Issues in Capital Budgeting by revitup2367

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									Real Options and Capital
                   Real Options
 • Traditional capital budgeting analysis:
         • estimates cashflows each period
         • discounts to get NPV
         • firm decides to invest/not invest

BIG PROBLEM:          Traditional analysis assumes that a firm’s
                      only choice is accept/reject the project.

              THIS IS NOT TRUE!!
 In a real business situation, firms face many choices with
 respect to how to operate a project, both before it starts
 and after it is underway.

      • use a production technology that is adaptable
      • can produce more than one product
      • if market for one product goes down, can switch production
      to the other

      • the option to change production if the firm wants
      to (the flexibility) is valuable
      • makes the project worth more
      • traditional NPV analysis assumes cashflows fixed,
      will not change with future business conditions – ignores
      the value of this option
      • firm invests in project
      • after a time the firm may be able to shut down production
      if things are not going well
      • option to abandon

  • traditional analysis assumes that the firm either takes
  the project and runs it for its life, or rejects it

  • But…the ability to start a project and shut it down
  (perhaps temporarily) if conditions warrant is valuable
       Option to Delay
       • traditional analysis assumes firm accepts project now
       or never invests
       • But…what if firm has choice to delay making decision?
       • Wait and see how things develop and then decide to invest
       or not
       • The choice to delay if the firm wants is valuable

• Other examples of valuable options (choices) a firm may have include:
           • option to expand/shrink production
           • option to move into new market
           • R&D gives the option to develop new products if
           they become viable
           • development options on natural resources
           • et cetera
                 Real Options
• Any time a firm has the ability to make choices, there is a
value added to the project in question

• traditional NPV analysis ignores this value

• the study of real options attempts to put a dollar value on the
ability to make choices
How are real options valued? Three major ways:
   1) Use methods developed for pricing financial options
            • Black-Scholes Model
            • Discussed in “What’s It Worth?” article
            • May be problems
   2) Decision trees
              • look at this method here

    3) Stochastic optimization problems
               • like (2) but using far more complicated
               (and realistic) models for the probability
               of different events occurring
                  Option to Delay
• simple example from “Irreversibility, Uncertainty and Investment”,
Robert Pindyck [Journal of Economic Literature, 1991]

   • for $800 a firm can build widget factory
   • makes 1 widget per year
   • factory is built instantly
   • investment is irreversible
   • if factory built, first widget produced immediately
   • no costs of manufacturing
   • no taxes
   • appropriate discount rate is 10%
               Option to Delay
• the price of widgets is currently $100

• next year the price will be either $150 (50% probability) or
$50 (50% probability)

• whatever price holds next year will hold forever after
 year 0          year 1         year 2

               Price = $150   Price = $150

Price = $100

               Price = $50    Price = $50
    Traditional NPV Analysis
 Expected year 1 price = E[price]
                       = 0.5($150) + 0.5($50) = $100

         NPV  800  100  
                            t 1 (1  r ) t
               800  100  
                             t 1 (1.1) t
               800  100 
               $300

Standard analysis says NPV > 0, so start project.
                  Option to Delay
• BUT… firm has another option. Delay the choice of whether
to invest or not.
        • Wait until next year to decide.
        • Can see what price turns out to be before making decision.

 • If you delay, you lose on the year 0 sales ($100).
         • The bad part of delaying – lost sales.

 • But, you get to see what price will be before making
 irreversible investment.
         • The good part of delaying, reduced uncertainty.

If delay and price turns out to be $50:

                  800  50
            NPV       
                    .     t 1 (11) t
                  800 50
                      
                   11    01 .
                 227.27

• NPV < 0 , so firm will not invest.
• From today’s perspective, NPV = 0 if price turns out to be $50.
If delay and price turns out to be $150:

                 800  150
           NPV       
                   .    t 1 (11) t
                 800 150
                     
                  11     01.
                772.73

 Firm will invest if the price goes to $150.
• the essence of the option to delay is that it allows the firm to avoid
 the “bad” outcome
• delay deciding until you see what the state of the world is:
            • you lose some sales on delay
            • if the market turns out to be bad, you do not invest
            and do not take the loss
             • does the avoided loss make the foregone sales
                                           Price = $150
                                           NPV = 772.73

                NPV = ??

                                             Price = $50
                                              NPV = 0
NPV in year 0 of delaying project
              = (0.5)(772.73) + (0.5)(0)
              = $386.36

• the NPV of delaying ($386.36) is more than the NPV of
starting immediately ($300)
       • therefore, firm should delay start of project

• the flexibility of being able to wait another year to decide
whether to invest or not is worth an additional $86.36

• Does this mean that firms should always delay projects?
       • No, if probability of high price in this example was
       90% it would be best to start immediately
            Option to Abandon
• ability to abandon a project if things are not going well is valuable

• allows firm to avoid bad outcomes

• value of the option to abandon can be calculated in similar
way to option to delay
        • see example handout
Capital Rationing
             Capital Rationing
• Usual assumption is that firm should accept all NPV>0-

• What if firm has a number of NPV>0 projects, but doe
  not have resources to take on all of them?

