Let us begin from the final period. If the option is still not exercised at t3, then the
optimal policy is as follows: to exercise if the sum of the NPV and the payout (i.e. the
payoffs obtained by exercising) exceeds the strike price; not to exercise, otherwise. Once
the payoffs at t3 (associated with the optimal exercise policy) are known, the value of the
option at t2 if not exercised can be computed by backward induction. At t2 the optimal
exercise policy is to exercise if the value of the payoffs received by exercising (payout +
NPV) exceeds the value of the unexercised option. By applying the same backward
induction we can find the American option value at all previous nodes.
To better understand the difference between the value of the option to invest when
exercised and when it is not, we can be decompose it into three components17. The first is
the “lost payout”. When the option has been stroke early, say at tn, the company collects the
payout (incremental revenues and cost savings) arisen at tn. If instead the company holds
the option for one extra period, it loses the payout at tn. On the other hand, by holding the
option for one more period, the company benefits from the postponement of the cash out-
flow: this is the second component. The third component is given by the value associated
with protracting the period in which it is possible to choose between the two alternatives: in
fact at the subsequent nodes the value of the unexercised option may still exceed the
payoffs (payout + NPV) gained by exercising. We will refer to this component as the
“reversibility component” which adds to the value of the option when not exercised. At the
date prior to expiry (i.e. t2) the company avoids incurring losses at expiry by postponing the
decision to invest. This is why in this case the reversibility component is referred to as the
protection value
We can now define the decision rule: an American option is rationally exercised when
the value of the payout exceeds the interest cost associated with an early disbursement of
the strike price (the “cash-out postponement”) plus the loss of the insurance against the
possibility that payoffs at expiry are less than the strike price (the “reversibility or
protection value”). In other words, according to the real option model, the investment is
carried out when the revenues gained from having implemented the project exceeds the
value of the marginal information obtained by waiting from time t0 to time t1 plus the
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