NPV and Other Investment Criteria

1
NPV and Other Investment Criteria

• P.V. Viswanath
• For an Introductory Course in Finance

2
Key Concepts and Skills

• The NPV Rule
• Understand the payback rule and its shortcomings
• Understand accounting rates of return and their
  problems
• Understand the internal rate of return and its
  strengths and weaknesses
• Understand the net present value rule and why it
  is the best decision criteria

3
Chapter Outline

• Net Present Value
• The Payback Rule
• The Average Accounting Return
• The Internal Rate of Return
• The Profitability Index
• The Practice of Capital Budgeting

4
Sources of Investment Ideas

• Three categories of projects
• New Products
• Cost Reduction
• Replacement of Existing assets
• Sources of Project Ideas
• Existing customers
• RD Department
• Competition
• Employees

5
Good Decision Criteria

• We need to ask ourselves the following questions
  when evaluating decision criteria
• Does the decision rule adjust for the time value
  of money?
• Does the decision rule adjust for risk?
• Does the decision rule provide information on
  whether we are creating value for the firm?
• The Net Present Value rule satisfies these three
  criteria, and is, therefore, the preferred
  decision rule.

6
Net Present Value

• The difference between the market value of a
  project and its cost
• How much value is created from undertaking an
  investment?
• The first step is to estimate the expected future
  cash flows.
• The second step is to estimate the required
  return for projects of this risk level.
• The third step is to find the present value of
  the cash flows and subtract the initial
  investment.

7
NPV Decision Rule

• 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 owner wealth, NPV
  is a direct measure of how well this project will
  meet our goal.
• NPV is an additive measure
• If there are two projects A and B, then NPV(A and
  B) NPV(A) NPV(B).

8
Project Example Information

• You are looking at a new project and you have
  estimated the following cash flows
• Year 0 CF -165,000
• Year 1 CF 63,120 NI 13,620
• Year 2 70,800 NI 3,300
• Year 3 91,080 NI 29,100
• Average Book Value 72,000
• Your required return for assets of this risk is
  12.

9
Computing NPV for the Project

• Using the formulas
• NPV 63,120/(1.12) 70,800/(1.12)2
  91,080/(1.12)3 165,000 12,627.42
• Do we accept or reject the project?

10
Estimating Project Cashflows

• Before the NPV decision rule can be applied, we
  need project cashflow forecasts for each year.
• These are built up from estimates of incremental
  revenues and associated project costs.
• Cash Flow Revenues Fixed Costs Variable
  Costs Taxes Long-term Investment Outlays
  Changes in Working Capital
• An equivalent formula is
• Cashflow Net Income Noncash expenses (that
  were included in the Net Income computation)
  (1-tax rate)Interest Long-term Investment
  Outlays Changes in Working Capital

11
Cost of Capital

• The cost of capital is the opportunity cost of
  capital for the firms investors and is used to
  discount the project cashflows.
• The cost of capital is also called the WACC and
  is computed as the firms after-tax weighted cost
  of debt and equity
• WACC (E/V)Re (D/V)Rd(1-t), where
• E, D are market values of the firms equity and
  debt V DE is the total value of the firm and
  t is the firms corporate tax rate
• The cost of debt Rd is multiplied by (1-t)
  because interest payments on debt are deductible
  for tax purposes.
• Since the tax advantage of debt is taken into
  account in the denominator, we do not include it
  in the numerator as well, thus avoiding double
  counting.

12
Sensitivity Analysis

• Since the firm will not know the future level of
  output, or the other cost parameters with
  certainty, it is important to know how the value
  of the project changes as these parameters are
  varied.
• This is called sensitivity analysis
• If the final decision on the project is very
  sensitive to a particular parameter, it would be
  more valuable to expend resources on obtaining
  more precise estimates of that parameter.
• The break-even point is the point of indifference
  between accepting and rejecting the project.
• With respect to sales, this is the number of
  units that have to be sold in order for the
  project to be in the black.

