projects cost, i.e.. how long will it take to
  get the businesss money back?

9
Payback for Project L (Long Most CFs in later
years)
2.4
0
1
2
3
10
80
60
-100
CFt
100
Cumulative
-100
-90
-30
50
0

PaybackL
2 30/80 2.375 years
10
Project S (Short CFs come quickly)
1.6
0
1
2
3
70
20
50
-100
CFt
100
Cumulative
-100
-30
20
40
0
PaybackS
1 30/50 1.6 years

11
What is the rationale for the payback period?

• Its a type of breakeven analysis. It tells
  us when the project will break even in a cash
  flow sense.

12
Strengths of Payback
1. Indication of a projects risk and
liquidity. 2. Easy to calculate and understand.
Weaknesses

• 1. Ignores time value of money (TVM).
• 2. Ignores CFs occurring after payback.
• 3. Ignores the pattern of returns.
• 4. Overvalues short projects

13
If maximum acceptable payback is two years, what
is the best decision if L and S are
independent? Mutually exclusive?

• If required payback is 2 years, Project S would
  be accepted and L would not.
• In this situation, it makes no difference whether
  the projects are independent or mutually
  exclusive.

14
Discounted Payback Uses discounted rather than
raw CFs.
0
1
2
3
10
10
80
60
CFt
-100
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.
15
Strength of Discounted Payback

• Unlike regular payback, it considers the time
  value of money.
• Like regular payback, it ignores the CFs
  occurring after payback.

Weakness
16
Should capital budgeters even look at payback?

• Some firms do calculate payback and give it some
  weight in capital budgeting decisions.
• Its not the primary criterion rather it is used
  as one measure of a projects liquidity and
  riskiness.

17
Accounting Rate of Return

• Examines the projects contribution to net income
  rather than its cash flow.
• ARR Average Annual Expected Income divided by
  Average Investment
• Does not consider the time value of money
• Overvalues longer projects
• Does not consider cash flows

18
NPV is the sum of the PVs of a projects inflows
and outflows.
n

CFt
?
NPV
(1 k)t
t 0
If all costs at t 0, then
CFt
n
- CF0
NPV
?
(1 k)t
t 1
19
Whats Project Ls NPV?
Project L
0
1
2
3
10
10
80
60
-100.00
9.09
49.59
60.11
18.79 NPVL
NPVS 19.98.
20
Calculator Solution
Enter in CFLO for L
-100 10 60 80 10
CF0
CF1
CF2
CF3
NPV
I
18.78 NPVL
21
Rationale for NPV method?

• NPV PV inflows - PV costs Net gain in
  wealth
• Accept project if NPV gt 0
• Choose between mutually exclusive projects on the
  basis of higher positive NPV. Adds most value.

22
Using the NPV method, which project(s) should be
accepted?

• If Projects S and L are independent, accept
  both NPV gt 0.
• If Projects S and L are mutually exclusive,
  accept S because NPVS gt NPVL.

23
Would the NPVs change if the cost of capital
changed?
CFt
n
NPV
?
(1r)t
t 0
YES NPV is dependent on k
If k , NPV If k , NPV
24
Internal Rate of Return IRR
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.
25
NPV Enter k, solve for NPV
IRR Enter NPV 0, solve for IRR
CFt
n

?
0
(1IRR)t
t 0
Please use your calculator or EXCEL.
26
Whats Project Ls IRR?
0
1
2
3
IRR ?
10
80
60
-100.00
PV1
PV2
PV3
0 NPV
Enter CFs in CFLO, then press IRR
IRRL 18.13.
IRRS 23.56.
27
Find IRR if CFs are constant
0
1
2
3
IRR ?
40
40
40
-100
INPUTS
3 -100 40 0 9.70
OUTPUT
Or, with CFLO, enter CFs and press IRR 9.70.
28
Q. How is a projects IRR related to a bonds
YTM?
A. They are the same thing. They both measure
percentage rate of return. A bonds YTM is the
IRR if you invest in the bond.
0
1
2
10
IRR ?
...
90
1,090
90
-1,134.2
IRR 7.08 (use TVM or CFLO).
29
Rationale for the IRR Method
If IRR gt WACC, then the projects rate of return
is greater than its cost-- some return is left
over to boost stockholders returns. Example WAC
C 10, IRR 15. Profitable.
30
IRR acceptance criteria

• If projects are independent,
• accept all projects with IRR gtk
• reject all projects with IRR lt k

31
Are S and/or L acceptable by IRR?

• If S and L are independent, accept both. IRR gt k
  10.
• If S and L are mutually exclusive, tentatively
  accept S because IRRS gt IRRL.

