Net Present Value

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Net Present Value Other Investment Criteria

• FIL 240
• Prepared by Keldon Bauer

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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?

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Discounted Payback - Example

• As the Chief Financial Officer of Spamway, Corp.,
  you have been presented with the following two
  potential projects. Assume a 9 discount rate.

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Net Present Value

• The philosophy behind the net present value (NPV)
  is how much should adoption of the project have
  on the overall value of the firm.
• NPV is the sum of all outlays in present value
  terms.
• Since outlays are negative, and inflows are
  positive, the net represents addition to value of
  the firm.

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Net Present Value

• 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.

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NPV - Example 1
321.45 Net Present Value
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NPV - Example 2
643.83 Net Present Value
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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.

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Decision Criteria Test - NPV

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

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Payback Period

• Meant to measure the time it takes to recoup the
  initial investment (ignoring the time value of
  money).
• The quicker the payback period (smaller the
  number), the better!
• To calculate payback period follow the following
  4 steps

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Payback Period - Steps

• Create cash flow time line.
• Add a line for cumulative cash flow.
• Identify the last year that cumulative cash flow
  is negative, we will call it A.
• Payback period is calculated as follows

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Payback Period - Example 1
Step 3 Last negative year is 3 È
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Payback Period - Example 2
Step 3 Last negative year is 3 È
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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?

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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

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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

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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
• The internal rate of return (IRR) represents the
  effective interest earned on the investment.

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Computing IRR For The Project

• If you do not have a financial calculator, then
  this becomes a trial and error process
• Calculator
• Enter the cash flows as you did with NPV
• Press IRR and then CPT
• IRR 16.13 gt 12 required return
• Do we accept or reject the project?

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Discounted Payback - Example

• As the Chief Financial Officer of Spamway, Corp.,
  you have been presented with the following two
  potential projects. Assume a 9 required return.

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IRR - Example 1
?
IRR 16.82
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IRR - Example 2
?
IRR 16.37
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IRR Problems

• IRR has two major problems.
• First, it assumes that all cash inflows will earn
  the IRR rate instead of the much more likely
  discount rate.
• Second, depending on the cash flow streams there
  can be more than one IRR.

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Multiple IRRs

• As an example of more than one IRR, lets assume
  you have a project that will return a net 4,000
  in year zero (salvage of old machine, and
  financing, etc.), nets a negative 25,000 in year
  one, and finishes with a positive 25,000 in year
  three.

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Multiple IRRs - Example

• Since the IRR is defined as the discount rate
  which yields an NPV of zero

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Multiple IRRs - Example

• Multiplying both sides by (1k)2 yields

Factoring the above polynomial
k IRR 25 or 400
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Multiple IRRs - Example
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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?

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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

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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

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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?

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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

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Modified Internal Rate of Return

• IRR has some problems that MIRR rectifies.
• There is only one MIRR for all projects.
• Reinvestment is assumed to be at k.
• MIRR can be seen as a more realistic return on
  invested capital.
• To calculate MIRR, you should follow 4 steps

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Modified Internal Rate of Return

• Create cash flow time line.
• Sum the present value of all cash outlays.
• Sum the future value of all cash inflows in the
  projects final period.
• Using only the present value from 2 and the
  future value from 3, calculate the interest rate.

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MIRR - Example

• As the Chief Financial Officer of Spamway, Corp.,
  you have been presented with the following two
  potential projects. Assume a 9 discount rate.

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MIRR - Example 1- Steps 1 2
Because all outflows are already in present
value, no adjustments are needed.
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MIRR - Example 1 - Step 3
Future Value 2,802.53
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MIRR - Example 1 - Step 4
MIRR 13.32
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MIRR - Example 2 - Steps 1 2
Because all outflows are already in present
value, no adjustments are needed.
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MIRR - Example - Step 3
Future Value 5,606.49
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MIRR - Example - Step 4
MIRR 13.32
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NPV Profiles

• To create an NPV profile, plot NPV on the Y axis
  and the discount rate on the X axis.
• Since the discount rate should be sensitive to
  changes in project risk, the NPV profile will
  show how sensitive the projected NPV is to the
  appropriate discount rate.

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NPV Profiles - Figure 8-3
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NPV Profiles

• The crossover rate is the rate at which both
  projects have the same NPV.
• If one knows the crossover rate, then one can
  assess the probability of the discount rate being
  that low (high), and can better rank the priority
  of potential projects.

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NPV Profiles

• The slope of the lines in an NPV profile measures
  the sensitivity of NPV to the discount rate
  chosen.
• In the books example the L represents a longer
  payback and S a shorter payback.
• The longer the payback the more sensitive the NPV
  will be to the discount rate.

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Independent Projects

• If two projects are independent, then adopting
  one does not affect the firms ability to adopt
  the other.
• If two projects are independent, all projects
  with positive NPV and/or IRR and MIRR greater
  than the discount rate should be adopted.

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Independent Projects

• All projects with positive NPV add value to the
  firm.
• All projects where IRR or MIRR are greater than
  the discount rate will bring more return than
  their cost of capital.

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Mutually Exclusive Projects

• If two projects are mutually exclusive, then the
  firm can only adopt one of the two projects.
• So which of the techniques should be used to
  decide which project to adopt?

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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

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Profitability Index - Example

• As the Chief Financial Officer of Spamway, Corp.,
  you have been presented with the following two
  potential projects. Assume a 9 discount rate.

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Profitability Index - Example

• Step 1 Calculate the present value of all
  future cash flows
• PV of G 1,821.45
• PV of Y 3,643.83
• Step 2 Divide the present value from step 1 by
  the initial outlay

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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

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What is a Real Option?

• Real options exist when managers can influence
  the size and risk of a projects cash flows by
  taking different actions during the projects
  life in response to changing market conditions.
• Alert managers always look for real options in
  projects.
• Smarter managers try to create real options.

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What are Some Types of Real Options?

• Investment timing options
• Growth options
• Expansion of existing product line
• New products
• New geographic markets

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Types of Real Options (Continued)

• Abandonment options
• Contraction
• Temporary suspension
• Flexibility options