13
Issues to keep in mind

• Sunk costs should be ignored. These costs have
  already been incurred and cannot be undone
  whatever the decision that is going to be
  currently taken.
• Only incremental cashflows should be considered.
  Hence if a machine is to be replaced by a new
  machine, only the additional flows implied by the
  new machine should be considered to make the
  decision of whether to buy the new machine.
• Only cashflows must be considered allocated
  expenses, such as depreciation are to be ignored
  because they reflect capital expenditures already
  made and are a kind of sunk cost.
• Of course, if there are any tax implications
  related to depreciation computations, these must
  be taken into account.

14
Projects with Unequal Lives

• Suppose we have to choose between the following
  two machines, L and S to replace an existing
  machine.
• Machine L costs 1000 and needs to be replaced
  once every four years, while machine S costs 600
  a unit and must be replaced every two years.
• The flows C1-C4 represent cost savings over the
  current machine, for the next four years.
• The discount rate is 10 percent.
• Project C0 C1 C2 C3 C4
  NPV
• --------------------------------------------------
  --------------------------
• L -1000 500 500 500 500
  584.93
• S -600 500 500 267.77

15
Projects with Unequal Lives

• Treating this problem as a simple present value
  problem, we would choose machine L, since the
  present value of L is greater than that of S.
• However, choosing S gives us additional
  flexibility because we are not locked into a
  four-year cycle. Perhaps better alternatives may
  be available in year 3.
• Furthermore, the present comparison is not
  appropriate because even if no better
  alternatives are available because we have not
  considered the tax savings in years 3 and 4 if we
  go with machine S we can always buy a second
  S-type machine at the end of year two!

16
Projects with Unequal Lives

• Consider the modified alternatives
• Project C0 C1 C2
  C3 C4 NPV
• --------------------------------------------------
  -----------------------------------------
• L -1000 500 500 500
  500 584.93
• S -600 500 500 267.77
• Second S -600 500 500
  220.66
• Combination S -600 500 -100 500
  500 488.43
• We see that the combination of two S-type
  machines are not as disadvantageous compared to
  one L-type machine, though the L-type machine
  still wins out.

17
Projects with Unequal Lives

• Alternatively, we can convert the flows for the
  machines into equivalent equal annual flows.
• Thus, we find X, such that the present value of L
  and L1 are equal.
• Project C0 C1 C2 C3 C4
  NPV
• --------------------------------------------------
  --------------------------
• L -1000 500 500 500 500
  584.93
• L1 0 X X X X
  584.93
• This is obtained as the solution to the equation
  PV(Annuity of X for 4 years at 10) 584.93
  and works out to 184.53

18
Projects with Unequal Lives

• Similarly, we convert the flows for machine S
  into equivalent equal annual flows.
• Thus, we find X, such that the present value of S
  and S1 are equal.
• Project C0 C1 C2 C3 C4
  NPV
• --------------------------------------------------
  --------------------------
• S -600 500 500
  267.77
• S1 0 Y Y
  267.77
• This is obtained as the solution to the equation
  PV(Annuity of Y for 2 years at 10) 267.77
  and works out to 154.29

19
Projects with Unequal Lives

• The values X and Y can simply be compared and the
  project with the lower equivalent annual flow is
  chosen.
• We are effectively making the choice betweenthe
  following two projects
• Project C0 C1 C2 C3 C4
• --------------------------------------------------
  --------------------------
• L1 0 X X X X
• S1 0 Y Y Y Y
• The advantage of this approach is that we dont
  need to explicitly construct two projects with
  the same project lives.

20
Internal Rate of Return

• This is the most important alternative to NPV
• It is often used in practice and is intuitively
  appealing
• It is based entirely on the estimated cash flows
  and is independent of interest rates found
  elsewhere

21
IRR Definition and Decision Rule

• Definition IRR is the return that makes the NPV
  0
• Decision Rule Accept the project if the IRR is
  greater than the required return

22
Computing IRR For The Project

• If you do not have a financial calculator, then
  this becomes a trial and error process
• In the case of our problem, we can find that the
  IRR 16.13.
• Note that the IRR of 16.13 gt the 12 required
  return
• Do we accept or reject the project?

