Alternative Investment Rules

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Alternative Investment Rules

• Chapter 7 Classes 1, 2 and 3

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Main Issues

• Capital budgeting decision
• Project Classification
• Evaluation criterion (advantages/disadvantage)
• Payback period.
• Net present value/Incremental NPV.
• Internal rate of return/Incremental IRR.
• Profitability Index/Incremental PI
• Why NPV is preferred capital budgeting criteria.

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What is capital budgeting?

• The capital budgeting decision is the process in
  which long term investments are generated,
  analyzed and undertaken. Long term is for more
  than 1 year
• Good investment decisions increase firm value.
  The value of the firm is increased only if the
  firm undertakes positive NPV projects.
• The goal of the firm is to maximize firm value.
  Maximizing value implies maximizing the present
  value of all future cash flows.
• Maximizing value is not the same as maximizing
  profits

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Two Companies with Identical Profits but a 60
Difference in Value
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Can Firm Maximize Value by Being Unethical?

• Not in the long run
• Think about WorldCom, Enron
• A 2003 study in Business Horizons confirms this
• Companies behaving in an illegal or
  irresponsible manner are hurt financially by such
  action

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Ethical Behaviour and Project Choice

• Consider the major stakeholders of a firm shown
  in the above diagram. What sort of actions,
  undertaken by the firm, ensure ethical project
  choice for each stakeholder group?

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What kind of projects do we consider?

• Classify projects by relationship
• Mutually exclusive - acceptance of 1 precludes
  adoption of 2nd.
• Example Deciding between 2 computer systems or 2
  production locations
• Independent - cash flows of 2 projects and
  decision to accept are unrelated.
• Example The proposal to upgrade a computer
  system is independent of building a new
  warehouse.

• Classify projects by type
• Expansion - are those designed to improve the
  firms ability to produce or market its products
  (increase product line, improve productivity).
  Most risky.
• Replacement - replace assets that have become
  obsolete.
• Mandatory - legislated by government or other
  regulatory body.

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The Capital Budgeting Process
1.Search for and identify growth opportunities.
Rejected opportunities
2.Estimate the magnitude, timing and riskiness
of cash flow
Improvements in identification or estimation
phases
3.Select or reject projects
4. Place project in capital budget
Rejected Projects
6.Control and post-competition and audit
5. Make investment outlays
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Criteria for Capital Budgeting Decision

• We assume managers maximize firm's value.
• What a good technique should do? The best
  technique will process the following essential
  property
• All of the cash flows should be considered
• Correctly ranks mutually exclusive projects
• The cash flow should be discounted at the
  opportunity cost of funds That is, takes into
  account the time value of money that near
  dollars are more valuable than far dollars and
  that a project has to cover its opportunity cost
  of funds.
• Firms use a variety of techniques or formulae to
  decide whether or not to accept a project. Well
  run through the most common ones. We will
  evaluate the advantages and disadvantages of
  different techniques.

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Acceptance/Rejection Criteria
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Evaluation techniques used by Canadian businesses
Not that the percentages do not add up to 100,
because many firms use multiple methods.
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Rainbow Products

• Rainbow Products is considering purchasing one of
  two paint-mixing machines to reduce labour costs
  Model L or Model S.
• Both machines cost 1,000 and are expected to
  last for 4 years.
• Rainbow's cost of capital is 10.
• The President of Rainbow wants you to advise him
  on best choice using
• Pay-back period,
• Discounted pay-back period
• Net Present Value
• Internal Rate of Return
• Profitability Index

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Annual After-Tax Cost Savings
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Payback Method

• Notation
• CFt after tax incremental cash flow in year t.
  
• At t0 the initial investment is made.
• Payback period is the number of years it takes a
  firm to recover its initial investment.
• Define ? such that

• T be the maximum acceptable payback period.
• Accept (reject) the project if ? lt (gt) T.

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Payback Period

• The payback period is the amount of time it takes
  for cash inflows to equal initial cash outflows.

The payback period for Model S is? The payback
period for Model L is? Suppose the firm set T
3, which project would be accepted?
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Payback Period

• If assume that the cash flow accrue uniformly
  throughout the year
• The payback period for Model S is?
• The payback period for Model L is?
• Suppose the firm set T 3, which project would
  be accepted?
• Model S

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Payback Method

• Disadvantages
• Doesnt take into account the time value of
  money.
• Doesnt consider all cash flows. (Ignores all
  cash flow occurring after the payback period.)
• Doesnt account for project risk.
• How does one set T?,

• Advantages
• Simple to calculate, easy to explain.
• Popular for small business and/or small projects.
• Favours short term projects, therefore biases
  towards lower risk and higher liquidity.

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Discounted Payback Period Rule

• Improves upon the Payback rule by accounting for
  the time value of money. Suppose k is the cost of
  capital

• And accept (reject) project if payback period ? ?
  (gt) T.
• From the Rainbow Products example, Suppose k
  10.
• What is the discounted payback period for Model
  S?
• What is the discounted payback period for Model
  L?
• Suppose the firm set T 3, which project would
  be accepted?

