Inverness Instruments Ltd is considering two major investment projects to cope with increased demand for its new, efficient removal vans. The first is to expand production of vans at its Inverness factory costing 100m and make small vans. The second is to start production at a new facility in Dundee at a cost of 200m to make large vans. The company has hired a consultant who has indicated that the performance of the two projects will depend on market conditions in the coming period. If the market grows strongly, then the Inverness expansion will yield a cash flow of 110m. If normal economic growth occurs, the cash flow will be 115m while if economic growth is poor, the vans will be very popular and the cash flow will be 120m.

The consultant has determined that the investment in Dundee will produce more varied results because of the different sized van produced. If economic growth is strong, the cash flow will be 300m; if economic growth is normal, a cash flow of 250m will be achieved while if economic growth is poor, the investment will only breakeven.

The consultant has estimated that for the coming period, there is a 30% chance of strong growth, a 40% chance of normal growth and a 30% chance of poor growth.

(i)Calculate the return for the two investments in each of the three economic growth scenarios: strong, normal and poor.

(ii)Calculate the expected return and the standard deviation of returns for the Inverness and Dundee investments and comment on which is the more attractive to Inverness Instruments Ltd.

(iii)Estimate the covariance between the pairs of returns.

(iv)If Inverness Instruments decides to enter into a joint venture with Dundee Designers plc and proceed with the two new investments, calculate the expected return and risk of a portfolio for Inverness Instruments Ltd composed of 80% of the Inverness project and 20% of the Dundee project.