Lecture Note 3

1
Lecture Note 3

• Chapter 6

2
Some alternative investment rules

• From this handout we will start learning capital
  budgeting, the decision-making process of
  accepting or rejecting project.
• The most useful decision rule is the net present
  value (NPV) rule where project is accepted when
  the net present value of the cash flow of the
  project is positive, and rejected if it is
  negative.
• See next page

3
Some alternative investment rules (contd)

• Although NPV rule is our preferred rule, there
  are other investment rules that are used in
  practices. These alternative investment rules had
  been used for several reasons These alternative
  rules may be easy to calculate, may be easy to
  understand, or may be used simply because it have
  been conventionally used.

4
Some alternative investment rules (contd)

• In this handout, we will learn some alternative
  investment rules.
• First, this handout summarizes some reason we may
  prefer NPV rules. Then, it will explain
• Payback Period Rule
• Average accounting return rule
• The internal rate of return
• Profitability Index

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Why use Net Present Value?

• A basic investment rule is to
• Accept the project if the NPV is greater than
  zero
• Reject the project if NPV is less than zero.

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Why use Net Present Value? (Contd)

• First reason we prefer NPV rule is that accepting
  positive NPV projects benefits the stockholders.
  Suppose that a firm has a productive asset worth
  V and has 100 of cash. Consider the following
  two strategies. The market interest rate is 0.06
• Use 100 of corporate cash to invest in the
  project. The 107 dividend will be paid as a
  dividend in one year.
• Forgo the project and pay the 100 of corporate
  cash as a dividend today.
• See next slide

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Why use Net Present Value? (Contd)

• If the firm takes strategy (1), the value of the
  firm today will be
• V107/1.06V100.94
  
• If the firm takes the strategy (2), the value of
  the firm today will be
• V100
• Clearly the firm value for strategy (1) is
  greater than the firm value for strategy (2) by
  the amount equal to the net present value of the
  project (0.94). Thus, accepting the positive NPV
  project will benefit the shareholder.

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Why use Net Present Value? (Contd)

• Second reason we prefer the NPV rule is that, the
  firm value will increase by the NPV. This can be
  seen from the example in the previous slides. The
  firm value for strategy (1) was higher than the
  firm value for strategy (2) by the amount equal
  to the NPV of the project.
• Thus, if the goal of the firm is to maximize its
  value, NPV rule gives clearer guidance than other
  alternative investment rules.

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Alternative Investment rule

• Although NPV method is our preferred method for
  capital budgeting, it is worthwhile to learn
  other alternative methods. It is worthwhile,
  first because learning other methods highlights,
  and second because these alternative methods are
  used in the real world.
• Next slides shows the extent to which these
  alternative methods are used in the real world.

10
The practice of capital budgeting

• According Graham, Campbell and Harvey The Theory
  and Practice of Corporate Finance Evidence from
  the Field Journal of Financial Economics 2000,
  the practice of capital financing decision of
  majority of the US and Canadian companies are
  given by the following table.

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Alternative Investment rule (1) The Payback
Period Rule

• Payback period rule is the decision rule where
  you accept the project if the initial investment
  can be paid back within pre-determined criteria
  period. For example, if the predetermined
  criteria period is 4 years, then you will accept
  the investment project if the initial investment
  can be paid back within 4 years.
• There are certain problem with this payback
  method
• When the payback period is computed (number of
  years to recover initial costs), typically the
  cash flow is not discounted
• Minimum Acceptance Criteria (criteria period) is
  set arbitrary by management
• There may be several projects that can be
  accepted. Then criteria to rank amount these
  project is set arbitrary by the management.

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Payback Period RuleExample

• Consider a project with the following cash flow.
• If the minimum criteria for payback period is 3
  years, is this project accepted?
• You could see that payback period rule gives an
  easy-to-understand, and easy-to-compute
  investment decision rule You do not have to
  consider the cash flow after the criteria period.
• However, this also causes a problem.
• See next page.

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Example 2

• Now consider the three project given in the
  table.
• Exercise
• If the minimum criteria is 3 years, which project
  will be accepted?
• This example shows some disadvantages of the
  payback period rule.