32
Are IRRs affected by changes in the cost of
capital?

• NO. IRRs are independent of the cost of capital.
• However, the acceptability of projects could
  change.
• Net Present Value calculations are affected by
  changes in the cost of capital.

33
Define Profitability Index (PI)
PV of inflows

PV of outflows
PI measures a projects bang for the buck.
34
Rationale behind the PI method?

• If PI gt 1 acceptIf PI lt 1
  reject
• The higher the PI, the better the project.

35
Which project is better if they are independent?
Mutually exclusive?

• Both franchises should be accepted if they are
  independent, but S should be selected if they are
  mutually exclusive because because NPVs gt NPVL.

36
Construct NPV Profiles
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)
37
NPV ()
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
38
NPV and IRR always lead to the same accept/reject
decision for independent projects
NPV ()
r gt IRR and NPV lt 0. Reject.
IRR gt r and NPV gt 0 Accept.
r ()
IRR
39
Mutually Exclusive Projects
NPV 80 60 40 20
L
r lt 8.7 NPVL gt NPVS IRRSgt IRRL CONFLICT r gt
8.7 NPVSgt NPVL IRRS gt IRRL NO CONFLICT
IRRL
S
IRRS
0 8.7 15 20 25 k
40
How do you find the crossover rate?

• Find the CF differences between the projects. See
  data at beginning of the case.
• Enter the differences in CFLO, then press IRR.
  Crossover rate 8.68.
• Can subtract S from L or vice versa, but better
  to have first CF negative.
• If profiles do not cross, one project dominates
  the other.

41
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 r is high, early CF
especially good, NPVS gt NPVL.
42
Reinvestment rate assumptions

• NPV assumes reinvestment at r (opportunity cost
  of capital).
• IRR assumes reinvestment at IRR.
• Reinvestment at opportunity cost, r, is more
  realistic, so NPV method is best. NPV should be
  used to choose between mutually exclusive
  projects.

43
Managers like rates- they can visualize IRR
better than NPV. Can we give them a better IRR?

• YES. MIRR is the discount rate which causes the
  PV of a projects terminal value (TV) to equal
  the PV of its costs. Since TV is found by
  compounding inflows at the opportunity cost of
  capital, MIRR assumes cash inflows are reinvested
  at WACC (r).
• MIRR is available as a financial function in
  EXCEL.

44
MIRR for Project L (r 10)
0
1
2
3
10
10.0
80.0
60.0
-100.0
10
66.0 12.1
10
MIRR 16.5
158.1
-100.0
TV inflows
PV outflows
MIRRL 16.5
45
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.
46
Why use MIRR vs. IRR?

• MIRR correctly assumes reinvestment at the
  opportunity cost of capital (WACC).
• MIRR also avoids the problem with multiple IRRs.
• Managers like rate of return comparisons, and
  MIRR is better for this than IRR.

47
Is MIRR better than NPV?

• NO. MIRR does not always lead to the same
  decision as NPV for mutually exclusive projects.
  In particular, small projects often have a higher
  MIRR, but a lower NPV than larger projects.
• NPV remains the conceptually best decision rule.

48
What is the difference between normal and
non-normal projects?

• Projects are normal if they have outflows or
  costs in the first year(s) followed by a series
  of inflows (One Change of signs)
• Projects are non-normal if there are 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.

