a)

A company has the options of building a full size plant or a small plant that can be expanded later. A market survey indicates that the probabilities of having a high and low demand over the next 10 years are 0.75 and 0.25 respectively. The immediate construction of a large plant will cost Rs. 5 million and a small plant will cost only Rs1 million. The expansion of the small plant 2 years from now is estimated to cost Rs4.2 million. Estimates of annual income for each of the alternatives are given as follows:

- Full size plant and high demand will yield Rs. 1,000,000 annually.

- Full size plant and low demand will yield Rs. 300,000 annually.

- Small plant and low demand will yield Rs. 200,000 annually.

- Small plant and high demand will yield Rs. 250,000 annually.

- Expanded small plant with high demand will yield Rs. 900,000 annually.

- Expanded small plant with low demand will yield Rs. 200,000 annually.

(Note: Small plant with low demand after 2 years will not be expanded)

(i) Draw a decision tree indicating the above information. (5 marks)

(ii) Using the decision tree in (i), calculate the expected income for each alternative. You are required to state and justify clearly the decision you take at each decision node if any. (8 marks)

(iii) What decision should the company make based on your calculations in (ii)? (2 marks)

Using the time series below, discuss briefly the trend and seasonality component.