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Appendix-II
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Appendix - II

Simple Model of Investment Timing in IT System

Assuming that the external environment is changing, at a stochastic rate. As time passes, the firm has the option of investing in IT. The firm does not know the date and type of change in the external environment. There is always the option of waiting, rather than investing in IT now, since the environment changes in a stochastic pattern. This timing choice will be exercised in light of two important considerations. First, IT investments are partially or completely sunk (i.e., costs cannot be recovered if the system proves to be ineffective or undesirable at a later time). Second, given the constraints of available funds, investing now often means giving up an option of investing later. That is, the choice of timing is irreversible. The function has the form:
where, v is a variable input (such as enforcement cost) and Q is the rule parameter whose value is determined stochastically. Assume that p is the fixed value of the benefit of the IT investment, per unit, and w is the fixed unit cost of the variable input cost. We consider a dynamic model with an infinite time horizon. At time 0, the state of the IT infrastructure is designated by:
Over time, as the external environment evolves, this parameter changes. Assume that this follows a jump process such that:
For simplicity, we assume that u is distributed uniformly, across the interval (0, u*). Adopting a new IT system means incurring a sunk cost of I, which is assumed to remain constant. The general problem facing the firm is choosing the right moment to switch to the new system. One extreme possibility is that the firm changes the system every time there is a change in the external environment; the other extreme is never to change the system. The former option would mean incurring the sunk costs for each change, which could be prohibitive. The latter could result in a system that is in effect obsolete and inefficient, since it does not address the needs of the firm. In between the two extremes, there should be a range of points where the benefits of the switch exceed the sunk cost of making the switch. According to traditional investment theory, the optimal timing of the investment should be the one that maximizes the net present value of the benefits from the new investment. Such a present value calculation, however, has been shown to ignore the option value of the investment decision (Pindyck, 1991). Using similar intuition one can show that the use of present value calculations in IT investment decisions omits to take into proper account the value of waiting in investment.
We consider the simple case of a single switch. There has been a change in the external environment. The firm could continue with the current system, or could adopt a new system. If the firm adopts the new system, the value of this new system is given by:
The value of v that maximizes the term above is given by:
This Means:
This can be rewritten as:
where
and
We obtain:
The termination payoff from adopting the new system, is equal to V(Q) - I.
To derive the optimal switching level, Q*, we have to consider the case where there is a positive probability that changing the system will be optimal after the next environmental change. First, we need to derive the Bellman equation. Combining the Bellman equation with at Q = Q*, and the value-matching condition (see Dixit and Pindyck, 1994) at the same point, we can arrive at the equation from which the optimal switching level can be calculated. The Bellman equation is:
where
Ignoring terms of dt with higher powers than one, the two equations give the following:
Dividing by (r+l),
we get:
From this we can derive the
Bellman equation for Q = Q*
The value matching condition indicates that, at this critical point, the firm would be indifferent between adopting a new system now, or waiting to adopt a more advanced system. This allows proceeding in the present “qualitative” analysis to explore the idea of evolution of IT systems in a dynamic framework. This model captures two essential elements in the adoption of a new IT system. First, the sunk costs in the new system are irreversible. There is also the cost of implementation, and disseminating information about the new system. Once the investment is made, these costs cannot be recovered. That is, the switch in the IT system is analogous to an irreversible investment in a new technology. Second, when the new system is adopted, the firm gives up the option of making the investment at some other time, using those same resources. Given some binding budget, or time there is an opportunity cost of adopting a new system, represented by the forgone possibility to introduce a new system in the subsequent time period.
As a result of these factors, the options of investing in new system has a value, an opportunity cost. If the analysis is extended to include the effects of such constraint-driven opportunity cost, the optimization problem should consider the forgone value of the option. Using a simple discounted, net present value rule would, in fact, yield an incorrect result of the optimal time to introduce new system, since it does not take into account the option value of the other environmental changes. The importance of the option in this context depends on the fact that, by waiting, the firm preserves the opportunity of making a better (or more informed) IT investment in the future, and not just that of not investing at all, as would be the case if the random events give new value to the existing system.
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