DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA

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Chapter 4

• DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA

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Contents

• Discounting
• Alernative Investment Criteria
• - Net Present Value Criteria
• - Benefit-Cost Ratio Criteria
• - Pay Back Period Criteria
• - Internal Rate of Return Criteria

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1.1 Discounting and Compounding

• Same amount of money "today" and "in future" do
  not have the same value.
• Finding the today value of a future amount is
  DISCOUNTING.
• Finding the future value a current amount is
  COMPOUNDING.

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1.1 Discounting and Compounding(contd)

• An investment of 1, with a discount rate r
• Value
  Value
• Present After One Year Present
  After n-Years
• B/(1r) B
  B/(1r)n B
• r is the discount rate
• 1/(1r) is the discount factor
• (1r) is the compound factor
• Ex Present value of 250 for 10 years at 6
  discount rate
• 4PV 250/ (10.06)10
• PV 250/ 1.79 139.6 or 250 1/(10.06)10
  139.6

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Example of Discounting

• Year 0 1 2 3 4
• Net Cash Flow -1000 200 300 350 1440

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1.1Discounting and Compounding(contd)

• Discounting Net Benefits
• - the period (number of years)
• - the size of the discount (r)
• NPVr0 (B0-C0)/(1r)0 (B1-C1)/(1r)1 ---
• (Bn-Cn)/(1r)n

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1.1Discounting and Compounding(contd)

• In ranking projects, the particular point in time
  to which all the net benefits in each period are
  discounted does not matter.
• Instead of discounting all the net benefit flows
  to the initial year (year 0), they can be
  dicounted to year k NPV at year k will be a
  constant multiple of NPV in year 0. It will be
  multiplied with (1r). This will not change the
  ranks of the projects, as all projects NPVs in
  year 0 will be multiplied with the same constant
  (1r).

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Table 4-1. Calculating the present value of net
benefits from an investment project
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1.2 Variable Discount Rate

• Discount rates may vary through time.
• Funds may be very scarce at the beginning of the
  project and the discount rates may be very high.
• This will fall in the following years as the
  supply and demand for funds return to normal

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1.2 Variable Discount Rates

• Adjustment of Cost of Funds Through Time

• For variable discount rates r1, r2, r3 in years
  1, 2, and 3, the discount factors are,
  respectively, as follows

1/(1r1), 1/(1r1)(1r2)
1/(1r1)(1r2)(1r3)
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1.3 Factors Affecting the Discount Rates for
Public Projects

• Discount rate for a private investment is the
  weighted average of
• Rate of return from the sale of equity
• The cost of borrowed funds
• Discount rate for a public sector investment is
  the Economic Opportunity Cost of Capital (EOCK).
  This rate reflects the opportunity forgone for
  not using the funds in an alternative public
  project. It considers the lost opportunity for
  the whole economy. It reflects the true cost of
  the resources (funds) used.
• EOCK is taken as 12 by the World Bank for
  developing countries.

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1.3 Factors Affecting the Discount Rates for
Public Projects (cont)

• If significant market distortions exits i.e.
  domestic distortions (taxes and subsidies), and
  external distortions (tariffs and subsidies for
  exports), the market price of inputs and outputs
  of the projects do not reflect the true costs of
  the resources. Their economic (shadow) prices
  should be used in public projects.
• For public sector projects, economic analysis
  (rather than financial analysis) is more
  relevant. Economic analysis uses the EOCK (rather
  than the discount rate) and the economic values
  (rather than the market prices).

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1.3 Factors Affecting the Discount Rates for
Public Projects (cont)

• Financial Analysis
  Economic Analysis
• Financial discount rates
  EOCK
• Market prices Economic values
• More relevant to private sector More rel.
  to public sector
• Owners and bankers point of view
  Economy point of view

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2. Alternative Investment Criteria

• First Criterion Net Present Value (NPV)
• What does net present value mean?
• Measures change in wealth
• Use as a decision criterion to answer following
• a. When to reject projects?
• b. Select project (s) under a budget constraint?
• c. Compare mutually exclusive projects?

