DISCOUNTED MEASURES OF PROJECT WORTH CONTINUED

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DISCOUNTED MEASURES OF PROJECT WORTH -CONTINUED

• Lecture 5

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Net Present Value (NPV)

• The cashflows estimated for the project are in
  the future they are not yet realised
• The future is not here yet, but decisions would
  have to be taken in the present time

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Net Present Value (NPV)

• The question then is, what is the value of these
  future estimated cashflows in the present or
  current period, or better still today?
• future estimated cashflows would have to be
  brought to the current or present period

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Net Present Value (NPV)
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Net Present Value (NPV)
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Net Present Value (NPV)
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Net Present Value (NPV)

• Decision Rule
• NPV gt 0 project is viable, accept.
• NPV lt 0 project is not viable, reject.
• NPV 0 project is neither viable nor not viable

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Net Present Value (NPV)

• The value of NPV suggests how much a project is
  adding in value terms to an existing entity or
  how much value the project is creating.
• A positive NPV means that the project is expected
  to add value to the firm and will therefore
  increase the wealth of the owners.

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Net Present Value (NPV)

• Since the goal of projects is to add value or
  increase owners wealth, NPV is a direct measure
  of how well this project will meet the goal.
• NPV has units of currency such as cedis () or US
  dollars (US).

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Net Present Value (NPV)
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Net Present Value (NPV)
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Net Present Value (NPV)

• Advantages
• Takes opportunity cost of money into account.
• A single measure, which takes the amount and
  timing of cashflows into account.
• With NPV one can consider different scenarios.

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Net Present Value (NPV)

• Results are expressed in value terms units of
  currency. So one is able to know the impact the
  value that the project would create.
• It is based on cashflows, which are less
  subjective than profits.

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Net Present Value (NPV)

• Disadvantages
• Complex to calculate and communicate.
• Meaning of the result is often misunderstood.
• Only comparable between projects if the initial
  investment is the same.

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Net Present Value (NPV)

• It can be difficult to identify an appropriate
  discount rate.
• Cashflows are usually assumed to occur at the end
  of a year, but in practice this is over
  simplistic.

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Net Benefit Investment Ratio

• Investments are required for project benefits to
  be realised.
• These investments in the project cashflow can be
  identified as negatives.

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Net Benefit Investment Ratio

• The procedure
• discount all the positive cashflows separately
• discount all the negative cashflows separately.
• Sum each of them
• The sum of positive discounted cashflows is
  divided by sum of negative discounted cashflows.

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Net Benefit Investment Ratio
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Net Benefit Investment Ratio

• The decision rule
• NBIR gt 1 accept
• NBIR lt 1 reject.

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Net Benefit Investment Ratio
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Net Benefit Investment Ratio

• NBIR is also referred to as Profitability Index
  by the accounting profession.
• It is often used for ranking projects especially
  if rationing is in place.

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Benefit Cost Ratio (BCR)

• A variant of the formula for NPV uses the
  subtraction of discounted cash outflow from
  discounted cash inflow.
• In the case of BCR, the discounted cash inflow is
  expressed in terms of the discounted cash
  outflow.

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Benefit Cost Ratio (BCR)
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Benefit Cost Ratio (BCR)

• This can be viewed as
• how many times the discounted cash inflow covers
  the discounted cash outflow over the project
  horizon.

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Benefit Cost Ratio (BCR)

• Decision criteria
• For a single project, a B/C ratio which is
  greater than 1 indicates acceptability
• For multiple (competing) projects, the project(s)
  with the highest B/C ratios (greater than 1)
  should receive highest priority

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Benefit Cost Ratio (BCR)

• NPV measures totals, indicates the amount by
  which benefits exceed (or do not exceed) costs.
• B/C measures the ratio (or rate) by which
  benefits do or do not exceed costs.
• They are clearly similar, but not identical.
• With multiple projects, some may do better under
  NPV analysis, others under B/C.

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Internal Rate of Return (IRR)

• IRR is the rate of return or discount rate that
  makes the NPV 0.
• Decision Rule
• Accept the project if the IRR is greater than the
  required return

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Internal Rate of Return (IRR)

• 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 cashflows
  and is independent of interest rates found
  elsewhere.
• Without a financial calculator, this becomes a
  trial and error process.

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Internal Rate of Return (IRR)

• A critical thing to note is that there should be
  at least one change of sign in order to realise
  IRR.
• there should be a negative net cashflow among
  positive net cashflows or a positive cashflow
  among negative cashflows.
• The change in sign is crucial.

