future.Assessedtoday,theexpectedpresentvalueofthecash
flowsfrominvestinginthefutureprojectisVandthetotal
investmentneededforthisprojectisX.Thefirmhasafixed
time horizon,attheendof whichithas tomake thefinal
decisiononwhethertomakethefutureinvestment.Finally,
thefirmcannotmoveforwardonthisfutureinvestmentifit
doesnotundertaketheinitialproject.Thisscenarioimplies
theoptionpayoffsshowninFigure12.4.Ascanbeseen,at
theexpirationofthefixedtimehorizon,thefirmwillexpand
intothenewprojectifthepresentvalueoftheexpectedcash
flows at that point in time exceeds the cost of expansion.
FIGURE 12.4The Option to Expand a Project
Inputs to Value the Option to Expand
To understand howto estimate the valueof the optionto
expand,letusbeginbyrecognizingthatthereareusuallytwo
projectsthatdrivethisoption.Thefirstprojectgenerallyhasa
negative net present value and is recognized as a poor
investment, even by the firm investing in it. The second
project isthepotentialto expandthatcomeswith thefirst