Net Present Value and Other Investment Rules

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Net Present Value and Other Investment Rules
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Percent of CFOs who say they use the following
rules to evaluate projects
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What Makes for a Good Investment Rule?

• Recognize the time value of money
• Should rely solely on expected future cash flows
  and the opportunity cost of capital
• -Manager discretion accounting numbers, are
  easy to manipulate
• Want to be able to rank projects, and evaluate
  portfolios of projects

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Potential Investment Criteria

• Payback Period
• Average Accounting Return
• IRR
• NPV

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Payback Period

• Definition The number of years before the
  projects cumulative future cash flows equal the
  initial investment.
• How long does it take the projects to pay for
  itself?
• Decision rule Accept projects whose payback
  period is less than a manager determined cut-off

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Payback Example

• Assume Payback cut-off is 1 year
• Which project do we take

Project Year 0 Year 1 Year 2 PB NPV _at_ 10
A -10 10 0
Cum. CF

B -10 0 15
Cum. CF
1
-0.91
0
0
-10
2
2.40
-10
5
-10
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The Payback Period Method

• Disadvantages
• Biased against long-term projects
• Ignores cash flows after the payback period
• Requires an arbitrary acceptance criteria
• Ignores the time value of money
• A Good project may destroy value
• Advantages
• Easy to understand
• Biased toward liquidity

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The Discounted Payback Period

• Cash flows are discounted before payback period
  is calculated
• Effectively pick positively NPV project
• Very conservative ? only very valuable projects
  accepted
• STILL ignores cash flows after the payback period

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Average Accounting Return

• Decision Rule If the calculated value is above a
  benchmark (Ex. the firms current return on book
  or the industry average) accept the project.
• Fatally Flawed because
• Based on Accounting Numbers

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AAR Example

• A project has net income of 1,200, and 1,600 a
  year over its 2-year life. The initial cost of
  the project is 5,000, which will be depreciated
  using straight-line depreciation to a book value
  of zero over the life of the project. What is the
  AAR for this project?

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AAR example

• A project has net income of 1,200, and 1,600 a
  year over its 2-year life. The initial cost of
  the project is 5,000, which will be depreciated
  using straight-line depreciation to a book value
  of zero over the life of the project. What is the
  AAR for this project?
• AAR
• 1,400 / 2,500 0.56 56

0 1 2 Ave
NI
BV
1,200
1,600
1,400
5,000
0
2,500
2,500
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Average Accounting Return

• Disadvantages
• Uses accounting numbers instead of cash flows
• Ignores the time value of money
• The benchmark is arbitrary.
• Advantages
• The accounting information is easy to obtain
• Easy to calculate

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Internal Rate of Return (IRR)

• Definition It is the discount rate that makes a
  projects NPV equal 0.
• Decision Rule Accept all projects with IRRs
  greater than the opportunity cost of capital.

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IRRs Underlying Assumptions

• All intermediate cash flows can be reinvested at
  the IRR
• Is this reasonable?
• That short-term interest rates are equal to
  long-term interest rates
• Does not address which to use if they are not
  equal

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IRR Notes

• To find the IRR of a project lasting t years,
  solve the following equation
• C0C1/(1IRR)C2/(1IRR)2.Ct/(1IRR)t0 
• NPV gt 0 implies that IRR gt Op Cost
• IRR gt Op Cost DOES NOT IMPLY that NPV gt 0
• IRR assumes that causality goes both ways

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IRR NPV Investment Example

• A firm has a project that requires an initial
  investment of 10m. In the first year, it will
  return 12m, what is the IRR?
• N 1, I/Y ???, PV -10, PMT0, FV12
• I/Y 20 ? IRR 20
• If r10 do we accept the project based on IRR
  and NPV?
• IRR gt Op cost ? Accept
• NPV -10 12/1.1 0.91m ? Accept

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Internal Rate of Return (IRR)

• Disadvantages
• No distinction between investing and borrowing
• May have multiple IRRs, or no IRR
• Problems with mutually exclusive investments
• Scale Problem
• Timing Problem
• Advantages
• Easy to understand and communicate

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Loan Example
C0 C1 IRR NPV _at_ 10
Project A -10 20 100
Project B 10 -20 100

• According to IRR which project do we pick?
• Both
• What about NPV?
• A creates value
• B destroys value

-1020/1.18.18
10(-20/1.1)-8.18
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No IRR

• Example of No IRR

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Multiple IRR

• If cash flows switch signs more than once then
  there exists multiple IRRs
• There will be as many IRRs as there are sign
  changes
• Which IRR do we use?

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The Scale Problem

• Would you rather make 100 or 50 on your
  investments?
• What if the 100 return is on a 1 investment,
  while the 50 return is on a 1,000 investment?

