Capital Budgeting: NPV and Other Investment Criteria

1
Lecture 8

• Capital Budgeting NPV and Other Investment
  Criteria

2
Lecture Outline

• The Capital Budgeting Process
• Investment Decision Criteria
• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• Payback Period
• Accounting Rate of Return
• Profitability Index (PI)
• Project Interactions and Other Special Cases in
  Capital Budgeting
• Mutually Exclusive Projects
• Investment Timing
• Capital Rationing
• Projects of Unequal Size
• Projects of Unequal Life
• Managerial Options
• Relevant Chapter RWJ-Ch. 9

3
The Capital Budgeting Process

• A good investment decision is one that raises the
  current market value of the firms equity,
  creating value for the firms owners
• Capital budgeting involves comparing the amount
  of cash spent on an investment today with the
  cash inflows expected from it in the future
• Discounting is the mechanism used to account for
  the time value of money
• Apart the timing issue, there is also the issue
  of the risk associated with future cash flows
• There is always some probability that the cash
  flows realized in the future may not be the
  expected ones
• Risk is incorporated into the discount rate, also
  called the opportunity cost of capital

4
The Capital Budgeting Process

• In order to evaluate investment opportunities (or
  projects) we need
• Estimated (amount and timing of) cash inflows the
  project will generate
• Estimated (amount and timing of) costs the
  project will incur
• An appropriate discount rate to compare the
  present value of the cash inflows and outflows.
• A technique to compare the projects under
  consideration.

5
Desirable Characteristics of Investment Decision
Criteria

• It should adjust for the timing of the projects
  expected cash flows
• It should adjust for the risk of the projects
  expected cash flows
• Overall, it should measure the value created by
  taking on the project

6
Net Present Value - Example

• Suppose we can invest 350,000 today and receive
  400,000 later today. What is our increase in
  value?
• Profit -350,000 400,000 50,000

Added Value 50,000
Initial Investment 350,000
7
Net Present Value - Example

• Suppose we can invest 350,000 today and receive
  400,000 in one year. What is our increase in
  value given a 7 expected return?

Added Value 23,832
Initial Investment 350,000
8
Net Present Value (NPV)
Net present value is the present value of all
future cash flows minus the initial investment.

• Some of the future cash flows can also be
  negative
• Alternative investments must be comparable in
• Riskiness
• Tax treatment
• Liquidity

Opportunity cost of capital is the rate of return
given up by investing in the project.
9
NPV Formula
10
The NPV Rule

• Managers increase shareholders wealth by
  accepting all projects that are worth more than
  they cost.
• NPV gt 0 ? Accept
• NPV lt 0 ? Reject

NPV Rule is to accept projects with positive NPV
and reject projects with negative NPV.
11
NPV Method - Example

• You have the opportunity to purchase an office
  building. You have a tenant lined up that will
  generate 16,000 per year in cash flows for
  three years. At the end of three years you
  anticipate selling the building for 450,000.
  How much would you be willing to pay for the
  building if your opportunity cost of capital is
  7?

12
NPV Method - Example

• If the building is being offered for sale at a
  price of 350,000, would you buy the building and
  what is the added value generated by your
  purchase and management of the building?

13
NPV Calculation usingTI BAII Plus Financial
Calculator

• If the cash flows are not the same for each
  intermediate period, then the CF function will
  need to be used. The sequence in that case is
• CF
• 2nd CLR Work
• CF0 -350000 ENTER ?
• C01 16000 ENTER ? F01 1 ?
• C02 16000 ENTER ? F02 1 ?
• C03 466000 ENTER
• NPV
• I 10 ENTER ?
• COMPUTE NPV 59,323.10

14
NPV Calculation using a Spreadsheet

• Enter all the cash flows and let Excel find the
  NPV

The NPV formula used NPV(0.07,C4C6)C3
15
NPV Measures Value Creation

• The present value of an assets expected cash
  flows at its cost of capital is an estimate of
  the assets market value
• This forms the basis of valuation
• By extension, the net present value of an
  investment represents the immediate change in the
  wealth of the firms owners if the project is
  accepted
• If NPV is positive, project creates value if
  negative it destroys value

