A Comparison of Capital Budgeting Techniques

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A Comparison of Capital Budgeting Techniques

• With definitions and exemplifications

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Capital budgeting

• Cost/benefit analysis
• Estimating the value of investment projects
• Making informed choices

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Capital Budgeting Techniques

• A collection of methods allowing the manager to
  choose among a variety of investment projects.

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Problem

• Value, rank and select investment projects

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Exemplification
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Clarifications

• Required rate a fair discount rate given each
  projects risk

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Methods

• Average Accounting Return
• Payback
• Discounted payback
• Internal Rate of Return
• Modified Internal Rate of Return
• Net Present Value
• Profitability Index

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Average Accounting Return

• AAR is the ratio of the Average Net Income to the
  Average Book Value.
• Decision rule
• Take the project if AAR is greater than some
  target ratio set by accountants.
• Disadvantages
• It has too many flaws, don't ever use it.

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Payback period

• PB is the time it takes to recover the initial
  cost of the investment

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Payback period

• Decision rule
• Take the project with the shortest payback period
• Disadvantages
• Ignores time value of money
• Ignores risk
• Ignores cash inflows beyond the cutoff point

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Payback period

• In our example
• project C 2.49 years
• project B 3.41 years
• project A 3.83 years
• All three projects are viable

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Discounted payback period

• DPB is the time it takes to recover the initial
  cost of the investment
• PB uses nominal CF
• DPB uses discounted CF

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Discounted payback period

• Decision rule
• Take the project with the shortest discounted
  payback period.
• Disadvantages
• DPB ignores cash inflows beyond the cutoff point

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Discounted payback period

• project A 4.94 years
• project B 3.76 years
• project C would need more than 5 years
• Only A and B are viable

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Internal Rate of Return

• IRR is the discount rate that makes the present
  value of the project equal to its initial cost.

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Internal Rate of Return

• Decision rule
• Take the project If the IRR exceeds the required
  rate of return
• Disadvantages
• Reinvestment rate assumption is unrealistic
• Multiple IRR
• IRR cannot rank mutually exclusive projects

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Internal Rate of Return Calculation

• Set Initial cost PV(project)?
• 5,045 400/(1r) 1,250/(1r)2 900/(r)3
  3,000/(1r)4 1,000/(1r)5
• r 8.

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Internal Rate of Return

• IRR(A) 8
• IRR(B) 8
• IRR(C) 5.
• Only A and B are viable

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Modified Internal Rate of Return

• MIRR is the discount rate that makes the future
  value of the project equal to its initial cost.
• MIRR requires a reinvestment rate.

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Modified Internal Rate of Return

• Decision rule
• Take the project if MIRR is larger than the
  required rate.
• Disadvantages
• MIRR cannot rank mutually exclusive projects.

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MIRR calculation

• Project A
• Set FV(at 5) 5,045(1MIRR)5
• MIRR 7

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MIRR calculation

• MIRR(A) 7
• MIRR(B) 6.54
• MIRR(C) 5
• Only A and B are viable

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NPV

• Net Present Value is the difference between the
  present value of a project and its initial cost
• NPV PV - Initial cost

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NPV

• Decision rule
• If NPV is positive, take the project.
• Disadvantages
• Very complex analysis, too many variables to
  forecast

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NPVCorollary

• Required Rate IRR ? NPV 0
• and vice-versa.

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NPV calculation

• project A
• PV 400/(1.077) 1,250/(1.077)2
  900/(1.077)3 3,000/(1.077)4 1,000/(1.077)5
  
• PV5,089.36
• NPV Present value - Initial Cost
• NPV 5,089.36 - 5,045 44.36

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NPV calculation

• NPV(A) 44.36
• NPV(B) 64.17
• NPV(C) -148.81
• Only A and B are viable
• B is better because it adds more value

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The Profitability Index

• The profitability index is the ratio of project
  PV to initial cost
• PI PV/Initial cost

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The Profitability Index

• Decision rule
• Take the project if PI gt 1
• Disadvantages
• PI cannot rank mutually exclusive projects.

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PI calculation

• Project A
• PI(A) PV(A)/Initial cost 5,089.36/5,045
• PI(A) 1.0088

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PI Calculation

• PI(A) 1.0088
• PI(B) 1.131
• PI(C) 0.9846
• Only A and B are viable

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Why cant PI rank the projects?Exemplification
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Why cant PI rank the projects?

• PI(x) lt PI(y)?
• but
• NPV(x) gt NPV(y)?

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Answer

• NPV rules.
• Always.

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Important side note

• In project valuation, measures of absolute wealth
  are more appropriate than measures of relative
  efficiency.

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