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Mutually Exclusive Projects

• Choosing between projects
• RANK all alternatives, and select highest IRR
• IRR ignore the amount of wealth generated
• Which project should we take according to IRR?
• INDIFFERENT
• Which project do investors prefer?
• A, creates more wealth

C0 C1 IRR NPV _at_ 10
Project A -100 150 50 36.36
Project B -75 120 50 34.09
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Resource constraint

• The firm has 100 to invest, what should it buy?
• IRR
• NPV

Project C0 C1 C2 IRR NPV 10
A -100 300 50 216 210
B -50 50 200 156 160
C -50 50 150 130 120
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Resource constraint

• The firm has 100 to invest, what should it buy?
• IRR A
• NPV

Project C0 C1 C2 IRR NPV 10
A -100 300 50 216 210
B -50 50 200 156 160
C -50 50 150 130 120
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Resource constraint

• The firm has 100 to invest, what should it buy?
• IRR A
• NPV B C
• 160120 280 gt 210

Project C0 C1 C2 IRR NPV 10
A -100 300 50 216 210
B -50 50 200 156 160
C -50 50 150 130 120
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Verdict on IRR

• Gives the same result as NPV if
• Flat term structure
• Conventional cash flows
• Independent projects
• Otherwise IRR can lead to BAD decisions

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The Profitability Index (PI)

• Minimum Acceptance Criteria
• Accept if PI gt 1
• Ranking Criteria
• Select alternative with highest PI

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Selection Example

• Which projects do we take?

Projects C0 C1 C2 NPV _at_ 10 PI
A -100 300 50 214
B -50 50 200 161
C -50 50 150 119
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Selection Example

• Which projects do we take?

Projects C0 C1 C2 NPV 10 PI
A -100 300 50 214 314/1003.14
B -50 50 200 161
C -50 50 150 119
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Selection Example

• Which projects do we take?

Projects C0 C1 C2 NPV 10 PI
A -100 300 50 214 314/1003.14
B -50 50 200 161 211/504.22
C -50 50 150 119
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Selection Example

• Which projects do we take?
• Take the projects with the highest PI B, then C

Projects C0 C1 C2 NPV 10 PI
A -100 300 50 214 314/1003.14
B -50 50 200 161 211/504.22
C -50 50 150 119 169/503.38
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The Profitability Index

• Disadvantages
• Problems when there are additional constraints
• Use linear or integer programming
• Advantages
• When funds limited (Capital Rationing), provides
  better rankings than NPV
• Easy to understand and communicate

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The Net Present Value (NPV) Rule

• Net Present Value (NPV)
• Total PV of future CFs Initial Investment
• Estimating NPV
• 1. Estimate future cash flows how much? and
  when?
• 2. Estimate discount rate
• 3. Estimate initial costs
• Minimum Acceptance Criteria Accept if NPV gt 0
• Ranking Criteria Choose the highest NPV

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Why We Love NPV

• NPV recognizes the time value of money
• NPV depends only on future cash flows and the
  opportunity cost of capital
• Present value, can be added up, thus allowing us
  to evaluate packages of projects or a single
  project
• Accepting positive NPV projects, increases wealth

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Capital Budgeting in Practice

• Varies by industry
• The most frequently used technique for large
  corporations are IRR or NPV
• However, many companies also consider payback

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Real World Capital Budgeting
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Example of Investment Rules

• Compute the Payback Period, NPV, and PI for the
  following two projects. Assume the required
  return is 10.
• Year Project A Project
  B
• 0 -200 -150
• 1 200 50
• 2 800 100
• 3 -800 150

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Example of Investment Rules

• Project A Project B
• CF0 -200.00 -150.00
• PV0 of CF1-3 241.92 240.80
• Payback
• NPV
• PI

1
2
90.80
41.92
241.92/200 1.2096
240.80/150 1.6053
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Summary Discounted Cash Flow

• Net present value
• Accept the project if the NPV is positive
• Has no serious problems
• Yields the best decision
• Internal rate of return
• Take the project if the IRR is greater than the
  required return
• Same decision as NPV with conventional cash flows
• IRR is unreliable with non-conventional cash
  flows or mutually exclusive projects
• Profitability Index
• Take investment if PI gt 1
• Cannot be used to rank mutually exclusive
  projects
• Should be used to rank projects in the presence
  of capital rationing

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Summary Payback Criteria

• Payback period
• Length of time until initial investment is
  recovered
• Take the project if it pays back in some
  specified period
• Does not account for time value of money, and
  there is an arbitrary cutoff period
• Discounted payback period
• Length of time until initial investment is
  recovered on a discounted basis
• Take the project if it pays back in some
  specified period
• There is an arbitrary cutoff period

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Summary Accounting Criterion

• Average Accounting Return
• Measure of accounting profit relative to book
  value
• Similar to return on assets measure
• Take the investment if the AAR exceeds some
  specified return level
• Serious problems and should not be used

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Quick Quiz

• Consider an investment that costs 100,000 and
  has a cash inflow of 25,000 every year for 5
  years. The required return is 9, and payback
  cutoff is 4 years.
• What is the payback period?
• What is the discounted payback period?
• What is the NPV?
• What is the IRR?
• Should we accept the project?
• What method should be the primary decision rule?
• When is the IRR rule unreliable?

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Why We Care

• Help you develop your finance intuition
• Showing you common mistakes, so that you wont
  make those mistakes