Capital Budgeting and Net Present Value

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Chapter 11

• Capital Budgeting and Net Present Value

Should we build this plant?
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Ch 13 Capital Budgeting Techniques

• Payback period rule
• Discounted Cash Flow Approaches
• Discounted payback period
• Net present value (NPV)
• Internal rate of return (IRR)
• Modified internal rate of return (MIRR)
• Profitability index (PI)
• Why is the NPV the best?
• NPV vs. Payback period
• NPV vs. IRR
• Mutually exclusive projects
• Multiple IRRs
• NPV vs. PI
• The practice of capital budgeting

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What is capital budgeting?

• Capital budgeting Total process of planning,
  evaluating, and selecting on capital expenditures
  for long-lived assets. Usually requires a large
  amount of capital expenditures. It could be
  anything that requires lots of money.
• In February 2000, Corning, Inc., announced plans
  to spend 170 million to expand by 50 percent its
  manufacturing capacity of optical fiber, a
  crucial component of todays high-speed
  communications networks.
• To do or not to do? That is the question!
• Is there any financial method that Corning can
  use to make this investment decision?

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Capital Budgeting Steps
1. Estimate CFs (inflows outflows). 2. Assess
riskiness of CFs. 3. Determine r WACC for
project. 4. Find NPV, IRR and/or others. 5.
Accept or reject project based on the results
from sep 4.

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Example 1

• Coca Cola and Procter Gamble just announced
  that they will consider a joint venture (JV) for
  new beverage and snack business. The new idea is
  to form a limited-liability company, with 50-50
  ownership, that will develop and market
  juice-based drinks and snacks. Coca-Cola will
  invest 2 billions and the investments will be
  deprecated on a straight-line basis with zero
  salvage value for four-year investment period.
  You are a CFO of Coca Cola and just created a pro
  forma income statement for this project.
  Previously, Coca Cola hired the consulting
  company to study market research for new beverage
  and snack business, and paid 300,000. The tax
  rate is 30 percent. The similar project with a
  similar risk level yields 10. Your job is to
  evaluate this project. Is this project
  acceptable?

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Coca Cola Pro Forma Income Statement
Year 2002 2003 2004 2005
Sales 2,000 2,000 2,000 2,000
Cost of Goods Sold 1,000 1,000 1,000 1,000
Gross Profit 1,000 1,000 1,000 1,000
Operating Expenses 50 50 50 50
Depreciation 500 500 500 500
EBT 450 450 450 450
Taxes (30) 135 135 135 135
Net Income 315 315 315 315
What is a pro forma income statement?
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Q1. What is the operating cash flow (OCF)?

• Operating Cash Flow (OCF)
• EBIT (1 T) Depreciation
• Why operating cash flow, instead of accounting
  income?

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Q2. Is the consulting fee of 300,000 relevant
in capital budgeting decision? What is the sunk
cost?
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Time Line for the Joint Venture
4
0
1
2
3
r 10
-2,000
815
815
815
815
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Q3. Is this project acceptable?

• We will use several capital budgeting techniques
  to evaluate new projects.
• Payback period
• Discounted cash flow (DCF) approaches
• Discounted payback period
• Net Present Value (NPV) - most important
• Internal rate of return (IRR) most popular
• Modified Internal Rate of Return
• Profitability index (PI)

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Q3. Is this project acceptable?Payback period

• Payback Period Length of time until initial
  investment is recovered, or How long will it
  take to recover initial investments?
• Computation Subtract the future cash flows from
  the initial cost until the initial investment has
  been recovered
• Decision Rule Accept if the payback period is
  less than some preset limit
• Payback period of JV

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Payback Period Computation
2.454
0
1
2
3
4
CFt
815
815
815
-2,000
815
-370
0
Cumulative
-2,000
-1,185
2 370/815 2.454 years
Payback

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Q3. Is this project acceptable?Discounted
payback period

• Discounted Payback Period Use discounted CFs
  rather than raw CFs.
• Computation Subtract the future discounted cash
  flows from the initial cost until the initial
  investment has been recovered
• Decision Rule Accept if the discounted payback
  period is less than some preset limit
• Discounted payback period of JV

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Discounted Payback Period
0
1
2
3
4
10
815
815
815
815
CFt
-2000
741
PVCFt
-2000
674
612
Cumulative
-2000
-1259
-586
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Discounted payback
2 586 / 612 2.96 yrs

Still this method requires arbitrary cut-off
point and ignores cash flows occurring later than
cut-off point
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Q3. Is this project acceptable?Net present
value (NPV)

• Net Present Value (NPV)
• PVs of inflows PVs of outflows, or
• PVs of inflows Initial Investment (usually
  occurs in year 0)
• Decision criteria If the NPV is positive, accept
  the project
• A positive NPV means that the project is expected
  to add value to the firm and will therefore
  increase the wealth of the owners.
• Since our goal is to increase owners wealth, NPV
  is a direct measure of how well this project will
  meet our goal.
• Should we accept or reject new joint venture
  proposal?

