Part 4: Investment Rules and Capital Rationing

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• Part 4 Investment Rules and Capital Rationing
• Organisation
• The Payback Rule
• The Internal Rate of Return
• The Profitability Index
• The NPV Rule Applications
• Capital Rationing

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4.1 Payback Rule Illustrated

• Initial outlay -1,000
• Year Cash flow
• 1 200
• 2 400
• 3 600
• Accumulated
• Year Cash flow
• 1 200
• 2 600
• 3 1,200
• Payback period 2 2/3 years

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4.2 Discounted Payback Illustrated

• Initial outlay -1,000 r 10
• PV of
• Year Cash flow Cash flow
• 1 200 182
• 2 400 331
• 3 700 526
• 4 300 205
• Accumulated
• Year discounted cash flow
• 1 182
• 2 513
• 3 1,039
• 4 1,244
• Discounted payback period is just under 3 years

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4.3 Internal Rate of Return Illustrated

• Initial outlay -200
• Year Cash
  flow
• 1 50
• 2 100
• 3 150
• Find the IRR such that NPV 0
• 50 100
  150
• 0 -200
  
• (1IRR)1 (1IRR)2
  (1IRR)3
• 50 100
  150
• 200
• (1IRR)1 (1IRR)2
  (1IRR)3

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4.4 Internal Rate of Return Illustrated
(concluded)

• Trial and Error (Technique for pre-Excel era)
• Discount rates NPV
• 0 100
• 5 68
• 10 41
• 15 18
• 20 -2
• IRR is just under 20 -- about 19.44

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4.5 Net Present Value Profile
Net present value
120
Year Cash flow 0 275 1 100
2 100 3 100 4 100
100
80
60
40
20
0
20
Discount rate
40
2
6
10
14
18
22
IRR
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4.6 Pitfalls of the IRR Rule

• Lending vs. borrowing
• Multiple IRRs
• No IRR

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4.7 Conventional (standard) Cash Flows

• The NPV of previous projects is not a monotone
  declining function of discount rate.
• For an independent project, when project cash
  flows are conventional - i.e., negative cash
  flows occur before positive cash flows, then the
  NPV is a declining function of discount rate. The
  IRR and the NPV rules lead to same
  accept-or-reject decision for conventional
  projects.

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4.8 Non-conventional Projects

• When project cash flows are non-conventional,
  then we are better not to use the IRR method,
  because we may find that there are no IRR, or
  multiple IRRs.
• Examples of non-conventional projects.

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4.9 Mutually Exclusive Projects

• If projects are mutually exclusive, additional
  complications can arise even when projects are
  conventional.
• Here, the NPV rule favors B while the IRR rule
  favors A.
• Project A costs less and has a greater return,
  but project B pays back more dollars.

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4.10 Profitability Index Illustrated

• When resources are limited, the Profitability
  Index (PI) provides a tool for selecting among
  various project combinations and alternatives.
• A set of limited resources and projects can yield
  various combinations.
• The highest weighted average PI can indicate
  which projects to select.

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4.11 Capital Rationing

• Have 350,000 to invest. Which ones to select?
• Proj PV(Inflow) Investment
  PI
• A 230,000 200,000 1.15
• B 141,250 125,000 1.13
• C 194,250 175,000 1.11
• D 162,000 150,000 1.08

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4.12 NPV Application

• Do not confuse average with incremental payoffs.
• Do not forget net working capital requirements
  and allocated overhead costs.
• Net working capital (often referred to simply as
  working capital) is the difference between a
  companys short term assets and liabilities.
• Overhead costs include supervisory salaries,
  rent, and utilities.

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4.13 NPV Applications (continued)

• Forget sunk costs but include opportunity costs.
• Sunk costs are past and irreversible. Opportunity
  costs are those foregone by investing in this
  project rather than in comparable projects or
  financial securities.
• Treat inflation consistently.
• Discount real cash flows with the real discount
  rate discount nominal cash flows with the
  nominal discount rate.

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4.14 Example

• Purchase price 42 000 Salvage value 1000 at
  end Year 3
• Net cash flows
• Year 1 31 000
• Year 2 25 000
• Year 3 20 000
• Tax rate is 34 Depreciation 20 reducing
  balance (not linear rule)
• Required rate of return 12

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SolutionDepreciation Schedule
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SolutionTaxable Income
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SolutionCash Flows
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SolutionNPV Conclusion
Conclusion NPV gt 0, therefore ACCEPT.
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4.15 Interest

• We separate investment and financing decisions.
  We analyze the project as if it were all-equity
  financed.
• Interest costs should not be included as an
  explicit cash flow.
• Interest costs are included in the required rate
  of return (discount rate) used to evaluate the
  project. Well elaborate on this issue later.
• Overall, financing is an NPV zero project itself
  in a competitive capital market.

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4.16 Treatment of Disposal of Assets and
Capital Gains (Losses)

• If the salvage value gt book value, a profit/gain
  is made on disposal. This profit/gain is subject
  to tax.
• If the salvage value lt book value, the ensuing
  loss on disposal is a tax deduction.
• Capital gains made on the sale of assets such as
  properties are subject to taxation.
• Capital losses are not a tax deduction but can be
  offset against future capital gains.

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4.17 Annual Equivalent Cost (AEC)

• When comparing two mutually-exclusive projects
  with different lives, it is necessary to make
  comparisons over the same time period.
• AEC is the present value of each projects costs
  calculated on an annual basis.
• Select the project with the lowest AEC.

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4.18 AEC Example

• Project A costs 3000 and then 1000 per annum
  for the next 4 years.
• Project B costs 6000 and then 1200 for the next
  8 years.
• Required rate of return for both projects is 10.
• Which is the better project?

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SolutionProject A

• Because we assume a replacement of an identical
  machine A after 4 years, there is no need to
  calculate the PV for the whole eight years when
  we have two machines of A to compare with one
  machine of B. Click the link here to see the
  excel spreadsheet for this comparison.

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SolutionProject B

• PVIFA Present Value Interest Rate Factor for
  Annuity.
• Project A is better because it costs 1946 per
  year compared to Project Bs 2325 per year.