16
NPV Method Advantages and Disadvantages

• Advantages
• is a direct measure of value creation
• adjusts for timing of the projects expected cash
  flows
• distant cash flows discounted with larger
  discount factors
• adjusts for risk of the projects expected cash
  flows
• riskiness of the project is reflected in the
  discount rate
• includes all cash flows over the life of the
  project
• is additive for independent projects
• Disadvantages
• requires estimation of cash flows for entire life
  of the project
• requires estimation of a discount rate

17
NPV A Caveat

• Applying the net present value rule is a
  straight-forward exercise
• The real issue is to determine
• the stream of future cash flows
• the appropriate discount rate

18
Internal Rate of Return - Example

• You can purchase a building for 350,000. If you
  know that you can sell the building for 400,000
  next year, what is the IRR on this investment?

19
Internal Rate of Return (IRR)
Internal rate of return is the discount rate that
results in a zero NPV.

• It can be thought of as the break-even discount
  rate
• IRR gt Opportunity Cost of Capital ? Accept
• IRR lt Opportunity Cost of Capital ? Reject

IRR Rule is to accept projects with IRRs higher
than the opportunity cost of capital and reject
projects with IRRs lower than the opportunity
cost of capital.
20
IRR Method Advantages and Disadvantages

• Advantages
• Percentages make more sense to most people.
• It is a simple way to communicate the value of a
  project to someone who doesnt know all the
  estimation details
• If the IRR is high enough, you may not need to
  estimate a required return, which is often
  difficult

21
IRR Method Advantages and Disadvantages

• Disadvantages
• Multiple IRRs Some projects will have multiple
  IRRs.
• Mutually Exclusive Projects Can lead to wrong
  choice when projects are mutually exclusive and
  projects have different scales or lives.
• Reinvestment Rate Assumption IRR method assumes
  all intermediate cash flows from the project are
  reinvested at the IRR. NPV method assumed they
  were reinvested at the opportunity cost of
  capital which is a better assumption. One way to
  get around this is to use MIRR but we will not go
  into that in this course.

22
IRR Method - Example

• You can purchase a building for 350,000. The
  investment will generate 16,000 in cash flows
  (i.e. rent) during the first three years. At the
  end of three years you will sell the building for
  450,000. What is the IRR on this investment?

IRR 12.96
23
Finding IRR using the NPV Profile
IRR12.96
24
IRR Calculation

• Calculating the IRR can be cumbersome. Without a
  financial calculator, you may have to go through
  a tedious trial and error process.
• Using a financial calculator or a spreadsheet
  will make the IRR calculation relatively straight
  forward.

25
IRR Calculation Using TI BAII Plus Financial
Calculator

• When the cash flows are the same throughout the
  project (except the last cash flow) then we can
  solve this using the TVM functions of the
  calculator.
• N 3
• I/Y ???
• PV -350000
• PMT 16000
• FV 450000

IRR 12.96
Make sure that the cash flows in the same
direction are entered with the same sign
26
IRR Calculation Using TI BAII Plus Financial
Calculator

• If the cash flows are not the same for each
  intermediate period, the previous method will not
  work. Instead, the CF function will need to be
  used. The sequence in that case is
• CF
• 2nd CLR Work
• CF0 -350000 ENTER ?
• C01 16000 ENTER ? F01 1 ?
• C02 16000 ENTER ? F02 1 ?
• C03 466000 ENTER
• IRR CPT
• IRR 12.96

27
IRR Calculation Using a Spreadsheet

• Enter all the cash flows and then let Excel find
  the IRR.

The IRR formula used IRR(B2B5)
28
IRR Calculation Trial and Error

• If you dont have your financial calculator or
  cant use a spreadsheet, you will need to go
  through several iterations of trial and error.
• You might get some help by using the approximate
  YTM formula, but you will then need to check to
  see if you get a close enough answer.

29
NPV vs. IRR

• NPV and IRR will generally give us the same
  decision
• Exceptions
• 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

30
NPV or IRRConflicting Recommendations
31
NPV Cross-over
IRRA14.23
IRRc-o12.26
IRRB12.96
32
IRR and Non-conventional Cash Flows

• When the cash flows change sign more than once,
  there is more than one IRR
• When you solve for IRR you are solving for the
  root of an equation and when you cross the x-axis
  more than once, there will be more than one
  return that solves the equation
• If you have more than one IRR, which one do you
  use to make your decision?