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NPV (continued)
Cost often is CF0 and is negative.
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Whats JVs NPV?
Project JV
4
0
1
2
3
r 10
815
-2,000
815
815
815
741
674
612
557
584 NPV
Since NPV gt 0, Accept!
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NPV (continued)Calculator Solution
Enter in CFj for JV
-2,000 815 815 815 815 10
CF0
CF1
CF2
CF3
CF4
NPV
I/YR
583.44
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Q3. Is this project acceptable?Internal rate
of return (IRR)

• Definition IRR is the return that makes the NPV
  0
• Decision Rule Accept the project if the IRR is
  greater than the required return
• Internal Rate of Return (IRR) of JV
• Should we accept or reject new joint venture
  proposal?

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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 r, solve for NPV.
IRR Enter NPV 0, solve for IRR.
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Coca Cola Example IRR
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Computing IRR For The Project

• If you do not have a financial calculator, then
  this becomes a trial and error process
• Calculator
• Enter the cash flows as you did with NPV
• Press IRR
• If IRR gt 10, required return, then accept the
  project.
• Should we accept or reject the new JV?

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Rationale for the IRR Method
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Q3. Is this project acceptable?Profitability
Index (PI)

• Definition
• PV of future cash flows _at_ R (discount rate)
  divided by Initial Investment
• Bang for the buck
• Benefit-cost ratio
• Decision rule If PI gt 1 then accept project
• PI of JV
• Should we accept or reject the JV?

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Profitability Index

• Measures the benefit per unit cost, based on the
  time value of money
• A profitability index of 1.1 implies that for
  every 1 of investment, we create an additional
  0.10 in value
• This measure can be very useful in situations
  where we have limited capital

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Q4 What are the relationships among NPV, IRR,
and PI?

• The discount rate is 10. Are the discount rate,
  opportunity cost, and cost of capital the same
  things?
• In this case, the IRR is 22.87. When you use
  22.87 as new discount rate, what is the new NPV?
• What if the discount rate is 20? What is the
  new NPV? What if the discount rate is 24? Does
  the higher discount rate means the lower NPV? If
  so, why ?
• When NPV gt 0, IRR gt r? When NPV gt 0, PI gt1?
• In general, if NPV gt 0, then IRR gt R and PI gt 1.

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So far,

• We learned payback period, discounted payback
  period, NPV, IRR and PI to evaluate new projects.
• Now, we will be making a case that the NPV is the
  best, and
• We will see why it is the best.
• Also, we will see some cases that NPV and other
  criteria lead us to conflicting results.

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Example 2 NPV vs. Payback period
Discount rate, r 10
0 1 2 3 4 Payback NPV
A -100 20 30 50 60 3 yr 21.52
B -100 50 30 20 60 3 yr 26.26
C -100 50 30 20 6,000 3 yr ?
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Advantages and Disadvantages of Payback

• Disadvantages
• Ignores the time value of money
• Requires an arbitrary cutoff point
• Ignores cash flows beyond the cutoff date
• Biased against long-term projects, such as
  research and development, and new projects

• Advantages
• Easy to understand
• Provides an indication of a projects liquidity.

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Special cases What is the difference between
independent and mutually exclusive projects?

• 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.

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An Example of Mutually Exclusive Projects
BRIDGE vs. BOAT to get products across a river.
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Example 3 NPV vs. IRR (Mutually Exclusive
Projects)

• Option 1 You give me 1 now and Ill give you
  1.50 back at the end of the class period.
• Option 2 You give me 10 now and Ill give you
  11 back at the end of the class period.
• You can choose only one of two options. Assume a
  zero rate of interest because our class lasts
  only 2 hours. Which option would you choose?

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Example 4 NPV vs. IRR (Mutually Exclusive
Projects)
Suppose r 5.
Project 0 1 2 3 IRR NPV _at_5
Long -100 10 60 80 18.1 33 Higher
Short -100 70 50 20 23.6 Higher 29
Which one should we take?
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Construct NPV Profiles
Enter CFs in CFj and find NPVL and NPVS at
different discount rates
NPVL 50 33 19 7
NPVS 40 29 20 12 5
r 0 5 10 15 20
(4)
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NPV ()
Double click on the icon
Crossover Point 8.7
IRRS 23.6
Discount Rate ()
IRRL 18.1
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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 CFj 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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Which project(s) should be accepted at r5?

• If S and L are independent, accept both. NPV gt 0.
  IRRS and IRRL gt r 5.
• If Projects S and L are mutually exclusive,
  accept L because NPVS lt NPVL at r 5, although
  IRRS gt IRRL . Conflict!!!
• Choose between mutually exclusive projects on
  basis of higher NPV. Adds most value in dollar.

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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
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Mutually Exclusive Projects
NPV
r lt 8.7 NPVLgt NPVS , IRRS gt IRRL CONFLICT
L
rgt 8.7 NPVSgt NPVL , IRRS gt IRRL NO CONFLICT
IRRS
S

r 8.7 r
IRRL
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Reinvestment Rate Assumptions

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

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Another Problem with IRR

• IRR has another problem so-called Multiple IRRs.