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Discounted Cash Flow
Remember k 10
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Discounted Cash Flow

• Therefore for S the payback period is
• And for L the payback period is
• Therefore if T is 3, accept project S but not
  project L.

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Alternative Cash Flow Timing Assumption.

• Cash flows occur at year end rather than accruing
  at a steady pace throughout the year.
• Payback period of S 3 years.
• Payback period of L 4 years.
• Discounted PP of S 3 years.
• Discounted PP of L 4 years.
• Look for first nonnegative entry in cumulative
  column.

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Net Present Value

• Using the firms WACC, k, the NPV is

• where the cash flows may be positive or negative.
• If NPV gt (lt) 0, accept (reject) project.
• If NPV gt0, firm has enough money to repay the
  initial investment at the return required by
  investors. Positive NPV projects increase firm
  value.

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Synonyms for WACC or K

• Discount rate
• (Weighted Average) Cost of Capital
• Opportunity Cost of Capital
• Minimum acceptable rate of return or minimum
  acceptable IRR
• Hurdle rate
• All these terms mean the same thing!

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Rainbow NPV

• Net Present Value (NPV) is the present value of
  the project's cash flows, both positive and
  negative, discounted at the project's opportunity
  cost of capital (10).

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Net Present Value

• Advantages
• Takes into account time value of money, accounts
  for risk in longer term projects.
• Uses all cash flows, takes account of the cost of
  capital, and provides the most consistent measure
  for ranking projects.
• The NPV is the project's contribution to firm
  value.

• Disadvantages
• What if firm does not know its cost of capital?

THEREFORE Choosing the project with the highest
NPV is consistent with maximizing firm value and
stock price.
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Internal Rate of Return

• The IRR, i, is the interest rate which sets the
  NPV to 0.

• If the project is a traditional project
  (negative outflows followed by positive inflows),
  then accept (reject) the project if i gt(lt) k, the
  firms cost of capital.
• The IRR is the effective yield to be earned over
  time on the portion of the initial investment
  that is still tied up in the project.
• If IRR gtk, that means that we can borrow funds
  for a cost k from our security holders and then
  reinvest them at a rate I gt k.
• The only way to solve for i is numerically -
  either trial and error or using a computer
  program.

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IRR for Rainbow

• Which project has higher IRR?
• IRR, rS, for project S satisfies

• Using Goal Seek in Excel rs 14.5
• IRR, rL, for project L satisfies

• Using Goal Seek in Excel rL 13.76

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Internal Rate of Return

• Advantages
• fairly easy to interpret.
• Disadvantage (Problems)
• 1. Multiple Rates of Return
• can give multiple rates of return for project
  with multiple sign changes in cash flows
• 2. Problems associated with mutually exclusive
  IRR
• NPV and IRR decision rule will always give same
  decision for independent projects that have only
  one sign change
• If firm has 2 mutually exclusive projects, 2
  methods may give different results when the sizes
  of the projects are considerably different (scale
  problem) and/or when the timing of the 2 projects
  are significantly different (timing problem).

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Problems with IRR I Multiple Rates

• If cash flows change from negative positive to
  negative, can get present value profile graph to
  the top right. None of the IRRs have any real
  meaning.
• Every time there is a change in the sign of cash
  flows from - to or to -, the NPV profile
  graph will cross the axis.
• We could be looking at a situation in which there
  is an initial investment for a project (-), and
  then the project earns positive returns for
  several years (), but at some point in the
  future projected upgrades/maintenance etc. create
  a negative return for that year. In this case the
  IRR method cannot be used, but NPV can still be
  used.

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IRR of a Financing Project

• Financing First cash flow positive, remaining
  cash flows negative, e.g. CF0100 CF1-130.
• There is a change in IRR decision rules.
• If IRRgtk, reject the financing.
• If IRRltk, accept the financing.
• No change in NPV decision rule.

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Investment Project with Multiple Cash Flow Sign
Changes

• Has a financing project embedded in it.
• If IRRgtk, is this good? Dont know.
• If IRRltk, is this good? Dont know.
• This is the reason why IRR cannot be applied to
  investment projects with multiple sign changes.

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Problems with IRR II Ranking Of Mutual Exclusive
Projects

• If 2 projects are mutually exclusive, the firm
  cannot undertake both of them. Ideally, the firm
  wants to undertake the project which increases
  the firm value the most.
• That is the project with the higher NPV should
  always be undertaken.
• But the higher NPV project is not necessarily the
  larger IRR project. This problem arises whether
  or not the projects differ in scale.

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IRR v. NPV - Example

• With a cost of capital of 10, which project has
  higher NPV?
• Which project (Model S or L) has higher IRR?

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Present Value Profile

• The present value profile graphs the present
  value of the project cash flows for different
  interest rates versus the different interest
  rates.
• The internal rate of return is where the profile
  crosses the X axis.

