Chapter 10: The Basics of Capital Budgeting: Evaluating Cash Flows

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Chapter 10 The Basics of Capital Budgeting
Evaluating Cash Flows

• Overview and vocabulary
• Methods
• Payback, discounted payback
• NPV
• IRR, MIRR
• Profitability Index
• Unequal lives
• Economic life

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MINICASE 10
3
What is capital budgeting?

• Analysis of potential projects.
• Long-term decisions involve large expenditures.
• Very important to firms future.

4
Steps in Capital Budgeting

• Estimate cash flows (inflows outflows).
• Assess risk of cash flows.
• Determine r WACC for project.
• Evaluate cash flows.

5
What is the difference between independent and
mutually exclusive projects?
Digression

• 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.

6
An Example of Mutually Exclusive Projects
BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.
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Normal Project
Nonnormal Project
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Normal Project
Cost (negative CF) followed by a series of
positive cash inflows.
Nonnormal Project
One or more outflows occur after inflows have
begun. Most common Cost (negative CF), 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



-
-
-
NN
-


-

-
NN
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c(1). What is the payback period?
11
What is the payback period?
The number of years required to recover a
projects cost, or how long does it take to get
our money back?
12
Payback for Project L(Long Most CFs in out
years)
2.4
0
1
2
3
CFt
10
80
60
-100
Cumul
-100
-90
-30
50
0
PaybackL 2 30/80 2.375 years. n.b. Assumes
CFs occur evenly over the year.
13
Project S (Short CFs come quickly)
1.6
0
1
2
3
CFt
70
20
50
-100
Cumul
-100
-30
20
40
0
PaybackS 1 30/50 1.6 years.
Payback is a type of breakeven analysis.
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Strengths of Payback
Weaknesses of Payback
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c(2). Strengths of Payback

• Provides an indication of a projects risk and
  liquidity.
• Easy to calculate and understand.

Weaknesses of Payback

• Ignores the TVM.
• Ignores CFs occurring
• after the payback period.

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c(3)Discounted Payback Uses discounted rather
than raw CFs. Apply to Project L.
2.7
0
1
2
3
10
CFt
10
80
60
-100
PVCFt
60.11
-100
9.09
49.59
Cumul
-41.32
-100
-90.91
18.79
Disc. payback
2 41.32/60.11 2.7 years.
Recover invest. cap. costs in 2.7 years.
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d(1) Net Present Value (NPV)
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Net Present Value (NPV)
Sum of the PVs of inflows and outflows.
n t0
CFt (1 k)t
NPV ????????????????
If one expenditure at t 0, then
n t1
CFt (1 k)t
NPV ? CF0.
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NET PRESENT VALUE

• NPV CF0 CF1/(1k) CF2/(1k)2
  ... CFn/(1k)n

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What is Project Ls NPV?
Project L (Beware use of comp. fns)
0
1
2
3
10
-100.00
10
80
60
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What is Project Ls NPV?
Project L
0
1
2
3
10
-100.00 9.09 49.58 60.11 18.78
NPVL NPVS 19.98.
10
80
60
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Calculator Solution
Enter in CFLO for L
-100 10 60 80 10
CF0
CF1
CF2
CF3
NPV
I
18.78 NPVL.
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d(2) Rationale for the NPV Method

• If NPV 0, project breaks even
• recovers cost of investment
• investors earn required rate of return (i.e.
  opportunity cost of capital)
• If NPV gt 0
• investors get above, plus additional .

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CONSIDER PROJECT LSUM OF undiscounted CFs
150

• Investors get 100 back
• Cover their 10 cost of capital
• and have 18.79 left over.
• Who does this 18.79 belong to?
• Stockholders.

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Rationale for the NPV Method
NPV PV inflows - PV of Cost Net gain in
wealth. Accept project if NPV gt 0. Choose
between mutually exclusive projects on basis
of higher NPV. Adds most value.
26
Using NPV method, which project(s) should be
accepted?

• If Projects S and L are mutually exclusive, ?
• If S L are independent, ?

27
Using NPV method, which project(s) should be
accepted?

• If Projects S and L are mutually exclusive,..
• If S L are independent, accept..
• What happens to the NPV as the cost of capital
  changes?