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Normal Cash Flow Project
Two kinds of Cash Flows
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.
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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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Example 5 NPV vs. IRR (Multiple IRRs)

• Greenspan Mining Co. is considering a project to
  strip mine coal. The project requires an
  investment of 22 million and is expected to
  produce a cash inflow of 15 million in each Year
  1 through 4. However, the Company is obligated to
  pay 40 million in Year 5 to restore the terrain.
  The Companys opportunity cost of capital is
  10. What are the IRR(s) and NPV?

0 1 2 3 4 5 NPV _at_5.62 NPV _at_27.78 NPV _at_10
-22 15 15 15 15 -40 ? ? 0.7M
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Multiple 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 6
lower IRR Now guess large IRR, say,
30 30 STO IRR 28 upper IRR
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Multiple IRRs (continued)

• The previous slides shows that there are two IRRs
  ? Multiple IRRs
• You need to recognize that there are
  non-conventional cash flows and look at the NPV
  profile
• Rely on NPV instead of IRR in this case

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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 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 assumes cash inflows are reinvested at
WACC.
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Example 6 Starbucks estimates the cash flows for
the new project, Mocha. Find MIRR. 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
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To find TV with a calculator, enter in CFj
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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Accept Project ?
YES. Reject because MIRR 16.50 gt r
10. Also, if MIRR gt r, NPV will be positive
NPV 18.78.
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Why use MIRR rather than 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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Advantages and Disadvantages of IRR

• Advantages
• closely related to NPV, often leading to
  identical decisions
• Knowing a return is intuitively appealing
• It is a simple way to communicate the value of a
  project to someone who doesnt know all the
  estimation details
• Disadvantages
• may lead to incorrect decisions in comparisons of
  mutually exclusive investments to be explained
  later
• May result in multiple answers (so-called,
  Multiple IRRs)

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Summary NPV vs. IRR

• NPV and IRR will generally give us the same
  decision
• Exceptions IRR is unreliable in the following
  situations
• Non-conventional cash flows cash flow signs
  change more than once
• Mutually exclusive projects
• Initial investments are substantially different
• Timing of cash flows is substantially different
• Whenever there is a conflict between NPV and
  another decision rule, you should always use NPV

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NPV (continued)

• Does the NPV rule account for the time value of
  money?
• Does the NPV rule provide an indication about the
  increase in value?
• Should we consider the NPV rule for our primary
  decision criteria?
• Does the NPV have serious flaws?

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Example 7 NPV vs. PIMutually Exclusive Projects
Suppose Project A and B are mutually exclusive.
0 1 2 PV_at_12 PI_at_ 12 NPV_at_12
A -20M 70M 10M 70.5M 3.52 50.5 Higher
B -10M 15M 40M 45.3M 4.53 Higher 35.3
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Advantages and Disadvantages of Profitability
Index

• Advantages
• Closely related to NPV, generally leading to
  identical decisions
• Easy to understand and communicate
• May be useful when available investment funds are
  limited (so-called, capital rationing, to be
  explained later)

• Disadvantages
• May lead to incorrect decisions in comparisons of
  mutually exclusive investments (To be explained
  later)

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Capital Rationing imposing maximum capital
expenditures

• 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.

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• Reason Companies want to avoid the direct costs
  (i.e., flotation costs) and the indirect costs of
  issuing new capital. Or companies avoid a high
  debt ratio or earnings dilution.
• 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. Or, Use profitability
  index, instead of NPVs.

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Capital Rationing Example
What if the company has only 700 million? Which project(s) should you choose?
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Capital Budgeting In Practice

• We should consider several investment criteria
  when making decisions.
• NPV and IRR are the most commonly used primary
  investment criteria.
• Payback is a commonly used secondary investment
  criteria.
• Use more than one
• Also exercise qualitative judgments in
  conjunction with quantitative analysis.

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Summary Discounted Cash Flow Criteria

• Net present value
• Difference between PV of future cash flows and
  cost
• Take the project if the NPV is positive
• Has no serious problems
• Preferred decision criterion
• Internal rate of return
• Discount rate that makes NPV 0
• Take the project if the IRR is greater than
  required return
• Same decision as NPV with conventional cash flows
• IRR is unreliable with non-conventional cash
  flows or mutually exclusive projects
• Profitability Index
• Benefit-cost ratio
• Take investment if PI gt 1
• Cannot be used to rank mutually exclusive
  projects
• May be useful to rank projects in the presence of
  capital rationing

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A challenging problem incorporating beta, WACC,
and capital budgeting.

• Returns on the market and Company Y's stock
  during the last 3 years are shown below
• Year Market
  Company Y
• 2001 24 22
• 2002 10
  13
• 2003 22
  36
• The risk-free rate is 5 percent, and the
  required return on the market is 11 percent. You
  are considering a low-risk project whose project
  beta is 0.5 less than the company's overall
  corporate beta. You finance only with equity,
  all of which comes from retained earnings. The
  project has a cost of 500 million, and it is
  expected to provide cash flows of 100 million
  per year at the end of Years 1 through 5 and then
  50 million per year at the end of Years 6
  through 10. What is the project's NPV (in
  millions of dollars)?

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