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2.1 Net Present Value Criterion

• a. When to Reject Projects?
• Rule Do not accept any project unless it
  generates a positive net present value when
  discounted by the opportunity cost of funds
• Examples
• Project A Present Value Costs 1 million, NPV
  70,000
• Project B Present Value Costs 5 million, NPV -
  50,000
• Project C Present Value Costs 2 million, NPV
  100,000
• Project D Present Value Costs 3 million, NPV -
  25,000
• Result
• Only projects A and C are acceptable. The
  country is made worse off if projects B and D are
  undertaken.

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2.1 Net Present Value Criterion (Contd)

• b. When You Have a Budget Constraint?
• Rule Within the limit of a fixed budget,
  choose that subset of the available projects
  which maximizes the net present value
• Example
• If budget constraint is 4 million and 4 projects
  with positive NPV
• Project E Costs 1 million, NPV 60,000
• Project F Costs 3 million, NPV 400,000
• Project G Costs 2 million, NPV 150,000
• Project H Costs 2 million, NPV 225,000
• Result
• Combinations FG and FH are impossible, as they
  cost too much. EG and EH are within the budget,
  but are dominated by the combination EF, which
  has a total NPV of 460,000. GH is also possible,
  but its NPV of 375,000 is not as high as EF.

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2.1 Net Present Value Criterion (Contd)

• c. When You Need to Compare Mutually Exclusive
  Projects?
• Rule In a situation where there is no budget
  constraint but a project must be chosen from
  mutually exclusive alternatives, we should always
  choose the alternative that generates the largest
  net present value
• Example
• Assume that we must make a choice between the
  following three mutually exclusive projects
• Project I PV costs 1.0 million, NPV 300,000
• Project J PV costs 4.0 million, NPV 700,000
• Projects K PV costs 1.5 million, NPV 600,000
• Result
• Projects J should be chosen because it has the
  largest NPV.

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2.1 Net Present Value Criterion (Contd)

• Constraints of Using NPV
• NPV, not only tells you whether the project will
  be accepted or rejected but also gives you the
  present value of the surplus or the deficit of
  the project. This is an advantage for NPV.
• If the life periods of the strickly alternative
  projects are not the same, adjustments have to be
  made, so that the projects will be compared for
  the same lenght of lives.
• It is not correct to compare the NPV of a gas
  turbine plant with a life of 10 years, to a coal
  plant with a life of 30 years. Their lenght of
  lives should be equated by repeating the gas
  plant for three times.

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2.2 Benefit-Cost Ratio

• It is a widely used by the analysts. Should be
  very careful, otherwise incorrect and misleading
  decisions can be made.
• Benefit-Cost Ratio (R) Present Value
  Benefits/Present Value Costs
• Basic rule
• If benefit-cost ratio (R) gt1, then the project
  should be undertaken.
• Problems?
• Sometimes it is not possible to rank projects
  with the Benefit-Cost Ratio
• Mutually exclusive projects of different sizes
• Mutually exclusive projects and recurrent costs
  subtracted out of benefits or benefits reported
  gross of operating costs
• Not necessarily true that RAgtRB that
  project A is better

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2.2 Benefit-Cost Ratio (Contd)

• First Problem
• The Benefit-Cost Ratio Does Not Adjust for
  Mutually Exclusive Projects of Different Sizes.
• For example
• Project A PV0of Costs 5.0 M, PV0 of
  Benefits 7.0 M
• NPVA 2.0 M RA 7/5 1.4
• Project B PV0 of Costs 20.0 M, PV0 of
  Benefits 24.0 M
• NPVB 4.0 M RB 24/20 1.2
• According to the Benefit-Cost Ratio criterion,
  project A should be chosen over project B because
  RAgtRB, but the NPV of project B is greater than
  the NPV of project A.
• So, project B should be chosen

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2.2. Benefit-Cost Ratio (Contd)