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The Payback Period Rule (continued)

• Disadvantages
• Ignores the time value of money
• Ignores cash flows after the payback period
• Biased against long-term projects
• Requires an arbitrary acceptance criteria
• A project accepted based on the payback criteria
  may not have a positive NPV
• Advantages
• Easy to understand

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Alternative investment rule (2)The Discounted
Payback Period Rule

• Since one of the problems with the payback method
  is that it does not discount the cash flow, one
  way to modify the method is to discount the cash
  flow and find out the payback period.
• However, major problems still remain You still
  have to arbitrarily set the criteria periods the
  decision still have a bias against long term
  project since it still ignores the cash flow
  after the criteria period.
• Also, by the time you have discounted the cash
  flows, you might as well calculate the NPV.

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Alternative investment rule 3Average accounting
return

• Another popular alternative investment method is
  the average accounting return (AAR) method. The
  average accounting return (AAA) is given by the
  following.

• The procedure of the AAR method is to accept the
  project if AAR is greater than a target return.
• Although this procedure has several problems
  (which will be described later), this method
  provides a percentage return of the investment.
  Thus, this method provides an easy-to-understand
  decision rule.

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Average Accounting Return RuleExample

• Consider a company that is evaluating whether to
  buy a new store in a new mall. The purchase price
  is 500,000. We will assume that the store has an
  estimated life of 5 years. We assume that the
  store will worth nothing at the end of the
  lifetime.
• Excel Sheet Average accounting return example
  shows the estimated cash revenue and expenses for
  each of the 5 periods.
• Use the file to compute the cash flow for each
  period by filling Table 1. Use straight line
  depreciation.

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Average Accounting Return RuleExample (contd)
Then, the average net income is given by Average
Net Income (100,000150,00050,0000-50,000)/550
,000
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Average Accounting Return RuleExample (contd)

• Now, compute the average investment of this
  project by filling Table 2 of Average Accounting
  Return exercise.

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Average Accounting Return RuleExample (contd)
We simply take the average of the investment.
Notice that investment occurs at date 0.
Therefore, there are 6 periods in this table.
The average investment is then determined by
Average Investment (500,000400,000300,000200,0
00100,0000)/6250,000
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Average Accounting Return RuleExample (contd)

• Thus, the average accounting return of this
  example is given by

• If the company has a target average accounting
  return smaller than 20 (say 15), the project
  will be accepted. If the company had a target AAR
  greater than 20, the project will be rejected.

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Problems with Average Accounting Return

• AAR uses accounting number. Since the decision to
  depreciate or expense a certain item depends on
  accountant judgment, the computed AAR is
  influenced by accountant judgment.
• Minimum acceptance criteria is set arbitrarily by
  management.
• AAR does not take into account the time value of
  money.

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Alternative Investment rule 4Internal Rate of
Return

• Similar to average accounting return, internal
  rate of return provides a single number (in
  percentage) summarizing the merit of the project.
  Thus, this method provides an easy-to-understand
  decision rule for investment.
• Internal Rate of Return, however, has several
  problems. These problems will be discussed later
  in this handout.

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Internal Rate of Return (IRR) Example

• To see the basic idea of IRR decision rule,
  consider a project that generates one time cash
  flow of 110 thousand dollars next year. Initial
  cost of this investment is 100 thousand dollars,
  which will occur at today. Then, what is the
  return on this investment. See next
  Page

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Internal Rate of Return (IRR) Example, Contd

• To answer the question, we will solve the
  following equation for y.

• Solution to y is called the Internal Rate of
  Return.
• Internal rate of return for this example is 10.
  This means that if the discount rate is lower
  than 10 (say 8), it makes sense for the firm to
  invest in the project the project provides a
  higher return than if the firm invests the money
  elsewhere.
• Thus, the basic IRR rule of investment is to
  accept the project if the IRR is greater than the
  discount rate.

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Internal Rate of Return -Decision Rule-

• Consider an investment project with the following
  cash flow.

• Internal rate of return (IRR) is the solution to
  the following equation.

• Decision rule
• The decision rule is to accept the project if
  IRR is greater than discount rate, and reject if
  IRR is smaller than the discount rate.

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Internal Rate of Return Example

• Let us consider another example given in the
  graph below.

• Although we can compute IRR by using excel
  function IRR(), let us find IRR manually.
• See next page.

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Exercise

• To compute the IRR, consider to compute Z, which
  is defined in the following equation, for many
  different value of y.

• Notice that IRR is the value of y that makes Z
  equal to zero
• Use Internal Rate of Return Exercise, fill the
  table, and graph Z against y to find the IRR.

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Answer

• IRR is computed as 19.44. Therefore, if the
  discount rate is smaller than 19.44, the project
  is accepted.