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e(1) What is the Internal Rate of Return (IRR)
0
1
2
3
CF0
CF1
CF2
CF3
Cost
Inflows
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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 forces PV inflows
cost. This is the same as forcing NPV 0.
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NPV Enter k, solve for NPV.
IRR Enter NPV 0, solve for IRR.
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What is Project Ls IRR?
0
1
2
3
IRR ?
10
80
60
-100.00
PV1
PV2
PV3
0 NPV
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What is Project Ls IRR?
0
1
2
3
IRR ?
10
80
60
-100.00
PV1
PV2
PV3
Enter CFs in CFLO, then press IRR
0 NPV
IRRL 18.13.
IRRS 23.56.
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e(2) How is a projects IRR related to a bonds
YTM?
0
1
2
10
IRR ?
90
1090
90
-1134.2
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How is a projects IRR related to a bonds YTM?
They both measure percentage (rate of) return. A
bonds YTM is its IRR.
0
1
2
10
IRR ?
90
1090
90
-1134.2
IRR 7.08 (use TVM or CFLO).
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e(3) Rationale for the IRR Method?
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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.
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IRR Acceptance Criteria

• If IRR gt k, accept project.
• If IRR lt k, reject project.

38
Using IRR method, which project(s) should be
accepted?
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Using IRR method, which project(s) should be
accepted?

• If S and L are independent, .
• If S and L are mutually exclusive, accept.
• What effect does a change in the cost of capital
  have on the IRR?

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f(1) Define Profitability Index (PI)
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Define Profitability Index (PI)
PV of inflows PV of outflows
PI .
PI measures a projects bang for the buck.
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Calculate each projects PI.


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Calculate each projects PI.
Project L
9.09 49.59 60.11 100
PIL
1.19.
Project S
63.64 41.32 15.03 100
PIS
1.20.
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PI Acceptance Criteria
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PI Acceptance Criteria

• If PI gt 1, accept.If PI lt 1, reject.
• The higher the PI, the better the project.
• For mutually exclusive projects, take the one
  with the highest PI. Therefore, accept L and S if
  independent only accept S if mutually exclusive.
• Any problems with using PI?

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g(1) Construct NPV Profiles
Enter CFs in CFLO and find NPVL and NPVS at
different discount rates
NPVL 50 33 19 7 (4)
NPVS 40 29 20 12 5
k 0 5 10 15 20
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NPV ()
NPVL 50 33 19 7 (4)
NPVS 40 29 20 12 5
k 0 5 10 15 20
50
40
Crossover Point 8.7
30
20
S
IRRS 23.6
10
L
0
Discount Rate ()
5
10
15
20
23.6
Vertical intercept horizontal intercept crossover
point
-10
IRRL 18.1
48
NPV and IRR always lead to the same accept/reject
decision for independent projects.
NPV ()
k gt IRR and NPV lt 0. Reject.
IRR gt k and NPV gt 0 Accept.
k ()
IRR
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g(2) Mutually Exclusive Projects
NPV
k lt 8.7 NPVL gt NPVS , IRRS gt IRRL CONFLICT
L
k gt 8.7 NPVS gt NPVL , IRRS gt IRRL NO CONFLICT
S
IRRs

k 8.7 k
IRRL
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To Find the Crossover Rate
1. Find cash flow differences between the
projects. 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 dont cross, one project
dominates the other.
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How do you calculate the crossover point?
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Which project do you choose?
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h(1) Why do NPV profiles cross?

• Size (scale) differences. Smaller project frees
  up funds at t 0 for investment. The higher the
  opp. cost, the more valuable these funds, so high
  k favors small projects.
• Timing differences. Project with faster payback
  provides more CF in early years for reinvestment.
  If k is high, early CF especially good, NPVS gt
  NPVL.

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Reinvestment Rate Assumptions

• NPV assumes reinvestment at k (opportunity cost
  of capital).
• IRR assumes reinvestment at IRR.
• Reinvestment 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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i(1) Managers prefer IRR to NPV. Can we give
them a better IRR?
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Managers prefer IRR to NPV. Can we give them a
better IRR?
Yes, modified IRR (MIRR) is the discount rate
which causes the PV of a projects terminal value
(TV) to equal the PV of costs. TV is found by
compounding inflows at WACC. Thus, MIRR forces
cash inflows to be reinvested at WACC.
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MIRR for Project L (k 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
158.1 (1MIRRL)3
100
TV inflows
PV outflows
MIRRL 16.5
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MIRR for Project L (k 10)
0
1
2
3
10
10.0
80.0
60.0
-100.0
10
66.0 12.1
10
158.1
0
0
-100.0

TV inflows
PV outflows
MIRRL 16.5
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EXCEL HAS MIRR FUNCTION!
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Why use MIRR rather than IRR?

