The Terra Firma Corporation is considering an investment into the aluminium industry that has a beta of 1.25. The risk-free rate is 3% and the average return on the market index is 7%. Assume that an investment of $100 into this industry has zero net present value if carried out today. The investment cost of $100 will remain constant over the next two years, but the present value of the investment will, each year, increase by 20% with probability one half and reduce by 4% with probability one half. An investment in this industry will not generate cash flows for the first two years of its duration.

1. Explain what we mean by risk neutral probabilities.

2. Find the risk neutral probabilities for the Binomial process described above?

3. Outline the optimal timing of the investment into this industry, making your decision contingent on the evolution of the present value of the investment. You should restrict your planning horizon to two years (which is as long as the investment cost remains constant).

4. What is the net present value of the optimal investment plan outlined in question (c), per $100 investment?

e.Give three real-world examples in corporate finance where option pricing theory is essential for analysing net present value.