Advanced Corporate Finance Making Investment by edk10782

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									Advanced Corporate Finance



Making Investment Decisions

      Finance 7330
       Lecture 2.1
     Ronald F. Singer
    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 financial undertake all
  positive NPV projects. Then we have to
  devise methods of choosing between
  alternative positive NPV projects.
   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?
    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(@ 10%) 36,000           77,700         41,700

• Notice the conflict that can exist between NPV and IRR.
  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
  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
   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.
        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)
                         (1+r)t
         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.
       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%.
        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?
       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.
     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.
            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:
           Repetitive Deals
• Mutually exclusive projects with different
  Starting Times
• Mutually exclusive projects with different
  Economic Lives
• Replacement Decision
• Management of Excess of Peak Capacity
•
examples:
 Alternatives with Different Lives


                3 Little Pigs



         Brick vs. Wood vs. Straw.
   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
  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.
   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
       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)
   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?
    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?
      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
     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
       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.
        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
      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%.
       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%
       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.
      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
            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.
            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.
              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
                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.
              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.

								
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