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Internal Rate of Return

• As can be seen from the example in the previous
  slides, internal rate of return provides a single
  number that summarizes the merit of the project.
• Since the IRR does not depend on the discount
  rate, this is called internal rate of return
  the number that is intrinsic to the project.
• Although IRR is attractive decision rule, it has
  several problems, which are summarized in the
  following slides.

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Problems with IRR approach (1)Multiple solutions

• Consider the following case.

• Exercise Use problem with IRR 1. Compute Z for
  each value of y, and graph Z against y.

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Answer

• There are two solutions to IRR. This typically
  occurs when negative cash flow occurs sometime
  after the initial period.
• Although such cash flow seems strange, it is not
  uncommon. For example, strip-mining project
  requires the excavation of the earth at the
  initial period. When all the mineral is
  extracted, the company will have to reclaim the
  land causing cash outflow. .

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Problems with IRR approach (1)Multiple
solutions, Contd

• When cash flow exhibits flip-flop pattern, (the
  project has negative cash flow, positive cash
  flow, and then negative cash flow), the multiple
  solution is likely to occur.
• Modified IRR method can be used for such a
  case. Consider the same example. The cash flow is
  -100, 230, -132
• Modified IRR combines the second cash flow (230)
  and the third cash flow (-132) using a discount
  rate so that there is only one change in sign.
  
• See next page

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Problems with IRR approach (1)Multiple
solutions, (modified IRR, contd)

• Suppose that the discount rate is 14. Then,
  modified IRR combines the second cash flow and
  the third cash flow by
• 230?132/(10.14)114.21
• After combining the second and third cash flow,
  the modified cash flow of the project looks like
  -100, 114.21
• Finally, you compute the IRR using the modified
  cash flow. If the resulting IRR is greater than
  the discount rate you used (14), the project is
  accepted.
• In this example, modified IRR is 14.21. Since
  this is greater than the discount rate 14, this
  project will be accepted.

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Problems with IRR approach (1)Multiple
solutions, (modified IRR, contd)

• The modified IRR may solve the problem. But this
  method violates the fundamental spirit of IRR
  that it does not depend on the discount rate.
• Also, if there are several negative cash flows,
  this modified IRR becomes difficult to implement.
• This problem shows one of the reasons why we
  prefer the net present value method over IRR
  rule.

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Problems with IRR approach (2)-Two period cash
flow, with negative cash outflow coming in second
period-

• Suppose a company conduct a seminar. The
  participants pay the fees in advance. Therefore,
  the cash inflow occurs at date 0 (today). The
  large expense occurs at the seminar date.
  Therefore, the negative cash flow occurs at date
  1 (1 period from today). See Next
  Page

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Problems with IRR approach (2)-Two period cash
flow, with negative cash outflow coming in second
period- Contd

• Suppose that the cash flow of the project is
  given by the following.

• Suppose that the cash flow of the project is
  given by the following.
• If you compute the IRR of this project, it will
  be 30
• See next page

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Problems with IRR approach (2)-Two period cash
flow, with negative cash outflow coming in second
period- Contd

• This particular case gives rise to the following
  unusual decision making rule.
• The decision making rule when the data 0 cash
  flow is positive and date 1 cash flow is negative
  is to accept the project if IRR is less than the
  discount rate, and reject if IRR is greater than
  the discount rate.
• The intuitive reason for this unusual decision
  rule is the following.

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Problems with IRR approach (2)-Two period cash
flow, with negative cash outflow coming in second
period- Contd

• Investing in this seminar project is like
  borrowing 100 at data 0, and paying back 130 at
  date 1. Internal rate of return on 30 is like
  borrowing 100 at 30 interest rate.
• Therefore, if the discount rate (market interest
  rate) is smaller than the IRR, (say 25), it
  makes more sense to borrow from the bank than
  investing in the project. This leads to the
  decision rule to reject the project when IRR is
  greater than the discount rate.
• As can be seen, this could cause a confusion for
  the decision making. This is another reason we
  prefer net present value method over IRR method.

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Problem with IRR (3)-Scale Problem-

• Another problem of IRR is that it does not take
  into account the scale of the project. For
  example, consider two projects, project A and
  project B. Project A is a small project (initial
  cost of 10,000) with 20 internal rate of
  return. Project B is large project (initial cost
  of 100 million) with 10 internal rate of
  return.
• Although the project B will bring larger cash
  flows, IRR decision rule would falsely make the
  project A appear more attractive. This is the
  basic illustration of scale problem.
  See next page.