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Explanation

• Look at the shape of the graph when the interest
  rate is 0, PV of future positive cash flows are
  high.
• As the interest rate increases, the initial
  negative outflow is not affect, but the PV of
  future positive outflows becomes smaller, thus
  the total NPV of the project goes from positive
  to negative.
• We can also see that when the cost of capital is
  less than the IRR, that the NPV of the project is
  positive, and therefore this project should be
  undertaken because it increases firm value.
• Look at interest rates less than 12.63. In this
  case, we would pick Model L over S as it has a
  higher NPV.
• This is a problem! If the firms interest rate
  were say 5, then NPV would say pick L, but IRR
  says pick S.

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Recap Problems with IRR
for mutually exclusive projects
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Summary Which is the best machine so far?

• Pay back period
• Discounted pay back period
• NPV
• IRR
• Are IRR and NPV consistent? In general, not!
• Explain?

• S or L?
• S or L?
• S or L?
• S or L?

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Why Can IRR and NPV Give Different Results?

• IRR assumes that intermediate cash flows can be
  reinvested at the internal rate of return.
• NPV assumes that intermediate cash flows can be
  reinvested at the firms opportunity cost of
  capital.
• The IRR method assumes that the intermediate cash
  flows in a project can be invested at a rate
  equal to the IRR. This is incorrect. The correct
  reinvestment rate is the WACC because it is the
  rate of return assigned by the market across
  projects with this risk level (opportunity cost
  of capital).
• Note If we could undertake them both (that is,
  if the projects are NOT mutual exclusive), we
  would. Both would increase firm value, so the IRR
  decision rule is not incorrect.

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Profitability Index PV bang per investment buck

• Ratio of the present value of future expected
  cash flows (excluding initial investment) divided
  by initial investment.

• For Rainbow PIS 1079 / 1000 1.079 and PIL
  1110 / 1000 1.11
• For independent projects Accept project if PIgt1.
• For mutually exclusive projects, prefer project
  with larger PI. But PI and NPV rankings are not
  the same if projects differ in scale. If
  projects are the same scale, PI and NPV rankings
  are the same.

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Scale Problems of IRR and PI A Simple Example

• Considering two projects with required rate of
  return 10
• IRR and PI focus exclusively on profitability
  (rate of return, bang per buck) ignoring the
  amount that can be invested in the project.
• NPV takes account of both profitability and
  amount that can be invested in the project.

Project A
-1000
1300
Project B
-2000
2400
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Scale problem of Profitability Index another
example

• Project B creates more present value bang per
  buck, but you can invest only a small amount in
  it.
• Project A creates less present value bang per
  buck, but you can invest lots in it.

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Incremental Project Example

• L is Challenger.
• S is Defender.
• Incremental project is Challenger minus Defender.
• Incremental project is an investment proposition.

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Incremental IRR or IIRR

• Use to correctly rank mutually exclusive
  projects.
• Tells you which you should prefer, not whether
  you should accept.
• Apply IRR to incremental cash flows. That will
  give us IIRR.
• If projects differ in scale, incremental project
  is bigger project minus smaller project.
• Use IIRR to rank projects. Then use IRR to
  decide whether you should accept the project
  ranked better.

• Decision rule
• If IIRRgtK, prefer bigger project. Accept bigger
  project if its IRR is also gt K.
• If IIRRltK, prefer smaller project. Accept
  smaller project if its IRR is also gt K.

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IIRR Approach when projects have same scale

• The incremental project must be an investment
  proposition, i.e., the first nonzero cash flow
  must be negative.
• Incremental project is Challenger minus Defender.
• Define one project as Challenger, the other
  project as Defender, so that the incremental
  project is an investment.

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Incremental IRRsExample

• IRR, rI, solves

• Using Goal Seek rI 12.63.
• Because the incremental IRR gt the cost of capital
  of 10, prefer project L. LChallenger,
  SDefender.

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Incremental PI

• Decision rule
• If IPIgt1, prefer larger project. Accept it if
  its PIgt1.
• If IPIlt1, prefer smaller project. Accept it if
  its PIgt1.

• Use to correctly rank mutually exclusive projects
  that differ in scale.
• If projects do not differ in scale, the PI and
  NPV rankings are the same.
• Use IPI only if projects differ in scale.
• Apply PI to incremental cash flows. That will
  give us IPI.
• Incremental project is larger minus smaller
  project.

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S vs. L, which is the better machine?

• Pay back period
• Discounted pay back period
• NPV
• IRR
• Incremental IRR
• PI (no need to apply IPI)

• S or L?
• S or L?
• S or L?
• S or L?
• S or L?
• S or L?

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Criteria for Independent Projects

• NPV always works, i.e., maximizes stockholder
  wealth.
• IRR consistent with NPV if project has only one
  sign change in CFs.
• What if multiple sign change? Cannot apply IRR.
• PI consistent with NPV, i.e, it always works.

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Criteria for Mutually Exclusive Projects

• NPV maximizes stockholder wealth.
• IRR ranking not consistent with NPV ranking
  whether or not project differ in scale. Must use
  IIRR. IIRR ranking is consistent with NPV
  ranking (if incremental project has only one sign
  change in cash flows).
• PI ranking not consistent with NPV ranking if
  projects differ in scale. If same scale, PI and
  NPV rankings are the same.