23
NPV Profile

• To understand what the IRR is, let us look at the
  NPV profile.
• The NPV profile is the function that shows the
  NPV of the project for different discount rates.
• Then, the IRR is simply the discount rate where
  the NPV profile intersects the X-axis.
• That is, the discount rate for which the NPV is
  zero.

24
NPV Profile For The Project
IRR 16.13
25
Decision Criteria Test - IRR

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

26
Advantages of IRR

• 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
• If the IRR is high enough, you may not need to
  estimate a required return, which is often a
  difficult task

27
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

28
IRR and Nonconventional 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?

29
Another Example Nonconventional Cash Flows

• Suppose an investment will cost 90,000 initially
  and will generate the following cash flows
• Year 1 132,000
• Year 2 100,000
• Year 3 -150,000
• The required return is 15.
• Should we accept or reject the project?

30
NPV Profile
IRR 10.11 and 42.66
31
Summary of Decision Rules

• The NPV is positive at a required return of 15,
  so you should Accept
• If you compute the IRR, you could get an IRR of
  10.11 which would tell you to Reject
• You need to recognize that there are
  non-conventional cash flows and look at the NPV
  profile.

32
IRR and Mutually Exclusive Projects

• Mutually exclusive projects
• If you choose one, you cant choose the other
• Example You can choose to attend graduate school
  next year at either Harvard or Stanford, but not
  both
• Intuitively you would use the following decision
  rules
• NPV choose the project with the higher NPV
• IRR choose the project with the higher IRR

33
Example With Mutually Exclusive Projects
Period Project A Project B
0 -500 -400
1 325 325
2 325 200
IRR 19.43 22.17
NPV 64.05 60.74
The required return for both projects is
10. Which project should you accept and why?
34
NPV Profiles
IRR for A 19.43 IRR for B 22.17 Crossover
Point 11.8
35
Conflicts Between NPV and IRR

• NPV directly measures the increase in value to
  the firm
• Whenever there is a conflict between NPV and
  another decision rule, you should always use NPV
• IRR is unreliable in the following situations
• Non-conventional cash flows
• Mutually exclusive projects

36
Additional Decision Rules

• In addition to the NPV and IRR rules, there are
  some other decision rules that are popularly
  used.
• These are conceptually flawed, but have the
  advantage of being easy to compute and use.
• They may, therefore, be used if a quick decision
  is necessary and not a lot is riding on the
  decision.
• Two examples of these alternative decision rules
  are the payback rule and the accounting rate of
  return.

37
Payback Period

• How long does it take to get the initial cost
  back in a nominal sense?
• Computation
• Estimate the cash flows
• 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

38
Computing Payback For The Project

• Assume we will accept the project if it pays back
  within two years.
• Year 1 165,000 63,120 101,880 still to
  recover
• Year 2 101,880 70,800 31,080 still to
  recover
• Year 3 31,080 91,080 -60,000 project pays
  back in year 3
• Do we accept or reject the project?

39
Decision Criteria Test - Payback

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

40
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
• Adjusts for uncertainty of later cash flows
• Biased towards liquidity

41
Justifying the Payback Period Rule

• We usually assume that the same discount rate is
  applied to all cash flows. Let di be the
  discount factor for a cash flow at time i,
  implied by a constant discount rate, r, where .
  Then di1/di 1r, a constant. However, if the
  riskiness of successive cash flows is greater,
  then the ratio of discount factors would take
  into account the passage of time as well as this
  increased riskiness.
• In such a case, the discount factor may drop off
  to zero more quickly than if the discount rate
  were constant. Given the simplicity of the
  payback method, it may be appropriate in such a
  situation.

42
Justifying the Payback Period Rule
43
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.

44
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?

45
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 criteria?

46
Advantages and Disadvantages of AAR

• 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

47
Summary of Decisions For The Project
Summary Summary
Net Present Value Accept
Payback Period Reject
Average Accounting Return Reject
Internal Rate of Return Accept
48
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

49
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

• Disadvantages
• May lead to incorrect decisions in comparisons of
  mutually exclusive investments

50
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

51
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 required
  payback is 4 years.
• What is the payback period?
• What is the NPV?
• What is the IRR?
• Should we accept the project?
• What decision rule should be the primary decision
  method?
• When is the IRR rule unreliable?