A General Approach to Real Option Valuation with ... - ICMA Centre

ICMA Centre Discussion Papers in Finance DP2012-040termsis˜w I t,T ′ = e(˜r−r)T ′ w 0 + ˜p t,T ′ − K t . (9)Note that if ˜r = r then also ∑ T ′s=t+1 e(˜r−r)(T ′ −s) CF s + p − T=˜p ′ t,T ′ in (8).Similarly, if the decision maker already owns the investment at time 0 and chooses tosell it at time t, the time 0 value of his wealth at time T ′ iswt,T S = ∑t−1e(˜r−r)T ′w ′ 0 + e (˜r−r)(T ′ −s) CF s + p + t − p 0 . (10)s=1Note that p 0 is subtracted here because we assume the investor has borrowed funds to investin the property. Alternatively, if there are no cash flows, or they are re-invested,˜w S t,T ′ = e(˜r−r)T ′ w 0 + ˜p 0,t − p 0 . (11)The wealth wt,T D ′ resulting from a defer decision at time t depends on whether he investslater on. This must therefore be computed using backward induction as described in the nextsub-section.3.3 Optimal Decisions and Real Option ValueAs in any decision problem, we shall compare the expected utility of the outcomes resultingfrom investment with the utility of a base-case alternative, which in this case is to do nothing. 8For brevity, we describe the backward induction step only for the decision to invest – it issimilar for the decision to divest, but replace I with S (for an existing investor that sells theproperty) and D with R (for an existing investor that remains invested).The option to invest at time t has time 0 utility value Ut,T I = U ( )w I ′ t,T , but since wI ′ t,T ′is random so is Ut,T I ′, and we use the expected utilityE [ U I s(t),T ′ ]=E[U(wIt,T ′)],as a point estimate. Then, given a specific decision node at time t, saywhenthemarketisinstate s(t), the potential investor chooses to invest if and only ifE [ U I s(t),T ′ ]> E[UDs(t),T ′],8 So, for the divestment decision we compare the expected utility of the outcomes resulting from remaininginvested with the utility of the alternative, to divest.Copyright c○ 2012 Alexander and Chen 10