Finance 402
Finance 402
49
Inflow () or Outflow (-) in year 0 1 2 3 4 5 N
NN - N - - NN - - - N
- - NN - - - NN
50
Pavilion Project NPV and IRR?
0
1
2
k 10
5,000
-5,000
-800
Enter CFs in CFLO, enter I 10.
NPV -386.78
IRR ERROR. Why?
51
We got IRR ERROR because there are 2 IRRs.
Nonnormal CFs--two sign changes. Heres a
picture
NPV Profile
NPV
IRR2 400
450
0
k
400
100
IRR1 25
-800
52
Logic of Multiple IRRs
1. At very low discount rates, the PV of CF2 is
large negative, so NPV lt 0. 2. At very high
discount rates, the PV of both CF1 and CF2 are
low, so CF0 dominates and again NPV lt 0. 3. In
between, the discount rate hits CF2 harder than
CF1, so NPV gt 0. 4. Result 2 IRRs.
53
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
54
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 _at_ 10 -4,932,231.40.
TV inflows _at_ 10 5,500,000.00.
MIRR 5.6
55
Accept Project P?
NO. Reject because MIRR 5.6 lt k 10. Also,
if MIRR lt k, NPV will be negative NPV
-386,777.
56
S and L are mutually exclusive and will be
repeated. r 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
57

• Note that Project S could be repeated after 2
  years to generate additional profits.
• Can use either replacement chain or equivalent
  annual annuity analysis to make decision.

58
S L CF0 -100,000
-100,000 CF1 60,000 33,500 Nj
2 4 I 10 10 NPV 4,132
6,190
NPVL gt NPVS. But is L better? Cant say yet.
Need to perform replacement chain (or common
life) analysis.
59
Project S with Replication
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.
60
Or, use NPVs
0
1
2
3
4
4,132 3,415 7,547
4,132
10
Compare to Project L NPV 6,190.
You could alternatively use the Equivalent Annual
Annuity Method.
61
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 lt NPVL 6,190. Now choose L.
62
Consider another project with a 3-year 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
63
CFs Under Each Alternative (000s)
0
1
2
3
1.75
1. No termination 2. Terminate 2 years 3.
Terminate 1 year
(5) (5) (5)
2.1 2.1 5.2
2 4
64
Assuming a 10 cost of capital, what is the
projects optimal, or economic life?
NPV(no) -123. NPV(2) 215. NPV(1) -273.
65
Conclusions

• The project is acceptable only if operated for 2
  years.
• A projects engineering life does not always
  equal its economic life.

66
Choosing the Optimal Capital Budget

• Finance theory says to accept all positive NPV
  projects.
• Two complications can occur when there is not
  enough internally generated cash to fund all
  positive NPV projects
• An increasing marginal cost of capital.
• Capital rationing

67
Increasing Marginal Cost of Capital

• Externally raised capital can have large
  flotation costs, which increase the cost of
  capital.
• Investors often perceive large capital budgets as
  being risky, which drives up the cost of capital.

(More...)
68

• If external funds will be raised, then the NPV of
  all projects should be estimated using this
  higher marginal cost of capital.

69
Capital Rationing

• Capital rationing occurs when a company chooses
  not to fund all positive NPV projects.
• The company typically sets an upper limit on the
  total amount of capital expenditures that it
  will make in the upcoming year.

(More...)
70

• Reason Companies want to avoid the direct costs
  (i.e., flotation costs) and the indirect costs of
  issuing new capital. (Reluctance to issue new
  stock)
• 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...)
71

• Reason Companies believe that the projects
  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. (Controlling estimation
  bias)
• Solution Implement a post-audit process and tie
  the managers compensation to the subsequent
  performance of the project.

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Post Auditing Already Committed Investments

• Compare actual results to those predicted in the
  request for funds
• Explanation of observed differences
• Improve Forecasts
• Improve Operations
• Identify Termination Opportunities

Finance 402
73
Conclusion

• Techniques of Capital Budgeting
• Payback
• Discounted Payback
• Accounting Rate of Return
• Net Present Value
• PI
• IRR
• MIRR
• Nonnormal Projects
• Economic Life
• Capital Rationing
• Post Auditing