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Problem with IRR (3)-Scale Problem-

• Scale problem becomes a problem when there are
  two mutually exclusive projects.
• Mutually exclusive projects Project A and B
  are called mutually exclusive if you cannot
  accept both project at the same time.
• If two projects are not mutually exclusive, you
  can accept both projects as long as both projects
  have IRRs greater than the discount rate.
• However, if two projects are mutually exclusive,
  you have to choose either project A or B. If IRR
  method is used for this purpose, scale problem
  may occurs.
• See the example in the next slide,

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Problem with IRR (3)-Scale Problem- Example

• Consider you produce a movie on either a small
  budget or a big budget. Then two plans are
  mutually exclusive.
• Exercise Fill in the blanks.

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Problem with IRR (3)-Scale Problem- Example

• IRR for small budget movie is 300, while IRR for
  a big budget movie is 160. However, net present
  value of the project B is greater.
• If we blindly apply IRR method to the decision to
  choose between small budget and large budget
  movies, we would choose low budget movie since it
  has higher IRR. However, it has a smaller net
  present value. This is the problem of scale
  problem in IRR method, and is one of the reasons
  NPV method is preferred over IRR method.
• We can somehow remedy this problem by using
  incremental IRR. See next page.

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Problem with IRR (3)-Scale Problem- Example contd

• Incremental IRR First you compute the
  incremental (or additional) cash flow from
  choosing small budget instead of large budget.
  Then compute incremental IRR.

?25m ?(?10m) ?15m
65m ? 40m 25m
Incremental IRR66.67
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Problem with IRR (3)-Scale Problem- Example contd

• In the previous slide, incremental IRR is 66.67.
  This means that choosing large budget movie
  instead of small budget move will brings
  additional return of 66.67. Put differently,
  increasing the budget from small to large will
  bring additional return of 66.67.
• Therefore, if 66.67 is greater than the discount
  rate, large budget movies should be accepted
  because 66.67 is the additional return from
  increasing the size of the project.

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Alternative Investment Rule 5-Profitability
Index (PI)-

• Profitability index also provides a single number
  that summarizes the merit of a project.
• Profitability Index is computed as

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Alternative Investment Rule 5-Profitability
Index Example-

• Consider a project with the following cash flows.
  Assume the discount rate of 12.

• Using this example, the profitability Index is
  computed in the following ways. See
  next slides.

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Alternative Investment Rule 5-Profitability
Index Example-

• First, you compute the present discount value of
  cash flows subsequent to the initial investment
  with discount rate of 12. This is given by

• Then, the profitability index is computed by
  dividing the above number (70.5) by the initial
  investment (20). Therefore, the Profitability
  Index (PI) for this example is given by

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Alternative Investment Rule 5-Profitability
Index Decision rules-

• Decision to accept or reject an independent
  project is given by the following.
• Decision rule Accept the project if PI gt1.
  Reject if PIlt1.

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A problem with the profitability index

• A problem occurs when we consider two mutually
  exclusive project. As was the case in the IRR
  method, profitability method does not take the
  size of the project into account.
• To illustrate the problem, consider the following
  two mutually exclusive project.

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A problem with the profitability index, Contd

• As an exercise, compute profitability index for
  both projects. Assume the discount rate of 12

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A problem with the profitability index, contd

• As can be seen, project 2 has greater PI.
  However, since profitability index is the ratio,
  PI misses out the fact that project 2 is a
  smaller project.
• Therefore, if the size of the projects are
  different, it is not necessarily the case that
  project with greater profitability index is more
  attractive project.
• We can remedy this weakness by using incremental
  cash flow.
• See next page.

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A problem with the profitability index, contd

• Exercise Profitability index for incremental
  cash folow Complete the following table

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A problem with the profitability index, contd

• The profitability index for the incremental cash
  flow was 2.52. This means that choosing project 1
  instead of project 2 will still increase profit.
  Put differently, increasing the size of the
  project from project 2 to project 1 will bring
  additional profit. Thus, project 1 is preferred.
• As can be seen, scale problem can be remedied by
  computing the PI for incremental cash flow.
  However, net present value method is more
  straightforward when choosing between mutually
  exclusive projects.

55
The practice of capital budgeting

• According Graham, Campbell and Harvey The Theory
  and Practice of Corporate Finance Evidence from
  the Field Journal of Financial Economics 2000,
  the practice of capital financing decision of
  majority of the US and Canadian companies are
  given by the following table.