FINC 3310

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FINC 3310

• Chapter Nine
• NPV and Other Investment Criteria

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Abbreviations and Symbols

• CF cash flow
• NPV net present value, a dollar measure
• IRR internal rate of return, a measure

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Getting Started

• Consider two projects that each cost 15,000.
• Cash flows A B
• 3,000 4,000
• 4,000 4,000
• 8,000 4,000
• -0- 4,000
• -0- 4,000
• Which project(s) should be taken? We will
  evaluate the projects using the following
  investment criteria

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Getting Started, continued

• A. Payback period
• B. Discounted payback period
• C. Net present value
• D. Internal rate of return

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A. Payback period

• Why? It's easy! The payback is defined to be
  the amount of time until cash flows recover the
  cost of investment (counted in years).
• Criteria Payback of x years or less (where x
  depends on management's discretion).
• Payback(A)
• Payback(B)

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A. Payback period

• Problems

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B. Discounted payback period

• This is designed to keep the ease of the payback
  method, but correct for the time value of money
  problem. Here, payback is again the length of
  time until cash flows recover investment, but the
  cash flows are discounted. Using the values for
  projects A and B, assume the appropriate discount
  rate is 10. What are the paybacks now?

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B. Discounted payback period

• Discounted CFs for A Discounted CFs
  for B
• 1
• 2
• 3
• 4
• 5
• Disc. Payback(A)
• Disc. Payback(B)

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B. Discounted payback period

• Problems

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C. Net present value, or NPV

• where
• CFt cash flow in year t
• IO initial outlay
• Criterion NPVgt 0 Þ accept project. Why?

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C. Net present value, or NPV

• Use the same cash flows for projects A B
  again, and again let the interest rate be 10.
  Which, if either, project is now acceptable?
• NPV(A) at 10
• NPV(B) at 10
• So, in this case, NPV gives OPPOSITE
  recommendation of the payback method!

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D. The Internal Rate of Return, IRR

• This is the rate that in the NPV equation makes
  NPV O, or IRR r " r '
• What does this mean economically? How do we
  interpret the IRR?

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D. The Internal Rate of Return, IRR

• These are the NPV Profiles for projects A and B.
  What can we say about the relationship between
  NPVs and IRRs?

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D. The Internal Rate of Return, IRR

• Recall, what is NPV decision criterion? NPVgt0
  Þ accept
• What you think this will mean for IRR?
• IRR gt RRR Þ accept
• Do you see the relationship?
• If IRR gt RRR ÞNPV gt 0
• If IRR lt RRR ÞNPV lt 0
• So for any single project, IRR and NPV provide
  the same accept or reject decision.

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D. The Internal Rate of Return, IRR

• IRR(A)
• IRR(B)
• Note that for any interest rate, Project A will
  have a negative NPV and an IRR lt RRR, so Project
  A should not be accepted. Recall that payback
  ranked A above B!

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D. The Internal Rate of Return, IRR

• How do you solve for the IRR?
• 1) If cash flows are even, this is like an
  annuity, so solve for factor and look it up in
  the tables.
• 2) If cash flows are uneven, you must take some
  special steps...called trial and error!
• 3) You may need to interpolate.
• Recommendation use a financial calculator!

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Solving for the IRR Example

• A 50,000 investment has 4 years of cash flows
  as follows 20,000 in year 1, 15,000 in years 2
  and 3, and 10,000 in year 4. What is the IRR?
• The first step is to create a pseudo-annuity to
  help us eliminate bad guesses.
• 60,000/4 15,000 "annuity"

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Solving for the IRR Example

• The second step is to find the interest rate that
  solves our pseudo-annuitys IRR
• 50,000 15,000(PFIVAr,4)
• 3.333 PVIFAr,4
• Looking up this factor, we find that the closest
  r is 8. This is not the IRR for our investment
  project! It is just our first guess! And it is
  not the best we can do! Why? Due to moving early
  cash flows to later ones in averaging, our 8 is
  too low. Go to 9.

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Solving for the IRR Example

• CASH FLOWS PVIF (8) Disc. Flow PVIF (9)
  Disc. Flow
• 20,000 .9259 18,518.52 .9174
  18,348.62
• 15,000 .8573 12,860.08 .8417
  12,625.20
• 15,000 .7938 11,907.48 .7722
  11,582.75
• 10,000 .7350 7,350.30 .7084
  7,084.25
• S 50,636.38 S
  49,640.83
• So, the IRR is between 8 and 9. Here is a
  chance to interpolate.

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Solving for the IRR Example

• Interpolating, or between the poles
• 8 9
• ½__________½___________½
• 50,636.38 50,000 49,640.83
• Interpolation is based on the relationship a/b
  c/d
• 636.38 C
• 995.55 1
• C .0064
• So, IRR .08 .0064.0864 8.64
• What if RR 10?

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Problems with IRR

• Multiple values are possible.
• No IRR is possible.

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Problems with IRR, continued

• When projects are mutually exclusive, conflict
  between IRR and NPV rankings is possible. This
  problem is based on size or lifetime disparity
  in projects, or patterns of cash inflows.

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Problems with IRR, continued

• Where do the NPV profiles cross? What does that
  tell us about the conflict?

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Problems with IRR, continued

• The reinvestment rate assumption may be less
  realistic