33
Internal Rate of Return - Pitfalls

• Pitfall 1 - Mutually Exclusive Projects
• IRR ignores the magnitude and the length of the
  project
• We will say more on this later

34
Internal Rate of Return - Pitfalls

• Pitfall 2 - Lending or Borrowing?
• With some cash flows (as given below) the NPV of
  the project increases as the discount rate
  increases.
• This is contrary to the normal relationship
  between NPV and discount rates.

35
Internal Rate of Return - Pitfalls
IRR20.00
36
Internal Rate of Return - Pitfalls

• Pitfall 3 - Multiple Rates of Return
• Certain cash flows can generate NPV0 at two
  different discount rates.
• The following cash flow generates NPV0 at both
  6 and 31.

37
Internal Rate of Return - Pitfalls
IRR15.94
IRR230.93
38
What to do when NPV and IRRgive conflicting
recommendations!

• NPV measures the value added by taking on the
  project being considered.
• When NPV gives conflicting recommendations with
  IRR, choosing the higher NPV project will
  generally work.
• Exceptions to this are when projects are
• Scalable investment size can be increased and
  all cash flows and NPV will increase in
  proportion
• Repeatable the project can be repeated when it
  ends and it will require the same investment and
  yield the same NPV when it is repeated.

39
Payback Period
Payback period is the time it takes for a firm to
recover its initial investment.
Payback rule is to accept projects if the payback
period is less than a specified cutoff period and
reject projects if the payback period is more
than the specified cutoff.

• Payback period lt Cutoff ? Accept
• Payback period gt Cutoff ? Reject

40
Payback Rule Advantages and Disadvantages

• Advantages
• Easy to understand
• Requires only the estimation of the cash flows up
  to the cutoff period
• Adjusts for uncertainty of later cash flows by
  ignoring cash flows after the cutoff period
• Allows quick evaluation by managers
• Disadvantages
• Ignores the timing and the riskiness of the cash
  flows
• Ignores cash flows beyond payback period
• Biased against long term projects

41
Payback Rule

• Applying the payback rule strictly is a bad
  financial management strategy
• Payback rule is only appropriate as a first pass
  approach in evaluating projects

42
Payback Method - Example
43
Discounted Payback Period

• The timing and riskiness of cash flows may be
  considered by applying the payback period method
  on discounted cash flows
• Still, cash flows beyond the cutoff period are
  completely ignored
• Still biased in favor of short-term investments
  and against long-term investments
• The inputs used in calculating a discounted
  payback period are the same as the ones needed to
  calculate the NPV (cash flows as well as the
  opportunity cost of capital) so why bother with
  the discounted payback!

44
Discounted Payback Method - Example
45
Discounted Payback Rule Advantages and
Disadvantages

• Advantages
• Includes time value of money
• Easy to understand
• Does not accept negative estimated NPV
  investments when all future cash flows are
  positive
• Biased towards liquidity
• Disadvantages
• May reject positive NPV investments
• Requires an arbitrary cutoff point
• Ignores cash flows beyond the cutoff point
• Biased against long-term projects, such as RD
  and new products

46
Average Accounting Return

• There are many different definitions for average
  accounting return
• The one used in the book is
• Average net income / average book value
• Note that the average book value depends on how
  the asset is depreciated.
• Need to have a target cutoff rate
• Decision Rule Accept the project if the AAR is
  greater than a preset rate.

47
Computing AAR For The Project

• Assume we require an average accounting return of
  25
• Average Net Income
• (13,620 3,300 29,100) / 3 15,340
• AAR 15,340 / 72,000 .213 21.3
• Do we accept or reject the project?

48
Decision Criteria Test - AAR

• Does the AAR rule account for the time value of
  money?
• Does the AAR rule account for the risk of the
  cash flows?
• Does the AAR rule provide an indication about the
  increase in value?
• Should we consider the AAR rule for our primary
  decision rule?

49
Average Accounting Return Advantages and
Disadvantages

• Advantages
• Easy to calculate
• Needed information will usually be available
• Disadvantages
• Not a true rate of return time value of money is
  ignored
• Uses an arbitrary benchmark cutoff rate
• Based on accounting net income and book values,
  not cash flows and market values

50
Profitability Index
Profitability index is the ratio of the present
value of cash inflows to the present value of
cash outflows.