• Second Problem
• The Benefit-Cost Ratio Does Not Adjust for
  Mutually Exclusive Projects where the Costs are
  treated in different ways.
• Project A Project B
• PV of gross benefits 2,000 2,000
• PV of operating Costs 500 1,800
• PV of capital costs 1,200 100
• B/C Ratio (Operating costs netted out of the
  benefits)
• RA (2000-500)/1200 1.15 RB
  (2000-1800)/100 2.0
• Project B is preferred to Project A (RB gt RA
  ).
• 2. B/C Ratio (Operating costs added to capital
  costs) RA 2000/(1200500) 1.18 RB
  2000/(1800100) 1.05
• Project A is preferred to Project B (RA gt RB
  ).
• NPV of a project is not sensetive to the way the
  acountants treat costs. Thus NPV is far more
  reliable than B/C ratio as a criterion for
  project selection.
• Conclusion The Benefit-Cost Ratio CANNOT be used
  to rank projects

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2.3 Pay-Out or Pay-Back Period

• It is widely used criterion as it is very easy to
  apply. Unfortunately it can give misleading
  results especially in cases of investment with a
  long life.
• In a simplest form, it measures the number of
  years it will take for the undiscounted net
  benefits (positive net cash flow) to repay the
  investment. If the number is greater than an
  arbitrary chosen year, the project is accepted.
• In more sophisticated form, it divides the
  discounted net benefits over a given year with
  the discounted investment costs. If the number is
  greater than 1, the project is accepted. One
  assumes that after the chosen net benefits are so
  uncertain (war and political inability) that they
  can be neglected. This assumption is not
  realistic in cases of bridges and roads, etc.

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2.3 Pay-Out or Pay-Back Period

• Project with shortest payback period is
  preferred by this criteria
• There is no reason to expect that quick
  yielding projects are superior to long term
  invetments.

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Figure 4.2 Comparison of Two Projects With
Differing Lives Using Pay-Out Period Criterion
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2.3 Pay-Out or Pay-Back Period (Contd)

• In such situations pay-back period criterion
  gives wrong recommendation for choice among
  investments.
• Assumes all benefits that are produced by in
  longer life project have an expected value of
  zero after the pay-out period.
• The criteria may be useful when project subject
  to high level of political risk.

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2.4 Internal Rate of Return Criterion

• IRR is the discount rate (K) at which the present
  value of benefits are just equal to the present
  value of costs for the particular
  project.....(IRR k) wkich equates the net
  benefits ti zero.
• NPVr 0 0 (B0 - C0 ) (B1 C1 )/((1k)1
  (B2 C2 ) / (1k)2
• Bt - Ct
• (1 K)t
• Note the IRR is a mathematical concept, not an
  economic or financial criterion
• Common uses of IRR
• (a). If the IRR is larger than the cost of funds
  then the project should be undertaken
• (b). Often the IRR is used to rank mutually
  exclusive projects. The highest IRR project
  should be chosen
• An advantage of the IRR is that it only uses
  information from the project
• Another advantage of IRR is that it does not
  require the calculation of EOCK. With NPV one has
  to calculate the EOCK in the economic analysis.

0
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2.4 Difficulties With the Internal Rate of Return
Criterion

• First Difficulty Multiple rates of return for
  project
• Solution 1 K 100 NPV -100 300/(11)
  -200/(11)2 0
• Solution 2 K 0 NPV -100300/(10)-200
  /(10)2 0

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2.4.1 Difficulties With the Internal Rate of
Return Criterion(IRR Makes Misleading Choice
under following conditions)

• For Single Projects
• If the net cash flow is negative in the initial
  year (due to initial investment) but all positive
  in the following years, then IRR has a unique
  solution i.e. One solution
• If negative net cash flows take place after the
  negative net cash flow in intial year, we cannot
  have a unique solution for the IRR. You will have
  two values for IRR (figure 4.3)
• If there is a large negative benefit in the
  final year of the project, there will not be a
  unique solution for IRR again.

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Figure 4.3 Time Profiles of the Incremental Net
Cash Flows for Various Types of Projects
Bt - Ct

time
-
Bt - Ct

time
-
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• Second difficulty Projects of different sizes
  and also strict alternatives

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2.4.3 Difficulties With The Internal Rate of
Return Criterion (Contd)
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2.4.4 Difficulties With The Internal Rate of
Return Criterion (Contd)