Acer, a Taiwanese computer company, started operations by serving the lower-price segments in Asia. Later, in its quest for a global expansion strategy, it ruled out competing in the high-price segments served by established PC giants. Rather, it decided to expand into emerging markets by serving other low-price segments in Mexico, South Africa, and Russia.

Postponing its global expansion had two benefits:

1. It allowed Acer to reduce initial capital requirements.
2. The company could learn more about the product and service needs of its Asian customers. With this knowledge, it could size and tailor its later capacity expansion to better fit the needs of these emerging markets.

The key reason for waiting is the belief that commercial success in emerging markets is highly correlated with success in the current Asian market. (Acer already has capacity in place to serve the Asian market. Aside from providing information regarding its future success, however, that capacity has no direct impact on our problem here.)

Demand from these emerging markets is highly uncertain; marketing and sales reports predict that Acer's low-price PC will either be a blockbuster, a success, or a dud. Assume that the demand forecast for those three scenarios is, respectively: 200 thousand units per year with likelihood of 25%, 100 thousand units per year with 50% likelihood, or 30 thousand units per year with 25% likelihood.

The cost structure is assumed to be as follows. Capacity expansion incurs a fixed cost of $8 million plus a marginal cost of $50 per unit of capacity; i.e., adding production capacity of 100,000 units per year costs $13 million. The process and product technology is commercially viable for four years (at that point a new technology would be needed, an issue we will ignore for now). Acer expects each PC to contribute about $80 in operating profits. A 25% discount rate is used for these types of investment projects.

How would you back up the statement: If Acer decides to expand now, the optimal size of capacity addition is 100 thousands units per year,?