Weber PLC is setting up a new factory to produce simple plastic chairs. The project costs $100$

million to set up$.$ Annual sales of $5$ million units at $10$ each are expected for a period of $8$

years, and the cost of production is $6$ per unit. The firm's management team is considering

the possibility that if the overall market for chairs expands sufficiently over the next $12$ months,

they could expand the factory to produce 'fancy' plastic chairs. The probability of this

occurring is $25\%$ in which case the company would need to spend $30$ million to expand the

factory, selling $1$ million 'fancy' chairs each year at $15$ each for the remaining $7$ years of the

project. The cost of production would be $8$ per unit. The discount rate is $7\%.$

Required:

a$)$ Calculate the NPV of the original project.

$(6$ marks$)$

b$)$ Calculate the value of the option to expand.

$(9$ marks$)$

c$)$ Discuss the features of a typical financial option contract and give a simple

example of such a contract.

$(4$ marks$)$

d$)$ Discuss the relationship between the price of the underlying asset and the value

at maturity for a typical call option. Explain why a holder of a call option would

benefit from a sudden increase in volatility of the underlying.