Advanced Corporate Finance Capital Budgeting Complications Finance 7330 Lecture 2.1 Ronald F. Singer

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Advanced Corporate FinanceCapital
Budgeting Complications Finance 7330Lecture
2.1Ronald F. Singer
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Making Investment Decisions

• We have stated that we want the firm to take all
  projects that generate positive NPV and reject
  all projects that have a negative NPV. Capital
  budgeting complications arise when you cannot,
  either physically or financially undertake all
  positive NPV projects. Then we have to devise
  methods of choosing between alternative positive
  NPV projects.

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Mutually Exclusive Projects

• IF, AMONG A NUMBER OF PROJECTS, THE FIRM CAN ONLY
  CHOOSE ONE, THEN THE PROJECTS ARE SAID TO BE
  MUTUALLY EXCLUSIVE.
• For example Suppose you have the choice of
  modifying an existing machine, or replacing it
  with a brand new one. You could not do both and
  produce the desired amount of output. Thus,
  these projects are mutually exclusive. Given the
  cash flows below, which of these projects do you
  choose?

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Mutually Exclusive Projects

• Time Modify Replace
  Difference
• 0 -100,000 -250,000
  -150,000
• 1 105,000 130,000
  25,000
• 2 49,000
  253,500 204,500
• IRR?

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Mutually Exclusive Projects

• Time Modify Replace
  Difference
• 0 -100,000 -250,000
  -150,000
• 1 105,000 130,000
  25,000
• 2 49,000
  253,500 204,500
• IRR .40 .30
  .25
• Assume the hurdle rate is 10

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Mutually Exclusive Projects

• Time Modify Replace
  Difference
• 0 -100,000 -250,000
  -150,000
• 1 105,000 130,000
  25,000
• 2 49,000
  253,500 204,500
• IRR .40 .30
  .25
• NPV(_at_ 10) 36,000 77,700
  41,700
• Notice the conflict that can exist between NPV
  and IRR.

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EXAMPLES OF CAPITAL BUDGETING COMPLICATIONS

• 1. Optimal Timing
• 2. Long versus Short Life
• 3. Replacement Problem
• 4. Excess Capacity
• 5. Peak Load Problem (Fluctuating Load)
• 6. Capital Constraints

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EXAMPLES OF CAPITAL BUDGETING COMPLICATIONS

• These Capital Budgeting Complications will stop
  the Firm from taking all possible positive NPV
  PROJECTS. Thus, the firm is faced with the
  choice of two possibilities.
• Remember Goal is still Max NPV of all
  possibilities

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EXAMPLES OF CAPITAL BUDGETING COMPLICATIONS

• We can divide these problems into three separate
  classes, each with their own method of solutions.
  
• (1) Once and for all deal.
• Choose the one alternative having the
  highest NPV.
• (2) Repetitive Deal.
• Choose the one alternative having the
  highest equivalent annual cash flow.
• (3) Capital Budgeting Constraint
• Choose the combination of projects
  having the highest NET PRESENT VALUE.

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Once and For all Deals

• INVESTMENT TIMING
• When is the optimal time to take on an
  investment project? Consider T possible times,
  where,
• t 1, ...T.
• Then each "starting time" can be considered a
  different project in a set of T mutually
  exclusive projects. Then find that t which Max
• NPV(t)
• (1r)t

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Once and For all Deals

• Example You are in the highly competitive area
  of producing laundry soap and detergents. You
  have a new product which you feel does a superior
  job in washing clothes, but you anticipate that
  the product will have difficulty being accepted
  by the consumer. Thus you expect that if you
  introduce the product now, you will have to
  suffer a few years of losses until the product is
  accepted by the consumer. A competitor is about
  to come out with a similar product. You feel
  that if you allow your competitor to come out
  with the product first, you can benefit from the
  time he spends acclimating your potential
  customers. However, you will then be giving up
  your competitive edge.

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Once and For all Deals

• The initial investment in the product has already
  been spent, is a sunk cost and can be ignored for
  this problem. The anticipated life of the
  productive process is ten years from the time the
  product is first produced. Thereafter, there
  will be so much competition that any new
  investment in this product will have a zero NPV.
  The discount rate is 15.

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Once and For all Deals

• Expected cash flows are
• CASH FLOW
  ( MILLIONS )
• year (from
• start of
• project 1 2 3
  4-10
  ___________________________________________
  ____
• immediately -4
  -3 -2 20
• If introduced after
• one year -1 1 3.5
  19.5
• If introduced after
• two years 0 2
  4 19
• WHAT SHOULD YOU DO?

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Once and For all Deals

• NPV(0) (Introduced Immediately) is 47.649
  million
• NPV(1) (Introduced in one year's time) is
  55.531 million
• NPV(2) (Introduced in two year's time) is
  56.118 million
• WHICH ONE OF THESE THREE OPTIONS SHOULD BE TAKEN?
• 47.649 55.531 56.118
• 0 1 2 3
  4 5
• Calculate NPV from time 0.

