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Corporate Finance Ch#22

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					                                                    Principles of
                                                  Corporate Finance
            Chapter 22                                   Eighth Edition




           Real Options


                                                               Slides by
                                                           Matthew Will


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                    Topics Covered
The Value of Follow-On Investment
 Opportunities
The Timing Option
The Abandonment Option
Flexible Production
Vary Output or Production




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                    Corporate Options
4 types of “Real Options”
1 - The opportunity to expand and make follow-up
   investments.
2 - The opportunity to “wait” and invest later.
3 - The opportunity to shrink or abandon a project.
4 - The opportunity to vary the mix of the firm’s
     output or production methods.

Value “Real Option” = NPV with option
                      - NPV w/o option

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                 Microcomputer Forecasts
    Example – Mark I Microcomputer ($ millions)


                                                                       Year
                                         1982          1983          1984         1985          1986          1987
After-tax operating cash flow (1)                       100           159          295           185             0
Capital investment (2)                     450            0             0            0             0             0
Increase in working capital (3)              0           50           100          100          -125          -125
Net cash flow (1)-(2)-(3)                 -450           60            59          195           310           125

NPV at 20% = - $46.45, or about -$46 million




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               Microcomputer Forecasts
    Example – Mark II Microcomputer

                          900
     PV (exercise price)  3  676
                          1.1

   OC  N (d1 )  P   N (d 2 )  PV ( EX )



              d1  log[ P / PV ( EX )] /  t   t / 2
                     log[.691 / .606]  .606 / 2  .3072
              d 2  d1   t  .3072  .606  .9134
         N (d1 )  .3793             N (d 2 )  .1805
   Call Value  [.3793  467}  [.1805  676]  $55.12million

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                    Microcomputer Forecasts
     Example – Mark II Microcomputer ($ millions)
                           Forecasted cash flows from 1982
                                                               Year
                                       1982   ……….           1985       1986        1987       1988        1989   1990
After-tax operating cash flow                                            220         318        590         370      0
Increase in working capital                                              100         200        200        -250   -250
Net cash flow                                                            120         118        390         620    250
Present Value @ 20%                     467                   807
Investment, PV @ 10%                    676                   900
Forecasted NPV in 1985                                        -93




            NPV(1982) =PV(inflows) -PV(investment)
                                = 467 – 676
                                = - $209 million



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               Microcomputer Forecasts
    Example – Mark II Microcomputer (1985)
               Distribution of possible Present Values
 Probability




                                                                                Present value in 1985
           Expected value             Required investment
               ($807)                          ($900)
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                    Option to Wait


    Intrinsic Value
   Option
   Price




                                                                                    Stock Price




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                    Option to Wait
Intrinsic Value + Time Premium = Option Value

Time Premium = Vale of being able to wait
Option
Price




                                                                              Stock Price




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                    Option to Wait
More time = More value



Option
Price




                                                                              Stock Price




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                              Option to Wait
Example – Development option

                    Cash flow
                    Office Bldg



                                    240
                    Office Bldg
                    NPV>0                         Wait


                                    100


                                                                                     Cash flow
                                               100            240
                                  NPV<0                                              from hotel
                                               Hotel NPV>0




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                    Option to Abandon
Example - Abandon
  Mrs. Mulla gives you a non-retractable offer to
  buy your company for $150 mil at anytime within
  the next year. Given the following decision tree
  of possible outcomes, what is the value of the
  offer (i.e. the put option) and what is the most
  Mrs. Mulla could charge for the option?

    Use a discount rate of 10%



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                    Option to Abandon
Example - Abandon
    Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil
    at anytime within the next year. Given the following decision tree of possible
    outcomes, what is the value of the offer (i.e. the put option) and what is the
    most Mrs. Mulla could charge for the option?

             Year 0           Year 1                      Year 2
                                                          120 (.6)
                              100 (.6)
                                                          90 (.4)
             NPV = 145
                                                          70 (.6)
                              50 (.4)
                                                          40 (.4)
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                    Option to Abandon
Example - Abandon
    Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil
    at anytime within the next year. Given the following decision tree of possible
    outcomes, what is the value of the offer (i.e. the put option) and what is the
    most Mrs. Mulla could charge for the option?

             Year 0           Year 1                      Year 2
                                                          120 (.6)
                              100 (.6)
                                                          90 (.4)
             NPV = 162                                                Option Value =
                                                                          162 - 145 =
                              150 (.4)
                                                                              $17 mil

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                    Option to Abandon
Example – Ms. East - Revenues

                                                        3.73


                            3.05


             2.50                                        2.50



                           2.05


                                                        1.68



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                    Option to Abandon
Example – Ms. East – Cash Flows

                                                        3.03


                            2.35


             1.80                                        1.80



                           1.35


                                                        .98



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                    Option to Abandon
Example – Ms. East – Value
                                     2.5
                               PV        $2.29million
                                    1.09

                                   3.05 p  2.05(1  p )
                 Expected return                         .06
                                           2.29
              Prob of up change  .382
            Prob of down change  .618

                            APV  -1.108 3.803  $2.695million


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                    Tanker Example

         Value of
         Tanker                           Value in
                                          operation


                                                       Cost of
                                                       reactivating




                                                            Value if
                    Mothballing                             mothballed
                    costs




                                                                      Tanker
                                                                      Rates



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                        Web Resources
                                                               Click to access web sites
                                                               Internet connection required




                    www.decisioneering.com




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