• This is situation of capital rationing
      • Limited amount of capital to invest
      • Must decide how to best invest the limited
           Sources of Rationing
Two types of capital rationing:

1.   Soft rationing: capital constraint imposed internally by
     the firm
       • Head office may assign a budget to each division
       • If soft rationing is leading to a division foregoing
            many NPV>0 projects, then the budget should be
2.   Hard rationing: capital constraint imposed on firm by
     the capital markets
       • Firm has limited internal cash, cannot borrow and
           cannot (or will not) issue new equity

       •   In a perfect world, there would never be
           externally imposed capital constraints

       •   In perfect world, firm could simply announce it
           had a good project to invest in, show investors
           the risk and return projections, and then
           investors would be willing to invest equity in/lend
           to the project
•    However, the world is not perfect.
•    There are several reasons that firms may be unable or
     unwilling to bring in external financing for a good

1.   Firm and investors may disagree on value of project
        • Management may lack creditability
        • Especially true for smaller, newer firms, or firms
          with poor records

2.   Flotation Costs
       • It costs money to issue new shares/bonds
       • The additional cost may make raising money to
           finance a project not worthwhile
       • Flotation costs are higher for smaller issues, so
           small firms are affected the most (also higher for
           equity issues compared to debt).
3. Underpriced shares
      • Firms shares may be trading below their true value
      • Management knows that the shares are
        undervalued (management has better info about
        firm than market = asymmetric information)
      • Selling shares to raise funds to finance a project
        means that shareholders get a good project, but
        are selling part of the firm at a discount
      • In some cases the project will not be worthwhile
        and firm will skip project

      • Biggest effect on firms with high degree of
        asymmetric information (complicated firms, new
        firms, firms with few analysts following them)
• Note: firms can benefit from having cash on hand

• Can fund NPV>0 projects that without accessing markets

• Do not have to skip a good projects because of reasons

• Assuming a firm is subject to capital rationing, how
  should it solve for the optimal investment strategy, given
  the constraint?
• Firm has $10 million available for investment, 3
  potential projects

                      Cashflows (millions)
   Project   Year 0         Year 1           Year 2   NPV @
     A        -10             30               5       21.4
     B         -5              5              20       16.1
     C         -5              5              15       11.9

• Simply choosing highest NPV means choose A
     • Uses up total budget
     • NPV = 21.4
• However you could take B and C instead
  – Uses up entire budget
  – Total NPV = 28
  – B and C is the better choice

• Best combination of projects is fairly obvious in
  this case, but may not be in more complicated
   Solving for Optimal Decision in
    Capital Rationing Problems
• Common way to approach capital rationing
  problem is to use the profitability index
             PV of project ' s FCFF
        PI 
              initial investment
• PI shows which projects give “most value for
  your money”
      • PI = value of project per dollar invested
• Choose project with highest PI, and keep
  choosing projects until your budget runs out
• From previous example:
      Project      PI
        A          3.1
        B          4.2
        C          3.4

• Solution by PI: choose B and C
Problems with Profitability Index
• If projects chosen via PI do not exhaust the
  budget, you may not get the optimal solution
• Required return = 10%, budget constraint =
        Year 0        Year 1   P.I.    NPV
          -5               8   1.454   2.27
          -5               7   1.272   1.36
         -100          120     1.091   9.09
Problems with Profitability Index
• PI says take first two projects for total NPV = 2.27 + 1.36
  = 3.63
• This leaves $90 of budget unspent

• Better to take third project by itself, for total NPV = 9.09

• Reason: PI has difficulty in comparing projects of
  different sizes
• Note: As long as your answer using PI uses up entire
  budget the NPV should be the maximum possible
Problems with Profitability Index
• PI also runs into problems if there is more than one
  constraint faced by firm
       • Projects are mutually exclusive (if you take one
         you cannot take the other)
       • Projects are dependant (you can only take on one
         project, if you have already taken another)
       • Budget constraints in more than one period
       • Etc.

• The usual approach to capital rationing situations is to
  solve for the optimal investment using optimization
  software on a computer
• Maximize an objective function subject to certain
• Can use “Solver” on Excel
Investments of Unequal Lives
  Investments of Unequal Lives
• When comparing mutually exclusive alternatives,
  NPV does not always give correct choice as to
  the best alternative if they are of different lengths
      • e.g. comparing Machine A to Machine B
        where B costs more but lasts longer

• NPV does not take into account the different
  lifespans of the projects
  Investments of Unequal Lives
  – Machine A costs $10,000 and increase profits
    by $5000/year. It lasts 6 years.
  – Machine B costs $5,500 and increases profits
    by $5000/year. It lasts 3 years
  – Discount rate = 10%
      NPVA  10000            t
                                    $11,776.31
                      t 1 (1.1)
      NPVB  5500            t
                                   $6,934.26
                     t 1 (1.1)
•   A has highest NPV
•   A is best choice if this is a “one time deal”
      • If you will only buy a machine once and
         never replace it

•  More commonly, machines have to be
   replaced as they wear out
• If replacement of machines as they wear out is
   relevant, there are two methods to correctly
   compare the alternatives
1. Project Replication
2. Equivalent Annuities
Project Replication
• Find a common multiple of the two life lengths
• Use this as total project length for both alternatives,
  where each alternative is repeated the appropriate
  number of times
• Calculate NPV over this common time frame and
Equivalent Annuities
• Equate the NPV of each alternative to an annuity
• The length of the annuity equals the life of the project
• Solve for annuity payment that would give the same NPV
• The annuity payment represents the value per year
  created by the project
• Since projects are now on a common time frame (per
  year), can simply compare
   Optimal Replacement Time
• It may sometimes pay to replace a machine
  before the end of its “natural” life
• May happen if:
      • Better machine becomes available
      • Salvage value is decreasing as machine
      • Machine becomes more expensive to
        operate or less efficient overtime
• Optimal time to replace a machine is just a
  special case of comparing projects of unequal

• A machine you always need for your production
• Lasts a maximum of three years before
  replacement needed
• It becomes less efficient over time
• When replaced, you will replace with an identical
  (but new) machine
• How often should you replace?
• Discount rate=10%
(example continued)

     Year                0       1       2       3
  Cashflow            -60000   40000   35000   25000
Salvage value                  30000   15000     0
 if sold this

• To solve, compare 3 projects of unequal lives:
            replace in year 1
      vs. replace in year 2
      vs. replace in year 3

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