$($b$)$ Project $B$ requires an initial investment of $$200.$ It pays either $$110$ or $$91$ in

one year's time. If it pays $$110$ in year $1,$ it will either pay $$121$ or $$100$ in year

If it pays $$91$ in year $1,$ it will then pay either $$100$ or $$82\mathrm{.}81$ in year $2.$ Each

pair of outcomes has equal chance. The cost of capital is $5\%$ per annum in the

foreseeable future.

$($i$)$ Calculate the net present value of Project B$.$ Would you accept this

project?

$(5$ marks$)$

$($ii$)$ If you can abandon Project B for $$100$ after one year, what is the value of

this abandonment? Is the project worthwhile with this abandonment

option?

$(7$ marks$)$

$($iii$)$ Suppose you can also invest another $$200$ at the end of year $2$ if Project

B can pay $$121$ at that time. It will then generate $$15$ in perpetuity from

year $3$ onward. What is the value of this expansion? Would you accept

Project $B$ which has both the abandonment and expansion options?

$(5$ marks$)$

$($iv$)$ Explain how a real option to expand could be analogous to an option,

specifying whether it is a call or a put option and identifying the specific

components of the option. Indicate clearly whether the option you

consider is an American option or not.

$(5$ marks$)$