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Once and For all Deals

• Shortcut
• Calculate the annualized rate of change of
  NPV. If delaying causes the NPV to increase by
  more than the discount rate, the project should
  be delayed. If not, the project should not be
  delayed.

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Once and For all Deals

• Caution
• This method assumes that the project cannot
  be reproduced at a positive NPV after the initial
  life of the project. Otherwise, you have to also
  account for the fact that the project that is
  started earlier can also be reproduced earlier.
  In that case, the alternatives look like
• START IMMEDIATELY
• 0 10 20
  30
• _______________________________
• ONE YEAR DELAY
• 0 1 11 21
  31
• _________________________________
• THIS LEADS TO THE SECOND CLASS OF PROBLEMS

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Repetitive Deals

• Mutually exclusive projects with different
  Starting Times
• Mutually exclusive projects with different
  Economic Lives
• Replacement Decision
• Management of Excess of Peak Capacity

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examples Alternatives with Different
Lives 3 Little Pigs Brick vs. Wood
vs. Straw.
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Alternatives with Different Lives

• Example YOU HAVE THE OPTION OF UNDERTAKING ONE
  OF TWO DIFFERENT WAYS OF ACHIEVING SOME GOAL.
  WHICH ONE SHOULD YOU TAKE?
• (A) A Bridge costing 5M lasts 15 years
• (B) A Bridge costing 4M lasts 10 years
• Both generate 1 Million in net revenues per
  year.
• Let the Discount rate 12 for each
  alternative.
• NPV (A) 1.81 Million
• NPV (B) 1.65 Million

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Alternatives with Different Lives

• Conceptually
• The NPV rule would say, take the project with the
  highest Net Present Value. This may be wrong.
• Consider what happens after ten years.
• In particular by year 30.

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Alternatives with Different Lives

• A
• 1.81 1.81
  1.81.....
• _____________________________________
• 0 5 10 15 20 25 30
  35
• B
• 1.65 1.65 1.65
  1.65
• _____________________________________
• 0 5 10 15 20 25
  30 35
• PV(A) over infinite horizon
• PV(A) 1.81 1.81 1.81
  2,214,900
  
• (1.12)15
  (1.1)30
• PV(B) over infinite horizon
• PV(B) 1.65 1.65__ 1.65__
  .. 2,435,700
  (1.12)10 (1.12)20

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Alternatives with Different Lives

• ALTERNATIVE
• EQUIVALENT ANNUAL CASH FLOW
• (EACF) or (NUS in Hewlett Packard)
• Note BMA talk about Equivalent Annual Cost, this
  is a more general concept.
• Consider the annuity having the same NPV and life
  of the project.
• EACF (A) That annuity having a Present
  Value of 1.81, lasting 15 years at a discount
  rate of 12.
• (A) PV(A) Annuity x PVFA(r, T)
• Annuity(A) 265,700 EACF(A)
• Annuity(B) 292,000 EACF(B)
  
  

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Alternatives with Different Lives

• This "Equivalent Annual Cash Flow" (or Cost) is a
  convenient way of examining the host of
  complicated, mutually exclusive capital budgeting
  problems listed above These all involve
• A TIMING PROBLEM
• (1) When to start project
• (2) When to "cash in"
• Forestry
• Wine
• (3) Replacement
• (4) Short vs. Long lived Project
• (5) When and how to increase capacity
• Can all be dealt with in a similar way?

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Mutually exclusive projects with different
Starting Times

• Instead of assuming that this is a once and for
  all deal, assume that the alternatives can be
  reproduced indefinitely. Note that this case
  differs from the Laundry Detergent Example
  treated above
• 1. How?
• 2. What impact will this have on the timing
  decision?

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Mutually exclusive projects with different
Starting Times

• Consider an example The mutually exclusive
  decision,
• when to cut down a forest
• In ten years with NCF of
  47,000
• In eleven years with NCF of 53,000
• In twelve years with NCF of 58,000
• If this were a one-time-only deal, you would
  simply calculate the NPV of each alternative
• NPV of cutting in ten years 15,132.74
• NPV of cutting in eleven years
  15,236.23
• NPV of cutting in twelve years
  14,887.16

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Mutually exclusive projects with different
Starting Times

• But, more realistically, you will be able to
  continue cutting down these trees every ten,
  eleven, or twelve years. Which is the best
  alternative as a repetitive procedure?
• The question is, what is better
• (1) receiving an annuity of 47,000 every ten
  years
• (2) receiving an annuity of 53,000 every eleven
  years
• (3) receiving an annuity of 58,000 every twelve
  years

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Mutually exclusive projects with different
Starting Times

• For any set of reproducible mutually exclusive
  projects with different lives, you can
• Find the NPV of each project through one
  repetition, and then find its Equivalent Annual
  Cash Flow (EACF), and choose the one with the
  highest EACF.
• Where EACF is calculated as that fixed
  payment (annuity) having the same value and life
  of the project.
• So
• EACF(10) 2,678.12
• EACF(11) 2,566.98
• EACF(12) You know this isn't the right one
  since it has a lower present value but takes
  longer to produce
• Thus you want to take the shorter lived project
  now.