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Internal Rate of Return (IRR)

• Using a spreadsheet
• Start with the cashflows.
• You first enter your range of cashflows,
  beginning with the initial cash outlay (negative).

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Internal Rate of Return (IRR)

• Call the IRR function
• Choose insert on the menu bar
• Select function
• Choose IRR from among the list
• Select the range of cashflows
• Enter a guess rate, but it is not necessary
  Excel will start at 10 as a default
• The default format is a whole percent you will
  normally want to increase the decimal places to
  at least two to get the most accurate output.

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Internal Rate of Return (IRR)

• NPV and IRR will generally give us the same
  decision.
• There are however some exceptions.
• Non-conventional cashflows
• cashflow signs change more than once
• Mutually exclusive projects
• Initial investments are substantially different
• Timing of cashflows is substantially different

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Internal Rate of Return (IRR)

• When the cashflows change sign more than once,
  there is more than one IRR.
• When we solve for IRR it would be noticed that we
  are solving for the root of an equation and when
  we cross the x-axis more than once, there will be
  more than one return that solves the equation.
• Therefore, IRR may be unreliable if we have any
  negative cashflows after our original investment.

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Internal Rate of Return (IRR)

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

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Internal Rate of Return (IRR)
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Internal Rate of Return (IRR)

• Mutually exclusive projects
• If you choose one, you cant choose the other
• Example You can choose to attend graduate school
  next year at either Legon or Central, but not both

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Internal Rate of Return (IRR)

• Intuitively you would use the following decision
  rules
• NPV choose the project with the higher NPV
• IRR choose the project with the higher IRR

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Internal Rate of Return (IRR)
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Internal Rate of Return (IRR)

• The required return for both projects is 10.
• Which project should you accept and why?
• (Accept Project A because of NPV)

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Internal Rate of Return (IRR)

• 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 cashflows
• Mutually exclusive projects

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Internal Rate of Return (IRR)

• Advantages of IRR
• It takes into account the time value of money,
  which is a good basis for decision-making.
• Results are expressed as a simple percentage, and
  are more easily understood than some other
  methods.
• It indicates how sensitive decisions are to a
  change in interest rates.

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Internal Rate of Return (IRR)

• Advantages of IRR
• 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.

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Internal Rate of Return (IRR)

• Advantages of IRR
• 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.

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Internal Rate of Return (IRR)

• Disadvantages
• For mutually exclusive projects timing and scale
  differences. This may lead to incorrect decisions
  in comparisons of mutually exclusive investments.
  
• Assumes funds are re-invested at a rate
  equivalent to the IRR itself, which may be
  unrealistically high.

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Internal Rate of Return (IRR)

• IRR will produce more than one mathematically
  correct rate for each year in which inflows are
  followed by outflows and vice versa. This is
  common with projects with unconventional
  cashflows. This can create some confusion to the
  user.

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Choice of Discount Rate

• Cost of capital - weighted average and marginal
  (financing rate)
• Opportunity cost of capital - what could they
  earn if that money was elsewhere
• Current capital position and expected capital
  position over next few years
• The rates of return for alternative investments.
• Market sentiments.

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Sources of discount rate

• Banks
• Long term government papers
• Ministry of Finance
• Sponsors

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Suggestions

• For industrial projects use market rate or cost
  of borrowing funds.
• For public sector projects use social time
  preference rate.
• For public projects to be funded from
  international loans use the cost of borrowing.

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Suggestions

• Generally, in financial analysis, the market rate
  is used, whilst the social time preference rate
  is used for public sector projects.
• When funding comes from various sources or from
  the same source but at different rates, then,
  compute and use the weighted average.

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Choosing Year 0 or Year 1

• World Bank
• World Bank believes that since investment is made
  and some returns may accrue from the first year,
  then discounting should start from 0 to first
  year.
• In this case, the initial year is Year 1.

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Choosing Year 0 or Year 1

• Others
• Other international originations use Year 0.
• Their argument is that investment must take place
  before benefits accrue.
• Thus, discounting should start from the second
  year.
• Choose any convention but be consistent.

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Deciding on a Project

• 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, but only because of its ease of use.

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Deciding on a Project

• For a single project, a positive NPV indicates
  acceptability.
• For multiple (competing) projects, the project(s)
  with the highest NPVs should receive highest
  priority.