• When the setting is an investment with an initial
  cash outflow followed by positive future cash
  inflows, the formula for the profitability index
  becomes

51
Profitability Index Rule
According to the PI Rule, accept projects when PI
is greater than 0 and reject projects when PI is
less than 0.

• PI will always give the same accept/reject
  decisions as the NPV but it may give conflicting
  results to the NPV when ranking projects.

52
Profitability Index Advantages and Disadvantages

• Advantages
• Closely related to NPV, generally leading to
  identical decisions
• Easy to understand and communicate
• May be useful when available investment funds are
  limited
• Disadvantages
• Problems when ranking mutually exclusive projects

53
Mutually Exclusive Projects

• Mutually exclusive projects are those where when
  one is chosen, the others must be turned down.
• An example is the choice of building a
  multi-level parking garage or an office building
  on a given piece of land.
• You can do one or the other but not both, even
  though both may be positive NPV projects.
• When you need to choose between mutually
  exclusive projects, the decision rule is
• to calculate the NPV of each project, and
• from those options that have a positive NPV,
  choose the one with the highest NPV.

54
Decision Making when Projects are Mutually
Exclusive

• With mutually exclusive projects
• the NPV rule will work well
• the IRR rule may fail
• see the examples below

55
Capital Rationing

• A firms investment budget may not be large
  enough to allow the firm to fund all its
  investment proposals that have positive NPVs and
  a limit may be set on the amount of funds
  available for investment.
• If limits are imposed, for some reason, by
  management, this is called soft rationing.
• If limits are imposed as a result of the
  unavailability of funds in the capital market,
  this is called hard rationing.
• If the firm is budgeting under capital rationing,
  the set of projects with the highest combined NPV
  is sought
• If investment outlays only occur at time 0, the
  projects should be ranked by their profitability
  index and they should be accepted in that order
  until the available funds are exhausted.
• If there are cash outflows also at future time
  periods, the question may become more complex to
  solve.

56
Projects of Unequal Size

• The usual NPV rule (choose the investment with
  the highest NPV) may fail to give the best
  results if projects with different funding
  requirements are evaluated and
• the projects are mutually exclusive, or
• there is capital rationing in place
• In such cases, a combination of projects yielding
  the highest total NPV should be selected
• If the restrictions apply only for the year when
  the projects are under review, this will be
  achieved by choosing the projects with the
  highest profitability indexes while staying
  within limitations

57
Projects of Unequal Size

• If there are cash outflows also at future time
  periods, the question becomes more complex to
  solve and turns into a constrained maximization
  problem which may be solved using linear
  programming
• Thus, a firm operating under capital constraints
  should not make todays investment decisions
  without considering investments that may be
  available tomorrow
• This might be more difficult to handle than it
  first seems because information about tomorrows
  investments may not be available today
• In such cases, choosing projects using the
  profitability index on the basis of currently
  available information may be the second best
  solution

58
Comparing Projects of Unequal Size Simple Case

• Suppose that a firm is limited to spending 10
  million in year 0.

59
Comparing Projects of Unequal Size Complex Case

• Suppose that the firm is limited to spending 10
  million both in year 0 and year 1.

60
Projects of Unequal Life Spans

• If projects have unequal lives, comparison should
  be made between sequences of projects such that
  all sequences have the same duration
• If projects have lives which are multiples of
  each other (e.g. 2 and 4 years), one project may
  be assumed to repeat to match the life of the
  other project
• This assumes that projects may be repeated as
  many times as we like
• The calculations may become tedious when project
  lives are not simple multiples of each other

61
Annuity Equivalent Cash Flows

• In cases where project lives are not simply
  multiples of each other (e.g. 3 years and 5
  years), it is possible to convert each projects
  stream of cash flows into an equivalent stream of
  equal annual cash flows with the same present
  value as the total cash flow stream
• The result is called the constant
  annual-equivalent cash flow (also called the
  annuity-equivalent cash flow, equivalent annual
  annuity, or equivalent annual cost)
• The decision may then be based on these
  annuity-equivalent cash flows

62
Comparing Projects of Unequal Life Spans
Replicating Projects
63
Comparing Projects of Unequal Life Spans
Annuity-Equivalent Cash Flows