QUESTION THREE

1. If the correlation between two risky assets A and B is positive, can the variance of a portfolio that comprises A and B be zero, when short positions can be taken? Explain.

2. If the correlation between two risky assets A and B is zero, can the variance of a portfolio that comprises A and B be zero, when short positions can be taken? Explain.

3. Suppose you are going on a skiing holiday and are considering buying insurance. Your assessment of the likelihood of incidents that need insuring is 5%. Such incidents cause a loss of 500 to your belongings and if there is no such incident, the loss is 0. Assume that you are an expected utility maximiser with a utility function u ( x ) = ln x where x is the monetary value of your belongings (this reflects the insurance premium and payment if you purchase the travel insurance). You plan to take belongings worth 3000 on your trip. Suppose there is only one insurance policy available. The policy pays you back the loss (i.e. 500) in full, and its premium is 25. Should you buy this policy? Explain.

QUESTION FOUR

1. You are a financial analyst at HE PLC and are evaluating a set of risky investment project, some features of which are noted below:

Project ID	Investment Outlay	Present Value of Future Cash Flows
A	1400	1875
B	2250	2800
C	2100	1800
D	3250	4425
E	4200	5500

The investment outlay and present value of the future cash flows are in millions. There is a limited budget of 6,250 million, such that all the projects cannot be chosen for investment and if need be, you can invest in fractions of a project. With supporting calculations, make your recommendation on the portfolio of projects that maximises the net present value for the company.

2. You own a small manufacturing operation that currently generates revenues of 2 million per year. Next year, based upon a pending decision by the government whether to award you a long-term government contract, your revenues will either increase by 30% or decrease by 25%, with equal probability and stay at that level as long as you continue operations. Running costs are 1.6 million per year. Your cost of capital is 10% per annum.

If you can sell the plant at any time to a large conglomerate for 5 million. What is the value of your company today?

3. Discuss the role of real options in the valuation of a company.