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Replacement Decision

• Return to the first example, you choose project
  (2), and now you are in the fifth year of that
  project. The project, as expected, is returning
  19.5 million this year. But production
  difficulties have resulted in a machine which is
  wearing out faster than anticipated. So that
  your expected cash flow for the next five years
  will be
• 0 1
  2 3 4 5
• Cash Flow 19.5 18 17 16 15
• NPV of operating
• Cash Flows 62.54 50.54 38.61
  26.24 13.39

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Replacement Decision

• A new production technology has been devised
  which will cost 100 million and generate 39
  million for the next 7 years, with an anticipated
  scrap value of 3 million at the end of the
  seventh year. Should you replace the machine
  now, never, or plan to replace it some time in
  the future?
• It is assumed that the scrap value of the old
  machine will be 0 if not replaced during the next
  5 years (the life of the old project), but can be
  sold for 3 million at any time during the next
  five years. The discount rate is assumed to be
  12.

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Replacement Decision

• Find the equivalent annual cash flow for the new
  machine, net of the current scrap value.
• Net Cash Flow of Replacement
  Machine
• 0 1 2 3 4 5 6 7
• -97 39 39 39 39 39 39 42
• NET PRESENT VALUE 82.344 million
• EQUIVALENT ANNUAL CASH FLOW 18.043 million
• IRR 35.56

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Replacement Decision

• Replace in the beginning of year 2. Note, simply
  comparing NPV will not give the right answer,
  neither will looking at incremental cash flow.
  This is because the replacement has a different
  life than the current process and they are
  obviously mutually exclusive. Furthermore, and
  more important, the alternatives of replacing now
  versus not replacing now is not the appropriate
  alternatives. You can also replace next year,
  the year after, etc. The alternative which gives
  the greatest incremental value relative to all
  the other possible alternatives could be
  calculated by looking at the incremental cash
  flows from each alternative. But it is easier to
  simply calculate the EACF and compare that to the
  current cash flow to see what to do.

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Replacement Decision

• In general, Equivalent Annual Cash Flow or Cost
  is used to consider a problem where the
  investment is considered ongoing and you have to
  examine what happens at the end of the project's
  life. All that EACF does is help you discover
  the decision which gives the highest NPV as a
  whole.
• STOP

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Capital Rationing

• In this situation, the decision maker is faced
  with a limited capital budget. As a result, it
  may not be possible to take all positive net
  present value projects. Under this scenario, the
  problem is to find that combination of projects
  (within the capital budgeting constraint) that
  leads to the highest Net Present Value.
• The problem here is that the number of
  possibilities become very large with a relatively
  small number of projects. Thus, in order to make
  the problem "manageable", we can systematize the
  search.

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Capital Rationing

• Since we have a constraint, what we want to do is
  invest in those projects which gives us the
  highest BENEFIT per dollar invested. (The
  highest bang per buck). What is the benefit?, it
  is the Present Value of the Cash Flows. So that
  we would want to choose that set of projects
  within the capital budgeting constraint that
  gives the highest
• Net Present Value
• INVESTMENT
• This ratio is called the profitability Index.

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Capital Rationing

• For example, suppose we have a 13 million
  capital budgeting constraint, with 7 alternative
  capital budgeting projects with the following
  projections.
• Project NPV Investment
  
• A 10 15
• B 8 10
• C 4 2.5
• D 6 5
• E 5 2.5
• F 7 5
• G 4.5 3

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Capital Rationing

• Rank by Profitability Index (NPV/INV
• Project Profitability Index
  Investment Total
• E 2.0
  2.5 2.5
• C 1.6 2.5 5.0
  
• G 1.5 3
  8.0
• F 1.4
  5 13.0 D
  1.2 5
• B .8 10
• A .667 15
• COMBINATION WITH HIGHEST PROFITABILITY INDEX
  WITHIN THE CAPITAL BUDGET
• (E,C,G,F) has a NPV of 20.5 million, and a cost
  of 13 million.

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Capital Rationing

• However, if the budget were 15 million rather
  than 13 million we would have a problem. Adding
  D would go over the budget and be infeasible, but
  the combination CDEF has a higher NPV (22
  million) than the chosen combination of ECGF.
  This is because the amount spent was only 13
  million leaving 2 million in unspent funds. In
  this case, we are better off choosing a
  combination which spends all the funds.
• THE ONLY WAY TO DO THIS RIGHT IS TO DO A FULL
  BLOWN LINEAR PROGRAMING PROBLEM WITH CONSTRAINTS.