• MIRR correctly assumes reinvestment at
  opportunity cost k.
• MIRR also avoids problems with multiple IRRs
  with nonnormal projects.
• Managers like rate of return comparisons, and
  MIRR is better for this than IRR.

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J Pavillion Project NPV and IRR?
0
1
2
k 10
5,000
-5,000
-800
What is NPV?, IRR?
What is MIRR?
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Pavillion Project NPV and IRR?
0
1
2
k 10
5,000
-5,000
-800
Enter CFs in CFj, enter I/YR 10.
NPV -386.78
IRR ERROR. Why?
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How do we find the IRR on a 12c?

• Make a guess for i and key it in i.
• RCL g R/S.

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We got IRR ERROR because there are 2 IRRs.
Nonnormal CFs with two sign changes. Heres a
picture
NPV
NPV Profile
IRR2 400
450
0
k
400
100
IRR1 25
-800
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Logic of Multiple IRRs

• At very low disc. rates, the PV of CF2 is large
  negative, so NPV lt 0.
• At very high disc. rates, the PV of CF1 and CF2
  are both low, so CF0 dominates and again NPV lt 0.
• In between, the disc. rate hits CF2 harder than
  CF1 , so NPV gt 0.
• Result 2 IRRs.

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When there are nonnormal CFs, 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
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j(2) Accept Project P?
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Accept Project P?
NO. Reject because MIRR 5.6 lt k 10. Also,
if MIRR lt k, NPV will be negative NPV
-386,777.
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NEW QUESTION Which of the following mutually
exclusive projects is better? (000s)
0
1
2
3
4
Project S (100) Project L (100)
60 33.5
60 33.5
33.5
33.5
70
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 common life analysis.
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• 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.

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Franchise S with Replication
Replacement Chain Approach (000s)
0
1
2
3
4
Franchise S (100) (100)
60 60
60 (100) (40)
60 60
60 60
NPV 7,547.
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Or, use NPVs
0
1
2
3
4
4,132 3,415 7,547
4,132
10
Compare to Franchise L NPV 6,190.
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Equivalent Annual Annuity(EAA) Approach

• Finds the constant annuity payment whose PV is
  equal to the projects raw NPV over its original
  life.

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EAA Calculator Solution

• Project S
• PV Raw NPV 4,132.
• n Original project life 2.
• k 10.
• Solve for PMT EAAS 2,381.
• Project L
• PV 6,190 n 4 k 10.
• Solve for PMT EAAL 1,953.

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• The project, in effect, provides an annuity of
  EAA.
• EAAS gt EAAL so pick S.
• Replacement chains and EAA always lead to the
  same decision if cash flows are expected to stay
  the same.

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If the cost to repeat S in two years rises to
105,000, which is best? (000s)
0
1
2
3
4
Franchise S (100)
60
60 (105) (45)
60
60
NPVS 3,415 lt NPVL 6,190. Now choose L.
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Types of Abandonment

• Sale to another party who can obtain greater cash
  flows, e.g., IBM sold typewriter division.
• Abandon because losing money, e.g., smokeless
  cigarette.

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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
80
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
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Assuming a 10 cost of capital, what is the
projects optimal, or economic life?
NPV(no) -123. NPV(2) 215. NPV(1) -273.
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Conclusions

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

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Conclusions

• The project is acceptable only if operated for 2
  years.
• A projects engineering life does not always
  equal its economic life.
• The ability to abandon a project may make an
  otherwise unattractive project acceptable.
• Abandonment possibilities will be very important
  when we get to risk.

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Choosing the Optimal Capital Budget

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

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

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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...)
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• Reason 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...)
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• Reason Companies dont 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...)
90

• 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.
• Solution Implement a post-audit process and tie
  the managers compensation to the subsequent
  performance of the project.